Adhesion-mediated cell migraton in three-dimensional matrices

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Adhesion-mediated cell migraton in three-dimensional matrices effect of spatial gradients of adhesiveness
Myles, Jennifer Lee, 1972-
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ix, 97 leaves : ill. ; 29 cm.


Subjects / Keywords:
Adhesives ( jstor )
Cell adhesion ( jstor )
Cells ( jstor )
Collagens ( jstor )
Gels ( jstor )
Integrins ( jstor )
Ligands ( jstor )
Matrices ( jstor )
Melanoma ( jstor )
Modeling ( jstor )
Chemical Engineering thesis, Ph.D ( lcsh )
Dissertations, Academic -- Chemical Engineering -- UF ( lcsh )
bibliography ( marcgt )
non-fiction ( marcgt )


Thesis (Ph.D.)--University of Florida, 1999.
Includes bibliographical references (leaves 89-96).
General Note:
General Note:
Statement of Responsibility:
by Jennifer Lee Myles.

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University of Florida
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University of Florida
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Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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42680713 ( OCLC )

Full Text







Copyright 1999


Jennifer Lee Myles


First and foremost, I wish to thank Dr. Richard Dickinson for his guidance and

support. Secondly, I wish to thank Brian Burgess for the development of tracking

algorithms and data analysis techniques using the persistent random walk model.

Additional help was provided by the Interdisciplinary Center for Biotechnology Research

at the University of Florida with peptide synthesis (Dr. Alfred Chung) and SEM

(Rosemary Davis). I also would like to thank Dr. David Muir at the University of Florida

for help in establishing cell culture and Dr. Daniel Mooradian at the University of

Minnesota for supplying the K1735 M4 murine melanoma cells. Additionally, I would

like to thank Dr. Julia Ross at the University of Maryland at Baltimore for advice on cell

adhesion experiments. Lastly, I wish to acknowledge the Whitaker Foundation

Biomedical Engineering Research Grant for financial support.



ACKNOWLEDGEMENTS ..................................................................... iii

LIST O F FIG U RES .............................................................................. vi

A B STR A C T ..................................................................................... viii


1 INTRODUCTION ........................................................................... 1

2 CELL ADHESION AND MIGRATION .................................................. 3
2-1 The Relation Between Adhesion and Migration .................................... 3
2-2 Receptor-Ligand Interactions ......................................................... 6
2-3 Directed Cell Migration ................................................................ 7
2-4 H aptotaxis ................... ......................... .................................... 8

3 C O LLA G EN .................................................................................. 11
3-1 Structure and Function ................................................................. 11
3-2 Cell Interaction with Collagen ........................................................ 12

4 RGD PEPTIDES .............................................................................. 14
4-1 RGD Adhesive Amino Acid Sequence............................................... 14
4-2 Modification of Surfaces with RGD Peptides....................................... 14

IN THREE-DINIENSIONAL MATRICES ............................................. 18
5-1 Specific G oals ........................................................................... 18
5-2 Experimental Techniques ............................................................. 18
5-2-1 Synthesis of Conjugated Collagen .......................................... 18
5-2-1-1 Reaction 1 ............................................................ 19
5-2-1-2 Reaction 2 ............................................................ 21
5-2-1-3 Quantification ................. .................................... 23
5-2-2 Automated Video Microscopy Incubation System ........ ...............24
5-2-3 Cell Culture ............................................... ........... 25
5-2-4 Adhesion Experiments ................................... .................... 26
5-2-4-1 Adhesion on BSA Coated Surfaces .............................. 26

5-2-4-2 Adhesion on Collagen Coated Surfaces ............................ 27
5-2-5 Cell Migration Experiments ................................................. 28
5-2-6 Formation of Spatially Adhesive Gradients ............................... 29
5-2-7 Preparation of Collagen Gels for Scanning Electron Microscopy..... 31
5-3 Experimental Results .................................................................. 32
5-3-1 Collagen Conjugation ........................................................ 32
5-3-2 Cell Adhesion Experiments ................................................. 35
5-3-3 Cell Migration Under Uniform Conditions ............................... 39
5-3-3-1 Data Analysis ...................................................... 39
5-3-3-2 Three-Dimensional Cell Tracking .............................. 41
5-3-4 Cell Migration in Spatial Gradients of Adhesiveness ................... 44

CELL MIGRATION ...................................................................... 47
6-1 Development of Model .............................................................. 47
6-2 Model Predictions ..................................................................... 53
6-2-1 Model Predictions for Uniform Conditions .............................. 53
6-2-2 Model Predictions for Spatial Gradients ................................ 55

7 D ISC U SSIO N ................................................................................ 61

8 SUMMARY AND CONCLUSIONS .................................................... 68

FUTURE WORK.......................................................................... 69
9-1 Conjugation to Alternative Matrices................................................ 69
9-2 Additional Gradient Work ........................................................... 71
9-3 Study of Integrin Specificity......................................................... 71
9-4 Cellular Labeling...................................................................... 72
9-5 Cellular Force Measurements........................................................ 72
9-6 Expansion of Modeling............................................................... 72





LIST OF REFERENCES ..................................................................... 89

BIOGRAPHICAL SKETCH ................................................................. 97


Figure page

2-1. Schematic of a motile cell ............................................. ................ 4

5-1. The reaction chemistry for the two step protein conjugation reaction. .......... 19

5-2. Schematic of the automated video microscopy system with incubation. ........ 25

5-3 Schematic showing the formation of spatial adhesion gradients.................... 31

5-4. Repeatable peptide substitution levels that were attainable for the
reactions ................................... ..................... ....... ............. .. 33

5-5. SEM micrographs of the various collagen matrices ................................ 34

5-6. Cell adherence to surfaces coated with various amounts of cross-lined
B SA .......................................... .. ....... .......................... ... 36

5-7. Cell adherence to collagen and conjugated collagen coated surfaces. ........... 38

5-8. Cell adherence to surfaces coated with various ratios ofRGd-grafted colagen. 38

5-9. Rate of cell dispersion quantified by the random motility coefficient ............. 42

5-10. Characteristic time of directional persistence quantified by the directional
persistence tim e ...................................................................... 43

5-11. Tortuosity of the cell path quantified by the persistence length ................. 44

5-12. Rate of translational motion quantified by the root-mean-square
cell speed. ............................................................................. 45

5-13. Biased cell migration in gradient gels quantified by measuring the
drift velocity toward the gradient direction ........................................ 45

5-14. The directional orientation bias is the mean angle of the displacements
relative to the gradient direction ................................................... 46

6-1. Force balance on the model cell ...................................................... 50

6-2. Schematic showing the effects of the polarity parameter, g, the direction
of pseudopod extension ............................................................. 51

6-3. Dimensionless retraction velocity ...................................................... 54

6-4. Simulation results of dimensionless random motility coefficient, speed, and
directional persistence time plotted vs. dimensionless ligand density...... 54

6-5. Simulated cell paths for high gradients of adhesion at various strengths
of adhesion ............................................................................. 56

6-6. Simulated cell paths for low and medium levels of adhesiveness showing
the minimum gradient necessary to produce a bias ............................... 58

6-7 Drift velocities for low and medium levels of adhesiveness showing
the minimum gradient necessary to produce a bias................................. 59

6-8. Simulated cell paths for medium levels of adhesiveness showing the
relative contributions of orientation bias and kinesis ............................. 60

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy



Jennifer Lee Myles

August 1999

Chairman: Richard B. Dickinson
Major Department: Chemical Engineering

Collagen, either alone or in combination with other materials, is an important

natural biomaterial used in applications such as vascular prostheses and bioartificial

organs. Spatially controlling the adhesiveness of collagen and/or other biomaterials may

allow controlled localization or redistribution of cells, thereby improving their chances of

serving as successful implants.

This dissertation describes a method to couple peptides which contain the well

characterized arginine-glycine-aspartic acid (RGD), adhesion sequence, and arginine-

glycine-glutamic acid (RGE), nonadhesive sequence, directly to collagen monomers prior

to fibrillogenesis. The average number of peptides substituted per monomer could be

controlled by changing the reaction conditions.

Scanning electron microscopy was used to examine the microstructure of RGD

modified collagen gels. Investigations of pore size, fibril size and fibril arrangement

showed no qualitative differences in collagen gel structure.

Cell adhesion strength was found to increase with both increasing degree of RGD

conjugation and increasing ratio of RGD-modified to unmodified collagen. Degree of

RGE conjugation was found to have no effect on cell adhesion.

