A QUANTITATIVE INVESTIGATION OF NONCOMPETITIVE
ELUTION IN AFFINITY CHROMATOGRAPHY USING
BOVINE a-CHYMOTRYPSIN AS A MODEL
WILLIAM ARTHUR GILBERT
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
I dedicate this dissertation to my first grade teacher,
Dorothy Jo Gonser, who opened up the world to me through the
beauty of reading. Her enthusiasm at my early age prompted me
to reach for a dream and to get there.
The author would like to express his deep appreciation to
Dr. Ben M. Dunn, his research director, for giving him the guidance
and freedom of thought during the completion of this work. Dr. Dunn's
open mindedness also allowed the author to develop skills outside of
the Department of Biochemistry., Wichout Dr. Dunn's cooperation this
author may not have been able to realize his full potential. The en-
vironment of Dr. Dunn's laboratory provided the author with the elements
required for productive work as well as for the development of deep
Special thanks are given to the author'5 advisory committee and
fellow graduate students of the Department of Bioch.mistry and Molecular
Biology for their suggestions and criticism during the execution of this
The author wishes to thank his parents for their years of under-
standing and for trust without which this work would have been impossible.
TABLE OF CONTENTS
LIST OF TABLES . . .
LIST OF FIGURES . .
KEY TO SYMBOLS NOT DEFINED IN TEXT .
ABSTRACT . . .
INTRODUCTION . . .
Background . .
Quantitive Affinity Chrocatography .
Affinity Chromatography of a-Chymotrypsin
MATERIALS AND METHODS ......
Chemicals .. . .
Equipment . ....
Spectroscopic Assay for a-Chymotrypsin .
Titrimetric Assay for a-Chymotrypsin .
Affinity Matrix Synthesi . .
Small Zone Elution Experijnents .
Large Zone Elution Experiments .
TPCK Inactivation of a-Chymotrypsin .
RESULTS . . .
Elution of the Affinity Matrix .
Soluble Ligand Experiments .
Determination of Dissociation Constants for
Soluble Complexes . .
. ..... vi
. . 1
. . 1
. . .
. . .18
. . .18
. . .19
. . .20
. . .20
. . .22
. . .25
. . .25
. . .28
. . . .iii
Quantitation of Matrix Bound Ligand . 45
DISCUSSION . . . 51
ABENDIX . . . 90
BIBLIOGRAPHY . . . 95
BIOGRAPHICAL SKETCH ...... ....... ........ ..... 97
LIST OF TABLES
I Dissociation constants for inhibitors of a-chymotrypsin
as determined from kinetics of the hydrolysis of BTEE .. 46
II Summary of predicted elution behavior in noncompetitive
affinity chromatography ... . ..... .. 62
III Comparison of soluble dissociation constants
obtained from affinity chromatography with
those obtained by solution kinetics ..... .. .. 78
LIST OF FIGURES
1 Affinity Chromatography .
2 Competitive Binding Scheme for Affinity
Chromatography . . .
3 Small Zone Versus Large Zone Elutio .
4 a-Chymotrypsin Binding to Affinity Matrix .
5 TPCK-Chymorrypsin Elution on Affinity Matrix .
6 a-Chymotrypsin Elution from the Affinity
Matrix . . .
7 a-Chymotrypsin on an Unsubstituted Matrix .
8 Small Zone Experiments for
Carbobenzoxyplenylalanine . .
9 Small Zone Experiments for
N-Acetyl-L-Phenylalanine . .
10 Small Zone Experiments for
Carbobenzoxyphenyialanine . .....
11 Large Zone Experiments for
Carbobenzoxyphenylalanine . .
12 Ultraviolet Spectra of 4-Phenylbutylamine and
Supernatant from Solvolysis of Matrix .
13 Ultraviolet Spectra of Unsubstituted Matrix and
Affinity Matrix After Solvolysis .
14 Dissociation Constants Present in Competitive
Elution Scheme . .
15 Expected Results for Small Zone Experiments in a
Competitive Elution Affinity Column .
16 Noncompetitive Elution Scheme for Affinity
Chromatography .. ..... .
.... .. 58
17 Simulation of Elution Behavior for
Noncompetitive Scheme . .... ... 61
18 Case I Type Noncompetitve Elution . 64
19 Case II Type Noncompetitive Elution .... 66
20 Case III Type Noncompetitive Elution .. 68
21 Linearized Form of the Case I Type Simulated
Results from Figure 18 . . 73
22 Results for Carbobenzoxy Deriviatives of the Aromatic
Amino Acids Plotted in Double Reciprocal Form .. 76
23 An Example of the Results Obtained from Solution
Kinetics Analyzed as a Double Reciprocal Plot
by the Method of Lineweaver and Burk ... .80
24 Linearized Form of the Case III Type Simulated
Results from Figure 20 . .. 82
25 Results for Carbobenzoxyalanylalanine Plotted
in Double Reciprocal Form . .... 85
26 The Structure of the a-Chymotrypsin Affinity
Matrix . . . 88
KEY TO SYMBOLS NOT DEFINED IN TEXT
A280 -Light absorbance at 280 nm
CBZ -Carbobenzoxy (prefix)
Abstract of Thesis Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy
A QUANTITATIVE INVESTIGATION OF NONCOMPETITIVE
ELUTION IN AFFINITY CHROMATOGRAPHY USING
BOVINE a-CHYMOTRYPSIN AS A MODEL
WILLIAM ARTHUR GILBERT
Chairman: -Ben M. Dunn
Major Department: Biochemistry and Molecular Biology
Affinity chromatography has become a widely accepted and powerful
technique in protein purification. However, the method was developed in
a shroud of empiricism based on unproven assumptions. Most often, an
investigator would opt for the highest substitution obtainable and
evaluate the affinity matrix only on an operational basis. There existed
no unambiguous way to quantitatively evaluate a newly synthesized affinity
This work presents a review of recent attempts in the development
of quantitative affinity chromatography and describes a widely accepted
method of zonal elution for determining intrinsic binding constants.
This method was applied to a system in which 4-phenylbutylamine was
immobilized to form an affinity matrix for a-chymotrypsin. a-Chymotrypsin
was passed through the column in the presence of varying concentrations
of known binding ligands. The results obtained were inconsistent with
those predicted for a simple competitive model.
A noncompetitive model involving two unique yet Interacting binding
sites was proposed. This model allows the enzyme to associate with the
column in either the free form, E, or as the complex, E-I.
Three types of elution behavior were predicted from the ratio of
column binding constants. Case I type of noncompetitive elution in-
volved soluble ligand retarded enzyme elation; case II type elution was
the degenerate case in which soluble ligand did not affect enzyme elution.
Finally, case III type elution involves soluble ligand facilitated enzyme
The experimental data obtained were found to fit Lhis model very
closely. Further, all three types of elution behavior were observed
and fit results predicted from the noncompetitive elution model.
This work is presented as a demonstration of the applicability of
quantitative affinity chromatography in examining sophisticated binding
This work is directly applicable to studies involving solid state
substrates. Examples of this are found in cell membrane, organelle and
Ben M. Dunn
Since the beginnings of the science we now know as biochemistry,
investigators have been concerned with the purity of the material with
which they were working. Methods for protein purification governed the
rate at which this science developed. The separation techniques developed
were based on the physical properties of the proteins. The differences
in these physical properties were exploited to separate proteins into
classes depending on ionic charge, solubility, molecular size and a
variety of other parameters.
