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Computational Studies for Conformational Change of Tetraglycine Loop Structure in Formyl-Coa Transferase Based on Molecu...

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Title: Computational Studies for Conformational Change of Tetraglycine Loop Structure in Formyl-Coa Transferase Based on Molecular Mechanics Approaches
Physical Description: 1 online resource (103 p.)
Language: english
Creator: Lee, Sangbae
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: charmm, dimb, fep, frc, md, mm, namd, nma, osrw, tetraglycine
Chemistry -- Dissertations, Academic -- UF
Genre: Chemistry thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The power of molecular dynamics simulation techniques is that they can be used to obtain detailed information on systems that are otherwise not amenable to experimental studies. Because of limitations on simulation times and the height of energy barriers to conformational transition, however, two alternative approaches were introduced in this thesis. We have attempted to analyze the conformational change of tetraglycine loop in formyl-CoA transferase by directly simulating the process of recognition from X-ray crystallographic enzymes as well as using simulation techniques to calculate differences in free energy between the open/closed states. Because conformational loop changes in protein represent motions that usually occur on a microsecond to millisecond time scale, the ability to obtain such information using nanosecond simulations is a significant advantage of the normal mode analysis and new free energy sampling strategy.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Sangbae Lee.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Richards, Nigel G.

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Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0042008:00001

Permanent Link: http://ufdc.ufl.edu/UFE0042008/00001

Material Information

Title: Computational Studies for Conformational Change of Tetraglycine Loop Structure in Formyl-Coa Transferase Based on Molecular Mechanics Approaches
Physical Description: 1 online resource (103 p.)
Language: english
Creator: Lee, Sangbae
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: charmm, dimb, fep, frc, md, mm, namd, nma, osrw, tetraglycine
Chemistry -- Dissertations, Academic -- UF
Genre: Chemistry thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The power of molecular dynamics simulation techniques is that they can be used to obtain detailed information on systems that are otherwise not amenable to experimental studies. Because of limitations on simulation times and the height of energy barriers to conformational transition, however, two alternative approaches were introduced in this thesis. We have attempted to analyze the conformational change of tetraglycine loop in formyl-CoA transferase by directly simulating the process of recognition from X-ray crystallographic enzymes as well as using simulation techniques to calculate differences in free energy between the open/closed states. Because conformational loop changes in protein represent motions that usually occur on a microsecond to millisecond time scale, the ability to obtain such information using nanosecond simulations is a significant advantage of the normal mode analysis and new free energy sampling strategy.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Sangbae Lee.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Richards, Nigel G.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0042008:00001


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COMPUT ATIONAL STUDIES FOR CONFORMATIONAL CHANGE OF TETRAGLYCINE LOOP STRUCTURE IN FORMYL-COA TRANSFERASE BASED ON MOLECULAR MECHANICS APPROACHES By SANGBAE LEE A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2010 1

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2010 Sangbae Lee 2

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To m y father, Manseok Lee, and my entire family 3

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ACKNOWL EDGMENTS There are many people who I would like to thank for number of reasons. First of all, I dont know how to thank my P h.D. supervisor, Dr. Nigel Richards. Without his help I would never have finished my thesis. I also have to thank my current committee members, Dr. Merz, Dr. Roitberg, Dr. Hirata and Dr. Hagen, for being patient with me and mana ging to read the entire thesis so thoroughly, at such short notice. I very much appreciate my collaborators cooperation: Dr. Perahia and Dr. Stote for providing and advising me about the CHARMM/D IMB technique, Dr. Yang and Dr. Chen for supporting a special version of CHARMM program and discussing my JACS manuscript, and Dr. Mulholland for supplying acetyl coenzyme A parameter. I also thank my past and current group members, even though be too manifold to enumerate. I owe special gratitude to my parents, brother and sisters. Last but not least, especially, I want to thank my wife Insook and my two tr easures (Taehee and John) for all their love. Sangbae, December 2010. 4

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TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ..........7 LIST OF FIGURES.........................................................................................................................8 LIST OF ABBREVIATIONS........................................................................................................10 ABSTRACT...................................................................................................................................12 CHAPTER 1 INTRODUCTION................................................................................................................. .14 Formyl-CoA Transferase........................................................................................................1 4 Research Goals................................................................................................................. ......23 2 MOLECULAR DYNAMICS SIMULATION OF FORMYL-COA TRANSFERASE.........24 Introduction................................................................................................................... ..........24 Materials and Methods...........................................................................................................24 CHARMM Force Field....................................................................................................24 Molecular Dynamic Methodology..................................................................................26 Molecular Dynamics Characteristics...............................................................................27 System Setup................................................................................................................... 28 Molecular Dynamics Simulation of FRC Enzymes........................................................30 Results and Discussions........................................................................................................ ..31 RMSD Analysis of FRC..................................................................................................32 Flexibility Changes upon Subs trate Binding and Unbinding..........................................33 Hydrogen Bond in CoA-binding FRC.............................................................................36 Intramolecular Trajectory Analysis.................................................................................40 Conclusions.............................................................................................................................44 3 CONFORMATIONAL PROPERTIES OF TETRAGLYCINE LOOP IN FORMYLCOA TRANSFERASE: LOW FREQUENCY MOTIONS...................................................45 Introduction................................................................................................................... ..........45 Methods..................................................................................................................................46 Normal Mode Analysis....................................................................................................46 Model Preparation...........................................................................................................49 Vibrational Motions in FRC Homodimer........................................................................50 Results and Discussion......................................................................................................... ..52 Minimized Structures......................................................................................................52 Normal Mode Calculation...............................................................................................53 5

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Analysis of Overall F luctuations.....................................................................................56 Correlation between the Atomic Fluctuations.................................................................59 Mutation Effects on the Dynamic Structure of Tetraglycine..........................................65 Conclusions.............................................................................................................................66 4 NEW FREE ENERGY SIMULATIONS OF ACTIVE SITE LOOP MOTIONS FOR FORMYL-COA TRANFERASE...........................................................................................69 Introduction................................................................................................................... ..........69 Methodology...........................................................................................................................70 Results and Discussion......................................................................................................... ..75 Conclusions.............................................................................................................................83 5 SUMMARY AND FUTURE WORKS..................................................................................85 Summary of Current Formyl-CoA Transferase Project..........................................................85 Future Works for Formyl-CoA Transferase Project...............................................................87 APPENDIX A NAMD PRODUCTION RUN FOR AP O STATE OF FRC ENZYME................................88 B NORMAL MODE CALCULATION INPUT USING CHARMM/DIMB............................90 C FREE ENERGY CALCULATION WITH OSRW ALGORITHM.......................................92 LIST OF REFERENCES...............................................................................................................95 BIOGRAPHICAL SKETCH.......................................................................................................103 6

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LIST OF TABLES Table page 2-1 Comparative fluctuation dynamics of the active site in FRC............................................34 2-2 Distance comparison of activ e site residues and CoA betw een X-ray crystal structure and average MD structure..................................................................................................38 3-1 Potential energy comparison between initial and optimized structur es in apo state and CoA-binding FRC..............................................................................................................52 4-1 Calculated free energy values for conforma tional inter-conversion of the tetraglycine loop and steady-state kinetic parameters for free FRC and alanine-containing FRC mutants...............................................................................................................................79 4-2 RMSD comparisons of the calculated G260A FRC mutant structures, with the tetraglycine active site loop in its open, cl osed and intermediate state, and the X-ray crystal structure of this FRC variant..................................................................................81 4-3 Crystallographic torsional angles observed for the four glycine re sidues in the active site loop of wild type FRC.................................................................................................83 7

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LIST OF FI GURES Figure page 1-1 Formyl-CoA transferase enzyme pathway in O. formigenes for transfer of CoA from formate to oxalate..............................................................................................................14 1-2 Crystal structure of the inte rtwined FRC dimer with bound CoA.....................................15 1-3 3-D representation of the crystal structure of FRC monomer............................................16 1-4 3D representation of active site resi dues of apoenzyme of FRC and CoA-binding FRC....................................................................................................................................17 1-5 Topology and sequence representation for the secondary structure of formyl-CoA transferase monomer..........................................................................................................18 1-6 Structure of Coenzyme A...................................................................................................1 9 1-7 Active site residues in apoand CoA-binding FRC...........................................................20 1-8 Catalytic mechanism for formyl-CoA transferase.............................................................21 1-9 Structural representations of each step in the catalytic mechanisms for formyl-CoA transferase..........................................................................................................................22 2-1 Representation of coenzyme A with atom names and their types necessary for CoA parameterization............................................................................................................... ..29 2-2 The simulated formyl-CoA transfer ase system with solvated waters................................30 2-3 The C RMS deviation representation in each monomer of FRC......................................32 2-4 Experimental versus calculated RMS fl uctuations for two FRC enzymes in first monomer and in the second monomer...............................................................................33 2-5 Experimental versus calculated RMSFs cen tering on tetraglycine loop structures in apo-FRC and CoA-binding FRC.......................................................................................35 2-6 Protein-CoA interactions based on the X-ray structure of CoA-FRC...............................37 2-7 Plots of the distances between active site residues and CoA.............................................39 2-8 Ten snapshot structures with 2 ns inte rvals for three enzymes, apo-FRC, CoA-FRC, and CoA-free FRC.............................................................................................................40 2-9 Schematic diagram of interaction of the tetraglycine loop struct ure of the B monomer with active site resi dues of A-monomer............................................................................42 8

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9 2-10 The time evolution of dihedral angle 1 (C-CA-CB-CG) of Trp48A................................43 3-1 Frequency coverage for the total 100 normal modes of apo-FRC and CoA-FRC structures..................................................................................................................... .......53 3-2 Average RMS coordinate fluctuations for 40 low frequency normal modes of apoand CoA-FRC....................................................................................................................54 3-3 Characteristics of the lowest 7th normal mode of apo-FRC and CoA-FRC.......................55 3-4 Average RMS fluctuations of the C atoms for the first monomer and second monomer of FRC...............................................................................................................57 3-5 Comparison of RMS fluctuation of the C atoms obtained experimentally from the B-factor of X-ray crystallography and by normal mode calculation.................................58 3-6 Intra-monomer and inter-monomer correla tion contours for apo-FRC and CoA-FRC.....60 3-7 Cross-correlation maps for inter-monomer fluctuations centering on the tetraglycine loop regions in apo-FRC and CoA-FRC............................................................................62 3-8 Inter-monomeric correlation contributions between active site residues of the A monomer and the tetraglycine loop fluctuations of the B monomer.................................64 3-9 RMS fluctuations of the C atoms for the wild-type and it s mutants for tetraglycines.....66 4-1 Cartoon representations of the FRC active site tetraglycine loop in its open and closed conformations.........................................................................................................70 4-2 Conformational sampling statistics for the variation in the reaction coordinate as a function of MD simulation time........................................................................................76 4-3 The free energy profiles computed for the tetraglycine loop from its open to closed conformations using the OSRW simulations.....................................................................78 4-4 Cartoon showing superimposed active site tetraglycine loops for the observed and the open, intermediate, and closed loop conformations calculated for the G260A mutant................................................................................................................................80 4-5 The phi and psi analyses in the wild type FRC and G260A variant for the last residue of tetraglycine loop............................................................................................................82

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LIST OF ABBRE VIATIONS ABNR Adopted Basis Newton-Raphson algorithm ADP Adenosine DiPhosphate apo-FRC apo state of FRC C alpha Carbon CHARMM Chemistry at HARvard Molecular Mechanics CoA Coenzyme A CoA-FRC CoA-binding FRC complex Conj Conjugate gradient DIMB Diagonalization In a Mixed Basis FEP Free Energy Perturbation FES Free Energy Surface FRC Formyl-CoA Transferase LJ LennardJones kDa kilo Dalton MD Molecular Dynamics NAMD NAnoscale Molecular Dynamics NMA Normal Mode Analysis OSRW Orthogonal Space Random Walk PDB Protein Data Bank PME Particle-Mesh Ewald method PMF Potential of Mean Force RMSD Root Mean Square Deviation RMSF Root Mean Square Fluctuation 10

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SD Steepest Descent SMD Steered Molecular Dynamics TI Thermodynamic Integration TIP3 Titratable Intermolecular Potential using 3-site water model vdW van der Waals VMD Visual Molecular Dynamics WT Wild Type 11

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Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy COMPUTATIONAL STUDIES FOR CONFORMATIONAL CHANGE OF TETRAGLYCINE LOOP STRUCTURE IN FORMYL-COA TRANSFERASE BASED ON MOLECULAR MECHANICS APPROACHES By Sangbae Lee December 2010 Chair: Nigel G. J. Richards Major: Chemistry Formyl-CoA transferase (FRC), purified from Oxalobacter formigenes is a crucial enzyme for catalyzing the transfer of coenzyme A (C oA) from formyl-CoA and oxalate to provide formate and oxalyl-CoA for oxalate degradation. One interesting feature of FRC is that a tetraglycine loop in the active si te can adopt two (open/closed) c onformations. The focus of this work is on understanding the dynamical properties of a mobile loop which is composed of four contiguous glycine residues. In this thesis, we report the structural (conformational) and thermodynamic (energetic) studies of the tetraglyci ne loop in the presence or absence of CoA. Molecular dynamics simulation was used to obtain structural or dynamic information for molecular systems in the FRC enzyme. Because of limitations on simulation times and on energy barriers to conformational tran sitions, however, two alternativ e approaches (normal mode analysis and free energy calculati on) were introduced for investig ation of the dynamic properties and the energetics of FRC enzyme. Normal mode analysis showed that the conformational change of open to closed state of tetraglycine loop structure is not driven by presence of any ligand su ch as CoA, but is related to inherent feature of free enzyme structure. In our X-ray crystal structure of FRC, the side chain of 12

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13 Trp48A, which is one of crucial active site residues and is thought to affect the conformational change of loop, rotates 90 in the open conformation of the tetraglycine loop. Because conformational loop changes in prot eins require simulation methods with the microsecond or millisecond time scales, a new fr ee energy sampling strategy, ORSW technique, was used to obtain such information usi ng nanosecond simulations. Our OSRW technique showed consistency with experimental steady-st ate kinetic properties of the wild-type FRC and the known FRC loop variants, and demonstrated the feasibility of using OSRW sampling to obtain quantitative information on the conformationa l preferences of loops within enzyme active sites. The method also correctly detected the side-c hain reorganization of the Trp48A residue. Through comparative studies by experimental and th eoretical results, we could illustrate that conformational change in the tetraglycine loop plays a cruc ial role in stabilization of intermediate structures and control of substrate access.

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CHAP TER 1 INTRODUCTION Formyl-CoA Transferase (FRC) As a member of a new family member of CoA-transferases, formyl-CoA transferase (FRC)[ 1 2 3 ] is an enzyme that can catalyze CoA (coenzyme A) transfer from formyl-CoA and oxalate to form two products ( formate and oxalyl-CoA )[ 4 ] in bacteria such as Oxalobacter formigenes .[ 5 6 ] The FRC enzyme is known to be involved in oxalate degradation in bacte rom formyl-CoA to oxalate,[ 11 ] giving oxalyl-CoA and formate as products as shown in Fig. 1-1. ria.[ 7 8 9 ] Free formyl-CoA transferase has ca. 47 kD a of monomeric mass with 428 residues.[ 10 ] In 1989 Anatharam and Maloney[ 4 ] experimentally proved that FRC catalyzes transfer of CoA f oxalate formyl-CoA oxalyl-CoA formate Figure 1-1. Formyl-CoA transf erase enzyme pathway in O. formigenes for transfer of CoA from and cture of CoAbound formate to oxalate. The structure of FRC from O. formigenes[ 5 6 ] was obtained by Richards and Lindqvist was the first crystal structure in the new Family III[ 12 13 14 15 16 ] of CoA transferases.[ 17 ] The structure is characterized by tw o spherically shaped monomers which forms an intertwined structure like an interlocked chain.[ 10, 18 19 ] Each dimer has two active sites on opposite sides of the structure, and defined by the cleft between the monomers (Fig. 1-2) The stru enzyme reveals that Trp48A, Tyr59A and Asp169A are the active site. 14

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For the understanding of the structure a nd m echanism of FRC enzyme, the crystal structures of the apo-enzyme of FRC (apo-FRC) and CoA-binding FRC complex (CoA-FRC) were solved at 2.2 and 2. 5 resolution, respectively.[ 17 ] Figure 1-2. Crystal structure of the intertwined FRC dimer with bound CoA. For clarity, the two The bound CoA molecules are shown as sp ace-filling models, while active site o C complex (PDB accession code 1p5r ) is identical to the apo state of FRC except for two CoA molecules. The mono mer structure of FRC is composed of three monom ers are colored yellow and gray, a nd are represented by molecular ribbons. residues are shown as bond representations. The apo-FRC (PDB accession code 1p5h) is a homo-dimer consisting of 854 residues (427 amino acids per monomer) with 530 water molecules. The first residue is not observed due t crystal disorder. The CoA-FR 15

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structural dom ains: a large (blue) and a small domain (red) that are connected by two linker regions (magenta) (Fig. 1-3). Figure 1-3. 3-D representation of the crystal structure of F RC monomer. Each monomer is is red, and the two linker -helices are colored magenta. The tetraglycine loop residues s with the N-terminal domain of the Aer. This highly intertwined arrangement is unusual, and the conformational changes that facilitate the assembly of the dimer are as yet unknown. shown as cartoon representati on. The large domain is colored blue, the small domain (Gly258 to Gly261) are hi ghlighted in green. Dimeric FRC enzyme consisted of two intertwined elongated ring structures. Thus, intermonomeric interactions should be considered betw een the active site residues of the first (A) monomer and the residues of second (B) monomer. The C-terminal domain of the A monomer folds around the B monomer to form non-covalent interaction monom 16

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Figure 1-4. 3D representation of active site residues of apoenzyme of FRC in blue ( left ) and CoA-binding FRC in magenta ( right ). The ball and stick model represents the coenzyme A (CoA) of CoA-FRC. Resi dues in red correspond to the long loop structures, including Gln231 to Ala257. The most distinctive feature of formyl-CoA transferase (FRC) is in the open/closed conformational change of a shor t flexible loop, called the tetraglycine loop, in small domain region. In apo-FRC, this tetragly cine loop (residues 258 to 261) is in the open state in the B monomer, but is in the closed state in the A monomer. In CoA-FRC, however, both monomers have the tetraglycine loop in th e closed conformation (Fig. 1-4). The names of all secondary elements consti tuting an FRC monomer are given in Fig. 1-5. Although crystal structures of the closed/open conformations of FRC are known, the mechanism of the conformational change in the te traglycine loop is still unclear. 17