A method was developed to track individual cells in three dimensions using an

automated video microscopy system with image analysis software. Cell migration was

quantified by analyzing the reconstructed cell paths. Parameters such as cell speed,

persistence time, and random motility coefficient were obtained by fitting the cell track

data to a persistent random walk model. The random motility of cells was found to be

biphasically dependent on the degree of conjugation of RGD peptides. No such

dependence was found for RGE modified collagen.

Gels were also cast with spatial gradients of adhesiveness. Studies of drift

velocity and orientation direction showed that there is a small bias in the direction of the


A mechanistic model of cell migration provides qualitative confirmation of the

experimental observations.

This modified adhesiveness data taken together with the data showing its

influence on cell motility support the hypothesis that haptotaxis may be a potential

mechanism for the controlled localization or redistribution of cells.


In 1990 alone over 83,000 people either died or were maintained on less than

optimal therapies due to the lack of donated organs in the United States[1l]. This lack of

availability and the risk for disease transmission associated with transplants has led to a

renewed effort in finding viable synthetic replacements for living tissue. However, to date

the biomedical research community is still very limited in the tissues that can be replaced

with high success rates due to the complicated hierarchical structures of these tissues and

the complex biochemical interactions between cells and tissues[2]. The major source of

complications and failures with synthetic replacements is poor biocompatibility with cells

in the tissue surrounding the implant[2]. Proper function of some implants requires

infiltration of surrounding tissue cells into the porous synthetic scaffold or onto the

biomaterial surface of the implant. One possible solution to promote cell infiltration or

ingrowth is to modify the surface of the biomaterial in order to promote the ingrowth of

the surrounding cells onto the biomaterial surface or into the porous structure of the

biomaterial[3]. Furthermore, by tailoring the specific adhesive properties of the

biomaterial, it may be possible to direct the migration of only a selected group of cells or

to promote the biased migration of cells in a particular direction by creating a gradient of

adhesiveness. The phenomenon of biased cell migration in an adhesion gradient is

known as haptotaxis[4], and is also believed to be important mechanism of biased cell

migration in several normal and pathological processes such as embryogenesis,

angiogenesis, wound healing, and tumor cell metastasis. It is therefore of great interest to

study the relationship between cell adhesion and cell migration in a three-dimensional

environment typical of tissue engineering scaffolds or extracellular matrix.

The goal of the work described in this thesis is to enhance the fundamental

understanding of adhesion-mediated three-dimensional tissue cell migration using

quantitative experimental techniques and mathematical modeling.

This dissertation describes the development of quantitative experimental

techniques for measuring the effect of adhesion on the migration of tissue cells in three-

dimensional matrices. Additionally, a stochastic mathematical model is developed to aid

in the interpretation of experimental results in terms of underlying physicochemical

mechanisms. Chapter 2 provides a brief background on the current state of knowledge

with respect to the biology underlying tissue cell adhesion and migration, a synopsis of

biased modes of cell migration and the current state of knowledge in the area of

haptotaxis. Chapters 3 and 4 discuss the relevant characteristics of collagen and the

adhesive peptides used in this study. Chapter 5 discusses the methodology used to

directly measure cell migration in three-dimensional matrices and to quantify the

migration response. Chapter 6 presents a mechanistic mathematical model for adhesion-

mediated cell migration. Chapter 7 discusses the relevance of the work with respect to

the current literature. Chapter 8 summarizes the key results and accomplishments and

Chapter 9 concludes with recommendations for future work.


2-1 The Relation Between Adhesion and Migration

Migration can be considered as a continual movement cycle of lamellipod

extension and subsequent cell body translocation into an extended lamellipod[5].

Mechanical forces needed to achieve locomotion are generated through polymer

filaments of the protein actin (Figure 2-1). Cell body translocation arises from a

contractile force produced within the submembrane cortex that is transmitted into traction

on the extracellular matrix or substratum via cell membrane interactions with the

surroundings[5]. This force is transmitted to the substratum by specific binding of cell

surface molecules (adhesion receptors) to binding sites ligandss) on the substratum.

Therefore, tissue cells must adhere to the underlying substratum or matrix in order to

generate the tractional force necessary to move across the substratum or through a three-

dimensional matrix. For an adherent cell to displace itself, pseudopods must be extended

in the direction of movement at which new attachments can be formed while the

attachments at the rear must be broken[6].

Cell migration and cell depend on the strength of transient cell-substratum

attachments[7]. Previous studies have demonstrated that variations in either absorbed

concentration of substratum bound ligands for integrins or integrin-ligand affinity affects

cell speed[6, 8, 9, 10].


Adhiesion.--wi 9 1 9 f
Ligand ,
Substratum Contractile Protein Network
Figure 2-1. Schematic of a motile cell. This figure shows the leading lammella,
contractile protein network and cell to substratum interaction necessary for cell migration
to occur.

Based on this research, three regions of motile behavior for a cell interacting with

a surface were predicted: (1) On weakly adhesive surfaces the cell is poorly spread and

the few cell-substratum attachments cannot provide enough traction for cell locomotion

to be possible; (2) on strongly adhesive surfaces, a cell is well spread and immobilized by

the large number of cell-substratum attachments; and (3) on intermediately adhesive

surfaces the balance between adhesive strength and traction force is such that locomotion

is possible. Dimilla and Lauffenburger developed a mathematical model, which

predicted that the key variable governing cell migration speed was the ratio of

intracellular motile force to cell-substratum attachment strength, and that migration speed

should exhibit a biphasic dependence on the attachment strength for a given level of

motile force[ 1]. In 1993, Dimilla and Stone directly observed this maximal migration of

human smooth muscle cells on surfaces of collagen and fibronectin at intermediate levels

of cell-substratum adhesiveness[8]. More recently Palecek et al. completed a study for

two-dimensional cell migration in which the relationship between cell-substratum

adhesiveness and cell migration was investigated using cell lines expressing different

levels of integrin and cell lines which possess different integrin-ligand binding affinities.

The same biphasic dependence of cell speed was observed with the optimum in cell speed

found at median cell-substratum adhesiveness for fibronectin and fibrinogen-coated


The adhesion and receptor-ligand bond breakage, coupled with the biomechanical

resistance imposed on the cell within a three-dimensional fibrous matrix is substantially

different than in the two-dimensional environment and requires the cell to respond

differently compared to migrating across planar surfaces[12, 13]. In addition, the cell

migratory behavior within three-dimensional matrices has been reported to vary distinctly

among different cell types[13]. For instance, for the highly adhesive integrin-mediated

migration of MV3 melanoma cells within three-dimensional collagen matrices, Friedl et

al. reported that cell migration resulted in a dynamic and permanent reorganization of

collagen fibers and receptor shedding[13]. However, it was reported that for the more

highly motile integrin-independent migration of T lymphocytes, correlating to a lowered

adhesion to the collagen fibrils, T lymphocytes were able to elastically bend the collagen

fibers and reduce their cell diameter in order to squeeze through narrow pore spaces

within the interwoven fibrous network[14]. Similar results have been observed for

dendritic cells migrating within three-dimensional collagen networks[15]. Using a

human breast carcinoma cell line, Keely et al. compared two-dimensional and three-

dimensional migration as a function of cell adhesiveness by reducing the number of c213i

integrins, a collagen and laminin receptor, expressed by cells[10]. For two-dimensional

migration across collagen coated filters, cell migration was optimally supported by

intermediate levels of adhesion. In contrast, cells cultured within three-dimensional

collagen gels expressing decreased amounts of a231 integrins did not organize in three-

dimensional collagen gels, suggesting the adhesion and motility was affected differently

compared to two-dimensional migration. Further, Kuntz and Saltzman measured the

three-dimensional migration of neutrophils within collagen matrices supplemented with

increasing concentrations of ECM proteins preceding collagen gelation[16]. They

reported neutrophil motility was a decreasing function of increasing adhesion and

increasing fibril pore spacing indicated through the random motility coefficient, a

measure of cell dispersion over time. Together, these studies suggest that the migration

of cells within the more highly complex three-dimensional environment may involve

different mechanisms than on two-dimensional substrata. However, to date most studies

of adhesion-mediated cell migration have been limited to two-dimensional substrata.