It is interesting to note that all of these separations were done
using properties which are secondary to the uniqueness of a protein. The
distinguishing feature of any protein is its specificity in the binding of
various ligands. Functions such as transport, catalysis, antibody recog-
nition and receptor binding all depend on ligands binding specifically to
the protein surface. This property was successfully used by uatCrecasas,
Wilchek and Anfinsen in 1968 to develop a method referred to as affinity
chromatography. The concept is realized by covalently attaching the ligand
to an insoluble matrix and packing the support into a chromatographic
column. Those macromolecules that display an affinity for the immobilized
ligand will be retained by the matrix, while those with little or no af-
finity will pass through unretardud. This is shown schematically in figure i,
where M is the insoluble matrix, L is the immobilized ligand which is
attached to the matrix, M, via a spacer arm assembly, S. This ligand marrix
3 X 0
C M/ J r ,C0
0 l1 .a
'O &- 4-1
U td N L)
*0 -4 f-( C P.
\ .- i-4 c
a 1- O)
CO CO 4 L
o -1 6
S > 0O
S 0 J 0 W
0O r0 0 -
0 01 -1 X z
C) a) a) 0 z
3 r-l 6
U r r 0 W 4 3
*4 *rq 0 IH t<
-- t >
(ia) ( cnr
conjugate has the element of specificity which would be unique for
the macromolecule to be isolated. The species which had been adsorbed
can then be desorbed by a change in the composition of the eluting buffer
to favor dissociation. These changes usually involve pH, ionic strength
This potentially easy, rapid and virtually limitless application of
affinity chromatography has promoted much growth in biochemistry over the
last decade. Wilchek and Jakoby (1974) list over 120 unique purification
applications. This technique can also be used to resolve and purify cells
and viruses (:urrr. t a i. 1972), chemically modified proteins (Wilkersor.
Mariano aRd~~S&76) and has potential use in the exploration of binding
sites, topographies and kinetic mechanisms (MareiniAzy et .1". 97r).
However, recent experience with affinity chromatography has given in-
vestigators a more cautious approach to this technique. An earl-y paper-by
Steers et al. (1971) describing the purif:c;tl n of 3-galactcsidase on
immobilized galactoside was later shown by, O'Carra. e al. (1973, 1974), to
be largely non-specific interactions with the spacer arm assembly. Such
phenomena can severely interfere with the true biospecific behavior and lead
to artifactual observations, such as electrostactic effects which may
attract non-specific proteins or repel the specific binding proteins. Care-
ful consideration must therefore be given to the nature of the matrix and
restrictions imposed by the immobilization of a ligand.
The selection of a matrix support is constrained by several factors,
The matrix should be composed of uniform spherical beads which are hydro-
philic, mechanically and biologically stable, and possess chemical groups
that can be easily modified without altering any of those properties.
Cuatrecasas and Anfinsen (1971) have reviewed the relative advantages
of cellulose, agarose, dextran, glass and polyacrylamide as affinity
The activation of hydrophilic polysaccharides by cyanogen bromide
is currently the most commonly employed procedure for the immobilization
of ligands having primary amino functions (Axmn -et nr---C96-4. This
procedure although widely accepted is not without its disadvantages. The
activation procedure introduces an isourea group as the link between the
ligand and the saccharide matrix. This group has a pKa of 10.4 which
gives a positively charged matrix at neutral pH. The resulting matrices
could exhibit an electrostatic interaction cfr the protein which may
alter or obliterate the specific interaction by the immobilized ligand
(Nishikawa & Bailon 1975). Wilchek (1973) has proposed that the charge
introduced by cyanogen bromide coupling of primary amines may be extin-
guished by the use of acrylhydrazides which yield a linkage to Agarose
which has a pKa of 4.0 and thus is uncharged at neutral pH. Tesser et al.
(1974) have pointed out another failing of the cyanogen bromide coupling
technique. They suggest that a small but continuous solvolysis of the
linkage between the matrix and the ligand is present at pH's above 5.
Wilchek (1973) has described the preparation of stable agarose derivatives
by coupling multivalent spacer molecules such as polylysine, polyornithine
or polyvinylalanine to Agarose. This polymer which serves as a spacer
arm is attached to Agarose by multiple isourea linkages. Thus, as these
linkages break down. the polymer will remain attached to the Agarose bead
through other linkages. Attachment of ligands to this spacer can be
achieved through the unreacted amino functions on the polymer. Wilchek
and Miron (1974) later combined the advantages of multipoint attachment
of spacer arms and the coupling of acylhydrazides to Agarose. His new
matrix synthesis method involved the coupling of polyacrylic hydrazide to
Agarose. The unr-acted hydrazide groups could be used to directly couple
carboxyl containing ligand or could be modified to accept ligands con-
taining other types of reactive groups. The most widely used modification
involves succinylation of the hydrazide moiety giving a carboxyl group
which could be used to couple ligands containing primary amines.
It seems therefore, that while cyanogen bromide activation is a very
simple and rapid procedure, it has a number of serious shortcomings for
use in affinity chromatography. However, these shortcomings have stimu-
lated the development of sophisticated methodologies in the design and
synthesis of affinity matrices.
A number of considerations govern the selection of the ligand for
affinity chromatography. The ligand to be coupled to the solid support
or spacer must display a unique affinity for the macromolecule to be puri-
fied. It can be a substrate, inhibitor, allosteric effector, cofactor,
hormone, antigen or any species that displays the required specificity.
Further, the ligand must possess functional groups that can be modified
for attachment to the solid support without blocking its recognition by
the complementary macromolecule. Most investigators have relied on em-
pirical guidelines -which had developed during the first half-decade of
affinity chromatography. These guidelines did not give investigators an
unambiguous method for quantitatively evaluating a newly developed chroma-
tographic matrix. This lack of information on the binding strength be-
tween the immobilized ligand and macromolecule often precluded any rational
design strategy and the highest attainable ligand concentration was
generally opted for. Further, a column's effectiveness was measured solely
on whether it worked and not on any quantitative criteria which could
be used by other investigators working on similar systems for comparison.
Quantitative Affinity Chromatography
In 1971, Akanuma et al. studied the affinity chromatography of
carboxypeptidase 3 on columns of immobilized basic amino acid and aromatic
amino acid derivatives. They were interested in the elution of the enzyme
from the column in a concentration gradient of eluting ligand. They
observed two interesting effects, first, carboxypeptidase B was eluted
from a column of immobilized e-aminocaproyl-D-arginine by an increasing
gradient of e-aminocaproic acid; secondly carboxypeptidase B was eluted
from a column of immobilized c-aminocaproyl-D-phenylalanine by a decreasing
gradient of e-aminocaproic acid. These two observations demonstrated two
binding schemes which could exist in affinity chromatography. The former
was a ligand-inhibited binding and the latter a ligand-facilitated binding.
Akanuma et al., however, made no attempt to quantitate these two binding
In this context, several attempts were made to devise a method for
the measuring of the parameters surrounding this technique. Andrews et al.