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Type Residue number Name aStrand Asn9 Asp12 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6 7 8 9 10 11 12 Helix Ala18 Phe28 1 Strand Asn32 Glu37 2 Helix Met44 Leu49 2 Helix Leu58 Thr61 3 Strand Arg68 Glu71 3 Helix Pro77 Lys89 4 Strand Val92 Glu95 4 Helix Ala101 Asn104 5 Helix Trp109 Leu115 6 Strand Ile20 Lys125 5 Helix Glu140 Ser146 7 Helix Ala150 Thr152 8 Helix Lue167 Thr190 9 Strand Lys195 Ala199 6 Helix Met200 Thr221 10 Helix Pro228 Ala230 11 Tetraglycine Gly258 Gly261 Strand Gly264 Lys268 7 Strand Tyr279 Thr283 8 Helix Trp289 Met295 12 Helix Pro299 Trp301 13 Helix Phe310 Arg313 14 Helix Leu317 Thr326 15 Helix Lys333 Ala341 16 Strand Cys347 Pro349 9 Helix Met353 His358 17 Helix Pro360 Lys364 18 bStrand Val368 Val371 10 Strand His379 Val382 11 Strand Phe386 Phe388 12 Helix Thr405 Leu412 19 Helix Asp416 Ala424 20 Figure 1-5. Topology and sequence representa tion for the secondary structure of formyl-CoA transferase (FRC) monomer. Shaded residues a and b represent N-terminal and C-terminal amino acids. The formyl or oxalyl form of CoA (formyl-CoA or oxalyl CoA) reacts with free FRC to form an acylated FRC intermediate. The covalent structure of CoA is shown in Fig. 1-6. CoA is composed of a pantetheine part (consisting of a pantothenate and -mercaptoethylamine group), which is attached to a 3-phosphorylated ADP moie ty. The CoA is close to the tetraglycine loop (Gly258 to Gly261) in the closed conformation. 18

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O N N N N NH2HO O O P O P O N P O-O O O OO OOH O N O SH 3-phosphate adenosine diphosphate Pantetheine Pantothenic acid mercaptoethylamine O N N N N NH2HO O O P O P O N P O-O O O OO OOH O N O SH 3-phosphate adenosine diphosphate Pantetheine Pantothenic acid mercaptoethylamine Figure 1-6. Structure of Coenzyme A (CoA). The only major difference between the struct ure of the apo-FRC (red) and the CoA-FRC complex (blue) is associated with the tetraglycine loop defi ned by residues Gly258 to Gly261, as shown in Fig. 1-7. In the apo-FRC dimer, this flex ible tetraglycine loop takes the open form in the B monomer, but it has the closed form in the A monomer. In the CoA-FRC complex, however, the tetraglycine loops of both monomers are in the closed conformation. Changes in the conformation of the tetraglycine loop are also correlated with the rotation of the Trp48A side chain (indole ring), in which location of the 1 (C-C-C-C) dihedral may affect the conformational motion of the tetraglycine loop. Only the thiol (-SH) group in CoA participates in the enzymatic reaction of FRC. The remaini ng parts of the CoA molecule may serve as recognition elements for binding by CoA-dependent enzymes. 19

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Figure 1-7. Active site residue s in apo(red) and CoA-binding FRC (blue). Bound CoA and the tetraglycine loop are rendered as ball-andstick model, and the crucial active site residues are modeled in sticks. The first catalytic mechanism for formyl-C oA transferase, proposed by Jonsson and Richards in 2003,[ 20 ] demonstrated that the active site residue Asp169 in the A monomer has an important role in the sequential mechanism st arting from formyl-CoA. The complete reaction mechanism for formyl-CoA:oxalate CoA transfer ase was reinvestigated in 2008 by Berthold et al.[ 21 ] as presented in Fig. 1-8. 20

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Figure 1-8. Catalytic mechanism for formyl-CoA transferase. Final produ cts are shown in red, while main compounds for reactions are in blue. In the reaction, formyl-CoA and oxalate as r eactants are converted to formate and oxalylCoA as the final products. This occurs via Asp169A, where CoASattacks aspartyl-formyl anhydride to form -aspartyl-CoA thioester (step 2), whic h is attacked by oxalate to form aspartyl-oxalyl anhydride (step3), which s ubsequently generates Asp169A with oxalyl-CoA (step4). The rate-determining step has not yet been determined, but is probably the release of the final product. The active site structural scenario fo r this mechanism is shown in Fig. 1-9.[ 21 ] According to proposed mechanism by Berthold et al., the tetraglycine loop in formyl-CoA transferase is initially in the open form (Fig. 1-9, A) around Gln17A, which is located behind Asp169A and is known to block the unusual intermed iate structure. This open conf ormation of tetraglycine is changed to the closed loop with formation of th e aspartyl-formyl anhydride complex (Fig. 1-9B), and the loop conformation is restored to the open form with the attack of CoASon the anhydride (Fig. 1-9C). 21

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Figure 1-9. Structural representati ons of each step in the cataly tic mechanisms for formyl-CoA transferase. A the active site residue motion incl uding open loop of tetraglycine in formyl-CoA. B the aspartyl-formy l anhydride (step 1). C -aspartyl-CoA thioester (step 2). D closed loop conformation with th e enzyme-CoA thioester in the B monomer. E the aspartyl-oxalyl anhydride (step 3). F final products of apoenzyme with closed loop conformation. Figure used with permission of Journal of Biological Chemistry, Vol. 283 (10), Berthold, C. L ., Toyota, C. G., Richards, N. G., and Lindqvist, Y. pp 6519-6529. Copyright 2008 Journal of Biological Chemistry.[ 21] From this step the oxalate from step 3 in Fig. 1-8 binds to the open conformation of the loop structure, resulting in the activated loop motion (Fig. 1-9D), in which formate is pushed down into the active site. The activated CoA conformation generates a cavity sufficiently large for oxalate to bind to -aspartyl-CoA thioeste r (Fig. 1-9E), and Asp169A and oxalyl-CoA are regenerated by attack of CoASon the aspartyl-oxalyl anhyd ride complex, returning the tetraglycine loop structure to the open form (Fig. 1-9F). 22

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23 Research Goals The goals of this research on formyl-CoA transferase (FRC) were to examine the conformational changes of the tetraglycine loop structure in the apo state (apo-FRC) and CoAbinding state of FRC enzyme (CoA-FRC). In the cas e of apo-FRC, the tetraglycine loop structure of the B monomer is in the open conformation, wh ile the loop conformation of the B monomer is in the closed state in the CoA-FRC. The studies in this thesis address three questions. (1) Can the dynamic motion of loop conformation be observed in th e range of molecular mechanics calculation? (2) How does substrate binding control the conformation of th e tetraglycine loop? (3 ) Can the conformational motion of the tetraglycine loop change between open/closed states in the presence/absence of substrate? (4) Are the glycine residues of the mo bile loop all of equal im portance in affecting loop movement and motional energetics? To satisfy the above questions and to reach the final research goal, three kinds of computational approaches and consequent spec ific aims were introduced (1) Simulating molecular dynamics[ 22 23 24 ] for the dynamic properties of a system in the nanosecond time scale (Chapter 2), (2) Performing low frequency normal mode analysis[ 25 ] to model the global (collective) motion of the FRC dimer (Cha pter 3), and (3) Computing the free energy differences[ 26 27 ] for the conformational changes betw een open/closed loop motion in FRC (Chapter 4).

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CHAP TER 2 MOLECULAR DYNAMICS SIMULATION OF FORMYL-COA TRANSFERASE Introduction We wanted to understand the role of the dynamic properties of the mobile loop in the catalytic mechanism of FRC. Through recent X-ray studies of the FRC enzyme,[ 17] we could determine the interactions of the active site resi dues and the tetraglycine loop structure of FRC. No experimental information, however, exis ts on the thermodynamics and detailed conformational motion for the loop of FRC enzyme Molecular dynamics (MD) simulations were initially used to model dynamic properties in FRC, so as to provide information on the interaction between protein and s ubstrate at a nanosecond time scale. We performed a comparative study of the a po state of FRC enzyme and the CoA-binding FRC complex. Molecular dynamics (MD) simulation[ 22 23, 24 ] using CHARMM force field[ 28 ] were utilized to determine the thermodynamics and detailed dynamical motions in the presence and absence of CoA. It was expected that the com puted trajectories would allow us to follow the conformational changes of the tetraglycine loop and to an alyze key nonbonded interactions between residues. Materials and Methods CHARMM Force Field Since molecular dynamics (MD) simula tion was developed in 1957 by Alder and Wainwright for condensed phase systems,[ 29 ] numerous MD program packages for biological systems have been developed, including CHARMM (Chemistry at HARvard Molecular Mechanics),[ 30 ] AMBER (Assisted Model Building with Energy Refinement),[ 31 ] GROMACS (GROningen MAchine for Chemical Simulations),[ 32 ] and X-PLOR.[ 33 ] 24

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As the first study of the confor mational motion of FRC in the nanosecond time scale, an atomic molecular dynamics (MD) s imulation was executed with CHARMM,[ 30 ] a representative molecular mechanics program, which was necessa ry for computing the detailed dynamic motions of FRC and for calculating the free energy profil es of the tetraglycine loop. The CHARMM 27 force field[ 28 ] represents the potential energy of larg e biomolecules as a function of nuclear positions using simple classical potentials.[ 28 34 35 36 ] vdW elec UB bE iji ij ij ij ij ij E iji ij ji E Bradley Urey ii UB E impropers ii E torsion E angle ii E bond iibrr r qq rrk k nk krrkrV 6 12 20, 3,13,1 2 0, 2 0, 2 0,4 )( )()]cos(1[)()()( (2-1) where represents the potential energy along the a function of at om ic coordinate, including bonding energy terms and non-bonding energy contributions. Bonding energy terms contain bond ( ri), angle ( )( rVi ), dihedral angle (i ), improper angle (i ), and Urey-Bradley ( ) contribution on the ith atomic position. Each value of k (,,, and ) represents the force constant for each b onding energy term, and 0 denotes the equilibrium state for each term. In particular, the Urey-Bradley term (additi onal 1,3 nonbonding energy term) is very useful for matching spectroscopic data. All bonding energy terms use the harmonic potential, while the dihedral angle term is expre ssed by a sinusoidal form, where n indicates the multiplicity and expresses the phase shift. The nonbonding energy terms (Eelec and EvdW) included the electrostatic energy using the Coulombic potentia l for the two point charge (qi and qj) and the van der Waals energy with Lennard-Jones 6-12 potential. In the electrostatic energy term, is the dielectric constant of medium, and ij is the minimum distance of the Lennard-Jones term. ir3,1 bk kkkUBk 25

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Molecular Dynamic Methodology In this study, the atomic trajectories of the apo-FRC and the CoA-FRC complex (about 18,000 atoms) were generated by direct numerical integration of Newton s equations of motion (Fi = miai) using the CHARMM potential: i iim F dt rd2 2 (2-2) where mi represents the mass of a particle i, Fi is the force on the particle i. The CHARMM potential energy, V(r), yields the force on each atom from the gradient of energy, i i idr rdV F )( Combining these equations yields, i i i idr rdV dt rd m )(2 2 (2-3) This equation describes the motion of a particle of mass mi as a function of the position ri with derivative of the potential energy ( V ). For integrating Newtons equation of motion, the Verlet algorithm[ 37 38 ] was introduced based on Taylor series expansion in a MD simulation as follows: )( 2 1 )()()(2tatttvtrttr (2-4) )( 2 1 )()()(2tatttvtrttr (2-5) Adding Eq. 2-4 and Eq. 2-5 gives )()()(2)(2tatttrtrttr (2-6) In Eq. 2-6, new position,)( ttr can be calculated us ing acceleration at time t and the previous position, ) ( ttr Although Eq. 2-6 in the Verlet algorithm does not include the 26

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velocity te rm, it can be calculated by divi ding the difference in positions at times tt and tt byt 2. t ttrttr tv 2 )()( )( (2-7) By integration of Newtons equations of motion, a trajectory can be calculated to describe the positions of particles as a function of time. For an MD simulation of a biomolecular system, it is necessary to define the initial configuration of the system, including the initial positions and the initial distribution of velocities. The initial positions may be obtained from experimental data such as the X-ray crystal stru cture of the protein or from a structure determined by NMR spectroscopy. The initial dist ribution of velocities was sel ected from a Maxwell-Boltzmann distribution at 300 K and corrected so there was no overall transl ational or rotational momentum. N i iivmP10 (2-8) The probability that an atom i has a velocity vx in the x direction at a temperature T is then: Tk vm Tk m vPB ixi B i ix 2 2/12 1 exp 2 ) ( (2-9) The temperature of a molecular system is calculated from the average kinetic energy using the relation KTNkvmB N i ii 2 3 2 11 2 (2-10) Molecular Dynamics Characteristics Time-dependent trajectories were displaye d graphically and analyzed by computing a number of properties, such as the Root-Mean-S quare (RMS) Deviation (R MSD) (Eq. 2-11) and 27

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Fluctuation (RMSF) (Eq. 2-12), f or comparison with the experime ntal crystallographic B-factor (Eq. 2-13).[ 39 ] The RMSD between two structures is an overa ll measure of the average deviation between two different conformations ( and ) of a given atom i N i ii i iirr N rr RMSD1 2 2)( 1 )( (2-11) While the RMSD is the difference between two structures for a specific set of atoms, RMSF can be understood as the fluctuation around an average position of particle i over a set of trajectories. N i iirr N RMSF1 2)( 1 (2-12) Finally, an experimental temperature fact or (called the B-f actor) of the X-ray crystallographic structure may be converted and compared with the calculated RMS fluctuations for a given position of the particle. 2 2)( 3 8 RMSF B (2-13) System Setup Two crystal structures of th e apo state of FRC (pdb code: 1p5h) and CoA-binding FRC complex (pdb code: 1p5r ) were used as the initial struct ures for molecular dynamics (MD) simulation from the Protein Data Bank.[ 40 ] The CoA parameter was modified from that of acetylCoA in citrate synthase[ 41 ] (Fig. 2-1) ; identical parameters were used in the 3-phosphorylated ADP and pantothenate groups, a nd the acetyl moiety from the -mercaptoethylamine group was changed to a hydrogen atom. Thus, atom types and atomic partial charges were, hence, derived 28

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by the analogy with present CHARMM 27 topo logy files. T he bond connectivity and angle information were referred to the closest match in the CHARMM parameter files. HN1 HN2 C4 N7 N6 C6P N1 C5P N3 C2P C8 N9 C1A C2A H2A O2A HOA C3A H3A O3A P3A O7O8 O9P C4A C5A H51 H52 O5A P1 O1 O2 O3 O4 P2O5P O6 C12 H12 H11 C11 C10 C9 N8 C7 C6 C5 N4 C3 C2 S1 H1 H22 H21 H31H32 H4 O5 H61H62 H72 H71 H8 O9 H10 O10 HO C13 C14 H16 H17 H18 H13 H14 H15 O4A H4A H1A H2P H8(HN1) (HN1) (NN1) (CN5) (NN3A) (CN4) (HN3) (NN3A) (CN5) (NN4) (CN4) (HN3) (NN2) (CN7B) (HN7) (HN7) (HN7) (HN7) (CN7) (CN7) (CN7) (ON5) (HN5) (ON5B) (ON2) (ON3) (ON3) (ON3) (P2) (P2) (P2) (ON3) (ON3) (ON3) (ON3) (ON2) (ON2) (CN8) (HN8) (HN8) (ON2) (CT2) (CT1) (CT3) (CT3) (CT1) (CT2) (CT2) (CT2) (CT2) (OH1) (H) (HA) (HA) (HA) (HA) (HA) (HA) (H) (NP) (NP) (H) (HA) (HA) (HA)(HA) (S) (HS) (C) (O) (O) (C) (HA) (HA) (HA) (HA) (HA) (HA) (HA) (CN5) (A) (B) (C) (D) (F) (A)Purinering part (B)Ribose ring part (C)3-phosphate part (D)5-phosphate part (E)Pantetheinicacid part (F)Beta-Mercaptoethylaminepart (E) Figure 2-1. Representation of coenzyme A (CoA) with atom names and their types necessary for CoA parameterization. As a control enzyme, CoA-free FRC enzyme (after removal of CoA from CoA-FRC complex) was prepared for structural comparison focusing on the tetraglycine loop structures of apo-FRC and CoA-FRC complex. All three simula tions for the apo-FRC, the CoA-FRC, and the CoA-free FRC enzymes were perfor med with identical procedures. 29

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All atom s, including hydrogens, were descri bed explicitly using the HBUILD routine[ 42 ] of the package.[ 30 ] The systems were then placed w ithin a cubic water box of length 108 (Fig. 2-2). All crystallographically resolved water oxygen positions were retained in the apo system as well as in CoA-binding system Two systems (apo-FRC and CoA-binding FRC) were completed by adding counter-i ons and solvent waters (TIP3P[ 43 ] molecules). Figure 2-2. The sim ulated formyl-CoA transferase system with solvated waters. The proteins are rendered as cartoons with each monomer in a different color (pink and blue). The counter-ions for neutralization of system are colored dark blue. The 33,952 randomly oriented water molecules (in red) ar e placed in a cubic box of length 108 Molecular Dynamics Simu lation of FRC Enzymes MD production simulations of 20 ns in leng th were carried ou t in explicit water surroundings[ 44 45 ] for the apo state, CoA-binding state, and CoA-free FRC state in order to explore the dynamic behavior of the enzyme. Three different systems were individually subjected to minimization, followed by short heating and equilibration steps before the production runs using NAMD2 version 2.6b1.[ 46 47 ] The SHAKE option[ 48 ] was used to remove 30