2-2 Receptor-Ligand Interactions

This adhesion and subsequent tractional force is mediated at least in part by

specific binding between cell surface receptors and complimentary ligands attached to the

substratum. Cell surface receptors are membrane proteins that possess an extracellular

domain, a transmembrane domain and an intracellular or cytoplasmic domain. Receptors

allow the cell sense the extracellular environment by binding to ligands in the

extracellular matrix. This binding usually results in a conformation change in the

intracellular region of the receptor molecule, which leads to transmission of the signal to

the cell interior and ultimately to a change in cell behavior. In this fashion, receptors are

able to direct such cell behaviors as proliferation, secretion, contraction, adhesion and


Integrins are a large family of cell surface receptors that have been shown to

mediate cell adhesion to other cells or to the extracellular matrix[17, 18]. Structurally,

integrins consist of a dimer of alpha and beta chains. Each subunit has a large N-terminal

extracellular domain followed by a transmembrane domain and a sort C-terminal

cytoplasmic region. Various integrins that recognize collagen as an adhesive ligand have

been identified including ca, 3, a213 1, and 3 13PI [17, 18]. Interestingly, the binding site for

integrins in several extracellular matrix molecules, including fibronenectin, vitronectin,

fibrinogen, von Willebrand factor, and collagen, consists of the three amino-acid

sequence, arginine-glycine-aspartic acid (RGD). Integrins that recognize the RGD

sequence include a513 I, tvpI, O.M32, IIb133, Xv133, avp35, aCv136[17, 18].

2-3 Directed Cell Migration

During locomotion, cells are polarized and extend and retract pseudopods

primarily in the direction of locomotion. For this reason, cells tend to persist for in the

same direction for short periods of time. However, over time, small changes in direction

or spontaneous reorientations of the cell lead to a meandering type path similar to a

random walk with direction persistence. In an isotropic environment, the random walk

has no net bias in direction and is analogous to molecular diffusion. This movement is

termed random motility. However, in anisotropic environments, the random walk may be

biased in response to external stimuli. Several types of biased migration have been

observed, including: chemotaxis (bias in the direction of a soluble attractant gradient),

contact guidance (bias based on a textual or structural anisotropy), haptotaxis (bias in the

direction of a surface bound adhesion gradient) and galvanotaxis (bias in the direction of

an electrical stimulus).

Several modes of biased cell migration have been proposed based on how the

underlying random walk behavior is modified to result in a net directional bias[19].

These include topotaxis (preferential turning toward the gradient direction), orthotaxis

(an enhanced speed in the direction of the gradient), klinotaxis (an enhanced persistence

in the direction of the gradient), orthokinesis (trapping in areas of higher stimulus due to

decreased speed), and klinokinesis (trapping in areas of higher stimulus due to decreased


2-4 Haptotaxis

Several mechanisms relating to the various modes of migration have been

proposed to explain how the phenomenon ofhaptotaxis may arise. Carter first observed

the directional movement of fibroblasts up a gradient of palladium coated on a cellulose

acetate surface[20]. He termed this movement "haptotaxis"; a word comprised of the

Greek roots "haptein" meaning "to fasten" and "taxis" meaning "arrangement". He used

this term to convey the idea that the movement of a cell could be controlled by the

relative strengths of its peripheral adhesions. He theorized that the bias could be

explained by the passive nature of cell extension and contact inhibition. He implied that

the movement of the leading edge of the cell involved intermolecular forces acting

between the surface of the cell and the surface of the substrate that could be due solely to

the differences in surface tension forces due to the differences in the coatings. He

hypothesized that cells migrating on plain glass slides exhibit some form of haptotaxis by

choosing not to return to spots they had previously occupied since these spots contained

traces of cellular proteins left behind by the migrating cell.

In 1973, Harris also studied the migration behavior of individual cells on biologically

non-relevant substrata of continuous variable adhesiveness [21 ]. Harris observed that

cells moved both up and down the gradient, although the cells did accumulate in regions

of greater adhesion. His observations did substantiate Carter's observations in that cells

did move preferentially from substrata of lesser to those of greater adhesiveness,

however, Harris suggested that this movement was the result of an active locomotory

process rather than some passive process. He hypothesized that although cells might

briefly travel down the gradient, the lamella attach more firmly in areas of higher

adhesiveness. This creates a sort of "tug-of-war" between competing cell margins;

therefore the cells become preferentially pulled in the direction of higher adhesion. This

is consistent with the mode of topotaxis.

In 1979, Keller et al. performed a series of experiments in which serum peptides

produced marked chemotactic orientation of human neutrophil granulocytes without

modifying the amount of cell attachment to the substratum[22]. Furthermore, they saw

that gradients of adhesion produced with gammaglobulins failed to induce morphological

orientation of neutrophils. Based on these results they hypothesized that haptotaxis may

simply be a specialized form chemotaxis. That is, a chemotactic response to a

substratum-bound chemical stimulus gradient (i.e, the cell does not respond specifically

to the adhesion differential but that the adhesion ligands differentially stimulate the

internal motile mechanisms of the cell.)

Still another mechanism was proposed by Lackie and Brown to explain the response

of neutrophil leukocytes to varying substratum adhesiveness[23]. Based on their results,

they proposed that haptotaxis may not even be a form of taxis at all. They hypothesized

that the redistribution results from a slowing of the cell in the highly adhesive area, which

in effect traps the cell in these regions. This is consistent with the mode of orthokinesis.

Additionally, studies of haptotaxis in response to physiologically relevant adhesion

molecules have been primarily limited to filter-based assays where direct observation of


the migration is impossible. McCarthy et al.[24], McCarthy and Furcht[25] and Varani et

al.[26] demonstrated biased migration on biologically-relevant adhesive proteins using a

modified Boyden chamber assay that consisted of two chambers separated by a thin

polycarbonate porous membrane filter. The extent of migration was measured by

counting the number of cells penetrating the filter. Biased migration was assessed by

comparing the migration in a positive gradient versus negative or no gradient conditions.

This method for assessing haptotactic response to adhesion molecules is widely used for

many cell types, however, the gradients are not well-controlled or quantifiable. In

addition it is likely that a portion of the adsorbed molecules desorb during the course of

the experiments[27], perhaps contaminating the results with a chemotactic response.

Furthermore, direct observation and characterization of biased cell movement is

impossible using this type of apparatus.

To eliminate the possibility of desorption and possible chemotactic influences,

Brandley and Schnaar covalently bound a peptide containing the RGD adhesion sequence

into a polyacrylamide gel and measured fibroblast redistribution on the gel surface[28].

Again, this method did not allow for the direct observation of the migration of individual

cells. Although haptotaxis may have contributed to some extent to the redistribution, an

equally likely explanation is the preferential removal of cells from the less adhesive

regions when the gels were rinsed prior to counting.

These later studies illustrate the difficulties is making conclusions about biased cell

migration without direct observation of the movements of individual cells. Therefore, it

is vital to combine a physiologically relevant system with one in which direct observation

of cell migration is allowed.


3-1 Structure and Function

The collagens are a group of complex structural proteins that exist in a large

number of different forms or types whose main function is to provide strength and

protection to biological structures. While there are many types, the differences in

morphology and biochemistry among the various types of collagen within a single

species and between different species are very small. The three most abundant forms of

collagen in the mammalian body are collagen type I, II and III. Type I collagen is found

in a variety of tissues and is the major component of tendons and cartilage and other

extracellular matrices. Therefore, type I collagen is the underlying substratum of interest

for in vivo applications and the rest of this thesis will focus on type I collagen.

Collagen fibers result from a hierarchical assembly process. The basic helix is

formed by a repeating secondary structure that is unique to collagen. The repeating

tripeptide sequence Gly-X-Pro or Gly-X-Hyp creates a left-handed helix with three

residues per turn. Three basic helices wrap around one another with a right-handed twist

to create the three-stranded molecule that is referred to as tropocollagen[29].

Tropocollagen is the fundamental structural unit of collagen. It is a molecular rod about

2600 Angstroms in length and 15 Angstroms in diameter with a molecular weight of

300,000 Daltons. Tropocollagen rods undergo a spontaneous aligning in a staggered head

to tail array to create the collagen fiber (fibrillogenesis). This alignment creates a

banded or striated pattern visible in electron micrographs that is unique to collagen.

3-2 Cell Interaction with Collagen

Reconstituted collagen has been used as a substrate for cell growth since the early

1900s in efforts to recreate some aspects of natural systems in tissue cultures[30]. Many

types of cells have since been shown to attach themselves to and move efficiently through

collagen matrices including human neutrophils[3 I], murine melanoma[32], human

fibroblasts[33], and rat hepatoma[34]. Due to its abundance and physiological relevance

collagen has long been the substratum of choice for studying relevant aspects of cell

adhesion and cell migration.