(1973) provided the first example of such a quantitative approach, using
immobilized a-lactalbumin to determine the equilibrium constant between
galactosyltransferase and glucose, Their simplified approach was only
applicable to a ligand facilitated binding system. Their experiments con-
sisted of immobilizing a-lactalburin to Sepharose and placing the modified
gel in a chromatographic column. The column was then pre-equilibrated with
a buffer containing a desired concentration of glucose. Galactosyitransferase,
in a small volume of the pre-equilibrating medium, was applied to the column:
fractions were collected and assayed for the appropriate activity. By
varying the concentration of glucose in the equilibrating buffer, a
family of elution volumes were generated for the protein. They observed
that by plotting the data as the reciprocal of the difference between
the observed elution volume, Ve, and Vo, the elution for the enzyme in the
absence of glucose, versus the reciprocal of the glucose concentration,
a straight line was obtained. Further, they showed that by dividing the
ordinate intercept by the slope, a value was obtained which was very close
to the known dissociation constant for the glucose.galactosyltransferase
complex. They repeated these experiments using N-acetylglucosamine as the
soluble ligand. Again, results fitting a straight line were obtained and
a value for the dissociation constant cf the N-acetylglucosamine-galacto-
syltransferase complex was obtained which matched the known value. Andrews
et al. made no mention of the relationship between the elution volume to
the degree of substitution of ligand on the matrix.
Nichol et al. (1974) expanded the theory of this quantitative approach
to encompass many possible equilibria involving an immobilized ligand,
soluble protein and soluble ligand(s). Nichol's equations provided a
complete theoretical consideration for affinity chromatography; however,
his derivation was also very cumbersome and lacked the necessary simplifi-
cations which would make its application experimentally feasible.
Dunn and Chaiken (1974) were working on the problem of quantitating
these parameters at the time of Nichol's derivations. Dunn and Chaiken,
however, had a technique which was better suited to an experimental
evaluation. Their column system consisted of an Agarose matrix of im-
mobilized thymidine-3'-aminophenylphosphate-5'-phosphate. The enzyme
staphylococcal nuclease was known to bind specifically with this matrix
(Cautrecasas, Wilchek and Anfinsen 1968). Their experimental approach
was to pre-equilibrate a column of the affinity matrix with a known con-
centration of soluble thymidine-3',5'-bisphosphate. This soluble ligand
would compete for the binding site on staphylococcal nuclease and pre-
vent interaction with the immobilized ligand. This scheme is shown in
figure 2 where E, I and =EF are the free enzyme, soluble ligand and im-
mobilized ligand, respectively; E-I and EtL-T are the possible binary
complexes formed in this system with KI and K]pg as their dissociation
constants. At low concentrations of soluble ligand the enzyme would
spend more of its time in the stationary phase, this would lead to re-
tardation of the enzyme by the column and a large elution volume for
the enzyme. On the other hand, at high concentrations of soluble ligand,
the enzyme would not be bound tc the immobilized ligand as much as to the
ubiquitous soluble ligand. This would lead to a situation in which the
enzyme would spend most of its time in the mobile phase and be eluted from
the column at a small elution volume. By carefully choosing the concen-
tration of soluble ligand they were able to establish an equilibrium for
the enzyme between the immobilized ligand (stationary phase) and the soluble
ligand (mobile phase) as it passed down the column.
They presented a derivation in which their final equation was re-
presented in experimentally obtainable values.
1 KT [T
Ve-V (V + [ -)( V -)
-e o o m) KI (Vo Vm)[L-7M
ca $ 0
(0) ) 0
N VU) >
44 W 0 0a
(U CO C
0 -4 Mc
N *rl H
Ld + 1r-- n
Where 1/(Ve Vo) is plotted versus [I] in which Ve, Vo and Vm are the
elution volume for the enzyme at a soluble ligand concentration, the
column void volume and volume of the mobile phase, respectively. K7--F,
KI, L- and I are as described. Here, the ordinate intercept divided by
the slope gives KI; K -= can be obtained from the ordinate intercept by
substitution of [L-M], Vo and Vm. A dissociation value for the nuclease
thymidine-3',5'-bisphosphate complex was obtained as well as a value for
the dissociation of the enzyme from the immobilized ligand. The measure-
ment of this latter value is very significant in that it could provide a
means of quantitatively expressing the ability of the column to bind pro-
tein. Further, the measurement of this value indicates that in an affinity
chromatographic system the enzyme is bound reversibly to the matrix and
exists in a dynamic equilibrium between the mobile phase and the stationary
phase. Thus in any affinity chromatographic system the protein will elute
at a finite volume, this volume being a function of the dissociation con-
stant between the enzyme, immobilized ligand, the concentration of im-
mobilized ligand, and the physical dimensions of the column.
This is somewhat different from the current attitude towards affinity
chromatography in which the adsorption process is maximized and not applied
quantitatively to the investigator's advantage. By the proper measurement
of the dissociation constant for the enzyme matrix interaction one could
rationally predict the behavior of the column and/or modify the ligand to
obtain the optimum behavior. The concept of a dynamic existence of the
enzyme between the two phases is extremely important and cannot be over-
emphasized when dealing with affinity chromatography.
Chaiken and Taylor (1976) used the analytical method of Dunn and
Chaiken to look at the behavior of ribonuclease A analogs. These analogs
were structurally competent complexes formed by allowing the cleaved S
peptide from ribonuclease A to reassociate with the remaining protein to
form a noncovalent complex which resembled the original enzyme. This
established a working base for determining binding constants for inactive
ribonuclease S, although catalytically nonfunctional, could recognize
substrates and substrate analogs.
Other attempts were made at developing quantitative affinity
chromatography. Kasai and Ishii (1975) did quantitative affinity chroma-
tography with a trypsin-glycylglycyl-L-arginine Agarose system; using
various concentrations of derivatives of L-arginine as the soluble ligand,
they generated a series of elution volumes for trypsin. Their results
fit the competitive binding scheme of Dunn and Chaiken. From these ex-
periments they obtained values for the Kl's of various inhibitors of trypsin.
Brinkworth et al. (1975) used quantitative affinity chromatography to
simultaneously determine the K,'s for NADH for the five isozymes of lactate
dehydrogenase. Their experiments point out the power an affinity system
would have when the intrinsic binding constants are known. By adjusting
the concentration of soluble ligand they were able to achieve maximum
separation of these isozymes from a tissue extract.
Finally, Brodelius and Mosbach (1976) developed a system in which
they could obtain the relative Km's for enzymes which bound to the same
affinity matrix. By applying all the enzymes to a column of immobilized
AMP, followed by an increasing gradient of soluble NADH, the bound en-
zymes were eluted as a function of their Km for NADH. The enzymes with
higher dissociation constants were found to elute first while the enzymes
with lower dissociation constants were eluted later.
They observed a linear relationship between the known Km's and con-
centration of NADH in the volume at which they eluted. From these re-
sults they were able to establish a calibration curve for their column.
They applied lactate dehydrogenase isozymes from various animal sources
and measured the eluting concentration of NADH against their calibration
Although this provided an empirical method for the determination of
soluble Km's, Brodelius and Mosbach did not derive a mathematical rela-
tionship for their calibration curve.
Affinity Chromatography of a-Chymotrypsin
Chymotrypsin is the product of tryptic activation of its inactive
precursor, chymotrypsinogen, which is produced by the pancreas. The iso-
lation of bovine chymotrypsinogen and its activation by trypsin were first
reported by Northrop and Kunitz (1932). The initial step involves the
splitting of the Arg(15) Ile(16) peptide bond leading to the formation
of catalytically active r-chymotrypsin. Subsequent autocatalytic events
give rise to S-, K-, and y-chymotrypsin as intermediates in the formation
of a-chymotrypsin (Wright et al. 1968; Miller er al. 1971). The final
species is the one most commonly encountered. All active forms of the
enzyme are known to exhibit a marked preference in catalyzing the hydrolysis
of peptide bonds on the carboxyl side of aromatic amino acid residues.