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high frequency vibration on polar hydrogen atom s. The particle-mesh Ewald (PME) method[ 49 50 51 ] was also used for the long-range electro statics with Coulombi c interactions. The van der Waals cutoff was set to 12 with a sw itching function that started at 10 In the heating phase, the simulation temperature was slowly raised in steps to 300 K, with the system preserving the crystallographic structur e. At the final required temperature (300 K), a short period of equilibration step (250 ps) was included to re-assign initial velocities for the desired temperature, because we were interested in the conformational changes of the flexible loop. The periodic boundary condition (PBC)[ 52 53 ] was used using a NPT (isothermal-isobaric) ensemble with a flexible cell and the hybrid Nos-Hoover Langevin piston method[ 54 55 ] to control the pressure (1 atm). The equilibrated structures of apo-FRC, CoA-FRC, and CoA-free FRC were very close to the crys tal structure, the RMSD of C atoms being only 0.35, 0.38, and 0.29 respectively. A shorter period of equilibration time was needed in all our simulations, since we were interested in the conformational changes of flexible loop that take place during the simulation. The equilibration periods were followed by longer periods of productive MD simulations with a time step of 2 fs. After obtaining 20 ns of production steps, all te n structures at 2 ns time-intervals were superimposed for trajectory analysis. The practical production step was performed by NAMD2 program. All MD simulations were carried out on the high CPU Linux cluster at the University of Florida. Results and Discussions The intra-monomer structural properties of FR C during the simulations are presented first, followed by the large-scale atomic motions as su ggested by the analysis of the inter-monomer motions. The effect of the inter-monomer fluctuations on access to active site is then described. 31

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As we are in terested mainly in the inter-monomer motions that affect the accessibility of the active sites to substrates, the following discus sion focuses on the tetraglycine loop structure (Gly258 to Gly261) of the B monomer and the cruc ial active residues of the A monomer (Trp48, Tyr59, and Asp169) only, if not otherwise indicated. RMSD Analysis of FRC Simulation Time (ps)RMSD ()A-monomer Simulation Time (ps)RMSD ()A-monomer Simulation Time (ps)RMSD ()B-monomer Simulation Time (ps)RMSD ()B-monomer Figure 2-3. The C RMS deviation representation in each monomer of FRC. The values of ApoFRC and CoA-FRC, and CoA-free FRC are colored in blue, magenta, and green, respectively The overall properties of three FRC enzy mes may be examined through Root-MeanSquare Deviation (RMSD) analysis, by which the displacements of residues can be monitored 32

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from their initial optimized positions. Generally, the RMS deviation plot shows a distinguishable increase in the initial phase a nd regular oscillations around the av erage value in the later phase. The structural RMS deviations of the three enzymes (apo-FRC, CoA-FRC, and CoA-free FRC) are plotted in Fig. 2-3. In the apo-FRC, CoA-FRC, and CoA-free FRC enzymes, the RMS deviations relative to the starti ng structures generally leveled o ff after ca. 3 ns, indicating that these structures provide reasonable initial paramete rs for the MD simulation. Fig. 2-3 shows that the free FRC (apo-FRC) has an average RMSD of 1.86 and CoA-FRC has an average RMSD of 1.59 in the B monomer. The CoA-binding FRC complex (CoA-FRC) showed more than 20% reduction in the average RMSD compared to apo-FRC. Flexibility Changes upon Subs trate Binding and Unbinding Compared with the free state of FRC (apoFRC), CoA-FRC simulation is expected to undergo structural changes due to the existence of CoA close to the active site residues of FRC. We then proceed to compare these changes with respect to the simulation results from the apoFRC simulation. residue numberRMSF ( )residue numberRMSF ( )050100150200250300350400450 0.0 0.5 1.0 1.5 2.0 2.5 3.0 apo-FRC (20 ns MD) CoA-FRC (20 ns MD) apo-FRC (X-ray) CoA-FRC (X-ray)050100150200250300350400450 0.0 0.5 1.0 1.5 2.0 2.5 3.0 apo-FRC (20 ns MD) CoA-FRC (20 ns MD) apo-FRC (X-ray) CoA-FRC (X-ray)Figure 2-4. Experimental vers us calculated RMS fluctuations for two FRC enzymes in first monomer ( left ) and in the second monomer ( right ). apo-FRC and CoA-FRC were shown as blue and magenta, respectively. Fig. 2-4 shows the results of dynamic fluctuatio ns of enzyme residues in apo-FRC and in CoAFRC. To identify the relative internal motions of the enzyme residues in the apo-FRC and CoA33

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FRC si mulations, the Root-Mean-Square fluctuations (RMSFs) were calculated based on the isotropic temperature factor (B-factor) of the X-ray structure according to Eq. 2-13. To characterize the influence of CoA binding on the flexibility of the enzymes, RMSFs of the C atom of each residue in apo-FRC and CoAFRC (bold solid line of Fig. 2-4) were compared with those based on X-ra y structures (circles in Fig. 2-4). The results for apo-FRC are shown in blue and those for CoA-FRC are in magenta, unless otherwis e indicated. Although the RMSF of the C atoms derived from the X-ray structures is higher for several of the residues, considerable similarities are observed for X-ra y structures and MD simulations between apoFRC and CoA-FRC. This confirms that the intr insic flexibility of the two enzymes is not sensitive to their precise structures, because only difference is the presence or absence of CoA. In general, fluctuation peaks based on MD simulation (bold solid line in Fig. 2-4) were more intensive compared to those based on X-ray structures (c ircles in Fig. 2-4), but these differences are understandable because the MD simulations in cluded the interactions between solute and solvent waters. In order to emphasize the roles of each of the active site re sidues of A monomer and the short loop structure of B monomer, RMSF result s for the crucial active site residues (Trp48, Tyr59, and Asp169) of A-monomer are compared w ith those for the tetraglycine loop structure of the B monomer in Table 2-1. Table 2-1. Comparative fluctuation dynamics of the active site in FRCa apo-FRC CoA-FRC CoA-free FRC Gly258B ~ Gly261Bb 0.99 0.76 1.54 Trp48A 1.10 1.70 0.89 Tyr59A 0.61 0.77 0.67 Asp169A 0.49 0.55 0.67 aAverage RMSFs (in angstrom) over the 20 ns dynamics simulation. bRMSFs centering on tetraglycine loop residues for apoand CoA-FRC are shown in Fig. 2-5. 34

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The RMSFs of tetraglycine loop structure (residues 258 ~ 261) show the typical trends of a nanosecond scale MD simulation. T he fluctuations of the apo-enzyme (0.99 ) are larger than those of the holo-enzyme (0.76 ), in which th e active site and CoA interact strongly. The distinguishable difference between MD simulation and X-ray struct ure are open to argument, and show the limitations of molecular mechanics technique with nanosecond time scale. The other active site residues, e.g. Tyr 59A and Asp169A, do not show significant fluctuation differences between apo-and CoA-binding FRC. Trp48A, howev er, shows a larger fluctuation upon binding to CoA (1.10 vs. 1.70 ). This can be explai ned as a rotation of the side chain of Trp48A affecting the conformational motion of tetraglycine loop to open state. residue numberRMSF ( )250252254256258260262264266268270 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 apo-FRC (20 ns MD) CoA-FRC (20 ns MD) apo-FRC (X-ray) CoA-FRC (X-ray)residue numberRMSF ( )250252254256258260262264266268270 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 apo-FRC (20 ns MD) CoA-FRC (20ns MD) apo-FRC (X-ray) CoA-FRC (X-ray)residue numberRMSF ( )250252254256258260262264266268270 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 apo-FRC (20 ns MD) CoA-FRC (20 ns MD) apo-FRC (X-ray) CoA-FRC (X-ray)residue numberRMSF ( )250252254256258260262264266268270 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 apo-FRC (20 ns MD) CoA-FRC (20ns MD) apo-FRC (X-ray) CoA-FRC (X-ray) Figure 2-5. Experimental versus calculated RMSFs centering on te traglycine loop structures in apo-FRC and CoA-binding FRC. Left and right represents the RMSF results for the A monomer and the B monomer, respectively. Apo-FRC and CoA-FRC are in blue and magenta, respectively. Top two thin dot-line plots are RMSF based on B-factors of Xray structures; bottom bold solid lines based on 20 ns of NAMD MD simulations. A closer look at tetraglycine loop fluctuat ions was necessary (Fig. 2-5) because the comparison of the C RMSF calculated from all-atom MD simulations with that of X-ray structures (Fig. 2-4) suggests that there are small but significant motional changes in the proximity of the tetraglycine loop region of B monomer. 35

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In m ost enzymes, the overall substrate binding complex simulation shows smaller structural deviations and fluctuat ions than the apo state of enzyme particularly in the active site residues.[ 56 57 58 ] This can be explained by the stabilizing interactions of the substrate moieties with these residues. The present MD simulations show reduced fluctuations in CoA-FRC (bold solid magenta line of Fig. 2-5) and increased peaks in apo-FRC (residues 250-270) (bold solid blue line of Fig. 2-5). The RMS fluctuations based on B-factor of X-ray structure (dot-line plots of Fig. 2-5), however, showed oppos ite peak trends relative to t hose of the MD simulation. Our MD simulation results may follow the general trend[ 56, 57 58] that the stabilizing interactions between substrate and protein in the holo-enzyme lo wers their fluctuations compared to those of free enzyme. In our MD simulation, CoA-bound FRC enzyme has a lower RMSF than the apo state of FRC enzyme (0.99 of apo-FRC and 0. 76 of CoA-FRC in Table 2-1). Nevertheless, these results are at variance with the X-ray re sults, which indicated that CoA-binding FRC has should have much larger fluctuat ions than those of apo-FRC. Hydrogen Bond in CoA-binding FRC An interesting feature of CoA-binding FRC complex (CoA-FRC) is the abundance of molecular non-covalent interactions between the activ e site residues and CoA, as seen in Fig. 2-6. In the X-ray structure of CoA-FRC (pdb code; 1p5r ), the adenine and ribose parts of CoA are exposed to the solvent surface, while the pantet heine long chain is covered by the large protein domain. The end of pantetheine arm (thiol group, -SH) is located near the small domain region, where the tetraglycine loop residue s are in the closed conformation. The adenine part of CoA is located near the side chain of Arg38 in the A-monomer. The phosphoribose interacts with FRC via two hydrogen bonds, one between O4A of CoA a nd NH1 atom of Arg38, the second between a phosphate oxygen atom (O7) of CoA and the side chain (NH1) of Arg104. The carbonyl 36

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moiety of the pyrophosphate (O1) and the hydrox yl group of pantethein e (O10) of CoA for m hydrogen bonds to the side chains of His15 and to the main chain carbonyl of Asn96. Asp169(OD1)Asp169(OD2)Gln17(N)Ala18(N)CoA (S1) His15(NE2)CoA(O1)CoA(O10)CoA(O4A)CoA(O7)Arg38(NH1) Arg104(NH1)Asn96 Asp169(OD1)Asp169(OD2)Gln17(N)Ala18(N)CoA (S1) His15(NE2)CoA(O1)CoA(O10)CoA(O4A)CoA(O7)Arg38(NH1) Arg104(NH1)Asn96 Figure 2-6. Protein-CoA inter actions based on the X -ray structure of CoA-FRC. Interactions between active site residues and CoA, which persist throughout CoA-binding FRC simulation, are shown. Active site residues were drawn as bond representation, while CoA was shown as ball-and-stick models. The thiol (-SH) group of CoA points towards the N-terminus of the -1 helix near to the mainchain amino group of Gln17A (N) and Ala18A (N) and also near to the side chain of Asp169A (OD1, OD2). Based on interactions between the active site residues and CoA (excluding hydrogens) in the X-ray structure of CoA-FRC, the molecular interactions with 20 ns of MDs are shown and compared to X-ray structures in Table 2-2 and Fig. 2-7. 37

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Table 2 -2. Distance comparison of activ e site residues and CoA between X-ray crystal structure and average MD structure. CoA Active site residues Average Crystal Diff. (a) Ribose ring (O4A) Arg38 (NH1) 3.34 3.85 -0.51 (b) 3-phosphate (O7) Arg104 (NH1) 3.53 2.42 1.11 (c) Pantetheine (O1) His15 (NE2) 8.30 3.60 4.70 (d) Pantetheine (O10) His15 (NE2) 5.91 2.78 3.13 (e) Pantetheine (O10) Asn96 (O) 7.05 5.33 1.72 (f) Thiol (S1) Asp169 (OD1) 4.47 3.78 0.69 (g) Thiol (S1) Asp169 (OD2) 5.51 3.18 2.33 (h) Thiol (S1) Gln17 (N of amide) 5.40 2.72 2.68 (i) Thiol (S1) Ala18 (N of amide) 5.51 2.65 2.86 The MD simulation of the CoA-FRC showed th e most significant and marked increase in considerable distances at the active site during the CoA binding simulations, e.g., centered on the carbonyl groups (CO-) of pantetheine side chain and thiol group (SH-) of CoA. His15CoA This residue results in losses of tw o hydrogen bonds to CoA. Two distances between CoA and His15 (e.g., CoA:O1His15:NE 2 and CoA:O10His15:NE2) showed initially close interaction (3.60 and 2.78 ), but their di stances were lengthened w ith average values of 8.30 and 5.91 after 3ns and 4ns production (( c) and (d) of Table 2-2 and Fig. 2-7). Thiol group of CoA The intermolecular distance between Asp169A(OD2) and CoA(S1) increases from 3.18 to a maxi mum distance of 8 ((g) of Tabl e 2-2 and Fig. 2-7), and the Ala18(N) CoA(S1) interaction weakens from an initial distance of 2.65 to a maximum distance of 7 ((i) of Ta ble 2-2 and Fig. 2-7). The remaining interactions between CoA and residues of active site, e.g., Arg38, Arg104, Asn96, and Gln17, maintained correlated distan ces (Fig. 2-7). These residues are in close proximity to CoA substrate but do not have strong interactions with it. 38

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(a) Ribose ring (O4A) -Arg38 (NH1) 02468101214161820 0 1 2 3 4 5 6 7 runnin g time ( in ns ) distance(in ) (b) 3-phosphate (O7) Arg104 (NH1) running time (in ns)distance(in )02468101214161820 0 1 2 3 4 5 6 7 8 9 10 (c) Pantetheine (O1) -His15 (NE2) running time (in ns)distance(in )02468101214161820 0 1 2 3 4 5 6 7 8 9 10 11 12 (d) Pantetheine (O10) His15 (NE2) running time (in ns)distance(in )02468101214161820 0 1 2 3 4 5 6 7 8 (e) Pantetheine (O10) -Asn96 (O) running time (in ns)distance(in )02468101214161820 0 1 2 3 4 5 6 7 8 9 10 (f) Thiol (S1) -Asp169A (OD1) running time (in ns)distance(in )02468101214161820 0 1 2 3 4 5 6 7 8 (g) Thiol (S1) -Asp169 (OD2) running time (in ns)distance(in )02468101214161820 0 1 2 3 4 5 6 7 8 9 (h) Thiol (S1) -Gln17 (N of amide) running time (in ns)distance(in )02468101214161820 0 1 2 3 4 5 6 7 8 9 (i) Thiol (S1) -Ala18 (N of amide) running time (in ns)distance(in )02468101214161820 0 1 2 3 4 5 6 7 8 9 Figure 2-7. Plots of the distances between active site residues and CoA. 39

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Intramolecular Trajectory Analysis As described earlier, the mobilities of the ac tive site residues of monomer A (e.g., Trp48, Tyr59, and Asp169) in apo-FRC and CoA-FRC have strong effects on the conformational change of the tetraglycine loop structure in monomer B of FRC. Fig. 2-8 shows the superimposition of the 10 snapshots at 2 ns intervals in the MD simulation. Even though active site residues su ch as Tyr59A and Asp169A in three enzymes show flexible movement, these motions were not significant compared to that of Trp48A, whose side chain fluctuates into the middle of the tetr aglycine structure in the presence of CoA in CoAFRC, especially (see Fig. 2-8B). Asp169 Tyr59 Trp48 CoA Asp169 Tyr59 Trp48 CoA Asp169 Tyr59 Trp48 Asp169 Tyr59 Trp48 Asp169 Tyr59 Trp48 Asp169 Tyr59 Trp48 Figure 2-8. Ten snapshot stru ctu res with 2 ns intervals for three enzymes, apo-FRC ( top left ), CoA-FRC ( top right ), and CoA-free FRC ( bottom ). 40

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These sim ilarities provide evidence for a crucia l role of Trp48A on the conformational change in the tetraglycine loop. Fig. 2-9 shows the distance between the atoms in the A monomer (C of Trp48 and oxygen of Asp169) that are closest to tetraglycine loop residues (C of Gly261) of the B monomer throughout the simulation. In the CoAremoval system from CoA-binding FRC (CoAfree FRC, green color), the binding site drift from the closed state (0-9 ns) to the open state (9-20 ns) was observed. However, apo-FRC (blue color) and CoA-FRC complex (magenta color) did not show any significant structural differences between two dist ances during all 20 ns of MD simulation. Trp48AGly261B The initial distance between C of Trp48A and C of Gly261B in CoAfree FRC system (green color) was 9.5 repres enting a closed conformational tetraglycine loop motion. This motion fluctuated in the range of 9 with an average distance of 11.2 After the first 9 ns of simulation this distance changed to 7.5 with an average of 8 during the final phase of the simulation (9 ns) indicating an open state. On the other side, apo-FRC and CoA-FRC both maintained their inherent distan ces during 20 ns of simulation, respectively. Asp169AGly261B The result has the same patte rn as Trp48A-Gly261B. Apo-FRC and CoA-FRC have their uniform distances (OD2 of Asp169A and C of Trp48A) indicating open state (10 in apo-FRC) and closed state (5 in CoA-FRC), while the distance of CoA-free FRC fluctuated mostly from 6 to up to 11 after 9 ns of simulation time. To investigate the adjunct impact factors that can induce tetraglycine loop conformational change in FRC, we visually inspected the effects of Trp48 of A monomer in the presence and the absence of CoA (CoA-FRC and apo-FRC, respectiv ely) and CoA-free FRC after the removal of CoA from CoA-FRC. 41

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Distance () Asp169 Gly261Simulation Time (ps) Simulation Time (ps)Distance ()Trp48 Gly261 Simulation Time (ps)Distance ()Trp48 Gly261 Figure 2-9. Schematic diagram of interaction of the tetraglycine l oop structure of the B monomer with active site residues of A monomer. ( Bottom ) C distance interaction between the last residue (Gly261B ) of tetraglycine loop and C of Trp48A (Trp48AGly261B). ( Top ) The same interaction between th e last residue (Gly261B) of the tetraglycine loop and position of oxygen (OD2) of Asp169A (Asp169A-Gly261B). As usual, apo-FRC, CoA-FRC, and CoA-fr ee FRC are shown as the color of blue, magenta, and green, respectively, unless otherwise provided. The conformational change in the side chain of Trp48A, in its turn, induces the indole ring of Trp48A in apo-FRC (blue) to move orthogonally to the conformation in CoA-FRC (magenta) after 6 ns of simulation. 42