The three-step model of cell migration consisting of protrusion of a leading

lamella, attachment to the substrate, and contraction of the cell body is well established

for migration across planar surfaces. However, it is not clear as to what extent the

migration of cells in a 3-dimensional tissue environment follows similar principles. Cell

migration may depend on integrin-mediated binding to extracellular matrix ligands,

including collagen. However, the extent and importance of this adhesion differs widely

with cell type.

This concept was confirmed by Friedl et al.[14, 35]. By combining a three-

dimensional collagen matrix model with time-lapse videomicroscopy, computer-assisted

cell tracking and confocal microscopy, these authors showed that the migration of highly

invasive MV3 melanoma cells in 3-dimensional collagen matrices follows the three-step

concept of migration but also results in characteristic reorganization of the extracellular

matrix. After incorporation in the lattice, MV3 cells spontaneously developed a slow

type of migration, leading to alignment of collagen fibers at attachment sites. In the

process of migration, the formation of focal clusters or stripes of alpha2 and betal

integrins co-localized with binding sites to collagen fibrils at the leading as well as the

trailing edge. This type of migration of MV3 cells in 3-dimensional collagen lattices

resulted in dynamic tissue reorganization and receptor shedding. However, they also

showed that T lymphocytes migrating in three-dimensional collagen matrices may utilize

highly transient interactions with collagen fibers of low adhesivity, thereby differing from

focal adhesion-dependent migration strategies employed by other cells.

In addition to the adhesive characteristics of the substratum and the cells, it has

previously been reported that the physical structure of the substratum can also affect cell

migration[16, 36]. More specifically, both the fibril pore size and fibril arrangement can

affect cell motility within collagen gels. Kuntz and Saltzman reported the migration of

neutrophils within collagen gels was a decreasing function of increasing pore size[ 16],

while Dickinson et al. reported that for oriented collagen fibrils, biased migration was

observed along the major axis of fibril orientation[36].

Furthermore, collagen is a typical substrate used in tissue engineering

applications. Tranquillo et al. took advantage of the behavior of tissue cells when

surrounded by a network of protein fibers, such as type I collagen gel for manufacturing a

tissue-equivalent[37]. The tissue-equivalent is characterized by the consolidation of the

fibrillar network, or gel compaction, resulting from traction exerted by the cells.


4-1 RGD Adhesive Amino-Acid Sequence

Until 1979 it had been widely reported that the attachment of cells to collagen

required the presence of a particular serum protein, fibronectin. At that time Schor and

Court showed that the serum-dependent mechanism of cell attachment described by

others was only the case for films of denatured collagen and that, in fact, cell attachment

to films or gels of native collagen occurred by a different, serum-independent

mechanism[32]. Since that time, the attachment activity of fibronectin has been localized

to a sequence of only four amino acids, arginine-glycine-aspartic acid-serine (RGDS).

Piersbacher and Ruoslahti showed that the cell attachment activity of fibronectin was

duplicated by small synthetic fragments of fibronectin which contained the RGDS

sequence[38]. This same tetrapeptide sequence has been shown to be present in other

proteins that interact with cells, including collagen, vitronectin and von Willebrand factor

and thus plays a role in cell attachment to these proteins as well[39]. Variations on this

sequence have also been found to be adhesive ligands. These include RGDA, RGDV and


4-2 Modification of Surfaces with RGD Peptides

In the study of such peptides as adhesion molecules and in the isolation of the

specific receptors necessary for cell adhesion to such peptides and ECM proteins, the

peptides and proteins have been previously coupled to a variety of surfaces including:

polystyrene, gelatin beads, and sepharose beads. The coupling of complete ECM

proteins to surfaces is done by activating the surface with cyanogen bromide (CNBr).

However, the coupling of the small synthetic peptides to surfaces was accomplished

using CNBr activated surfaces or a heterobifunctional cross-linker, 3-(2-

pyridyldithio)propionic acid N-hydrosuccinimide ester. The coupling of peptides with

the various surfaces, mostly through cysteine termini, showed no loss of their adhesive

activity. The use of a heterobifunctional reagent is a logical extension of a chemical

method that has been used extensively to modify proteins[41], create protein-protein

conjugates[42], create antibody-toxin conjugates[42], create fluorescently labeled

antibodies[43], to prepare immunoabsorbants for liquid chromatography[44], for the

immobilization of antibodies on solid surfaces[45] and a number of other unique

applications. In addition, collagen and its fragments have been coupled extensively to

liquid chromatography supports without loss of receptor binding activity in many studies

whose goal is to isolate and characterize the integrin family of receptors[46, 47]. RGD-

containing peptides had also been previously linked with BSA and shown to increase the

adhesivity of BSA to the level of fibronectin[48]. Therefore it seemed promising that

these same techniques or variations could be used to couple RGD containing peptides to

collagen to create an even more adhesive substrate.

The conjugation of RGD containing peptides had been used to modify the

adhesive properties of a variety of substrates for cell adhesion studies. Massia and

Hubbel cross-linked several synthetic peptides (Gly-Arg-Gly-Asp-Tyr and Gly-Tyr-Ile-

Gly-Ser-Arg- Tyr, which contain Arg-Gly-Asp (RGD) and Tyr-Ile-Gly-Ser-Arg

(YIGSR)) to a nonadhesive modified glass surface[49]. These modified substrates

supported the adhesion and spreading of cultured human foreskin fibroblasts

independently of adsorbed. This study showed that chemically stable substrates could be

produced which may be useful in studying receptor-mediated cell adhesion, as the

quantity of peptide available at the surface may be precisely measured and controlled.

They also completed a study in which glass was examined as a model cell-nonadhesive

substrate prior to modification, and polyethylene terephthalate (PET) and

polytetrafluoroethylene (PTFE) were examined as representative materials for biomedical

applications[50]. Prior to peptide grafting, all surfaces were unable to support cell

adhesion without the presence of serum proteins. Following the modification all surfaces

supported cell adhesion irrespective of adsorbed proteins. They concluded that since the

peptide grafting is quite easily controlled and is temporally stable, peptide grafting may

be advantageous over other approaches employed to improve long-term cell adhesion to


Additionally, the conjugation of RGD containing peptides had been used to

modify the adhesive properties of a variety of substrates for cell motility studies. Olbrich

et al evaluated the cell population motility and adhesion of rat skin glass modified with

covalently-immobilized biologically active peptides, specifically, either arginine glycine-

aspartic acid-serine (RGDS) or tyrosine-isoleucine-glycine-serine- arginine-glycine

(YIGSRG)[51]. Fibroblast population motility was decreased and adhesion was

increased on substrates modified with covalently immobilized RGDS peptide compared

to substrates with the covalently immobilized nonadhesive peptides arginine-glycine-

glutamic acid-serine and arginine-aspartic acid-glycine-serine. This study suggested a

possible use for RGD-modified substrata to study adhesion-mediated cell migration.

Furthermore, RGD had been previously linked to substrates in other studies

whose goals were to elucidate possible mechanism of haptotaxis. Brandley and Schnaar

derivatized polyacrylamide surfaces with quantifiable gradients of a nonapeptide

containing the adhesive RGD sequence[28], that is, they were able to take an otherwise

inert surface that had been used previously for cell growth and make it highly adhesive to

melanoma cells. They hypothesized that this gradient of adhesion was enough to cause

spontaneous redistribution of cells via haptotaxis, since they observed that cells

accumulated in areas containing higher concentrations of the grafted RGD peptide.

Additionally, one solution presented in the literature to promote the successful

function of a bioartificial implant is to modify the surface of the biomaterial in order to

promote the ingrowth of the surrounding cells onto the biomaterial surface or into the

porous structure of the biomaterial. Previous studies have shown that synthetic

polymeric biomaterials could be made more adhesive to cells by grafting various

adhesive peptide sequences on their surfaces (a review is provided by Ikada[3]). By

modifying the surface of a material, which already has excellent biofunctionality and

bulk properties (collagen), it may be possible to produce a more clinically applicable



5-1 Specific Goals

The goal of this research was to develop a quantitative relationship between cell

adhesion and cell migration in three-dimensional collagen matrices using a combination

of experimental techniques with mathematical modeling. This work may aid

fundamental understanding of the role of adhesion in cell migration as well as lead to

ways to control cell infiltration, localization or redistribution in tissue engineering

scaffolds. The specific goals are to (1) develop a method to covalently link RGD-

containing peptides, specifically GRGDSPC peptide which contains the tetrapeptide

sequence RGDS which has been well characterized as an adhesion ligand, to the collagen

monomer prior to fibrillogenesis, (2) measure the effect of this conjugation on cell

adhesion; and (3) measure the effect of this conjugation on cell migration in both uniform

and gradient concentrations of the conjugated collagen.