While the procedures for the isolation of chymotrypsin and chymotryp-
sinogen in a highly homogeneous state have been developed (Keller et al.
1958), the preparation of chymotrypsinogen devoid of chymotrypsin is dif-
ficult to achieve, even after repeated purification procedures. Cuatrecasas
et al. (1968) approached this purification through the use of their newly
developed affinity chromatography technique. They were able to selectively
adsorb chymotrypsin to Sepharose gels containing covalently bound e-amino-
n-caporyl-D-tryptophan methyl ester. Enzyme was adsorbed at pH 8.0 when
applied to this column. This adsorption was selective in that chymotryp-
sinogen, subtilisin, diisopropyl-phosphoryl-trypsin and pancreatic ribo-
nuclease were not bound. The a-chymotrypsin was not ad:orbed by a column
of unsubstituted Sepharose.
The possibility of coupling inhibitors other than E-amino-n-caporyl-
D-tryptophan methyl ester to Sepharose was considered by Stevenson and
Landman (1971), who studied the properties of Sepharose-4-phenylbutyl-
anine columns. Their choice of this molecule was based on the known binding
of the hydrophobic phenyl moiety to chymotrypsin and on minimization of
steric effects by virtue of the bucyl spacer arm in the molecule. Their
studies with Sepharose-4-phenylbutylamine were in accordance with these
expectations. The column was capable of adsorbing a-chymotrypsin from
solutions at pH 8.0 with recovery by elution at pH 3.0. The selectivity
of the adsorbent was further confirmed by its inability to adsorb porcine
trypsin, bovine trypsinogen and a-chymotrypsin inhibited with tosylpheny-
lalanine chloromethyl ketone (TPCK). The Sephiarose-4-phenylbutylaminne
columns were found to be effective in the isolation of chymotrypsin-like
proteases from extracts of moose (Alces alces) pancreas. The use of
4-phenylbutylamine is advantageous over that of e-amino-n-caproyl-D-
tryptophan methyl ester in that the synthesis of the later is a time-
consuming and tedious synthesis. Further, once synthesized it is subject
to degradation by light.
Hofatree (1973) investigated non-specific binding of negatively charged
proteins to column of Sepharose substituted with n-alkylamine or with
4-phenylbutylamine (PBA). Of the proteins tested, the only exception to
nonspecific binding was a-chymotrypsin which showed a strong affinity for
PBA-substituted material even in the presence of reagents which disrupted
the non-specific binding. By contrast, biidirg did not occur when the
ligand was an n-alkylamine. He concluded that although many of the proteins
he was testing were binding because of bydrophobic and/or electrostatic
forces that the binding of ut-chymotrypsin was a specific event involving
the complementarity of the contours (i.e., fit) of the interacting mole-
There is also much known about the kinetics and mechanism of a-
chymotrypsin (Boyer, the Enzymes, 1970). Work with synthetic inhibitors
by Morihara and Oka (1977) shows that the active center of the enzyme can
accommodate four to five amino acid residues along with the aromatic resi-
due which fits near the catalytic site. This is supported by X-ray
crystallographic work which shows the binding site in chymotrypsin as an
elongated groove capable of binding several amino acid residues (Segal
et al. 1971; Robertus et al. 1972).
The amount of information available on the affinity chromatography
of a-chymotrypsin with immobilized 4-phenylbutylamine makes this system
a logical choice in which to further investigate the binding constants
involved in affinity chromatography. The system has been shown to be both
specific and devoid of any interfering interactions. Further, the amount
of information available on a-chymotrypsin and its inhibitors encourages
the choice of this system for quantitative study. By further developing
the technique of quantitative affinity chromatography through the use of
an established system, we hope to extend this method to systems in which
the phenomena of immobilized binding are not well understood. This in-
volves enzymes whose substrates are actually substructures of very large
macromolecules such as cell walls or ribosomes. Most important of all
we hope to remove some of empiricism which surrounds affinity chromatography
and provide some rational approach in evaluating an affinity system.
MATERIALS AND METHODS
Bovine a-chymotrypsin was obtained from Sigma Chemical Company as
a three times crystallized and lyophilized solid with a specific acti-
vity of 43 Units per milligram. N-Benzoyl-L-tyrosine ethyl ester, car-
bobenzoxy (CBZ) amino acid derivatives and N-acetyl amino acid deriva-
tives were also obtained through Sigma Chemical Company. 4-Phenylbuty-
amine and 4-phenylbutyric acid were obtained from Aldrich Chemical Com-
pany. Succinylated polyacrylic hydrazide Agarose was obtained through
Miles-Yeda, Ltd. (51 pmole succinyl groups per ml, Lot No. SPAH3). All
other chemicals used were reagent grade and purchased from common suppliers.
The column used in these experiments was a Chromatoflo Series A
borosilicate glass type (0.9 x 25cm) purchased from Pierce Chemical
Company. A sample injection port and adjustable plungers for variable
bed volumes were also obtained from Pierce. An LKB 2120 Varioperpex
peristaltic pump was used to maintain a uniform eluant flow through the
column. Fractions were collected using an LKB Redirac Fraction Collector.
The eluant from the column was passed through a ISCO Model 226 Absorbance
Monitor for recording the amount of 280 nanometer absorbing material.
Chromatograms were recorded using a Model 1310 strip recorder from Bio-Rad
Spectrophotometric activity assays were performed using a Gilford
Model 250 spectrophotometer. Titrometric activity assays and syntheses
involving titration were performed using a Radiometer TTT60 Autotitrator.
Spectroscopic Assay for a-Chymotrypsin
Fractions were assayed for a-chymotrypsin activity by the method of
Hummel (1959). N-benzoyl-L-tyrosine ethyl ester (6.7 mg) was dissolved
in 20 milliliters of methanol. Twenty-two milliliters of 0.08 M tris.HCl-
0.1 M calcium chloride (pH 7.8) were then added and mixed. Nine-hundred
microliters of this assay buffer was placed in a one milliliter cuvette and
the absorbance of the substrate at 256 nanometers electronically subtracted.
The assay is started by adding 100 microliters of test solution (0.1 to
2.0 micrograms a-chymotrypsin) to the cuvette and mixing the contents. The
rate of enzymatic hydrolysis of N-benzyol-L-tyrosine ethyl ester is mea-
sured by a linear increase in absorbance at 256 nanometers. One unit of
enzyme activity is equivalent to one micromole of substrate hydrolysed per
minute at pH 7.8 and 250C.
Titrimetric Assay for a-Chymotrypsin
An alternative method for determining the activity of a-chymotrypsin
has been described by Morihara and Oka (1977) which involves measuring
the proton release, uptake of base, by a pH stat method. Reactions were
carried out in 2 mM N-benzoyl-L-tyrosine ethyl ester, 0.1 M in calcium
chloride with 0.01 N sodium hydroxide as titrate. A pH of 7.8 was main-
tained during the hydrolysis of substrate by the addition of sodium hy-
droxide. The rate at which titrant was added to the test solution is
measured on a servorecorder. One unit of enzyme activity is equivalent
to one micromole of substrate hydrolysed per minute at pH 7.8.
Affinity Matrix Synthesis
The affinity matrix used in this study was based on the immobiliza-
tion of 4-phenylbutylamine according to Stevenson and Landman (1971).