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running time (picosecond)Chi1 (Trp48)05000100001500020000 -180 -90 0 90 180 Figure 2-10. The time evol ution of dihedral angle 1 (C-CA-CB-CG) of Trp48A. The apo-FRC is shown in blue, the CoA-FRC in magenta, and the CoA-free FRC in green. In CoA-FRC, this happens after 15 ns of simula tion time as shown in Fig. 2-10, which is a plot of the time dependence of 1 dihedral angle (C-CA-CB-CG) of Trp48A for the entire 20 ns run. This figure shows that the fluctuation in 1 angle of Trp48A in the CoA-free FRC simulation (green) is much smaller than that in the apo FRC (blue) and CoA-FRC (magenta), and maintained its open conforma tion during the entire 20 ns of simulation. In contrast, in the apo-FRC simulation where the mi nimum dihedral angle in the Trp48A was 167 in the crystal structure, 1 fluctuated mostly between 160 and 180 (c losed state) to up to 45 to 90 (open state) after 5.5 ns of simulation time. Likewise CoA-binding FRC also displayed its closed to open state fluctuation after 11 ns of simulati on with short splits (at 11.6 to 13.2 ns). The above results indicate that the rotation of the side chai n of Trp48A can have a strong influence on the conformational change of tetraglycine loop m ovement, although we were unable to determine a significant conformational change of the tetraglycine loop structure with MD simulation at the nanosecond time scale. 43

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Conclusions Molecular dynamics simulation is suitable for investigating the mobility or flexibility of proteins or enzymes, occurring within the na nosecond time scale of the computer technique. Protein mobility or flexibility can be not only an inherent property in bi omolecules, but also an index of the catalytic mechanism of enzymes. Ou r study of MD simulations allowed us to gain important insights into the flexible behavior of FRC enzyme. It is believed that this is first attempt to investigate computationally a detaile d open and closed conformational motion of FRC even though there are a large amount of e xperimental data. The detailed survey on conformational changes a nd interor intra-monomer interac tion between two monomers of the FRC enzyme could be a crucial index in the und erstanding of the catalytic mechanism of FRC. It is an undeniable fact that experimental elucidation alone is not capable of probing the binding site of a protein and its substrate, the interactions betw een crucial active site residues, and the cross-interaction between long-range in ter-domain residues. In this study, we have computationally proved that FRC enzyme prom otes the interaction between protein (e.g. tetraglycine loop structure) a nd substrate (coenzyme A). We ha ve also described the possible mechanistic roles of Trp48A, Tyr59A, and Asp169A residues in the opening and closing dynamics of the FRC. Our 20 ns MD calculations provide typica l insights into the dynamic and energetic mechanisms of FRC with CoA bound, even thou gh these results did not agree with the normal mode analysis (Chapter 3). This indicates that conformational change for any loop motion should be investigated at a time scale longer than that of a nanosecond approach. We think nonequilibrium mechanical approaches such as steered or biased MD simulation,[ 59 ] or normal mode analysis[ 25 ] may be appropriate alternatives to MD simulation. 44

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CHAP TER 3 CONFORMATIONAL PROPERTIES OF TETRAGLYCINE LOOP IN FORMYL-COA TRANSFERASE: LOW FREQUENCY MOTIONS Introduction Large-scale conformational cha nges in enzymes involve the co llective motions of groups of atoms and therefore typically take place on microsecond timescales. Modeling such motions using conventional MD simulation methods is ve ry difficult because these approaches model small, localized movements that occur on the nanosecond timescale.[ 60 61 62 ] In an effort to overcome this limitation of MD simulations, st rategies based on analyzing the normal mode vibrational motions of large pr oteins have been developed.[ 25, 63 ] Thus, normal mode analysis (NMA) provides information on the low-frequenc y vibrations of the protein, which correspond to motions exhibiting the largest amplitude,[ 64 ] thereby providing a qualitative picture of the collective atomic motions that take place on the microsecond timescale. In NMA, vibrational motions of the system are obtained directly by assuming that the potential energy function varies qu adratically on an energy minimum,[ 65 ] and the harmonic dynamics of the molecule can be determined in cost-effective computational times. NMA has been widely used for modeling confor mational changes in several proteins[ 66 67 ] and for analyzing the complex path of dynamic interactions.[ 68 69 ] Recent advances in methodology of NMA have extended the application of this method to large proteins.[ 70 71 72 73 74 ] NMA calculations have several advantages ove r MD simulations. NMA is a relatively rapid computational technique in comparison with regular MD simulations; calculated fluctuations based on NMA can be compared w ith experimental values from the isotropic temperature factor ( B -factor) of the X-ray structure; and low-frequency modes can be analyzed into the conformational fluctuation. 45

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In this chapter, we inves tigate the open to cl osed conformational change in the tetraglycine loop regions of FRC in terms of harmonic motions determined by normal mode investigation for apo-FRC and CoA-FRC. In particular, the X-ray crystallographic data of CoA-FRC suggest the hypothesis that CoA-binding may stabilize the clos ed conformation of the tetraglycine loop, whereas the loop in the apo-FRC is in an open conformation. For the validation of this NMA study, we calculated the root-mean-square (RMS) fluctuations from normal mode data, and compar ed them with the actual RMS fluctuations derived from the temperature B-factor of X-ray cr ystallography. To test this hypothesis and to determine the extent to which dynamics influence the conformational change of tetraglycine loop motion, we calculated the internal molecular cont ributions using a glycineto-alanine mutation in its wild type (apo-FRC) and mutant forms such as G258A, G259A, G260A, and G261A. Methods Normal Mode Analysis Tetraglycine loop motions in apo-FRC and the CoA-FRC complex result in the opening/closing of a cleft between the regi on comprising the active site Asp169 and Trp48 residues of monomer A, and the four c ontiguous glycine resi dues (Gly258-Gly259-Gly260Gly261) of monomer B. Modeling such collec tive motions in this large system using conventional MD simulation is difficult due to the computational inefficiency of computing trajectories of sufficient length to show large scale changes.[ 75 76 77 ] A better method to investigate such collective (global) mo tions is normal mode analysis (NMA),[ 25] which describes dynamics in terms of a superimposition of normal mode coordinates. As usual, the potential energy function ( V ) can be expanded at an energy surface minimum ( r0) using Taylor expansion series. 46

PAGE 47

ijk k j i rr kji ij j i rr ji i rr i irrrrrr rrr V rrrr rr V r V rrrVrV ))()(( !3 1 ))(( !2 1 )()()(0 0 0 3 0 0 2 0 00 0 0 (3-1) In the expression of harmonic vibrational an alysis with a system corresponding to an energy minimum, the first term, V ( r0), is defined to be zero, and second term also vanishes from the gradient of the potential func tion (first derivative term) because the molecule is at an energy minimum. In addition, third and higher order de rivatives are excluded for small displacements treated in vibrational analys is. The harmonic approximation, by which normal modes and their frequencies are calculated, ther efore allows the potential en ergy to be represented as a summation of the second derivatives at small displacements from r0. ij j i rr jirrrr rr V rV ))(( !2 1 )(0 0 20 (3-2) The frequency of the normal mode could be started from the mass-weighted Hessian matrices (F). 1/2 MV 1/2 MF (3-3) In Eq. 3-3, the Hessian matrix (V ) contains second derivatives of the potential energy at r = r0, i.e. 0/)(2 rr jirrrV V, and the matrix M is a diagonal matrix with the given positions. The dynamical motions about an energy minimum struct ure can be qualitatively described using the eigenvector ( ) and the associated eigenvalue ( ) com puted from the Hessian matrix. iQiiQFQ (3-4) To obtain the eigenvalue in a system, the secular equation 0 IF is used and the eigenvector is obtained by diagonalizing Hessian matrix F. From the eigenvalue the 47

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vibrational frequency of norm al mode ( ) is then calculated as 2 / (i.e. from ) For a protein containing N atom s, there are 3N -6 vibrational normal modes, and the size of the matrix that must be diagonalized is (3 N6) (3N6), which is often too large for direct calculation. 2 24/ To address these problems, many approxima te NMA methods have been described, including the elastic network model (ENM),[ 73 78 ] the rotation-transition block (RTB) model,[ 79 ] and the VIBRAN and DIMB (Diagonaliz ation in mixed basis) method.[ 80 81 82 ] The use of allatom empirical potential energy descriptions with CHARMM/VIBRAN[ 83 84 85 86 ] becomes computationally inefficient for large system due to huge memory requirements. However, since our purpose was to investigate in teraction between the active site residues of protein and the substrate stuck in the inner part of active site hole, we decided that th e normal mode method with all-atom potential energies should be appropriate for describing the collective motions of FRC enzyme and for comparing with crystallographi c temperature factor (called B-factors). For our normal mode calculati on, we used CHARMM/DIMB module[ 80 81 ] to calculate low frequency normal modes only. As a reduced ba sis NMA technique, DIMB (Diagonalization in a mixed basis) method was develope d by Perahia and his coworkers[ 80 ] in order to reduce the computational cost to diagonalize all of the potential energy of th e Hessian matrix. In order to reduce the size of the Hessian matrix, an itera tive diagonalization pro cess was performed to extract a few low frequency normal modes, represen ting global vibrational motions in the protein or enzyme, based on the convergence criterion usi ng the magnitude of the quantity C, as follows: VA VAV CT 1 (3-5) 48

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where V is the approximate eigenvector, TV is its transpose, and A is the exact Hessian matrix. When this expression is equal to zero, then full convergence is achie ved meaning that the approximate low-frequency vibrational modes are a very good representation of those that would be calculated from the full Hessian matrix. The DIMB method requires less memory space to obtain the Hessian matrix than an allatom NMA method such as CHARMM/VIBRAN, a nd it provides exactly the same vibrational normal modes in the low frequency regions. Model Preparation Two crystal structures of apo state of FRC (apo-FRC) and Co A-binding FRC complex (CoA-FRC) at the re solution of 2.2 and 2.5 were used. Th e atomic coordinates used in this study were obtained from pdb entry 1p5h for the apo-FRC and from pdb entry 1p5r for the CoAFRC. X-ray crystal water molecules were incorporated, resulting in 530 and 260 water molecules in apo-FRC and CoA-FRC complex, respectively. In the CoA-FRC, two CoA substrates are located near to each of active site residues, Trp48A, Tyr59A, and Asp169A. In this way, two models were prepared initia lly: the apo-FRC with the cl osed/open tetraglycine loop conformation in each monomer, and the CoA-FRC with the closed/closed conformation in both monomers. In addition, another structure from the CoA-FRC afte r the removal of CoA (called CoA-free FRC) was prepared to determine the CoA contribution to the loop conformation. Finally, in order to investigate the effect of the tetraglycine, additional normal mode calculations were performed for a glycine-to-alanine mutation in the tetraglycine loop structure (G258A, G259A, G260A, and G261A). All results fo r glycine-to-alanine mutant variants were compared with those of the wild type of FRC (apo-FRC). 49

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For all normal m ode calculations of apoFRC and CoA-binding FRC complex, we used CHARMM program (version c33b2)[ 30] with an all-atom 27 protein force field.[ 28 ] For investigation of interactions between the active site residues and substrate (CoA), the coenzyme part was re-parameterized (Fig. 2-1) from that of the original acetyl-C oA of citrate synthase[ 41] using a CHARMM topology file and parameter file. All polar hydrogen atoms were explicitly added to initial X-ray structures of apo-FRC and CoA-binding FRC complex w ith the HBUILD module[ 42 ] of CHARMM and the nonbonded interactions were truncated at 14, and the van der Waals interactions switched between 10 and 12.[ 87 ] Vibrational Motions in FRC Homodimer The three normal mode calculations me ntioned above were performed using the CHARMM/DIMB program.[ 80] The consecutive minimization algorithms such as SD (steepest descent)[ 88 ] and CONJ (conjugate gradient)[ 89 90 ] were performed by applying the different harmonic constraints with a mass weight force co nstant to all atoms, which were gradually reduced from 250 to 0 kcal/mol/2 by atomic mass unit. Finally, after removing all cons traints, the system was re-minimized using the ABNR (adopted basis-set Newt on-Raphson) algorithm[ 30 91 ] until the potential energy reached the gradient tolerance of 10-5 kcal/mol/. The same minimization procedures were applied to apoFRC, CoA-FRC, and CoA-free FRC, respectivel y. The consequent input file for the normal mode calculation using CHARMM/DIMB method is provided in appendix B. Iterations were continued to a convergence criterion of 0.06 (arbitrary number) on the eigenvectors of each mode. From NMA/DIMB re sults, atomic RMS fluctuations corresponding to the vibrational contribution of a given atom i at a temperature T can be calculated by eigenvectors and eigenvalues w ith following contribution: 50

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2/1 7 3 1 2 2 2/1 2)( )( N k ki ,ki B iM a Tkr (3-6) In which kB is the Boltzmann constant, k is the frequency of the kth mode starting from 7th (lowest) vibrational motion, is the displacement of the ith atom from the minimum energy position, Mi is the diagonal mass matrix, and is the component of the kth normal mode corresponding to the coordinate ( = x y and z ) of atom i For the vibrational motion of proteins, the unit of frequency (ir ,kia ) is converted to wavenumber ( ) (cm-1) by the following equation; where c indicates th e speed of light with unit of cm/s. 2 2c2 2244 The atom ic RMS fluctuations of NMA obt ained from normal mode calculation were compared to those based on the X-ray temperature B-factor ( Bi) using Eq. 2-13 in chapter 2. The contribution of N modes to cross-correla tion fluctuations between ith and jth atoms were derived and contoured from modes and frequencies as follows. N k kji kiki B jiMM aa Tkrr7 3 1, 22/12/1 ,, (3-7) A normalized quantity (called the correlation coefficient) for N modes is given by 2 2)()( ))(( ))((),( j i ji N jirr rr rrjiC (3-8) where each of the indices and runs from 1 to 3. In this approach, the values of C ( i j ) fall between -1 and 1. To examine the correlated or anti-correlated motions involving residue pairs throughout the protein, we employed maps in which the values of C were plotted as a function of ( i j ) where i and j are the numbers of the residues. 51

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Results and Discussion Minimized Structures Refinement of the enzyme crystal structure is critical for direct normal mode calculations because initial X-ray structure may have in correct non-bonding contacts and poor internal geometries, depending on the enviro nment during enzyme crystallization. In this study, the two initial structures corres ponded to X-tray structures available for the apo-FRC and the CoA-FRC. Also, the CoA-FRC complex structure after th e removal of CoA (called CoA-free FRC) was prepared as a third structure to compare with the tetraglycine loop mo tion of apo-FRC and CoAFRC complex. At the end of minimization, th e RMS energy gradients for the two individual structures reached 10-5 kcal/mol/, where the low value of the RMS energy gradient is essential for computing normal modes in the all-atom representation. With consecutive minimization algorithms, the internal geometries of the two enzymes were greatly improved as shown in Table 3-1, where each energy term of the initially and finally minimized structures are presented for each of two enzymes. Table 3-1. Potential energy comparison between initial and optimized st ructures in apo state and CoA-binding FRC. Initial structures Minimized structures apo-FRC CoA-FRC apo-FRC CoA-FRC Total potential energy 58910.17 74946.18 -8242.29 -8272.09 Bond energy 1271.72 1054.29 324.84 341.12 Angle energy 12604.06 14323.26 1322.62 1392.02 Dihedral energy 3955.26 3614.60 3352.42 3501.29 Improper energy 21.89 6.26 50.73 53.63 UREY-Bradley 6008.46 6581.67 92.60 84.54 Electrostatic energy -6609.18 -7036.58 -8478.72 -8594.11 Van der Waals energy 41657.95 56402.69 -4906.78 -5050.58 RMS energy gradient 0.00001 0.00001 The units of all energies are kcal/m ol with gradients in kcal/mol/. In apo-FRC and CoA-FRC, the RMS coordinate deviations between crystal structures and minimized structures were 1.22 and 1.26 between the backbone atoms such as N, C, and C, respectively. These large values of RMS deviat ion in apo-FRC and CoA-FRC indicate that the 52

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initial crys tal structures were not energetically desirable for a reasonable starting model for the vibrational analysis. Normal Mode Calculation For all-atom normal mode analysis of apo-FRC and CoA-FRC enzyme, the frequencies for total 100 normal modes were initia lly determined (Fig. 3-1). The frequency regions of apo-FRC were slightly higher than thos e of CoA-FRC for modes greater than 50, but these differences were not significantly meaningful. The 1st to 6th normal mode regions with almost zero frequencies (less than 8.8-3 cm-1) were not included in our normal mode analysis, because these frequencies are in rotational and translational motion regions. 010203040506070809010 0 0 2 4 6 8 10 12 14 apo-FRC CoA-FRCMode NumbersFrequency (cm-1)010203040506070809010 0 0 2 4 6 8 10 12 14 apo-FRC CoA-FRCMode NumbersFrequency (cm-1) Figure 3-1. Frequency coverage for the to tal 100 normal modes of apo-FRC (blue line) and CoA-FRC (magenta line) structures. 53

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In Fig. 3-1, the highest norm al mode (100th) in apo-FRC and CoA-FRC had a frequency less than 12 cm-1. In order to determine the number of low fr equencies indicating th e global (collective) motion of FRC enzymes, the average RMS fluctu ation was plotted versus normal mode numbers (Fig. 3-2) after omitting the first 6 modes. Figure 3-2. Average RMS c oordinate fluctuations for 40 low frequency normal modes of apoand CoA-FRC. RMS fluctuations of C atoms for apo-FRC and CoA-FRC are in blue and magenta, respectively. In Fig. 3-2, the contributions to the average RMS fluctuations are very similar for apo-FRC (blue) and CoA-FRC enzyme (magen ta). The lowest 40 normal modes (7th to 46th normal mode) from all 100 modes ( < 12 cm-1) were extracted for computi ng the low-frequency normal modes of FRC enzyme due to the mode depende nce of RMS fluctuations. These average RMS fluctuations diminish drastically to 28th normal mode. Overall, it drop s from 0.01 to just above 0.001 from the 7th to 40th normal modes, drops to below 0.001 after the 40th mode, and then 54