5-2 Experimental Techniques

5-2-1 Synthesis of Conjugated Collagen

Type I collagen was cross-linked with glycine-arginine-glycine-aspartic acid-

serine-proline-cysteine (GRGDSPC) peptide via the heterobifunctional reagent

' I wish to acknowledge the support of Brian Burgess for his work with cell tracking protocols and data

Sulfosuccinimidyl 6-[3'-2-(pyridyldithio)-propionamido]hexanoate (Sulfo-LC-SPDP).

The procedure involves a two step reaction with purification and concentration after each

reaction. The reaction chemistry is shown in Figure 5-1.

o0 'H NHr(a:) -o N H N +
~ + NH2-c~2?~ ~+ HO- iSOa
0 -'-OM/ (Lf^CHd -C-CH.).-C-NfA \_SO)VO
SPDP Amine Containing Derivative
Reaction 1

0 0
|01 ) ? H 4 + MSO\ o.. 9 H ? 2 -"^ r
S (+CH zaC N.(CH ijC4W7^ < -SCH -C-*CH +

Derivative Sulthydryl Conjugate H
Containing Protein Pyridine-2-thione

Reaction 2

Figure 5-1. The reaction chemistry for the two-step protein conjugation reaction.
Reaction 1 shows the dervitization of an amine containing protein (collagen monomer) by
reaction with SPDP to form amide bonds. Reaction 2 shows the conjugation of a
sulfhydryl containing protein (GRGDSPC peptide) to the collagen derivative through the
formation of disulfide bonds.

5-2-1-1 Reaction 1

First, the N-hydroxysuccinimide group of the Sulfo-LC-SPDP linker was reacted

with primary amine groups of collagen monomers to form stable amide bonds and create

a derivatized collagen. This reaction was carried out at pH 2.0 in phosphate buffered

saline (PBS buffer) for 24-48 hours at room temperature under constant stirring. The

PBS buffer was made from a pre-packaged mix that yields pH 7.2 buffer at a final

composition of 0.1 M sodium phosphate and 0.15 M sodium chloride. This pre-packaged

buffer was lowered to pH 5.0 by adding glacial acetic acid and 0.5% sodium azide was

added to help prevent bacterial contamination. Then, PBS buffer and cross linker were

added to a 3 mg/ml Vitrogen 100 collagen solution (Collagen Corporation, Palo Alto,

CA) in the ratio of 50 d.1 of cross linker to 2 ml buffer to 3 ml collagen to create the

reaction mixture. The reaction mixture was lowered in pH a second time to pH 2.0 to

prevent spontaneous fibrillogenesis of the collagen by adding glacial acetic acid.

After the 24 or 48 hour incubation, the excess linker was removed from the

derivatized mixture by liquid chromatography on the Biorad Econo System. The reaction

mixture was separated on a 5 ml desalting column (Sephadex G-25 Superfine) and eluted

with PBS/EDTA buffer[41]. The column was equilibrated with buffer for 30 minutes at a

flow rate of 1 ml/min. The derivatized collagen sample was loaded into the sample loop

and applied to the column at a flow rate of 0.5 ml/min. Elution of 1 ml fractions from the

column was done at a flow rate of 0.5 ml/min. Thirty fractions were collected to give a

total elution time of 1 hour. Detection of the collagen derivative was done by UV

absorbance. The derivative was contained in the first absorbance peak.

The fractions corresponding to this absorbance peak were pooled and divided into

several Centricon-30 micro-concentrators[52] for concentration as each concentrator can

hold up to 2.0 ml of sample. The concentrators were spun at 4000xg in a centrifuge for

30 minutes. This concentration also served as an additional purification step as the

concentrators are fitted with molecular weight filters which exclude any material below

30,000 Daltons or in the case of small scale preparations the concentration served as the

only purification step. In the small scale case, after the first 30 minutes, the supernatant

was rediluted with PBS (pH 5.0) and spun at least a second time to ensure adequate

removal of unreacted linker. In either case, the samples were spun in 30 minute intervals

until the final combined volume of supernatant in the concentrators was approximately to

volume of the original amount of collagen added. The supernatant were combined and

now contained all the purified derivatized collagen.

5-2-1-2 Reaction 2

Second, the 2-pyridyl disulfide group of the Sulfo-LC-SPDP linker on the

derivatized collagen was reacted with the sulfhydryl group on the cysteine residue of the

GRGDSPC peptide to form disulfide bonds and create the collagen-RGD conjugate. This

reaction was also carried out at pH 2.0 in PBS buffer for 24-48 hours at room temperature

under constant stirring. The supernatant from the concentrators was added to pH 5.0 PBS

buffer with sodium azide (made as described in section 5-2-1-1) and GRGDSPC peptide

in the ratio of 2 ml of buffer to 3 ml of supernatant to X mg of GRGDSPC peptide (X was

varied from 0.5 mg to 5 mg depending on the degree of conjugation desired). Refer to

Figure 5-3 for the amount of peptide corresponding to the desired conjugation level. This

reaction mixture was also lowered to pH 2.0 to prevent spontaneous fibrillogenesis of the

collagen by adding glacial acetic acid.

After the 24 or 48 hour incubation, the unreacted peptide was removed from the

conjugated mixture by gel filtration on an 80 ml Sephadex G-200 column by elution with

PBS buffer. The column was equilibrated with buffer for 1 hour at a flow rate of 1

ml/min. The conjugated collagen sample was loaded into the sample loop and applied to

the column at a flow rate of 0.5 ml/min. Elution of 2 ml fractions from the column was

done at a flow rate of 0.5 ml/min. Sixty fractions were collected to give a total elution

time of 4 hours. Detection of the conjugated collagen was done by UV absorbance. The

conjugated collagen was the first absorbing peak.

The fractions corresponding to this absorbance peak were pooled and divided into

several Centricon-30 micro-concentrators. The concentrators were spun at 4000 g in a

centrifuge for 30 minutes. This concentration served as an additional purification step in

this instance as well since the RGDSPC peptide is well below the 30,000 Dalton

exclusion limit or, again in the case of small scale preparations, the concentration served

as the only purification step. In the small scale case, after the first 30 minutes, the

supernatant was rediluted with PBS (pH 5.0) and spun at least a second time to ensure

adequate removal of unreacted peptide. In either case, the samples were spun in 30

minute intervals until the final combined volume of supernatant in the concentrators was

approximately that of the original amount of supernatant added.

The supernatant was pooled and tested for collagen concentration using

bicinchoninic acid protein assay reagent (BCA) which forms a blue copper complex in

the presence of proteins[53]. The protein determination reagent was prepared by adding

1 part copper (II) sulfate pentahydrate (4% solution) to 50 parts bicinchoninic acid

solution. Protein determination reagent was added to the supernatant in various dilutions

and the mixture was vortexed and incubated at 37C for 30 minutes. The absorbance was

measured at 562 nm and compared to a standard absorbance curve made by treating

collagen solutions of known collagen concentration with various dilutions of the protein

determination reagent to ensure a good range of absorbances for comparison with the

unknown sample. At this point, BCA testing and 30 minute concentrations were

alternated until the concentration of the pooled supernatants were at the original collagen

solution concentration (3 mg/ml). Both the supernatant and the filtrate were reserved for

tests to determine the degree of conjugation.

5-2-1-3 Quantification

Quantification of the amount of substitution of covalently linked peptide was

accomplished spectrophotometrically. The second reaction releases pyridine-2-thione

which has a specific molar absorptivity of 8.08 X103 M'cm'1 at 343 nm[54]. The

absorbance of this species was measured on the Spectronic 2D spectrophotometer. The

concentration can be obtained using

A = cs (5-1)

where A is the absorbance, c is the concentration and e is the molar absorptivity. The

concentration of released pyridine-2-thione is equivalent to the concentration of disulfide

residues formed in the conjugate (1:1 correspondence) and therefore equivalent to the

concentration of peptide substituted (also 1:1 correspondence).

Additionally, an independent test was run on the filtrate from the concentration

steps to measure the amount of unreacted peptide by measuring the free sulfhydryl

groups. This spectrophotometric test was done by treating the sample with Ellman's

Reagent which forms a yellow complex in the presence of free sufhydryl groups.