Twenty milliliters of settled succinylated polyacrylic hydrazide Agarose
(51 micromoles succinyl groups per milliliter, 1.02 mmoles total) was
washed with water to remove the storage buffer and taken up in dioxane/
water (4:1). 4-phenylbutylamine (15.3 mile, 2.28 g) was added and the
pH adjusted to 6.0 with 1 M hydrochloric acid (HC1). The coupling rea-
gent, l-ethyl-3(3-dimethyl-aminopropyl)-carbodiimide (4 g), was added in
0.2 gram units into the stirred Agarose. The pH is maintained at 6.0
during these additions by dropwise titration with 1 M HC1. The reaction
was allowed to proceed for 10 hours with gentle mixing by using a stirring
bar and motor. At no time during the reaction should the gel be stirred
violently as this leads to a mechanical shearing of the gel particles,
thus reducing their porosity. The coupling was terminated by washing the
gel sequentially with water, 0.1 M sodium carbonate (pH 9.5), 0.1 M sodium
acetate and finally 40 mM tris.HC1-50 mM calcium chloride (pH 7.8); all
of the washing buffers contained 25% (v/v) methanol to aid in solubilizing
Small Zone Elution Experiments
A solution of a known amount of ligand was prepared by first dis-
solving the ligand in about one milliliter of methanol. This was necessary
because of relative insolubility of the ligand in water. This was then
added to 40 mM tris-HC1-50 mM calcium chloride (pHI 7.8) 25% (v/v) methanol
and brought to a final volume of 200 milliliters. The solution was degassed
under vacuum and the affinity column pre-equilibrated with this buffer.
The eluant was monitored spectrophotometrically at 280 nm for the emergence
of ligand through the column. A stepped increase in the absorbance of
eluant was taken to indicate equilibration of the column. To insure full
equilibration no less than four column volumes were run after this initial
detection of ligand. An enzyme solution (1 mg/ml) was prepared in which
the ligand concentration had been adjusted to be the same as that of the
equilibrated column. One hundred microliters of this enzyme solution was
applied to the column via the sample injection port. The fraction col-
lector, peristaltic pump and strip chart recorder were started simultan-
eously; one minute fractions containing 0.74 milliliters were collected.
A run was terminated by the detection of enzyme elution from the eluant
monitor. The column was washed with the methanolic tris-Ca++ buffer to
remove soluble ligand and to prepare the column for the next determination.
The activity in the fractions was determined by using the spectrophotometric
assay as described above. One hundred microliters was taken from each
fraction and added to 900 microliters of substrate was sufficient to over-
come the effect of inhibition by that ligand. Results of activity assays
and A280 tracings were plotted and the elution volume defined as the volume
at which the enzyme is half-eluted, that is, the top of the eluting peak.
Large Zone Elution Experiments
In large zone experiments, the column was pre-equilibrated as in the
small zone experiments. The enzyme solution was prepared by first dis-
solving (37.5 mg) a-chymotrypsin into one milliliter of 0.001 M hydrochloric
acid to aid initial solubilization. This was then brought to a final
volume of 150 milliliters with the pre-equilibration buffer to give a final
concentration of 0.25 mg/ml c-chymotrypsin. This solution was passed through
the column, fractions were collected and the eluant monitored as in small
zone experiments. The enzyme was eluted as a front of increasing absorbancy
and reached a plateau corresponding to 0.25 mg/ml enzyme. The column was
then washed with methanolic-tris Ca++ buffer as in small zone experiments.
Activity assays were performed on each fraction as previously described.
The results were plotted along with the A280 tracings and the elution
volume was taken as the volume at which the activity is one-half that of
the plateau, or the centroid of the enzyme front.
Figure 3 gives a comparison of the expected elution profiles for
small zone and large zone experiments.
TPCK Inactivation of a-Chymotrypsin
a-chymotrypsin was inactivated by the method of Stevenson and Smillie
(1968). Enzyme (200 mg, 8 moles) was dissolved in 250 ml of 0.1 M tris-HCl-
50 mM CaC12 (pH 7.5). After removing 1 ml of solution to serve as a refer-
ence, 7.5 ml of ethanol were slowly introduced followed by the addition of
28 mg (80 moles) of tosylphenylalanine chloromethyl ketone (TPCK) in 5.0
ml of ethanol to give a final molar ratio of TPCK/enzyme of 10/1. The
solution was stirred at room temperature for 2.5 hr and assayed for re-
sidual activity. The enzyme preparation contained iess than 5% of the
initial activity. The reaction mixture was freeze-dried and passed over
a Sephadex G-25 column to remove the excess reagents and salts.
M I -*
0 0 4
C a) ri 4-
> 0 0 0
0 *4 *- b C
N 0 0 O0
00 0 O
0 0 4-i 0
N n) en o o
S a o0
a < Xo M >
g, Pc L1
CL ^^ C
Q Y opz
Evaluation of the Affinity Matrix
The primary concern in using a newly synthesized affinity matrix is
to test for non-specific binding effects. A column was poured with fresh
4-phenylbutylamine-polyacrylhydrazide Agarose and washed with methanolic
tris.Ca+ buffer until a stable baseline was obtained on the eluant moni-
tor. This was to remove any 4-phenylbutylamine which may have leaked
from the column during storage. One hundred microliters of an a-chymo-
trypsin solution (1.0 mg/ml) were added to the column via the injection
port to give a small zone of enzyme passing through the column. An initial
peak of A280 absorbing material was observed on the eluant monitor. Sub-
sequent activity assays gave no indication of active enzyme in these
fractions. This is consistent with observations by Wilkerson, Mariano
and Glover (1976) who showed that this initial peak corresponds to low
molecular weight autolysis products present in the enzyme preparation.
The serendipitous presence of this peak provided us with an excellent
internal marker for column experiments. After the elution of this initial
peak the eluting buffer was changed to 0.1 M acetic acid, pH 3.0, resulting
in elution a larger peak of A280 absorbing material which was shown by
activity assay to be active enzyme (Figure 4).
A sample of a-chymotrypsin which had been inactivated by TPCK provided
us with an enzyme containing a blocked active site. This was applied to
the affinity column which had been shown to bind active ac-chymotrypsin.
1. 0-0 0 c a O
4-1 4J J
1 '1j3 M1
. o s- T
r 0 14 1C 0
0 < r C0 *
C O (0 *C
I *" 03 >C
*r 00 0
I 3 -J3 4J
CQ UQl rt J U
0a 0 0 t
Ce a n
'I-I 3 a -
o Gz 14
(Q--.) irOls! u
o i ci 0 i
o o o o
In this experiment a large peak of A280 absorbing material was obtained
as an initial peak. We were not able to show that this was a-chymotrypsin
by activity assay but did show that it corresponded to all of the A280
absorbing material which was applied. A change in pH after this initial
peak gave a very small peak (less than 5%) of active a-chymotrypsin
(Figure 5). We assumed this to be unreacted c'-chymotrypsin. These results
are consistent with Stevenson and Landman (1971).
One hundred microliters of a 1.0 mg/ml c-chymotrypsin solution were
applied to the affinity column. After the initial peak of inactive material
the buffer was not changed to 0.1 M acetic acid but allowed to continue.
This will lead to the eventual elution of the sample as broad, shallow
peak. This is shown in Figure 6. The elution volume for enzyme through
the matrix under these conditions was used as a measure of the relative
amount of immobilized ligand present. Throughout the course of this project
the method of Figure 6 was used to monitor changes in the column due to
ligand leakage and to provide a reference for experiments involving soluble
ligands. The elution profiles determined from A280 tracings and activity
assays show good correspondence to each other. Both methods were used to
evaluate the peak position in subsequent experiments. This was done to
give a cross check on the two procedures.