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decreases very slowly and finally converges at ca. 0.001 after the 47th mode. This shows that the long time scale motions of apo state of FRC and the FRC/CoA complex should be adequately modeled by vibrational modes 7th ~ 46th. A) 01000200030004000500060007000 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 apo-FRC01000200030004000500060007000 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 apo-FRC CoA-FRCNumber of IterationsC01000200030004000500060007000 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 apo-FRC CoA-FRCNumber of IterationsCB) Figure 3-3. Characteristics of the lowest 7th normal mode of apo-FRC (blue line) and CoA-FRC (magenta line). (A) and (B) represent, respectively, the frequency dependence and eigenvector convergence C as a function of the iteration number of simulation. In Fig. 3-3, the frequencies and corresponding C quantities for lowest 7th normal mode are plotted versus iteration number for apo-FRC and CoA-FRC. Th e frequencies of the lowest CoA-FRCNumber of IterationsLowest Frequency (cm-1)01000200030004000500060007000 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 apo-FRC CoA-FRCNumber of IterationsLowest Frequency (cm-1) 55

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vibrational norm al modes were 7.5 ~ 7.9 cm-1 initially and decreased to 2.3 ~ 2.5 cm-1 at the end (Fig. 3-3A). The eigenvector conv ergence (ca. 0.06) based on Eq. 3-5 was also derived in order to reduce the main memory requirements. Analysis of Overall Fluctuations The average RMS fluctuations of the C atoms of each residue at 300 K for all 40 modes are given in Fig. 3-4 and Fig. 35. In the average RMS fluctua tion result for NMA of FRC (Fig. 3-4), the major divergence of the RMS fluctua tions between both monomers is in the loop residues of apo-FRC, which shows smaller fluc tuations in the A monomer than in the B monomer. The most distinguishable regions co rrespond to the long flexible loop (residue 231257) between the 11 helix and the 7 strand of the FRC enzyme. In the second (B) monomer especially, fluctuations of these long loop resi dues of apo-FRC are considerably higher than those of the CoA-FRC complex. RMS fluctuation results from normal mode calculation show slight differences in magnitude with experimental B-factor results (Fig. 3-5). This is not unexpected because NMA uses a simple harmonic representation of the system, excluding the solvent soaking or the effect of counter-ions. However, according to Guilbert et al.[ 82 ] and Karplus et al.,[ 92 ] RMS fluctuation based on experimental B-factor may have larger values than other calculated fluctuations[ 93 ] due to the low resolution of X -ray crystallography and corresponding crystal defects. In Fig. 3-5A, RMS fluctuations based on the NMA study are compared with those from the crystallographic B -factor. Even though RMS fluctuations based on X-ray B-fact or (top two lines) show larger values than our normal mode cal culations (bottom two lines), there are good qualitative similarities between the two RMS fluctuation results. 56

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Figure 3-4. Average RMS fluctuations of the C atoms for the first monomer (A) and second monomer (B) of FRC. Two different colors show the apo-FRC (blue line) and CoAFRC (magenta line), respectively 57

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Figure 3-5. Comparison of RMS fluctuation of the C atoms obtained experimentally ( top two bold lines) from the B-factor of X-ray crystallography and by normal mode calculation ( bottom two thin lines ). Two different colors show the apo-FRC (blue) and CoA-FRC (magenta). Top figure (A) is homo-dimeric structure of FRCs, and bottom (B) is the tetraglycine loop structure of FRCs. It is generally known that the RMS fluctuations obtained from X-ray B-factor are larger than those of calculated NMA results.[ 94 95 ] Evolved peak regions except for the C-terminal and N-terminal parts show patterns similar to those observed in other protein systems.[ 69 96 97 98 ] Here, we need to focus on the tetraglycine loop motion of the B monomer in the apo-FRC and CoA-FRC, as shown in Fig. 3-5B, wher e the theoretical RMS fluctuations of C atoms centering on tetraglycine loop residues (residue 250 to 270) are i llustrated. The experimental RMS fluctuations based on the B-factor (upper two dotted lines) and calculated one by NMA 58

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(bottom two solid lines) are compared. Even though the absolute RMS fluctuations of experimental and calculated were significantly different, they showed corresponding patterns. In the NMA result, the RMS fluctuations of apo-FRC (blue color) of the A monomer (left) are very similar to those of the CoA-FRC comple x (magenta color). In the B monomer (right), however, the loop motion of CoA-FRC is considerably greater compared to that of apo-FRC. In the apo-FRC structure (blue color), the loop conf ormation is in the open form, whereas in the CoA-FRC complex (magenta color) this tetraglycine loop has the closed form. This result shows that the conformational change of the tetr aglycine loop structure can be observed by NMA/DIMB method with remarkable agreement with the X-ray structures. Based on RMS fluctuation results, we can conclude that the loop conformational change s from open to closed form appears to be an intrinsic motion of the free FRC enzyme, although the CoA parts have effectively contributed to the fluctuati ons of tetraglycine loop structure. Correlation between the Atomic Fluctuations In order to describe inter-monomeric relations among fluctuations of different parts of the enzyme, the normalized correlation coefficient, C ( i j ), obtained between pairs of C atoms using Eq. 3-8 is shown in Fig. 3-6, where CoA-FRC (upper triangle) was compared to the apo-FRC (lower triangular part). In general, correlation coefficient values range between C ( i j ) = -1 and 1. The lower limit of -1 (dark blue) means the perfectly anti-correlated motions with opposite directions in the ith and jth C atoms, where C ( i j ) = 1 (dark red) represents perfectly correlated motions in the same directions, and C ( i j ) = 0 (white region) indicates that there in no relationship between the motions in the ith and jth C atoms (uncorrelated). 59

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Figure 3-6. Intra-monomer and inter-monome r correlation contours for apo-FRC (lower triangle) and CoA-FRC (upper triangle). (A ) and (D) show the cr oss correlations of inter-monomeric interactions between Amonomer and B-monomer in apo-FRC and CoA-FRC, respectively. (B) and (C) represent intra-domai n correlations within each monomer. Anti-correlated motions are in dark blue and perfect correlations are in dark red. According to Levitt et al.,[ 99 ] inter-monomeric correlations within 20 can be predicted in proteins, and especially within less than 9 significant correlations ar e predictable with C ( i j ) > 0.5. Simonson et al.[ 69 ] also demonstrated that strong inter-monomeric correlations appear within the distance of 6 whereas weaker corre lations occur at considerable distances of 12 with a correlation value of more than 0.2. 60

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In this FRC study, the overall cross-correlations of protein are very sim ilar to apo-FRC and CoA-FRC as expected, and the correlations concerning the -strand regions are larger than those of the -helical structures with minimum correlation value of -0.2. (A) and (D) represent interdomain cross-correlation interaction between two monomers, while (B) and (C) parts show intra-domain correlation w ithin one monomer. The intra-monomeric interaction of FRC (see (B ) and (C) of Fig. 36) shows that the Nterminal regions of apo-FRC and CoA-FRC (residues 2-199) exhibit larger correlations than the C-terminal parts of the protein chain (resi dues 367-428). The important correlation regions appear in the small domain regions of FRC enzyme ( 11 and 1415 helix). A short helix ( 11) and successive long loop (residues 248-259) are directly coupled to 78 helix which makes a protrusion towards the small domain ( and ), and 1415 loop was in turn coupled to the 11 helix, which is a short helix starting the small domain ( and ). Additional dynamic coupling is observed at the N-terminal helix residues; 9 helix appears to be coupled to the 33 loop ( & ). Final representative inter-monomeric interactions occur in the second monomer; the 812 loop affiliated with the small domain is coupled to the 1011 loop, which is the interface region be tween the large and small domains (). It is noteworthy that correlation occurs in the second monome r (FRCB) of apo-FRC only. More interestingly, inter-domain interactions between two monomer residues are observed, as shown in (A) and (D). In or der to focus on the cross correlations of the active site residues of the A monomer with the tetraglycine loop struct ure of the B monomer, expanded contours (Fig. 3-7) were necessary to empha size the inter-monomeric interaction between FRCA and FRCB monomer (black dotted box of (A) and (D) of Fig. 3-6). 61

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62 Figure 3-7. Cross-correlation maps for inter-mono mer fluctuations centering on the tetraglycine loop regions in apo-FRC (A) and CoA-FRC (B ). X-axis includes two magenta dottedlines representing the tetraglycine region of B monomer, and Y-axis means the active site residues of A monomer.

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In Fig. 3-7, the cross correlation m aps s how residues 1 to 200 of the A monomer, which are mainly around the active site, and residues 200 to 400 of the B monomer, including the tetraglycine loop structure. The largest correlation in FRC can be seen in the black dotted boxes in Fig. 3-7: inter-monomeric interact ion between the second linker helix ( 17-18) of the B monomer and a protrusion helix ( 7-8) that are towards located the small domain but practically belong to large domain in the A monomer. A dditional peculiar coupl ing is found at the 812 loop of the B monomer and Trp48 of A-monomer in the apo-FRC only (small red dotted box of apo-FRC in Fig. 3-7). The role of Trp48A is worthy of notice, whic h is involved in an inter-domain interaction with the Gly258B-Gly261B tetrag lycine loop is noteworthy (Fig 3-8). It is known that a (closed/open) change in the conformation of the tetraglycine loop is related to a rotation of Trp48A away from loop Gly258B-Gly261B. Therefor e, this coupling calculated by NMA/DIMB method can help verify our expe rimental results. In Fig. 3-8 (C) and (D), Trp48 of the A monomer has a strong correlation with te traglycine residue Gly260B and Gly261B (C ( i j ) > 0.5). In particular, the cross correlation contour of Trp48A and Gly261B ((D) of Fig. 3-8) shows a different trend compared to the other correlations. It is possi ble that the Gly261B residue may play a more important role in the conformational change compared with other glycine residues because Gly261B is closer to Trp48A than the othe r three glycine residues of tetraglycine (258 to 261). Even though some other residues (His 15~Cys19, Leu72~Lys75, Asn96, Ala101~Arg104, and Leu136~Tyr139) are in the active site of the A monomer, thes e cross correlation contributions to tetraglycine loop (, and ) are beyond our concern because they are far from the tetraglycine residues and are rather accessible to the adenin e and pyrimidine ring of CoA (brown and green colors of Fig. 3-7 and Fig. 3-8). 63

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Figure 3-8. Inter-m onomeric correl ation contributions between active site residues of the A monome r (FRCA) and the tetraglycine loop fluctuations of the B mono mer (FRCB). (A) ~ (D) represent the interactions between the active site residues and each glycine residue of loop regions (Gly258 ~ Gly261). The intensities of correlati on of apo-FRC and CoA-FRC are colored blue and magenta, respectively.(0.327/0.293) (0.582/0.494) (0.673/0.640) (0.625/0.715) 64

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This is corresponded to our experim ental data[ 17] that the thiol (-SH) group on the long side chain of pantetheine of CoA is near to tetraglycine loop (Gly258-Gly261) in the closed conformation of CoA-FRC complex. Lastly the cross-correlation between Asp169 of the A monomer and the tetraglycine loop residues (Gly258B ~ Gly261B) is represented in & (blue circles of Fig. 3-7 and Fig. 3-8). From our crystallographic information for Asp169A,[ 17 ] whose side chain is located near to the thiol (-SH) group of CoA, a deep cavity that can ho ld an oxalate molecule is observed in the apo state of the enzyme. Mutation Effects on the Dynamic Structure of Tetraglycine In order to explore the roles of the individual glycine residue s which are thought to affect the conformational motions of the tetraglycine loop, all 40 normal mode calculations were performed for four mutant variants (G258A, G259A, G260A, and G261A) using the same methods as that for the wild type (WT) apo-FRC. Fig. 3-9 shows average RMS fluctuations for WT apo-FRC (blue) and its four mutants (G258A, magenta; G259A, green; G260A, orange; G261A, brown). In itial structures for four mutants were obtained by graphica l modification of the appropriate glycine residue to alanine in each of the energy minimized reference structures of wild type FRC using Maestro/MacroModel.[ 100 ] The resulting structures were then energy minimized in CHARMM using an identical procedure to that outlined for the wild type enzyme. For the WT and its four mutants, the distributions of normal modes were determined centering on the tetr aglycine loop by diagonali zation of the Hessian matr ix. Nearly identical frequency distributions were obs erved for WT FRC and the four mutants (not shown here). 65

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250252254256258260262264266268270 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Apo-FRC G258A G259A G260A G261AResidue numbersFluctuations ( )(A) FRC A-monomer 250252254256258260262264266268270 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Apo-FRC G258A G259A G260A G261AResidue numbersFluctuations ( )(A) FRC A-monomer 250252254256258260262264266268270 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Apo-FRC G258A G259A G260A G261AResidue numbers (B) FRC B-monomer 250252254256258260262264266268270 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Apo-FRC G258A G259A G260A G261AResidue numbers (B) FRC B-monomer Figure 3-9. RMS fluctuations of the C atoms for the wild-type (apo-FRC, blue) and its mutants for tetraglycines, (G 258A, magenta; G259A, green; G260A, orange; and G261A, brown) The first six mode representations of the mutants, corresponding to translational and rotational motion, were excluded in this normal m ode calculation. All 40 modes of tetraglycine mutants show frequency range from 2.21 ~ 2.43 cm-1 to 7.71 ~ 7.87 cm-1, very similar to frequency range of WT (2.44 ~ 7.89 cm-1). Except for Gly-254 residue in the A monomer, the shape of the frequency distributio ns for the four mutants were quite similar to our established two NMAs (See Fig. 3-5), and t hose reported for other proteins.[ 67, 101 102 103 104 ] Conclusions In this chapter, the results of a normal m ode calculation on the formyl-CoA transferase centering on the conformational motions of apo state and CoA bindi ng enzyme were presented. This study was undertaken to observe the dynamic mo tions of the tetraglyci ne loop, which were unable to be simulated by a nanosecond time scal e approach such as MD simulation. Our CHARMM/DIMB normal mode analysis could uncover the conformational change of tetraglycine loop regions in F RC enzyme, and these findings were conjectured to provide new opportunities to probe the catalytic m echanism inquiry of the FRC enzyme. 66

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For our norm al mode calculation, the 40 lowest frequency modes (7th to 46th) in apo-FRC and CoA-FRC were extracted from 100 normal modes of consideration, due to the large hard memory consumption and the convergence of th e RMS fluctuations. These small numbers of modes represent only 0.07% of the total number of modes [53,994 (3 N -6)] of the system, but it is believed that only low fre quency normal modes can provide information about global or delocalized motions of proteins or enzymes.[ 66, 67 105 106 107 108 ] All normal mode calculations we have performed have frequencies less than 8 cm-1 and displayed large amp litude (global) motions that produce significant rearrange ments within the protein. From our RMS fluctuation analysis of apoFRC and CoA-FRC, we realized that two results from NMA and X-ray crys tallography have qualitative sim ilarities, even though the X-ray temperature factor shows larger fluctuation than our NMA cal culations. In particular, the conformational change of tetrag lycine loop structure obtained vi a normal mode calculations has remarkable accordance with that determined from the X-ray structure. Based on the correspondence between thes e two results, it appears that the change of loop conformation from the open to closed form is an intrinsic motion of free FRC en zyme, although the CoA parts have effectively contributed the fluctuatio ns of tetraglycine loop structure. Lastly, the role of Trp48A, which is inter-m onomerically coupled with the tetraglycine loop structure, was reproduced using inter-domain correlation between the two monomers of FRC. A different conformational motion of the te traglycine loop is related to a side chain rotation of Trp48A away from loop structure. Therefore, this c oupling interaction calculated by normal mode analysis provides further s upport for our experimental results. Although the use of NMA calcula tions to explore the large-scale motions of FRC does provide useful information on the intrinsic dynami cs of the tetraglycine loop, the omission of 67

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protein/so lvent interactions in the model a nd the assumption that the potential energy surface remains harmonic as the protein explores conformational space preclude any quantitative insights into loop energetics. On the other hand, the qualitative agreement of the calculated and observed fluctuations in this study does suppor t the idea that this NMA study has provided information on how dynamical motion may be altere d when CoA is bound with in the active site. 68

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CHAP TER 4 NEW FREE ENERGY SIMULATIONS OF ACTIVE SITE LOOP MOTIONS FOR FORMYLCOA TRANSFERASE.[ 109 ][ ] Introduction Understanding the conformational energetics a nd the dynamical properties of flexible loop structures in the catalysis and binding aspects of enzyme[ 110 111 ] requires the use of novel free energy calculations. Free energy calculations usin g established molecular dynamics methods, such as free energy perturbation (FEP)[ 112 113 114 ] or thermodynamic integration (TI)[ 115 116 117 ]result in H amiltonian lag,[ 118 ] which arises from the relativel y long times that are needed for the protein environment to relax in a given stat e. Therefore, Yang et al developed an orthogonal space random walk (OSRW) sampling algorithm,[ 119 120 ] in which coincident sampling of an order parameter is coupled to rapid protein re organization. The OSRW method was used to compute the co nformational energetics of the functionally important tetraglycine loop in the active site of formyl-CoA transferase.[ 20] Free energy profiles using the OSRW technique were performed for conformational cha nges between open and closed state of tetraglycine loop and compared with the stea dy state kineti c properties of FRC.[ 111 121 ] Berthold et al. have report ed extensive crysta l structures for FRC corresponding to various snapshots of the catal ytic cycle of the enzyme.[ 21 ] These X-ray results illustrated that conformational change in the tetraglycine loop (blue and magenta network shapes in Fig. 4-1) plays a crucial role in stabilization of intermediate structures[ 20 21] and control of substrate access.[ 122 ] [*] Reproduced in part with permission from Journal of the American Chemical Society, Vol. 132 (21), Lee S, Chen M, Yang W, and Richards NGJ. Pages 7252-725 3. Copyright 2010 American Chemical Society 69

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Figure 4-1. Cartoon representa tions of the FRC active site tetraglycine lo op (G258-G259-G260G261) in its open ( left ) and closed ( right ) conformations. Coordinates are taken from the crystal structures of apo-FRC (1p5h) and the Co A-FRC complex (1p5r) after removal of CoA.[ ] Methodology Theoretical Background of OSRW According to Yang and co-workers,[ 119 120 ] the orthogonal space random walk (OSRW) algorithm can accelerate motion along a path de scribed by a pre-defined order parameter ( ) and its coupled environmental respons e. In OSRW, as for free energy techniques such as adaptive umbrella sampling,[ 123 ] adaptive biasing force,[ 124 ] and meta-dynamics,[ 125 ] the original potential energy function ( U0) is modified by the addition of a biasing energy function fm( ) as follows: ) (0 m mfUU (4-1) [] Figure reprinted with permission from Journal of the American Chemical Society, Vol. 132 (21), Lee S, Chen M, Yang W, and Richar ds NGJ. pp. 7252-7253. Copyright 2010 American Chemical Society.[109] 70