Ellman's reagent was made by dissolving 400 mg of 5,5'-dithio-bis(2-nitrobenzoic acid)

in 100 ml of reaction buffer. Reaction buffer was 0.1 M sodium phosphate at pH 8.0.

The absorbance of the treated filtrate was measured at 412 nm. The concentration of

unreacted peptide was determined by comparing the filtrate absorbance to a standard

absorbance curve made by treating cysteine solutions of known concentrations with

Ellman's reagent.

A third independent test was performed on the supernatant from the filtration

steps. It was also treated with Ellman's reagent (as described above for the filtrate) to

determine if there was any residual unreacted peptide in the conjugated collagen sample.

Ifpeptide remained, the conjugated collagen was separated and concentrated a second


Although sodium azide was used as a bacterial control, some contamination was

inevitably introduced into the samples. After all reaction, purification, concentration and

quantification steps, the conjugated collagen solutions were filtered through 0.2 p.m

syringe filters to remove any contaminating bacteria.

5-2-2 Automated Video Microscopy Incubation System (AVMIS)

Cell motility and adhesion experiments were performed using a Nikon Diaphot

200 inverted microscope equipped with computer controlled motorized stage and focus

for automated x, y, z-positioning. Images were viewed using a CCD camera and Optimas

image processing software. A library of functions was written in Optimas macro

language, which communicated to the motorized stage and performed image processing

steps to extract data from images in real time (Appendices A and B).

To maintain cells at physiological conditions during experiments for up to 24

hours, a novel stage incubation system (Figure 5-2) was developed which mounts onto

the microscope body maintaining physiological conditions: temperature at 37C, high

humidity level (relative humidity>85%) and 5% carbon dioxide level. Construction of

the incubator was from acrylic (Plexiglas) with an enclosed volume of approximately 3.5

ft3. Heat was maintained and controlled by a closed loop re-circulating system in which

humidified air was circulated across heater coils and then re-circulated to the incubator

mounted on the stage via insulated tubing. Carbon dioxide levels were controlled using a

separate controller. Relative humidity was maintained using a humidifier and a wall

mount sensor. Using a data acquisition board, Visual Basic software, and constructing a

circuit to regulate power input, relative humidity levels were controlled at desired

settings. To prevent any hot or cold regions inside the incubation system, air was well

mixed using two 4" circular fans. To insure that physiological conditions were

maintained inside the incubation system during the time course of all experiments, a data

acquisition program recorded the temperature, carbon dioxide level and humidity level

inside the incubator and exported them to an output file approximately every 30 seconds.

The output file could be reviewed to determine if any experiment was subject to less than

ideal conditions.

Automated Video Microscopy System
Data Acquisition

ii i-F

U L-J IVIFE 11_.-7

Figure 5-2. Schematic of the automated video microscopy system with incubation.

5-2-3 Cell Culture
A highly metastatic clone (M4) of the K1735 mouse melanoma line was provided
by Dr. Daniel L. Mooradian (University of Minnesota, Departments of Laboratory

Medicine and Pathology, Minneapolis, Minnesota). The cell line was maintained by in

vitro culture in low-glucose DN I EN I with L-glutamine, 110 mg/L sodium pyruvate and

pyridoxine hydrochloride which was supplemented with 10% heat inactivated calf serum

and 1.2% penicillin/streptomycin (10,000/10,000 units). Passages were made at 70-80%

confluency by washing twice with 5 ml of IX PBS, pH 7.4, releasing with 2 ml of

trypsin-EDTA and then replating 1:5 in low-glucose DMEM with serum. The number of

passages was limited to 16 in order to minimize phenotypic drift of the cell population.

Cells were harvested for use in experiments by the same procedure, however, they were

resuspended for use in experiments in serum free DMEM.

5-2-4 Adhesion Experiments

All adhesion tests were performed using multiple wells for each condition in 24-

well tissue culture plates. All cells in adhesion tests were suspended in serum-free cell

culture media. All cell suspensions were counted manually using a standard Petroff

Hauser chamber and bright field microscope. A computer program was written using

Optimas software which exploited the motorized stage and image analysis software

(Appendix A). The program scanned each tissue culture well in an automated fashion

and determined a cell density per microscope field by counting the number of cells in 25

fields within each well of the culture plate. These cell densities were reported to an

output file for each field. Tests were done on surfaces of bovine serum albumin (BSA)

and collagen that had been conjugated with RGDSPC peptide.

5-2-4-1 Adhesion on BSA Coated Surfaces

BSA was conjugated to GRGDSPC peptide using Sulfo-LC-SPDP following the

procedure described for collagen in Section 5-2-1. Quantification of the conjugation was

also accomplished using Ellman's reagent as described in Section 5-2-1-3. A set of five

BSA solutions (10 mg/ml total protein content) containing (1) 0% cross-linked BSA, (2)

25% cross-linked BSA, (3) 50% cross-linked BSA, (4) 75% cross-linked BSA and (5)

100% cross-linked BSA were prepared. Each BSA solution (0.25 ml/well) was added to

four wells in a 24 well tissue culture plate. The plate was incubated at 37C for one hour

to allow for protein adsorption. The wells were aspirated and stored in PBS at 4C until

ready for use. Prior to use, the PBS was aspirated and the wells were filled with serum

free DMEM. Cells were added to each well at a concentration of 30,000 cells per well

and incubated at 37C for 1.5 hours to allow attachment. Non-adherent cells were

removed by gently aspirating and replenishing media to attached cells. Final cell

densities in each well were obtained in an automated fashion using the program described

above and in Appendix A.

5-2-4-2 Adhesion on Collagen Coated Surfaces

Dilute solutions of collagen in 0.5 M glacial acetic acid (0.24 mg/ml) were made

of unconjugated collagen and of each of the conjugation levels. Each collagen solution

(0.25 ml/well) was added to four wells in a 24 well tissue culture plate. The plate was

incubated at room temperature for one hour to allow for protein adsorption. Wells were

rinsed with several milliliters of PBS buffer to remove excess acetic acid. To block any

exposed polystyrene (due to incomplete adsoprtion), 0.25 ml of a 0.5% w/v solution of

BSA, was then added to each well and incubated at room temperature for one hour. Each

well was rinsed with several milliliters of PBS to remove any non-adherent protein. As

control measures, a set of wells coated only with BSA and a set of wells washed only

with PBS were also prepared. Cells were added to each well at a concentration of 25,000

cells per well and incubated at 37C for 30 minutes to allow attachment. Initial cell

densities were counted using the automated computer program described above and in

Appendix A. Samples were then placed on a Rotomix at 100 RPM (inside the incubation

system) and spun for 20 minutes to remove approximately 50% of attached cells from

unconjugated collagen coated surfaces. Detached cells were removed by gently

aspirating and media was replenished to attached cells. Finally, cells were fixed using

neutral buffered formalin (10%) fixing solution and recounted to obtain final cell

densities. Final cell densities were compared to initial cell densities to obtain a fraction

of cells removed.

5-2-5 Cell Migration Experiments

Collagen gels were prepared with the following composition (on a volume basis):

67% collagen solution, 13% 10OX DMEM, 5% 4.4% w/v sodium bicarbonate, 10% 0.1M

NaOH, and 5% cell solution (cells suspended in serum free DMEM). Solutions were

well mixed to insure uniform dispersal of cells in collagen solutions and brought to a

final pH of 7.2. The final cell concentration was 104 cells/ml to minimize collagen gel

contraction induced by cell traction forces. Collagen solutions were heat polymerized in

a cell culture incubator at 37C, 5% C02, and high relative humidity for two hours to

allow for complete polymerization and initial cell spreading in the matrix. After

polymerization, gels were supplemented 0.2 ml of serum free DMEM to provide

additional nutrients for cells during the course of the tracking experiments. The samples

were then transferred to the pre-heated and humidified microscopy and incubation system

as described in Section 5-2-2. Cell tracking began once the samples were secured on the

microscope stage.