A final experiment involved passing a-chymotrypsin over a column of
unreacted succinyl polyacrylic hydrazide Agarose. Active enzyme was
shown to elute in the column void volume (Figure 7).
Soluble Ligand Experiments
The column was pre-equilibrated as previously described with solu-
tions containing a known amount of carbobenzuxy (CBZ) phenylalanine.
V C C .4
o c* 0)
SC rl Q) 4J
H co 4
PN U 43
<0 C) 0
0 4 d 41
4J 44 4 r. C
- o o 0d
04 0 a)C 0
*| p, c a -4
a -' co 1
0 d Cd 4 4)
3o oU (0 (
ft r-l 0 t-1
Q o o
Q 0 0
(-) 08 v
d C d o
4J 4 4
0 00 0 >
41 a) am -r
44 4J U
H 0 C
C Td H CO
0) C )
) O C
0 ca r-i 0
Q Q Q Q
I I 4
-4 C4 N-
Small zone experiments were performed using 100 microliters of a 1 mg/ml
a-chymotrypsin solution. This solution contained the same concentration
of CBZ-phenylalanine as the pre-equilibrated affinity column. The re-
sults for various concentrations of this soluble ligand and for enzyme
in the absence of ligand are shown in Figure 8.
Small zone analyses were also done using CBZ-tyrosine and CBZ-trypto-
phan. These soluble ligands gave elution patterns similar to CBZ-phenyla-
lanine. Although the general trend of increasing elution volume with
increasing soluble ligand concentration was maintained, the amount of
retardation for a given concentration of soluble ligand varied with the
ligand used. Small zone experiments were done in triplicate for each
concentration of each inhibitor. Values obtained within a set of triplicates
did not differ more than 5 percent from the average of the set of triplicates.
Small zone analyses were done using N-acetyl-L-phenylalanine as
the soluble ligand. For concentrations of ligand from 0.5 mM to 8 mM each
experiment gave an elution profile identical to that obtained for zero
concentration of inhibitor. A composite of the A280 tracings are shown
in Figure 9 along with a zero concentration experiment.
N-Acetyl-D-phenylalanine, N-acetyl-L-tyrosine and N-acetyl-L-phenylala-
nine were also used as soluble ligand for small zone experiments. Over
the concentration range tested (0.5 mM to 10 mM) the elution volumes did
not differ from those obtained for enzyme at zero concentration of ligand.
Soluble 4-phenylbutylamine and phenylbutyric acid were tested over
a concentration range of zero to 50 mM; again the elution volumes obtained
corresponded to those obtained for enzyme in absence of inhibitor.
Carbobenzoxyalanylalanine was used as a soluble inhibitor over a
concentration from 0.5 to 8.0 mM. The results shown in Figure 10 show
ra) *c 0
4 Cd 0S
P- 1-1 4-1 UE-
0 EU 0 C
r*j 410 P, l
N c00 O C
0 CM C
m a) 0
0-4 0 r 04
W w 0
20 40 60
m 0 '
*-I c i -
I co 0 U
3 CJ Uc
I 41 c
C.) c oJ
r-G( c0 *r
w (3 10
O *r4 X
0 H U-4
S0 H- 0
20 40 60 80
VOLUME E mi
C n *h
0 0 CO
H c *H*
CN 4M1 1
(s a) o
0 01 0n,
0 E- 0 W
OH a c.)
iH 0 u
H a c p.
41 C tv w
r-! OT-I 4>
CBZ ALA ALA
20 40 60 80
that with increasing concentration of soluble ligand there is a decrease
in the elution volume for the enzyme. It is also noted that for con-
centrations of CBZ-alanylalanine greater than 2.0 mM the elution volume
remains constant at a position between the column void volume and the
elution volume of enzyme with no inhibitor. Note that the column void
volume is represented in each experiment by the peak of inactive autoly-
sis products endogenous to enzyme preparation.
Large zone analysis was done using CBZ-phenylalanine over the same
ligand concentration range as for the small zone experiments done with
this inhibitor. These results are shown in Figure 11 as a composite of
the elution fronts obtained from this type of analysis. In agreement
with the small zone experiments the elution volume for the centroid po-
sition of the enzyme front increased with increasing concentration of
Determination of Dissociation Constants for Soluble Complexes
Dissociation constants for the soluble ligands and a-chymotrypsin
were determined by the method of Lineweaver and Burk (1934). Titra-
metric assays were done using a varying concentration of benzoyl-L-
tyrosine ethyl ester as substrate and a constant concentration of soluble
ligand. The experiments were repeated at two other concentrations of
soluble ligand to establish the type of inhibition involved. From a plot
of the reciprocal of the activity (velocity) versus the reciprocal of
soluble ligand concentration, three straight lines were obtained each
corresponding to a constant soluble ligand concentration. From the resulting
plot it was seen that the three lines intersected on the ordinate axis
w w a)
- EE E
O LO o 0
indicating competitive inhibition. The dissociation constant (KI) for
enzyme-ligand complex could be graphically obtained. These results are
shown in Table I.
Quantitation of Matrix Bound Ligand
The immobilized 4-phenylbutylamine was removed from the matrix by
solvolysis over a period of 5 months at 40C. The supernatant was removed
from the matrix by filtration followed by washing of the matrix with
methanolic tris.Ca+ buffer. The washings were combined and an absorption
spectra taken. Figure 12 shows a composite spectra of pure 4-phenylbutyl-
amine and the supernatant from the matrix. Figure 13 shows composite
spectra of matrices suspended in buffer. The break at 270 nm is where
the scan was stopped and the matrix resuspended by mixing. The results
show the successful solvolysis of ligand from matrix thus providing a
method for determining the degree of substitution of the matrix.
0 0C0 0 0 0 0 c
c4 r- oD rr. Co r- U- r
i CS r-l r-t C, 6 CM
*& $% 4
0 4-H .
44I Z 0 .,
wIri T L4
-0 0 a)
4 N1d I I
Si m m O
0 J a a z
(f4 4-1 -H W
< z a- 1 w <
4 >- U>0 1 Z -
0 0. I- z r
o 4 0 >-0
B < rI I I Z
___ __ __ __ -- -- I
240 260 280
The rationale involved in choosing the system was based on its es-
tablished performance in other laboratories. The matrix synthesis was
relatively simple and methods involved in testing for specific binding
had been established and were easily applied to this system with satis-
factory results. It was anticipated that by using the approach of Dunn
and Chaiken for obtaining column binding constants this system would be
easily quantitated. The information obtained will add both to the under-
standing of the 4-phenylbutylamine column and the applicability of
quantitative affinity chromatography for evaluating affinity matrices.
Dunn and Chaiken proposed the scheme shown in Figure 2, in which E,
I and L-R are the enzyme, soluble ligand and the immobilized ligand,
respectively. E-I and ERL-M are the binary complexes formed where KI and
KL-H are their dissociation constants as defined in Figure 14. Using
their experimental approach of pre-equilibrating the column followed by
passing a small zone of enzyme through this column, one would expect the
results shown in Figure 15. At low concentrations of I the enzyme would
exist predominantly as the free form, E; this free form would be able to
interact with the immobilized ligand. Through its binding to the im-
mobilized ligand, its passage down the column would be retarded giving a
large elution volume for the enzyme. At high concentrations of I, rela-
tive to KI, the enzyme would exist predominantly as the E-I complex,
this complex would be unable to bind to the immobilized ligand and pass
through the column very quickly. For this situation the elution volume
would be equivalent to the column void volume, Ve.