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In Eq. 4-1, fm( ) is equal to ) (0 G which is the negative of the free energy profile along so that random walks in the order parameter space can be achieved. Since random sampling moves defined by the order parameter are blocke d by slow environmental relaxations, the OSRW method has been formulated to further remove hidden free energy barriers[ 126 ] that are strongly related to the moves. This allows faster relaxa tion of the protein environment. Specifically, an additional biasing energy term is a dded to give the following equation. ) ,()(0 FFfUUm m m (4-2) where the generalized force is defined to be F 0U. In this case ) ,( FFmis expressed as ),('0 FG which is the negative of the free energy profile along ) ,( F corresponding to the potential function of )0(0 GU According to Yang et al.,[ 120 ] the generalized force can describe the direction in which the collective environmental relaxation occurs at each state described by the order parameter. In our calculations, the order parameter space ( ) is defined as a co mplicated function of the form 0 02 RMSD RMSD RMSD Here represents the post-supe rim position RMS deviation between the loop structures in the open and closed confor mations in WT FRC, while is the difference of the post-superim position RMS deviation including loop from the ones in the reference (open and closed) structures. The RM SD values are computed by superimposing a given conformation of the tetraglycine backbone atoms with the corresponding atoms in the open and closed reference structures (shown in Fig. 4-1). If 0RMSDRMSD 0 20 0 RMSD RMSD RMSD (that is, ), its conform ation corresponds to the open conformational state, and 0RMSD RMSD 71

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otherwise if 1 20 0 RMSD RMSD RMSD (that is, 0RMSD RMSD ), this represents the closed state. The Hamiltonian then takes the form: m p RMSD RMSD RMSD 22 0 0 KHH 2 2 1 '2 00 (4-3) in which the target order parameter is restrained to an exte nded dynamic variable in a dynamics-type approach.[ 127 128 ] As a result, calculating free en ergies along the target order parameter is reduced to the problem of calculating the free energy profile ) (0 G0H along based on the exten ded Hamiltonian ( ) rather than the original Hamiltonian ( ). Thus, the extended dynam ics of the particle are realized in a Lange vin dynamics scheme, for which the temperature is set to be identical to that of the real particle dynamics, i.e. 298.15 K. The mass of the particle is defined as 500 a. m.u., and the force constant K is set to 1,000 kcal/mol. The theoretical justification for this approach has been described previously.[ '0H109] Accordingly, the OSRW simulations on FRC employed an extended potential ( ) as f ollows. 'mU ,)(''0U FfUUm mom (4-4) 2 where 0 0 02 2 1 RMSD RMSD RMSD KUUo (4-5) Here ) ( mf can also be represented by ) (0 G which is the negative of the free energy profile along and ,0U Fm is equal to ,0U G '0, i.e. the n egative of the free energy profile along U'0 in the canonical ensem ble corresponding to ) (00 GU 72

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This stand ard OSRW recursion procedure is em ployed to achieve the targeted functions of )( mf and ,0U Fm.[ 119 120 ] More specifically, ,0U Fm is obtained by repeatedly adding a small Gaussian-shaped repulsive poten tial as in the work of Laio and coworkers[ 125 ] given below: 2 2 2 0 0 2 1 22 )( '' exp 2 )( exp w t UU w t hi i (4-6) which is centered at )( ),(0 i it U t thereby discouraging the system from adopting conformations that have been visited often in earlier simulation steps. In Eq. 4-6, represents the tim e-step at which the i -th update is scheduled. This recursion method for computing ) (it ,0U Fm, developed by Yang and co-workers[ 119 120 ] is similar to that used in meta-dynamics implementations.[ 129 ] Using this repetitive procedure, the overall biasing potential is then obtained cumulatively as: it i i mw t UU w t h U F2 2 2 0 0 2 1 2 02 )( '' exp 2 )( exp (4-7) For the FRC simulations, the height h of Gaussian function was 0.001 kcal/mol, and the two widths ( w1 and w2) were chosen to be 0.001 kcal/mol and 20.0 kcal/mol. Our Gaussian update frequency was every 2 fs, because the choice of Gaussian height h was relatively small. In 73

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the O SRW recursion, the value of fm( ) was then updated from ,0U Fm at 5 ps intervals in the production run using the following two equations: )'( exp )'( exp '0 00 0 0 0 0 U m U mU F U F U U d dG (4-8) )()(' 0 0 d d dG Gfim (4-9) Computational Details for FRC/OSRW CHARMM/OSRW simulation was performed on w ild type FRC and four mutant variants (G258A, G259A, G260A, and G261A). For the syst em setup of the free energy calculation on wild type FRC, a truncated octahedral box was made with ca. 5,600 water molecules, in which hydrogen atoms were added using the HBUILD function[ 42] of CHARMM. Counter-ions were added to neutralized the system, and the initia l structure was optimized with steepest descent (SD)[ 88] and the adopted-basis Newton Raphson (ABNR) algorithm[ 30 91] using CHARMM (version c32b2).[ 30 ] These calculations and subsequent OSRW simulations employed the allhydrogen CHARMM27 force field for proteins[ 28] and TIP3P water molecules.[ 43] The optimized FRC structure was then e quilibrated at 298.15 K prior to running production OSRW simulations, with the simulation temperature being slowly raised while the protein heavy atoms were constrained to their minimum energy positions. After reaching the final temperature, the system was equilibrated for 20 ps with a time step of 2 fs. These calculations employed periodic boundary conditions (PBC),[ 52, 53 ] with the long range Coulombic interactions being modeled by the particle-mesh Ewald (PME) method.[ 49] Short-range non74

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bonded interactions were switched at a distance of 10 and truncated when atom s were separated by more than 12.0 The procedure[ 48] was used for applying the constraints of bond lengths including polar hydrogen atoms. Af ter equilibration, the free energy profile for wild type FRC was computed using the OSRW (Orthogonal Space Random Walk) module implemented in CHARMM (Appendix C). In these OSRW simulations, the value of the reaction coordinate was computed within 0 and 1 by evaluating the RMSD of the heavy atoms of loop structure with two energy minimized structures in the open and clos ed states. The order parameter was defined as 0 02 RMSD RMSD RMSD, as described in methodology section. MD simulations, using the parameters outlined above except for the use of a 2 fs timestep, were then performed for the system at this value of the reaction coordinate for 50 ps. Initial structures for the G258A, G259A, G260A and G261A FRC mutants were obtained by graphical modification of the appropriate glycine re sidue to alanine in each of the energy minimized reference structures of w ild type FRC using Maestro/MacroModel.[ 100 ] The resulting structures were then energy minimized in C HARMM using an identical procedure to that outlined for the wild type enzyme. Results and Discussion Sampling Enhancement for the Free Energy Convergence Free energy simulations on the w ild type FRC dimer and the f our mutant variants were carried out for the open to closed conformationa l transition in tetragly cine loop (residue 258 ~ 261) structure. The differen ce of free energy change ( G ) for the conformational movement can be expressed as 75

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G = G (closed) G (open) (4-10) Each G represents the free energy change in the open and the closed conformation, respectively. Eq. 4-10 indicates that the relative free energy difference between the open and closed state of the tetraglycine loop structur e in wild type FRC can be calculated from subtracting the free energy value in each open/closed state. The free energy difference values in each of the four mutant variants (G258A, G259A G260A and G261A) were calculated using the same procedures as for the wild type enzyme. Figure 4-2. Conformational sampling statistics for the variation in the reaction coordinate as a function of MD simulation time, showi ng the extent to which different loop conformations were sampled during the co mputation of the free energy profiles for wild type (WT) FRC and the G258A, G259A, G260A and G 261A FRC mutants. An equilibrated homodimer with open loop confor mation was used as the initial structure and simulated until free energy profil e converged over the sampling range = 0 = 1. All structures were sampled at 1 ps intervals of production trajectory, and the free energy simulation 76

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with OSRW was continued until the convergence of the free energy profile. The final free energy results including wild-type and four mutant variants coul d be obtained in less th an 2 ns (Fig. 4-2). This result shows that a conve rged free energy profile for changing the open conformation of the loop to its closed conformation could be obtained by sampling all values of the order parameter in a single return trip. At the beginni ng of the OSRW simulation of the wild-type FRC and mutant variants, the order parameter was set as = 0, in which the loop was in its open conformation. Because the target free energy va lue is negative, the order parameter quickly moved to the other end with = 1, which represents the loop in the closed conformation. Free Energy Profile for FRC The free energy difference as a function of the pro cessing of the order parameter is given in Fig. 4-3 for the wild-type FRC dimer and four mutant variants. The general trends shown in this figure are the two verified local minimum energy pathways between two conformations, representing the open and closed state conformations. The OSRW simulations performed in five different free energy changes included the open and closed conformations in the entire oneround-trip of the order parameter. The use of this parameter may underestimate free energy barrier heights.[ 126 ] OSRW free energy profiles calculated for th e tetraglycine loop conformations in the G258A (red), G259A (magenta), and G260A (cyan) FRC mutant varian ts showed different energy profiles from those for the wild type (blue) FRC and G261A (brown) mutant. For the wild-type and four mutant enzymes the closed conformation of tetraglycine l oop structures is generally less stable than the open conformation (See Table 4-1). 77

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0.00.10.20.30.40.50.60.70.80.91.0 -40 -30 -20 -10 0 10 20 WT G258A G259A G260A G261AScaling parameter ( ) G (kcal/mol)0.00.10.20.30.40.50.60.70.80.91.0 -40 -30 -20 -10 0 10 20 WT G258A G259A G260A G261AScaling parameter ( ) G (kcal/mol) Figure 4-3. The free energy profiles com puted for the tetraglycine loop from its open to closed conformations using the OSRW simulations reported above. Color code: WT FRC, blue; G258A, magenta; G259A, red; G260A, cyan; G261A, brown. The G260A structure on the free energy profile at = 0.45 was superimposed on the crystal structure of this enzyme (pdb code 2vjn )[ 21 ] as seen in Fig. 4-4. The CHARMM/OSRW simulation found the additiona l minima that were intermediate in shape between the open and closed loop conforma tions and comparable in free energy (red, magenta, and cyan in Fig. 4-3). Two distinct local minima describing the open and closed state of the loop structures appeared in all free energy profiles except for the G259A FRC mutant, for which there were three stable minima. In Table 4-1, the free energy difference between WT and four mutants are presented based on the ORSW module and compared with steady-sta te kinetic parameters that were obtained experimentally.[ 21 ] In the free energy calculation of WT FRC and mutants, we found out that open conformation in loop structure was preferred to the closed conformation by 4.8, 5.3, 2.2, 2.5, and 3.7 kcal/mol, respectivel y, of free energy difference. 78

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Table 4-1. C alculated free energy values (kca l/mol) for conformational inter-conversion of the tetraglycine loop and stea dy-state kinetic parameters for free FRC and alaninecontaining FRC mutants.[ ] Ga G kcat (s-1)b Enzyme WT 4.8 13.0 (Exp.16.3) 5.3 0.1 5.3 23.0 c G258A G259A 2.2 9.0 1.9 0.1 G260A 2.5 9.3 0.23 0.02 G261A 3.7 10.5 1.65 0.01 aAll calculated free energies are in kcal/mol. G = G (closed) G (open), and G is the barrier relative to the open conformation. bExperimental steady-state kinetic parameters at 30 C have been published previously [21] and are included here for ease of comparison. cTechnical problems in expressing and purifying the G258A FRC mutant have precluded its characterization. The inter-conversion of free energy barriers fr om kinetic parameters was computed from Himos work, by which the energetic barrier related to experimental rates can be calculated if the transition state (TS) of the reaction is found:[ 130 ] )/ exp( RTG Ak (4-11) Here, the pre-exponential factor A is defined to be h TkB, where kB is the Boltzmann constant and h is Plancks constant. In addition, is the free energy difference between the trans ition state (TS) and ope n conformation (reactant). GIn w ild type FRC, the energy barrier relativ e to the structure with open conformation was 13 kcal/mol, which is lower than the experiment al free energy of 16.3 kcal/mol at 303.15 K assuming a value of 612 s-1 for the pre-exponential factor. Th e G259A (9.0 kcal/mol), G260A (9.3 kcal/mol), and G261A (10.5 kcal/mol) mutants show intermediate-favorable structures as compared with the wild type FRC (13.0 kcal/mol ) and G258A variant (23.0 kcal/mol). Especially, the energy barrier relative to open conformation in the G259A and G260A FRC mutants is slightly lower than that of the wild type FRC. This agrees with our X-ray results in that the [] Table reprinted with permission from Journal of the Amer ican Chemical Society, Vol. 132 (21), Lee S, Chen M, Yang W, and Richards NGJ. pp. 7252-7253. Copyright 2010 American Chemical Society.[109] 79

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catalytic activities of the G259A and G260A FRC m utant variants were reduced relative to the wild-type FRC.[ 21] For G259A and G260A, the catalytic activity for th e experimentally crucial loop conformation was consistent with the computed free energy calculation. OSRW simulations of the loop conformational change describing the open/closed state in the wild type FRC and in the G261A FRC mutant gave a similar free energy profile (Fig. 4-3, blue and brown). This similarity in the two fr ee energy profiles agrees with the experimental observation that the experimental kinetics of the G 261A FRC (5.3 s-1) variant are essentially unchanged from those of the wild type enzyme (1.65 s-1). Figure 4-4. Cartoon showing supe rimposed active site tetraglyci ne loops for the observed (pdb code; 2vjn ) (cyan) and the open (blue), intermed iate (black), and closed (red) loop conformations calculated fo r the G260A mutant, together with the associated positions of the active site residues Trp48A, Tyr59A, and Asp169A.[ ] [] Figure reprinted with permission from Journal of the American Chemical Society, Vol. 132 (21), Lee S, Chen M, Yang W, and Richar ds NGJ. pp. 7252-7253. Copyright 2010 American Chemical Society.[109] 80

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In order to inspect the predic tive power of our free energy ca lculations, the experim ental crystal simulation for the G260A mutant was compared with the one calculated by ORSW (Fig. 4-4). The experimental G260A F RC variant (cyan) with the loop structure was extracted from Xray crystallography (pdb code; 2vjn ),[ 21 ] expressing the free energy profile at = 0.45 (See Fig. 4-3). In the G260A intermediate analysis, onl y 2.06 of RMS deviation was observed between computation and experiment (Table 4-2). This result may help verify our X-ray intermediate result for G260A, even though no information about this new loop conformation had been included in our OSRW simulations. Table 4-2. RMSD comparisons of the calcula ted G260A FRC mutant structures, with the tetraglycine active site loop in its open, cl osed and intermediate state, and the X-ray crystal structure of th is FRC variant (2vjn). Intermediate Open Closed 2.06 (1.70)a 3.01 (1.65) 3.71 (1.86) G260A (2vjn) G260A (open) 3.58 (0.96) 4.10 (0.93) aRMSD values are computed based on the C positions of the four residues (Gly258B ~Gly261B) in the active site loops of the superimposed structures. Parentheses show the cognate RMSD for all C atoms in the superimposed dimers. Additionally, the importa nce of the influential role of Trp48A was reproduced in our OSRW results. In Fig. 4-4, the active reorienta tion of the side chain of Trp48A was observed as the loop changed conformation. However no sign ificant conformational changes were observed in Tyr59A and Asp169A. This flexible move ment of Trp48A indicates that the loop conformational change can accommodate the side chain motions in the protein with a small number of simulation steps at a given value. 81

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Dihedral Trajectory for Tetraglycine Loop One other important structural event during the inter-conversion between open and closed state is the comparison of dihedral change between the wild-type and its mutants. 0200400600800 1000120014001600 -180 -90 0 90 180 phi () psi ()02004006008001000120014001600 -180 -90 0 90 180 phi () psi ()Running time (ps) Running time (ps) Wild Type G260A0200400600800 1000120014001600 -180 -90 0 90 180 phi () psi ()02004006008001000120014001600 -180 -90 0 90 180 phi () psi ()Running time (ps) Running time (ps) Wild Type G260A Figure 4-5. The phi ( ) and psi ( ) analyses in the wild type FRC ( left ) and G260A variant ( right ) for the last residue (Gly261) of tetraglycine loop. Phi( ) and psi ( ) dihedral were represented as the blue and magenta, respectively, to illustrate the extent to which conformations may be differentiated. In Fig. 4-5, the last loop resi due (Gly261) of wild-type FRC and G260A mutant were chosen for dihedral analysis, because the Gly261 re sidue may have greater influence on the conformational change than the other glycine residues (See Fig. 3-9 of chapter 3). For better understanding of dihedral expression for the Gly261 residue, the torsional angles expressing open and closed conformations we re compared from two crysta llographic FRC structures (pdb code of 1p5h for apo-FRC and 1p5r for CoA-FRC) (See gray color in Table 4-3). Two time-dependent dihedrals show that the major conformational transition was not started until 300 ps in the wild-t ype and 200 ps in the G260A si mulation, representing one-waytrip movements in scaling parameter evaluations. Conformational changes from the open to closed state of the tetraglycine loop then continued until 800 ps (wild-type) and 1 ns (G260A). 82

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These corresponded to our X-ray results, which s howed open to closed confor mational changes (e.g., -78.5 to -139.5 for -dihedral and -5.9 to -173.2 for -dihedral). From 800 ps and 1 ns of time evaluation, th e wild type FRC and G260A having a closed type of dihedral angle began to stray out of uniform trajectory. These trends of random walk in dihedral expression suggest that efforts to improve free energy calculations for macromolecules must focus on the random sampling treatment for conformational movement. In conclusion, this sampling of Gly261 residue resulting from the free energy calculation with OSRW techniqu e corresponded to X-ray FRC result with the open and closed state of apo-FRC (Table 4-3). Table 4-3. Crystallographic torsio nal angles observed for the four glycine residues in the active site loop of wild type FRC. Residue opena closedb Gly-258 Gly-258 -58.6 -35.5 -64.3 -35.1 Gly-259 84.4 -6.6 66.4 -108.3 Gly-260 -138.1 -147.3 -82.9 9.6 Gly-261 -78.5 -5.9 -139.5 -173.2 a and b values are observed in pdb code of 1p5h (apo-FRC) and 1p5r (CoA-FRC), respectively. Conclusions A number of ingeni ous efforts for free energy development have been attempted previously to overcome the problems of the large energy barrier and the lack of accurate intermediate predictions. However, due to th e low simulation efficiency resulting from Hamiltonian lagging,[ 118 ] the non-synchronizing between st ructural relaxation and order parameter were problematic. With the application of the OSRW module to the macromolecu le system such as our FRC enzyme, the free energy efficiency in the confor mational change could be improved. We utilized 83