To track cells in an automated fashion, a computer algorithm using Optimas

programming language was developed (Appendix B). First, a number of cells,

determined by desired time-lapse increment and required image processing time per cell,

were selected by manually scanning the collagen gel to determine and store initial

positions, rt [x y z]. Once all initial positions were stored, the computer program

returned in an automated fashion to the initial position of the first cell selected. The

previous coordinates, centered within the region of interest box, were, in general,

different than the current position of the cell (i.e. off-center and out-of-focus), indicating

that the cell had moved some distance in the time interval. The motorized stage

autofocus feature was used to determine the new plane of focus by scanning the z-plane

in 3 [im step increments. The plane that provided the highest optical contrast was defined

as the new z-coordinate of the cell position. The updated x- and y-coordinates were

determined by completing a series of image processing features to determine the area

centroid of the cell (the center of mass for a two-dimensional projection of the cell). The

stage was recentered such that new x- and y-coordinates were centered within the region

of interest box. The updated positions, rt+At, were then recorded and exported to an

output file. The program returned to each cell position for each time increment over the

course of the experiment. Anywhere from 20 to 100 cells could be tracked for times

from 10 to 24 hours.

5-2-6 Formation of Spatially Adhesive Gradients

Gradients were poured in an automated fashion using the gradient former and

peristaltic pump of the BioRad Econo liquid chromatography system. This unit could

control the amounts of two solutions, A and B, that were being mixed at any point in

time. The system could be programmed to pour various types of gradients by simply

inputting the flow rates and the percentages of solution A and B desired at various times

in the pumping cycle. To quantify the gradients, collagen gel solutions were made

containing various amounts (from 0% to 100%) of BCA. Collagen gels containing

gradients of BCA protein determination reagent were poured with the automated system

where solution A was collagen containing 0% BCA reagent and solution B was collagen

containing 100% BCA protein determination reagent (this would create a gradient of the

copper complex as the collagen gelled and thus giving a gradient of absorbance). The

gradient former was programmed to linearly increase the amount of B in the mixture over

the 30 minute pouring cycle. Figure 5-3 shows the specially designed pumping chamber,

a wedge shaped teflon spacer sandwiched between two glass microscope slides, which

was designed to eliminate mixing while pumping into the chamber. The mixture of the

two solutions was pumped into the chamber at 0.25 ml/min to minimize mixing during

the pumping stage. After the pumping cycle the chamber was sealed with wax and

placed in the cell culture incubator at 37C for 2 hours to allow for complete gelation.

After 2 hours, the gels were removed from the incubator and sliced into thin pieces. The

pieces were dissolved under gentle sonication. The absorbance of each slice was then

compared to the collagen standards (as described in Section 5-2-1-2) to test the linearity

of the gradient. It was found that linear gradients could be poured in a reproducible

fashion. This pumping technique was also used for the collagen matrices used in cell

tracking experiments, where solution A was an unconjugated collagen gel solution and

solution B was a solution of RGD conjugated collagen. In these cases, the gradient

former was programmed to pour various steepnesses of linear gradients of adhesiveness.

Capped with
Two 1x3"
glass slides
With a 0.2" thick
pTFE spacer

II ifjni 1111 ________________ __ 11111

Collagen Collagen

Figure 5-3. Schematic showing the formation of spatial adhesion gradients. To
minimize dispersion, collagen solutions were pumped very slowly a with gradient
controller from a liquid chromatography system.

5-2-7 Preparation of Collagen Gels for Scanning Electron Microscopy

Collagen gel solutions were prepared with the following composition (on a

volume basis): collagen solution (either unconjugated or conjugated) (67%), 10X

DMEM (18%), 4.4% w/v sodium bicarbonate (5%), and 0.1 M NaOH (10%) to give a

total protein content in each gel of 2 mg/ml. All solutions were pre-filtered using a

0.1 p.m porous filter. The pH of the gel solution was adjusted to 7.4 by adding

concentrated sodium hydroxide as needed. The samples were prepared for scanning

electron microscopy using a protocol that minimizes but does not eliminate shrinkage of

the collagen gel microstructure as described previously by Kuntz and Saltzman[16]. A

few drops of liquid gel solution were placed on polylysine coated coverslips. These were


placed in a 37 C incubator to allow the solution to gel. The resulting gels were fixed in

2% gluteraldehyde and washed in PBS. Specimens were dehydrated through a series of

graded ethanol solutions and critical point dried. Specimens were sputter coated with

gold/palladium and viewed using a Hitachi SR400 FE scanning electron microscope at

2,000 times and 10,000 times magnification. Multiple micrographs were taken at varied

magnification levels to study the microstructure. Using OptimasTM image analysis

software, gels were characterized by measuring the fibril diameter and fibril spacing of

50 sample regions per micrograph.

5-3 Experimental Results

5-3-1 Collagen Conjugation

The conjugation was easily controllable due to the choice of a heterobifunctional

cross-linker. SPDP was chosen because it contained one N-hydroxysuccinimide and one

2-pyridyl disulfide group, which were able to react with primary amines on the collagen

monomers and sulfhydryl groups on the GRGDSPC peptide, respectively. Since the two

reactive groups were directed toward different functional groups, the coupling and cross-

linking could be conducted in separate sequential steps with purification between steps.

This was especially true in the case of collagen since collagen monomers contain no

sulfhydryl groups (cysteine residues). Also, by using a heterobifunctional reagent, inter-

molecular cross-linkages were easily introduced without concomitant formation of intra-

molecular cross-linkages[41]. Liquid chromatography confirmed this for each reaction

step. After reaction one, only two absorbing peaks were obtained corresponding to

unreacted SPDP and a collagen/collagen derivative mixture. After reaction two, only two


absorbing peaks were obtained corresponding to the collagen derivative and the collagen-

RGDSPC conjugate. No contaminating peaks were seen.

The average degree of peptide substitution to collagen was found to vary with the

amount of peptide added, the amount of linker added and the time of incubation in each

reaction step. By repeating various reaction conditions we found that reproducible

peptide substitution levels of 6-8, 13-15 and 22-25 peptides per collagen monomer could

be obtained. A conjugation level of(1) approximately 3 peptides per monomer was

obtained for two different sets of reaction conditions, (2) approximately 7 peptides per

monomer was obtained for four different sets of reaction conditions, (3) approximately

15 peptides per monomer for four different sets of reaction conditions and (4)

approximately 23 peptides per monomer for two different sets of reaction conditions.

The reaction conditions necessary for these levels are shown in Figure 5-4. It was found

that we could maximize the amount of linkage while minimizing the amount of reactants

necessary by allowing both reaction one and two to proceed for 48 hours.

E 25
M 20-
S15 ,

7 5
4 10-

I 0 I 0-I
0 1 2 3 4 5
Peptide Added (mg)
25 ul linker/24 hours incubation w 50 ul linker/24 hours incubation
25 ul linker/48 hours incubation 50 ul linker/48 hours incubation

Figure 5-4. Repeatable peptide substitution levels that were attainable for the reactions.
Quantities shown in the figure are based on reaction with 10 mg of collagen and a 20 mM
stock solution of SPDP cross-linker.

This conjugation did not significantly alter the properties of the collagen. All

modified collagens were found to have similar gelation times and viscosities.

Additionally, scanning electron microscopy was used to probe the microstructure of the

collagen gels. These micrographs were taken to determine if the gel microstructure was

disrupted, as it has been previously reported that variations in pore sizes can alter the

migration of cell through collagen gel matrices[16]. Measurements of fibril size,

alignment and spacing show no qualitative or quantitative differences in gel structure

(Figure 5-5). Plain collagen gels were found to have an average pore size and fibril size

of 621 57 nm and 121 7 nm, respectively. Gels of modified collagen had average

pore sizes of 602 55 nm, 619 47 nm, 637 57 nm for 8 peptides/monomer, 15

peptides/monomer and 23 peptides/monomer, respectively. Their average fibril sizes

were 113 12 nm, 116 7 nm, 126 7 nm, respectively.

Collagen gel 8 peptideslmonomer



15 peptides/monomer 23 peptides/monomer

Figure 5-5. SEM micrographs of the various collagen matrices. No significant
differences in fibril size, orientation or structure were found. All images were taken at
2,000 times magnification. The gray bar represents a scaling of 15 gm.

5-3-2 Cell Adhesion Experiments

Two types of tests were performed: (1) to test the peptide independent of collagen

to determine if the K1735 M4 cells expressed receptors specific for the peptide chosen by

covalently linking the peptide to a nonadhesive blood protein (BSA); (2) to test the

conjugation reactions by determining if the adhesiveness of collagen was modified by

conjugation with GRGDSPC peptide. Cell adhesion was found to be directly related to

the presence of GRGDSPC peptide for both BSA and collagen coated surfaces.