5 f +
Thus, in a competitive elution scheme the observed elution volume
will vary as a function of the inverse concentration of soluble ligand
and at saturating concentrations of soluble ligand the elution volume
will be approach the column void volume.
The results obtained from the small zone experiments with the
4-phenylbutylamine column (Figures 8, 9 and 10) do not agree with the
competitive binding scheme presented by Dunn and Chaiken. The results
are, however, consistent with the early observations of Akanuma et al.
(1971) with carboxypeptidase B on columns of immobilized e-aminocaproyl-
D-phenylalanine in which they demonstrated the ligand-enhanced binding
of carboxypeptidase B to the column in the presence of e-aminocaproic
Based on the assumption by Akanuma et al., this type of elution
behavior was due to the presence of two unique, yet interacting sites on
the enzyme, the binding scheme shown in Figure 16 was hypothesized to
explain the results obtained. We shall refer to this type of binding
scheme as non-competitive elution as compared with the nomenclature of
Dunn and Chaiken of competitive elution for their scheme. This scheme
is similar to the one involving a competitive site, with the addition
of the E-I complex binding to the immobilized matrix with dissociation
constant Ky'g for the resulting complex. A mathematical evaluation of
these schemes is given in the Appendix. This derivation was based on the
starting assumptions presented by Dunn and Chaiken (1974). Their starting
equations were used only with the addition of I.E.L-M complex and appro-
priate substitutions involving Kf~r.
, d 0
U r4 1
l4 r4 C
r(3 d f
tf E3 d
Equation 14 of the Appendix gives the elution volumes, binding
ratios and ligand concentrations in terms of dimensionless ratios.
Ve- Vo= K=7 1 [I] > 0
1 + 1 + KI
This equation was used to generate a family of curves shown in Figure
17. The elution volume is corrected for the column void volume and ex-
pressed relative to VT=-, the volume at which an enzyme would elute in
the absence of soluble ligand after correction for the column void volume.
The concentration of soluble ligand is expressed relative to KI. The
two column binding constants are expressed as a ratio of each other.
The point at which all of the lines intersect on the volume axis is that
point at which the concentration of soluble ligand is zero. For ratios
of KL./K 4I=z greater than one the elution volume will increase with in-
creasing ligand concentration; for KgL-/K=- equal to one there will be
no effect on the elution volume by ligand; finally, when K-r=/Kgr is
less than one the elution volume will decrease with increasing ligand
concentration (Table II). Figures 18 through 20 illustrate these three
types of elution patterns expected from this scheme for typical small
zone experiments. We have chosen to refer to them as Case I, Case II
and Case III for column binding ratios greater than, equal to and less
than one, respectively.
Let us examine each case in detail from the standpoint of the en-
zyme species. First, Case i (Figure 18) describes the situation in
WA -^ 0
-I I L> mJ
which the binding of E-I to the matrix is tighter than the binding of
free E to the matrix, that is, KIr- > K=-. At high concentrations of
soluble ligand the enzyme will exist predominantly as the E*I complex.
As this complex, the enzyme will bind tighter to the immobilized ligand
than in the free form. Further, as saturating concentrations of I are
approached the elution volume will approach a finite value determined
by the dissociation constant KI-R. This is similar to the passage of
free E through a column in the absence of soluble ligand. This elution
is determined solely by the column dissociation constant KL-=, the nature
of the affinity matrix and the column dimensions. By causing the enzyme
to spend more time in the stationary phase, this will enhance the re-
tardation through the column, subsequently increasing the elution volume.
At concentrations near the KI of the enzyme the elution volume will vary
as a function of the concentration of soluble ligand.
Case II (Figure 19) presents us with some rather uninteresting data.
We find that the elution volume is independent of the concentration of
soluble ligand. In this case it does not matter which form the enzyme
is in. With KL-= equal to K=_p the free form of the enzyme will bind to
the column with the same affinity as the E.I complex.
It is important to nota that these results would be obtained for
soluble ligands which do not form binary complexes with the enzyme. In
these types of experiments the enzyme would exist in the free form giving
an elution volume corresponding to Vo. One would have to determine by
an independent method, such as inhibition assays that the binary complex
was formed with a finite value of KI before these results could be pro-
perly interpreted as Case II.
Finally, Case III non-competitive elution patterns (Figure 20) will
be obtained when KL=_ < Kj~R. As the concentration of soluble ligand is
increased in the pre-equilibrating buffer the enzyme will again exist
predominantly as the binary complex, E-I. The column will not bind this
complex as tightly as the enzyme in the free form. This will cause the
enzyme to spend more of its time in the mobile phase and will facilitate
elution. The enzyme will appear in the eluting stream at a volume less
than Vo but greater than Vo. Here we find that the elution volume will
vary inversely with the concentration of soluble ligand.
Although the results which would be obtained for Case III elution
appear to resemble the elution patterns obtained for competitive elu-
tion, a very subtle difference exists. In competitive eiution, when the
concentration of soluble ligand is saturating with respect to the KI, the
E.I complex will not interact with the matrix and the elution volume will
correspond to the column void volume. At saturating concentrations of
soluble ligand in non-competitive elution the E-I complex will interact
with the matrix and elute at a finite elution volume determined by the
column dissociation constant KL-M.
For Case III elution behavior it is interesting to note that as
K "- approaches infinity, i.e. no binding, the results predicted will
approximate those for competitive elution. Thus, competitive elution
can be shown to be a subset predicted from the noncompetitive model.
To be useful in obtaining quantitative results equation 14 must be
manipulated into a linear form. This leads to equation 16 of the Appendix
Ve- Vo 1 K [I]
1 = +
Vz-=R LIj + KI
which can be converted to a straight line equation having the form
y = mx + b by taking a double reciprocal to give:
1 + K
i = +
V, Vo K_-1~ KE--=
-1 1 [I]
VL-M K_= KC
This equation will give a straight line when the left side of the equa-
tion is plotted with respect to the reciprocal of the concentration of
soluble ligand, I. This is shown for theoretical data in Figure 21
where [I] and KI would have the same units. From the above linear equation
a line would have a slope of KI/((K -=/K-M)-I) and an ordinate intercept
of 1/((KI=-/K=-)-I). The quotient from the slope divided by the inter-
cept would give the value for KI, the dissociation constant for the E-I
Equation 16 from above can be expressed in terms of observed elu-
tion volumes by substituting in the definition, Vo = V-E= + Vo.
This substitution yields equation 19,
Ve Vo = VL- [I + KI
This is similar to equation 16 in which the volume term is slightly re-
arranged to give a value which can be expressed directly from experimen-
tally obtained values; Ve is the elution volume at for a finite concen-
tration of I and Vo is the elution volume in the absence of I.
Equation 16 can be linearized by taking a double reciprocal to give,
S K + 1
Ve Vo K i Kr-1
VLM K VL.M K
J ----'' -- ----
This equation will yield a straight line when elution volumes are plot-
ted as l/(Ve V') versus the reciprocal of the concentration of soluble
ligand. The values for the intercept and slope will be 1/V-r(KL-I/KR_')-I)
and K!/V-=V ((K-z/K='q)-l, respectively. Again the quotient from the slope
divided by the intercept will give KI, the dissociation constant for the
Figure 22 shows the data for the elution volumes obtained from small
zone experiments with the carbobenzoxy (CBZ) derivatives of phenylala-
nine, tyrosine and tryptophan plotted in this manner.