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this a lgorithm to compute the conformational energetics of the functionally important tetraglycine loop in the active site of Oxalobacter formigenes formyl-CoA:oxalate CoA transferase (FRC). As the result, OSRW-derived free energy profiles could be computed for the inter-conversion of the open and closed loop stru ctures in FRC and correlated with the steadystate kinetic properties[ 21 ] of the enzyme. In general, the conformational change of the loop usually occurs on a microsecond or millisecond time scale in computational free ener gy aspects. The ability to determine these conformational changes of loop st ructure in nanosecond time scal e, therefore, would be an advantage of the OSRW sampling strategy. Currently, this OSRW approach has been a pplied by our group for CoA-FRC enzyme to investigate the conformational change of tetraglycine from closed to open state in the presence or absence of CoA. Based on the success of ORSW simulation using the fr ee state of FRC as demonstrated in the current chapter, we belie ve that the refined free energy calculation using CoA bound FRC enzyme can also create comparable results with the apo state of FRC in the near future. 84

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CHAP TER 5 SUMMARY AND FUTURE WORKS Summary of Current Formyl-C oA Transferase Project The overall goal of this research project was to model the dynamic motion of the tetraglycine loop in FRC. We anticipated that the tetraglycine loop would have different conformations and energetics in the apo state of FRC and in the CoA-binding FRC complex.[ 17 ] In particular, we were interested in the dynamic motion of the tetraglycine loop in the presence/absence of substrate, the controlling factor(s) of loop conformations, and how each glycine residue in the loop residues affects loop movement and motional energetics. The first specific project was to investigate the conformational motion of the tetraglycine loop on the nanosecond time scale using molecular dyna mics simulation. The results of 20 ns of molecular dynamics[ 131 132 ] indicated that the dynamic inte r-conversion of two separate and distinctly different binding s ite conformations of FRC was di fferent from the experimental binding conformation of FRC, especially in th e protein-substrate interactions. The crucial mechanistic roles of active site residues such as Trp48A, Tyr59A, and Asp169A in the environment of the open and closed dynamics of the FRC were also described. Unfortunately, these MD studies on the dynamic a nd energetic mechanism of FRC were not in accordance with findings from X-ray crys tallography for FRC. Normal mode analysis was then used to investigate the dynamic inter-conversions of two different conformational states, open a nd closed, of the tetraglycine loop.[ 25] The binding of coenzyme A to the apo state of FRC was hypothe sized to induce a confor mational movement of the active site resulting in closing of the tetraglycine loop structure. Our results suggested that the calculat ed normal modes produce root-mean-square fluctuations for the atoms that correspond to thos e derived from the crys tallographic temperature 85

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factors. Some of the m odes resulted in changing the collective motion of the protein in such a way that open/closed conformational change wa s induced in the tetrag lycine loop site. The conformational change of open to closed state in the tetraglycine loop stru cture is not concerned with presence of any ligand such as oxalate, but is related to the inherent enzyme structure. Also, the influence of individual gl ycine residues on the conformationa l motions in the tetraglycine loop was studied by the glycine to alanine mutations The obtained results show that the glycine residue of the mobile loop does not influence the open-to-closed loop movement and motional energetics. Finally, the unique role of each glycine residue in the tetraglycine loop was studied using a new free energy application, OSRW[ 109 ] to compute the conformational energetics of the functionally important tetraglycine loop in wild -type FRC and four FRC mutant variants, in which the glycine residues were replaced one-b y-one with alanine. This procedure made it possible to evaluate the energetic effects of altering the accessibility of allowed backbone torsion angles in the loop. Computationa l results were consistent with our experimental steady-state kinetic properties of the wild -type FRC and the known FRC loop va riants, and demonstrated the feasibility of using OSRW sampling to obtain quantitative information on the conformational preferences of loops within enzyme active sites. Detailed analysis of structures generated during the OSRW simulations showed that the sampling algorithm was able to model side chai n reorientation correc tly, even though these motions were not defined explicitly in the reaction coordinate or driven by prior knowledge of their positions in the FRC crystal structure. Because such changes represent motions that usually occur on a microsecond to millisecond time scale, the ability to obtain such information using nanosecond simulations is a significant advantag e of the OSRW sampling strategy. This new 86

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algorithm may contribute to the de velopment of free energy calcula tions in crucial chemical and biochemical problems, considering our success w ith large molecule, such as FRC enzyme. Future Works for Formyl-CoA Transferase Project As mentioned in previous chapters, formyl -CoA transferase enzy me has retained the distinctive structural characteris tics such as interlocked homo-di meric structure and accompanied strong inter-monomeric interactions between two monomers.[ 17 ] We are confident that features indigenous to the FRC enzyme were well dem onstrated using three consecutive molecular mechanics methods: molecular dynamics,[ 30 ] normal mode analysis,[ 25 ] and final free energy calculation.[ 119 120 ] Future research will expand on the present computational results using current or advanced molecular mechanics programs. One very obvious project will be to repeat OSRW for the FRC/CoA complex and other structur es determined by X-ray crystallography. In chapter 4, we demonstrated the free ener gy calculation for conformational change of the tetraglycine loop in free FRC en zyme and verified the result s by comparing them with our established X-ray results.[ 109 ] On the basis of differently predictive results in the case of the apo state of FRC via bindi ng free energy calculation[ 133 134 ] for CoA-bound FRC complex, the role of substrate (coenzyme A) could be predicted in the binding or unbinding to FRC. By extending the free energy calculations to the CoA-bound FRC complex, the role of coenzyme binding can be determined, so that the other factors that can a ffect the conformational change of tetraglycine loop could be discussed as second candidates. As mentioned in chapter 2, the conformati onal changes of the loop or inter-monomeric interactions in active s ite residues of FRC were not demonstr ated in the nanosecond time scale of molecular mechanic methods. Free energy calcul ation with our OSRW module, however, is a good technique, not only for observing the conformati onal change of flexible loop, but also for predicting inter-monomeric or pr otein-substrate interaction. 87

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APPENDIX A NAMD P RODUCTION RUN FOR AP O STATE OF FRC ENZYME ############################################################# ## JOB DESCRIPTION ## ############################################################# # apo-FRC production step (20 ns MD) ############################################################# ## ADJUSTABLE PARAMETERS ## ############################################################# structure apofrc_pbcsetup_xp.psf coordinates openEQ_fin.coor outputName openMD20ns_fin set temperature 298 # Continuing a job from the restart files set inputname openEQ_fin binCoordinates openEQ_rst.coor binVelocities openEQ_rst.vel extendedSystem openEQ_rst.xsc #firsttimestep 0 ############################################################# ## SIMULATION PARAMETERS ## ############################################################# # Input paraTypeCharmm on parameters par_all27_prot_na.prm temperature $temperature # Periodic Boundary conditions # NOTE: Do not set the periodic cell basis if you have also # specified an .xsc restart file! cellOrigin 0 0 0 cellBasisVector1 108.0 0 0 cellBasisVector2 0 108.0 0 cellBasisVector3 0 0 108.0 wrapWater on wrapAll on # Force-Field Parameters exclude scaled1-4 1-4scaling 1.0 cutoff 12. switching on switchdist 10. pairlistdist 14. 88

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# Integrator Parameters timestep 2.0 ;# 2fs/step rigidBonds all ;# needed for 2fs steps nonbondedFreq 1 fullElectFrequency 2 stepspercycle 10 #PME (for full-system periodic electrostatics) PME yes PMEGridSizeX 120 PMEGridSizeY 120 PMEGridSizeZ 120 # Constant Temperature Control langevin on ;# do langevin dynamics langevinDamping 5 ;# damping coefficient (gamma) of 5/ps langevinTemp ;#$temperature langevinHydrogen no ;# don't couple langevin bath to hydrogens # Constant Pressure Control (variable volume) useGroupPressure ye s ;# needed for 2fs steps #useFlexibleCell no ;# no for water box, yes for membrane #useConstantArea no ;# no for water box, yes for membrane langevinPiston on langevinPistonTarget 1.01325 ;# in bar -> 1 atm langevinPistonPeriod 100. langevinPistonDecay 50. langevinPistonTemp $temperature restartfreq 500 ;# 500steps = every 1ps dcdfreq 500 xstFreq 500 outputEnergies 250 outputPressure 250 outputTiming 2500 run 10000000 ;# 10ns (x 2fs time step) 89

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APPENDIX B NORM AL MODE CALCULATION INPUT USING CHARMM/DIMB ... GENERATED by Sangbae Lee on March (2007) FRC CoA enzyme Crystal Structure & NMA/VIBRAN + DIMB bomlev -1 open read card unit 10 name top_all27_prot_na_co.rtf read rtf card unit 10 open read card unit 12 name par_all27_prot_na_co.prm read param card unit 12 close unit 12 open read card unit 12 name coa-frc.psf read psf card unit 12 close unit 12 open read card unit 12 name coa-frc-initial.pdb read coor resi pdb unit 12 close unit 12 updat inbfrq -1 atom rdiel shift vswitch cutnb 14.0 ctofnb 12. ctonnb 10. eps 2.0 e14fac 0.4 wmin 1.5 ener coor copy comp cons harm sele all end force 250.0 mass mini sd nstep 1000 tolgrd 1.0 cons harm sele all end force 250.0 mass mini CONJ nstep 100 tolgrd 1.0 cons harm sele all end force 100.0 mass mini CONJ nstep 100 tolgrd 1.0 cons harm sele all end force 50.0 mass mini CONJ nstep 100 tolgrd 1.0 cons harm sele all end force 25.0 mass mini CONJ nstep 100 tolgrd 1.0 cons harm sele all end force 10.0 mass mini CONJ nstep 100 tolgrd 1.0 cons harm sele all end force 5.0 mass mini CONJ nstep 100 tolgrd 1.0 cons harm sele all end force 0.0 mass mini CONJ nstep 1000 tolgrd 0.01 cons harm sele all end force 0.0 mass mini ABNR nstep 30000 tolgrd 0.00001 coor orient rms mass 90

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updat inbfrq -1 atom rdiel shift vswitch cutnb 14.0 ctofnb 12. ctonnb 10. eps 2.0 e14fac 0.4 wmin 1.5 ener mini abnr tolgrd 0.00001 nsteps 10000 savf 100 -> Every 100 iterations the modes are written open write file unit 41 name apo-dimb.mod vibran nmod 200 dimb iter 5000 tole 0.06 iunmod 41 dwin pard 400 savf 100 end stop 91

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APPENDIX C FREE E NERGY CALCULATION WITH OSRW ALGORITHM GENERATED BY SANGBAE LEE on Mar, 25. 2009. INPUT FILE FOR NPT DYNAMICS W/ OSRW OF apo-FRC !Read topology open read unit 10 card name top_all27_prot_na.rtf read rtf unit 10 card !Read parameters open read unit 20 card name par_all27_prot_na.prm read para unit 20 card !Read PSF and Coordinates open read unit 10 card name apofrc_pbcsetup.psf read psf unit 10 card open read unit 10 card name apofrc_EQ.crd read coor unit 10 card !read ref1 open read unit 10 card name apofrc_open.crd read coor unit 10 card REF1 !read ref2 open read unit 10 card name apofrc_closed.crd read coor unit 10 card REF2 Setup PBC (Periodic Boundary Condition) stream apofrc_pbcsetup.str open read unit 10 card name apofrc_crystal_image.str CRYSTAL DEFINE @XTLtype @A @B @C @alpha @beta @gamma CRYSTAL READ UNIT 10 CARD !Image centering by residue IMAGE BYRESID XCEN 0.0 YCEN 0.0 ZCEN 0.0 sele resname TIP3 end IMAGE BYRESID XCEN 0.0 YCEN 0.0 ZCEN 0.0 sele ( segid @posid .or. segid @negid ) end Nonbonded Options nbonds atom vatom vfswitch bycb nbonds atom vatom vfswitch ctonnb 10.0 ctofnb 12.0 cutnb 16.0 cutim 16.0 inbfrq -1 imgfrq -1 wmin 1.0 cdie eps 1.0 ewald pmew fftx @fftx ffty @ffty fftz @fftz kappa .34 spline order 6 energy !use a restraint to place center of ma ss of the molecules near the origin MMFP GEO rcm sphere Xref 0.0 Yref 0.0 Zref 0.0 XDIR 1.0 YDIR 1.0 ZDIR 1.0 harmonic FORCE 1.0 select .not. ( hydrogen .or. resname TIP3 .or. segid @posid .or. segid @negid ) end END !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 92

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!!!!!! O S R W !!!!!!!!!! !setup lambda-dynamics ilmd nlamb 2 two Lambda particles temp 300.0 temperature xlamb 1.0 0.0 initiated coordinates whose first coordinates computed mlamb 500.0 500.0 the mass of Lambda particles blamb 500.0 500.0 friction factor of lambda particles !!setup reaction coordinates rcls fitpart noshow select .not. ( resid 255:266 .or. resid 44:52 .or. resid 2:10 .or. resid 240:248 ) .and. type CA end rcls: rmsd cluster rcls select ( ( segid PROB .and. ( resid 258:261) ) .or. ( segid PROA .and. ( resid 48) ) ) .and. ( .not. type H*) end !!setup Fourier path orpa orthogonal space path orpa ndime 1 nbead 32 astate -2.4 A state bstate 2.4 B state path 28 the predefined path between A state and B state in gromestry nprt 10 the write out frq. of Lambda and geometry reaction coordinates trajectory type 5 GFOR 10.0 kfor 1000 the restrain constant !setup orth-meta gmeta: gaussian metaMD gmeta ndim 2 nsor 2 hgau 0.05 # dimension of reaction coordinates nste 1 hred 0 extg 0 following is for other purpose, but don't remove mgau 0.0001 accf 0 wlf 0.85 metf 0.7 gcut 5 type 50 the type of generated reaction coordinate nprt 50000 the frq. of Gaussian Energy profile write out npro 5000 the frq. of Free Energy print out ngat 0 gval 1.0 eval 20.0 the max of Gaussian energy could be added min 0 max 1 wbin 0.001 wgau 0.002 peri 0 hass 0 smin 0 smax 0 extl 1 extr 1 kres 10 min -2000 max 2000 wbin 20.0 wgau 40.0 peri 0 hass 0 smin 0 smax 0 extl 1000.0 extr 1000.0 kres 0 NPT dynamics : estimate Pmass from SYSmass (total system mass) scalar mass stat calc Pmass = int ( ?stot / 50.0 ) shake tolerance 1.0e-06 bonh param open write unit 12 card name wt_run1.rst open write unit 13 file name wt_run1.dcd DYNA CPT leap start time 0.002 nstep 5000000 nprint 100 iprfrq 1000 ntrfrq 1000 iunread -1 iunwri 12 iuncrd 13 iunvel -1 kunit -1 nsavc 500 nsavv 0 echeck -1.0 PCONSTANT pref 1.0 pmass @Pmass pgamma 20.0 93

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isvfrq 5000 HOOVER reft 300.0 tmass 2000.0 tbath 300.0 firstt 300.0 open write unit 10 card name wt_run1.pdb write coor unit 10 pdb open write unit 10 card name wt_run1.crd write coor unit 10 card close unit 10 stop 94

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LIST OF REFERE NCES 1. Allison, M. J.; Littledike, E. T.; James, L. F. J. Anim. Sci. 2008, 45, 1173. 2. Brunger, A. T.; Adams, P. D.; Clore, G. M. ; DeLano, W. L.; Gros, P.; Grosse-Kunstleve, R. W.; Jiang, J. S.; Kuszewski, J.; Nilges, M.; Pannu, N. S.; Read, R. J.; Rice, L. M.; Simonson, T.; Warren, G. L. Acta. Crystallogr. D Biol. Crystallogr. 1998, 54, 905. 3. Chohnan, S.; Furukawa, H.; Fujio, T.; Nishihara, H.; Takamura, Y. Appl. Environ. Microbiol. 1997, 63, 553. 4. Anatharam, V.; Allison, M. J.; Maloney, P. C. J. Biol. Chem. 1989, 264, 7244. 5. Heider, J. FEBS Lett. 2001, 509, 345. 6. Baetz, A. L.; Allison, M. J. J. Bacteriol. 1990, 172, 3537. 7. Duncan, S. H.; Richardson, A. J.; Kaul, P.; Holmes, R. P.; Allison, M. J.; Stewart, C. S. Appl. Environ. Microbiol. 2002, 68, 3841. 8. Stewart, C. S.; Duncan, S. H.; Cave, D. R. FEMS Microbiol. Lett. 2004, 230 1. 9. Baetz, A. L.; Allison, M. J. J. Bacteriol. 1989, 171, 2605. 10. Sidhu, H.; Ogden, S. D.; Lung, H. Y.; Luttge, B. G.; Baetz, A. L.; Peck, A. B. J. Bacteriol. 1997, 179, 3378. 11. Berthold, C. L.; Moussatche, P.; Richards, N. G.; Lindqvist, Y. J. Biol. Chem. 2005, 280, 41645. 12. Dickert, S.; Pierik, A. J.; Linder, D.; Buckel, W. Eur. J. Biochem. 2000, 267, 3874. 13. Engemann, C.; Elssner, T.; Pfeifer, S.; Kr umbholz, C.; Maier, T.; Kleber, H. P. Arch. Microbiol. 2005, 183, 176. 14. Foster, J. W. Nat. Rev. Microbiol. 2004, 2 898. 15. Kim, J.; Darley, D.; Selmer, T.; Buckel, W. Appl. Environ. Microbiol. 2006, 72, 6062 6069. 16. Leutwein, C.; Heider, J. J. Bacteriol. 2001, 183, 4288. 17. Ricagno, S.; Jonsson, S.; Richards, N. G. J.; Lindqvist, Y. EMBO J. 2003, 22, 3210. 18. Gogos, A.; Gorman, J.; Shapiro, L. Acta. Crystallogr. D Biol. Crystallogr. 2004, 60, 507 511. 95