The data shown represents the triplicate values obtained for each
concentration of I with multiple points shown where the data from the
The value for KL=-/K=~y could be determined from the intercept by
substituting in the value of V'=-, which was shown to be 1.49 for each
of the CBZ-derivatives shown. From equation 13 in the Appendix, where
[I] = 0 the elution volume is,
(Vo Vm)[ =]
Ve V =
Vo and Vo can be determined from the passage of enzyme through the column
in the absence of soluble ligand. The column void volume, Vo, would be
the elution volume for the autolysis products. Vm is volume of mobile
phase of the column and is determined at the volume at which a very large
molecular weight marker, such as Blue Dextran 2000, will elute. The im-
mobilized ligand concentration was obtained from extended solvolysis of
matrix, representing the amount of ligand physically substituted to the
Pa H H
vuir [ -
For the column used to analyze the CBZ-derivatives Vo, Vm, [-M]
and Ve were 17.3 ml, 3.7 ml, 30.4 mM and 65.5 ml, respectively. These
data give a value of 8.57 mM for the column dissociation constant,
Ki-. From the data giving the ratios of the column binding constant a
value of 5.75 mM was obtained for KM- using each of the CBZ-derivatives.
The linearity of the fit for these data suggest that the model im-
plemented to account for these data is correct. Further, the Kl's ob-
tained from the chromatography experiments agree with those obtained
through inhibition kinetics. These are compared in Table III.
Data obtained for N-acetyl-D-phenylalanine, N-acetyl-L-phenylala-
nine, N-acetyl-L-tyrosine, 4-phenylbutylamine and phenylbutyric acid as
soluble inhibitors cannot be analyzed graphically since no difference
between Ve and Vo is obtained. However, inhibition kinetics showed a bi-
nary complex between the enzyme and the ligand is formed at concentrations
used in our elution experiments. Figure 23 shows representative results
obtained with CBZ-phenylalanine as the soluble ligand. On the basis of
this determination, these ligands could be said to give authentic Case II
non-competitive elution in the immobilized 4-phenylbutylamine system.
Referring again to the linearized form of equation 15, Figure 24
shows simulated results for Case III behavior in which the column binding
constant, KL-= is less than the constant K]y. These results are charac-
terized by a leftward shift in the elution volume with increasing soluble
The values obtained for ordinate axis will have a negative sign.
This is because the results are normalized to give VL-= a value of unity.
When elution volumes less than VTL-_ are considered, this results in a
4 0 0
i ,-4H 0
co1 0 0
a) 4 PN u
0 ) u1 (U3 4 44J
4 0 w 0
4C10 00 0 0
10 0) 1 4-1 4 -1 4J
c rd to to w 33
4- 4 -3 0 C w)
34 O 0 l4 rM-
td 0 W Q0 *
1 o 0 0 00 C .
d o > q *W
o .o C-4
S 10 Q a) 0 m
0 r4 0) CU-H
to 4 IU >
w0 0 U 3 3
4r *H A *H0a)
4 O N C *U 4- -C
S (0 (a 0 cl cd
0) u pn 1a r-14.
4 1 4 4 3 (.u 0 C1 i
41 0 0 CC 3 fu oS
4 U 0-0 0 w 0 W 0
0 w z 4.0 0 rC
(I N a E 0 3U 0 31
o Q q Q
fraction which when subtracted by one gives a negative value. The slope
and ordinate intercept will, however, have the same definition as before.
Further, K-=/K -= and KI are determined in the same way as for Case I
plots. The only difference here is that the values which are obtained
directly from the graph are negative. This is analogous to Lineweaver-
Burk plots in which the intercept on the 1/[S] axis is negative. Proper
substitution of these values will give rational results.
The results for a-chymotrypsin elution in the presence of CBZ-
alanylalanine are shown in Figure 25 plotted as the reciprocal of the
difference between Ve, observed elution volume, and Vo, versus the re-
ciprocal of CBZ-alanylalanine. The results are consistent with those
predicted in Figure 24. Note that the ordinate intercept and the slope
are both negative values.
From an intercept value of -.072 which is equal to an ordinate in-
tercept of l/VL=_((Ky-I/K=P-)-l), where Vyr- is equal to 31 ml, the
value of KI-E/K'^ is 0.55. This value is less than 1.0 which explicitly
demonstrates Case III noncompetitive elution. By substitution of the
previously determined value for KL-= equal to 8.57 mM, we find that Ki='
is 15.6 mM. Finally, the soluble dissociation constant for CBZ-alanyla-
lanine can be obtained by dividing the slope by the ordinate intercept.
This gives 2.5 mM which compares well with the value obtained from in-
hibition kinetics of 2.3 mM.
A model has been presented which satisfies all of the observations
obtained in this work. The data have been shown to fit closely the be-
havior predicted by this model and constants for the soluble binary com-
plexes were obtained which are in agreement with results from an independent
oO O O
method. However, the initial assumptions made about the a-chymotrypsin--
4-phenylbutylamine Agarose system do not lead a prior to this model.
Soluble 4-phenylbutylamine has been shown by Stevenson and Landman (1971)
and by our work that it binds as a competitive inhibitor. However, when
this molecule is immobilized to succinylated polyacrylic hydrazine Agarose
it takes on new properties. It has been shown by our work with soluble
4-phenylbutylamine that the immobilized ligand and the soluble ligand bind
in such a way as not to affect the elution volume, i.e., Case IT results.
What evidence then would support this model and the observation
that 4-phenylbutylamine behaves differently when immobilized through its
Morihara and Oka (1977) have shown that the active center in
a-chymotrypsin corresponds to at least five or six amino acid residues.
Their results showed that CBZ-glycylprolylphenylalanine (KI = 0.044 mM)
bound much tighter than acetyl-L-phenylalanine (KI = 0.57 mM). These re-
sults indicate the presence of multiple binding sites at the active center
of a-chymotrypsin other than the hydrophobic center long thought to be
responsible for binding. Evidence from X-ray crystallographic work by
Robertus et al. (1972) shows the active center to be an elongated groove
of anti-parallel B-sheets. Further, this active center appears to contain
charged groups for ionic interaction and small hydrophobic regions which
would provide ample opportunity of the binding of multiple species.
In free solution 4-phenylbutylamine exists as a positively charged
molecule with a hydrophobic tail. When immobilized to succinylated poly-
acrylic-hydrazide Agarose the molecule has the structure shown in Figure
26. The positively charged amine has now become a structure analogous
II I II
O='U I U=O I U=O
i I I
' I I j
z 1 z
to a peptide bond. Also there exist other chemical functions capable of
binding to the active center groove. Finally, the phenylbutylamine molecule
could be held in such a position by the matrix that it can only orient one
way into the active center. These factors could contribute to the observed
behavior of immobilized 4-phenylbutylamine with respect to a-chymotrypsin.
Further, soluble ligands could bind to the enzyme and enhance the inter-
action between the matrix and enzyme. This was seen with the CBZ-derivatives
of the aromatic amino acids. Alternatively, the soluble ligand cculd dis-
turb that interaction as was seen with CBZ-alanylalanine. The soluble
ligand could bind and not affect the column interaction as was seen with
the n-acetyl derivatives and the phenylbutyl derivatives.