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19. Gruez, A.; Roig-Zamboni, V.; Valenc ia, C.; Campanacci, V.; Cambillau, C. J. Biol. Chem. 2003, 278, 34582. 20. Jonsson, S.; Ricagno, S.; Lindqvi st, Y.; Richards, N. G. J. J. Biol. Chem. 2004, 279, 36003. 21. Berthold, C. L.; Toyota, C. G.; Richards, N. G. J.; Lindqvist, Y. J. Biol. Chem. 2008, 283, 6519. 22. Alder, B. J.; Wainwright, T. E. J. Chem. Phys. 1959, 31, 459. 23. Brooks, C. L. III.; Karplus, M.; Pettitt, B. M. Proteins : A theoretical perspective of dynamics, structure and thermodynamics ; John Wiley & Sons: New York, 1998. 24. McCammon, J. A.; Harvey, S. C. Dynamics of proteins and nucleic acids ; Cambridge University Press: Cambridge, UK, 1987. 25. Tirion, M. M.; ben-Avraham, D. J. Mol. Biol. 1993, 230, 186. 26. Lybrand, T. P.; McCammon, J. A.; Wipff, G. Proc. Natl. Acad. Sci. U. S. A. 1986, 83, 833. 27. Won, Y. Bull. Kor. Chem. Soc. 2000, 21, 1207. 28. MacKerell, A. D.; Bashford, D.; Bellott, M.; Dunbrack, R. L.; Evanseck, J. D.; Field, M. J.; Fischer, S.; Gao, J.; Guo, H.; Ha, S.; Joseph-McCarthy, D.; Kuchnir, L.; Kuczera, K.; Lau, F. T. K.; Mattos, C.; Michnick, S.; N go, T.; Nguyen, D. T.; Prodhom, B.; Reiher, W. E.; Roux, B.; Schlenkrich, M.; Smith, J. C.; Stote, R.; Straub, J.; Watanabe, M.; Wirkiewicz-Kuczera, J.; Yin, D.; Karplus, M. J. Phys. Chem. B 1998, 102, 3586. 29. Alder, B. J.; Wainwright, T. E. J. Chem. Phys. 1957, 27, 1208. 30. Brooks, B. R.; Bruccoleri, R. E.; Olafson, B. D.; States, D. J.; Swaminathan, S.; Karplus, M. J. Comput. Chem. 1983, 4 187. 31. Weiner, P. K.; Kollman, P. A. J. Comp. Chem. 1981, 2 287. 32. Van Der Spoel, D.; Lindahl, E.; Hess, B.; Groenhof, G.; Mark, A. E.; Berendsen, H. J. J. Comput. Chem. 2005, 26, 1701. 33. Brnger, A. T. X-PLOR, version 3.1 : A system for X-ray crystallography and NMR ; The Howard Hughes medical institute and department of molecular biophysics and biochemistry: Yale university, 1992. 34. Schlenkrich, M.; Brickmann, J.; Mackerell, A. D.; Karplus, M. Empirical potential energy function for phospholipids : Criteria for parameter optimization and applications. 96

PAGE 97

In biological membranes : A molecular perspective from computation and experiment ; ed. Merz, K. M.; Roux, B. Birkhauser: Boston, 1996, pp 31. 35. MacKerell, A. D.; Wiorkiewicz-Kuczera, J.; Karplus, M. J. Am. Chem. Soc. 1995, 117, 11946. 36. Reiling, S.; Schlenkrich, M.; Brickmann, J. J. Comput. Chem. 1996, 17, 450. 37. Verlet, L. Phys. Rev. 1967, 159, 98. 38. Verlet, L. Phys. Rev. 1968, 165, 201. 39. Kuriyan, J.; Petsko, G. A.; Levy, R. M.; Karplus, M. J. Mol. Biol. 1996, 190, 227. 40. Bernstein, F. C.; Koetzle, T. F.; Williams, G. J. B.; Meyer, E. F. Jr.; Brice, M. D.; Rodgers, J. R.; Kennard, O.; Shimanouchi, T.; Tasumi, M. J. Mol. Biol. 1977, 112, 535 542. 41. Mulholland, A. J.; Richards, W. G. Proteins Struct. Funct. Genet. 1997, 27, 9. 42. Brnger, A. T.; Karplus, M. Proteins Struct. Funct. Genet. 1988, 4 148. 43. Jorgensen, W.; Chandrasekhar, J.; Madur a, J. D.; Impey, R. W.; Klein, M. J. Chem. Phys. 1983, 79, 926. 44. Levy, R.; Gallicchio, E. Annu. Rev. Phys. Chem. 1998, 49, 531. 45. Rognan, D.; Zimmermann, N.; Jung, G.; Folkers, G. Eur. J. Biochem. 1992, 208, 101 113. 46. Kal, L.; Skeel, R.; Bhandarkar, M.; Brunner, R.; Gursoy, A.; Krawetz, N.; Phillips, J.; Shinozaki, A.; Varadarajan, K.; Schulten, K. J. Comp. Phys. 1999, 151, 283. 47. Phillips, J. C.; Braun, R.; Wang, W.; Gumbar t, J.; Tajkhorshid, E.; Villa, E.; Chipot, C.; Skeel, R. D.; Kale, L.; Schulten, K. J. Comp. Chem. 2005, 26, 1781. 48. Ryckaert, J. P.; Ciccotti, G.; Berendsen, H. J. C. J. Comput. Phys. 1977, 23, 327. 49. Darden, T.; York, D.; Pedersen, L. J. Chem. Phys. 1993, 98, 10089. 50. Cheatham, T. E.; Miller, J. L.; Fox, T.; Darden, T. A.; Kollman, P. A. J. Am. Chem. Soc. 1995, 117, 4193. 51. Essmann, U.; Perera, L.; Berkowitz, M. L. ; Darden, T.; Lee, H.; Pedersen, L. G. J. Chem. Phys. 1995, 103, 8577. 97

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52. Rapaport, D. C. The art of molecular dynamics simulation ; Cambridge University Press: Cambridge, 1995. 53. Cramer, C. J. Essentials of com putational chemistry; John Wiley & Sons: New York, 2002. 54. Feller, S.; Zhang, Z.; Pastor, R.; Brooks, B. J. Chem. Phys. 1995, 103, 4613. 55. Hoover, W. G. Phys. Rev. A 1985, 31, 1695. 56. Amaro, R. E.; Minh, D. D. L.; Cheng, L. S.; Lindstrom, W. M.; Olson, A. J.; Lin, J. H.; Li, W. W.; McCammon, J. A. J. Am. Chem. Soc. 2007, 129, 7764. 57. Pauli, I.; Timmers, L.; Caceres, R. A.; Basso, L. A.; Santos, D. S.; de Azevedo, W. F. Jr. J. Mol. Model. 2009, 15, 913. 58. Gumbart, J.; Wiener, M. C.; Tajkhorshid, E. J. Mol. Biol. 2009, 393, 1129. 59. Park, S.; Khalili-Araghi, F.; Tajkhorshid, E.; Schulten, K. J. Chem. Phys. 2003, 119, 3559. 60. Case, D. A. Molecular dynamics and normal mode analysis of biomolecular rigidity In rigidity theory and applications ; Edited by Thorpe and Duxbury; Kluwer Academic / Plenum Publishers: New York, 1999, pp 329. 61. Hafner, J.; Zhenga, W. J. Chem. Phys. 2009, 130, 194111. 62. Bahar, I.; Lezon, T. R.; Bakan, A.; Shrivastava, I. H. Chem. Rev. 2010, 110, 1463. 63. Hayward, S.; Go, N. Annu. Rev. Physiol. Chem. 1995, 46, 223. 64. Case, D. A. Curr. Opin. Struct. Biol. 1994, 4 285. 65. Janei D.; Venable, R. M.; Brooks, B. R. J. Comput. Chem. 1995, 16, 1554. 66. Brooks, B. R.; Karplus, M. Proc. Natl. Acad. Sci. U. S. A. 1985, 82, 4995. 67. Gibrat, J. F.; G N. Proteins Struct. Funct. Genet. 1990, 8 258. 68. Seno, Y.; G, N. J. Mol. Biol. 1990, 216, 95. 69. Simonson, T.; Perahia, D. Biophys. J. 1992, 61, 410. 70. Tirion, M. M. Phys. Rev. Lett. 1996, 77, 1905. 71. Haliloglu, T.; Bahar, I.; Erman, B. Phys. Rev. Lett. 1997, 79, 3090. 98

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72. Delarue, M.; Sanejouand, Y. H. J. Mol. Biol. 2002, 320, 1011. 73. Tama, F. Prot. Pept. Lett. 2003, 10, 119. 74. Wang, Y.; Rader, A. J.; Bahar, I.; Jernigan, R. L. J. Struct. Biol. 2004, 147, 302. 75. Wade, R. C.; Davis, M. E.; Luty, B. A.; Madura, J. D.; McCammon, J. A. Biophys. J. 1993, 64, 9. 76. Wade, R. C.; Luty, B. A.; Demchuk, E.; Madura, J. D.; Davis, M. E.; Briggs, J. M.; McCammon, J. A. Nat. Struct. Biol. 1994, 1 65. 77. Peters, G. H.; Olsen, O. H.; Svendsen, A.; Wade, R. C. Biophys. J. 1996, 71, 119. 78. Tama, M. M.; Wriggers, W.; Brooks, C. L. III. J. Mol. Biol. 2002, 321, 297. 79. Tama, F.; Gadea, F. X.; Marques, O.; Sanejouand, Y. H. Proteins Struct. Funct. Genet. 2000, 41, 1. 80. Mouawad, L.; Perahia, D. Biopolymers 1993, 33, 599. 81. Perahia, D.; Mouawad, L. Comp. Chem. 1995, 19, 241. 82. Guilbert, C.; Pecorari, F.; Perahia, D.; Mouawad, L. Chem. Phys. 1996, 204, 327. 83. Brooks, B. R.; Janei D.; Karplus, M. J. Comput. Chem. 1995, 16, 1522. 84. Barton, N. P.; Verma, C. S.; Caves, L. S. D. J. Phys. Chem. B 2002, 106, 11036. 85. Rios, P. D. L.; Cecconi, F.; Pretre, A.; Dietler, G.; Michielin, O.; Piazza, F.; Juanico, B. Biophys. J. 2005, 89, 14. 86. Gaillard, T.; Martin, E.; Sebastian, E. S.; Cosso, F. P.; Lopez, X.; Dejaegere, A.; Stote, R. H. J. Mol. Biol. 2007, 374 231. 87. Loncharich, R. J.; Brooks, B. R. Proteins Struct. Funct. Genet. 1989, 6 32. 88. Fedoryuk, M. V. Method of steepest descent, in Hazewinkel, Mich iel; Encyclopaedia of Mathematics: Springer, 2001. 89. Fletcher R.; Reeves, C. M. Comput. J. 1964, 7 149. 90. Press, W. H.; Flannery, B. P.; Te ukolshy, S. A.; Vetterling, W. T. Numerical recipes : The art of scientific computing ; University Press: Cambridge, 1987. 99

PAGE 100

91. States D.; Karplus, M. Unpublished results 92. van Vlijmen, H. W. T.; Karplus, M. J. Mol. Biol. 2005, 350, 528. 93. Brooks, C. L. III.; Karplus, M.; Pettitt, B. M. In A theoretical perspective of dynamics, structure, and thermodynamics ; Prigogine I., Rice S. A., Eds.; Advances in Chemical Physics: Wiley, New York, 1988, vol. LXXI. 94. Cheng, X.; Lu, B.; Grant, B.; Law, R. J.; McCammon, J. A. J. Mol. Biol. 2006, 355, 310 324. 95. Cheng, X.; Ivanov, I.; Wang, H.; Sine, S. M.; McCammon, J. A. Biophys. J. 2007, 93, 2622. 96. Ma, J.; Karplus, M. J. Mol. Biol. 1997, 274, 114. 97. Miller, D. W.; Agard, D. A. J. Mol. Biol. 1999, 286, 267. 98. Schmid, F. F.; Meuwly, M. J. Mol. Biol. 2007, 374, 1270. 99. Levitt, M.; Sander, C.; Stern, P. S. J. Mol. Biol. 1985, 181, 423. 100. Mohamadi, F.; Richards, N. G. J.; Guida, W. C.; Liskamp, R. M. J.; Lipton, M.; Caufield, C. E.; Chang, G.; Hendrickson, T. F.; Still, W. C. J. Comput. Chem. 1990, 11, 440. 101. Dauber-Osguthorpe, P.; Osguthorpe, D. J.; Stern, P. S.; Moult, J. J. Comput. Phys. 1999, 151, 169. 102. Brooks, B. R.; Karplus, M. Proc. Natl. Acad. Sci. U. S. A. 1983, 80, 6571. 103. Bone, R.; Silen, J. L.; Agard, D. A. Nature 1989, 339, 191. 104. Whitmire, S. E.; Wolpert, D.; Markelz, A. G. ; Hillebrecht, J. R.; Galan, J.; Birge R. R. Biophys. J. 2003, 85, 1269. 105. Marques, O.; Sanejouand, Y. H. Proteins Struct. Funct. Genet. 1995, 23, 557. 106. Mouawad, L.; Perahia, D. J. Mol. Biol. 1996, 258, 393. 107. Thomas, A.; Field, M. I.; Mouawad, L.; Perahia, D. J. Mol. Biol. 1996, 257 1070. 108. Thomas, A.; Field, M. J.; Perahia, D. J. Mol. Biol. 1996, 261, 490. 109. Lee, S.; Chen, M.; Yang, W.; Richards, N. G. J. J. Am. Chem. Soc. 2010, 13, 7252. 110. Loria, J. P.; Berlow, R. B.; Watt, E. D. Acc. Chem. Res. 2008, 41, 214. 100

PAGE 101

111. Boehr, D. D.; McElheny, D.; Dyson, H. J.; Wright, P. E. Science 2006, 313, 1638. 112. Zwanzig, R. W. J. Chem. Phys. 1954, 22, 1420. 113. Beveridge, D. L.; Dicapua, F. M. Annu. Rev. Biophys. Biophys. Chem. 1989, 18, 431. 114. Kollman, P. A. Chem. Rev. 1993, 93, 2395. 115. J. G. Kirkwood. J. Chem. Phys. 1935, 3 300. 116. Kstner, J.; Senn, H. M.; Thiel, S.; Otte, N.; Thiel, W. J. Chem. Theory Comput. 2006, 2 452. 117. Straatsma, T. P.; Berendsen, H. J. C. J. Chem. Phys. 1988, 89, 5876. 118. Kollman, P. A.; Pearlman, D. A. J. Chem. Phys. 1989, 91, 7831. 119. Zheng, L.; Chen, M.; Yang, W. J. Chem. Phys. 2009, 130, 234105. 120. Zheng, L.; Chen, M.; Yang, W. Proc. Natl. Acad. Sci. U. S. A. 2008, 105, 20227. 121. Eisenmesser, E. Z.; Millet, O.; Labeikovsky, W.; Korzhnev, D. M.; Wolf-Watz, M.; Bosco, D. A.; Skalicky, J. J.; Kay, L. E.; Kern, D. Nature 2005, 438, 117. 122. Toyota, C. G.; Berthold, C. L.; Gruez, A.; Jonsson, S.; Lindqvist, Y.; Cambillau, C.; Richards, N. G. J. J. Bacteriol. 2008, 190, 2556. 123. Bartels, C.; Karplus, M. J. Comput. Chem. 1997, 18, 1450. 124. Darve, E.; Pohorille, A. J. Chem. Phys. 2002, 115, 9169. 125. Laio, A.; Parrinello, M. Proc. Natl. Acad. Sci. U. S. A. 2002, 99, 12562. 126. Rosta, E.; Woodcock, H. L.; Brooks, B. R.; Hummer, G. J. Comput. Chem. 2009, 30, 1634. 127. Martyna, G. J.; Tuckerman, M. E. ; Tobias, D. J.; Klein, M. L. Mol. Phys. 1996, 87, 1117 1157. 128. Kong, X. J.; Brooks, C. L. III. J. Chem. Phys. 1996, 105, 2414. 129. Ensing, B.; De Vivo, M.; Liu, Z. W.; Moore, P.; Klein, M. L. Acc. Chem. Res. 2006, 39, 73. 130. Himo, F. Theor. Chem. Acc. 2006, 116, 232. 101

PAGE 102

131. Brooks, C. L. III.; Karplus, M.; Pettitt, B. M. Proteins : A theoretical perspective of dynamics, structure and thermodynamics ; New York: John Wiley & Sons, 1988. 132. Nelson, M. T.; Humphrey, W.; Gursoy, A.; Dalke, A.; Kal, L. V.; Skeel, R. D.; Schulten, K. Comput. Appl. 1996, 10, 251. 133. Oostenbrink, C.; van Gunsteren, W. F. Proteins Struct. Funct. Bioinf. 2004, 54, 237. 134. Villa, A.; Zangi, R.; Pieffet, G.; Mark, A. E. J. Comp. Aid. Mol. Design 2003, 17, 673 686. 102

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103 BIOGRAPHICAL SKETCH Sangbae Lee was born in Kangwondo, Republic of Korea, and grew up in Seoul, Korea. He spent a very active youth with his parents and his elder brothe r and two elder sisters, and he graduated from Wooshin High School in 1987. In 1988, Sangbae began his undergraduate studies in chemistry at Hanyang University, Seoul, Korea. During his senior year, an internship with a local pharmaceutical company introduced Sangbae to a higher level of research-driven chemistry and inspired him to pursue a masters degree in chemistry. He earned his B.S. and M.S. in chemistry from Hanyang University, Korea, in 1995 and 1998, respectively. After graduating in February 1998, with his M.S. in chemistry, Sangbae was employed by the Choongwae pharmaceutical company as a scientist at Suwon, Korea in March 1998. At that time, Sangbae had a wedding ceremony with his wife (Insook Yoon). In 2005, he began the pursuit of his doctoral degree at the University of Florida, under the guidance of Dr. Nigel G. J. Richards. Sangbaes graduate re search is focused on using computational methods with the goal of recogni zing catalytic mechanisms in proteins. With Nigels advice, Sangbaes time in Gainesville bro ught success in the form of papers published, awards, and fellowships. After completing his Ph .D. in December, 2010, Sangbaes family plans to move to Indiana, where Sangbae will take a po stdoctoral fellowship at Indiana University at Bloomington, IN.