As the percentage of conjugated BSA in the coatings increased, the number of

cells adhering increased up to 3-4 times greater than for BSA alone (Figure 5-6). The

coatings containing 25% conjugated BSA increased adhesion 2.5 times over that of BSA

alone. The coatings containing 50% and 75% conjugated BSA increased adhesion 3.5

and 3 times, respectively, over that of BSA alone. These results suggest that the cells

adhere directly to the GRGDSPC peptide independent of an adhesive substratum and

therefore the peptide is active in implementing K1735 mouse melanoma cell attachment.

The leveling off between 50% and 75% conjugated BSA in the coating suggests that at

this level a maximum in augmentation of cell adherence to BSA was reached for the

cross-link density of 14 peptides per BSA molecule. This data suggests that K1735 M4

cells possess integrins that are specific for GRGDSPC peptide. This was not unexpected

as others have shown numerous cell lines express integrins which are specific for RGDS

peptide. Such lines include: normal rat kidney cells[55], transformed rat kidney

cells[55], human fibroblastic cells[55], human endothelial cells[55], rat hepatocytes[56],

rat cardiac fibroblasts[56], B16-F10 murine melanoma cells[57] and others. It has also

been shown that the M2 metastatic clone of the K1735 cell line expresses the integrin


complex which is necessary for RGDS-dependent attachment[58]. Additionally,

extensive research has shown that RGDS peptide affects both cell attachment to and

detachment from various substrates in a dose dependent manner[38, 59].



0 3 -
< .

0 i

0.00 0.25 0.50 0.75 1.00
Ratio of RGD-Conjugated BSA to Unconjugated BSA

Figure 5-6. Cell adherence to surfaces coated with various amounts of cross-linked BSA.
The results are normalized to the adherence for BSA alone. The crosslink density for all
experiments was 14 peptides per BSA molecule.

Cell adhesion strength on surfaces coated with monomeric collagen (conjugated

and unconjugated) was also found to increase with increasing conjugation (Figure 5-7).

At the conjugation level of 8 peptides per collagen monomer, the number of cells

removed decreased by over 50% from plain collagen substratum. At 14 peptides per

collagen monomer, the removal percentage slightly increased from the level obtained for

8 peptides per collagen monomer but was still nearly 50% lower than plain collagen.

This may have been due to inconsistencies in the force applied during aspiration. The

removal percentage at 22 peptides per collagen monomer was below both that at 8 and 14

peptides per monomer indicating that the conjugation level of 22 was the most adherent.

The overall trend demonstrated that at each conjugation level the collagen was more

adhesive. All conjugated collagen coatings were significantly more adhesive than BSA

or collagen alone. It is interesting to note that the 22 peptide per collagen level

approached the adhesiveness of tissue culture polystyrene. A similar trend was found for

K1735 cell adhesion to surfaces coated with fibrillar collagen. These results suggest that

the peptide is active in affecting cell adhesion even in the presence of a highly adhesive

substratum. This may be due to differential receptor expression. It has been shown that a

recognition sequence for collagen attachment is RGDT peptide, a ligand which is specific

for different integrins than RGDS[60]. It has also been shown that RGDS in solution is

ineffective at removing attached cells from collagen[55].

As a control measure, a similar set of experiments was done for collagen that was

covalently linked to a well-characterized nonadhesive peptide, glycine-arginine-glycine-

glutamic acid-serine-proline-cysteine (GRGESPC) using the procedure described above

for GRGDSPC. No significant differences in the adhesion to surfaces coated with RGE

grafted collagen were found (Figure 5-8). This lack of response is expected, as

GRGESPC is a well-documented nonadhesive control peptide in adhesion experiments.

The fact that there is no decrease in adhesion indicates that we have not disrupted any of

the normal mechanisms of cell adhesion to collagen by conjugation with GRGESPC

peptide. It can be assumed that these mechanisms are likewise not disrupted by

conjugation with GRGDSPC peptide. The fact that there is no increase in adhesion

indicated that the conjugation procedure itself does not increase the adhesiveness of the

collagen substrate. Therefore, the increase in adhesion found for collagen linked with

GRGDSPC peptide can be inferred to be solely due to the presence of the peptide.



5 10 15 20
Number of Peptides Conjugated Per Collagen Monomer

Figure 5-7. Cell adherence to collagen and conjugated collagen coated surfaces. The
adherence to collagen containing 22 peptides per monomer approaches that of tissue
culture polystyrene.




( .
0 1.00

0.75,1 1 1-
0.00 0.25 0.50 0.75 1.00
Ratio of RGD-Conjugated Collagen to Unconjugated Collagen

Figure 5-8. Cell adherence to surfaces coated with various ratios of RGD-grafted
collagen. Cell adhesion increases as the total amount of RGD in the coatings increases.

5-3-3 Cell Migration Under Uniform Conditions

Results represent data from multiple tracking experiments pooled (as described in

section 5-3-3-1). The mean-squared displacement, , was obtained from cell

tracks and fit to a correlated random walk model, Equation (5-2), using generalized

nonlinear regression program. Random motility (analogous to molecular diffusion term

for cells), persistence time (characteristic time a cell persists in one direction) and cell

speed were estimated from each set of experiments.

5-3-3-1 Data Analysis

A common statistical characterization of cell migration in an isotropic

environment, is mean-squared displacement

= < d(t)* d(t) > (5-1)

where d(t) is the displacement vector over time period, t.

Given an isotropic environment, cell movement may be characterized by two

asymptotic limits. For lower time limit (t ->0) cells persist in the same direction, while

over longer time (t -+oo) cell movement can be best described by random directional

changes, analogous to the Brownian motion of a particle. This has led researchers to

mathematically model this type of cell behavior as a persistent random walk. The model

applied in this research is a persistent random walk model augmented with a parameter

accounting for positioning error. The analysis of cell track displacements and model

have previously been described[61].

< d(t)2 >= 2nul(t P(l e )) + 2y (5-2)

where p is known as random motility coefficient, analogous to molecular diffusion term

for cells. P is directional persistence time that characterizes how long a cell persists in


one direction. y is mean-squared positioning error, which accounts for stage positioning

error and imaging resolution inaccuracies, n, represents the number of dimensions the

data is analyzed.

Dunn[62] has previously shown the direct relationship of p. to P and mean speed,


t =- S2p (5-3)
lim t-- ///

Briefly, mean-squared displacement, from cell tracks was determined by

applying method of non-overlapping time interval lengths

<'' >= d(t)2 (5-4)

where n, is the number of time intervals for a given interval length, and nt is the total

number of time intervals.

To maximize available data for a given time interval, displacements from cell

tracks may be averaged as pooled mean-squared displacement for a given interval length.

This is valid if cell population is homogeneous. To test for homogeneity, cell population

was subdivided and analyzed to determine if significant differences arose. No

differences were found, therefore the cell population was considered homogeneous. This

was accomplished by
< ) > (5-5)


where is averaged square displacement for a given interval for cell track m, M

is the total number of cell tracks and Wm, is a weighting factor to account for tracks of

unequal time length given by

W"., = -M (5-6)

where nf/ is the number of intervals for a track m.

Data from repetitive experiments for a given treatment were pooled to increase

statistical confidence in cell migrational parameters, by

< d(t)' >= IM, < d(t)" >](-7
"^^ < (5-7)

where is mean-squared displacement of interval length i for repetitive

experiment e, Exp is total number of repetitive experiments for a given treatment, and Mt

is total number of cells for repetitive experiments.

5-3-3-2 Three-Dimensional Cell Tracking

Using generalized nonlinear regression to fit the model to the data, estimates for

random motility coefficient, p, were obtained. A modal dependence of p on the degree

of RGD conjugation was observed (Figure 5-8). For the range of conjugated peptides

linked to collagen tested, an optimal increase of p was found in 8x gels (39% increase in

p from collagen). For conjugation of adhesion peptides greater than eight peptides per

collagen monomer, a significant decrease in u was observed. In fact, for an increase of

six peptides (over the optimal 8) linked to collagen monomer, a 57% decrease in p. was

observed. However, in the control experiments (RGE cross-linked gels) no dependence

was found. This strongly suggests that the three-dimensional cell migration is

biphasically dependent on substratum adhesiveness. The trend in Figure 5-7, suggests

the diffusional properties of cells may be enhanced or reduced by controlling the

adhesive properties of collagen and that the maximum occurs at intermediate


adhesiveness. These results are similar to the results DiMilla and Stone[8] and Kuntz and

Saltzman[ 16] have found for two dimensional tracking of human smooth muscle cells on

a range of surface concentrations of fibronectin and type IV collagen and PMNINs on

collagen gels or collagen gels supplemented with various concentrations of laminin,

fibronectin and heparin.

2.5 -


0 1.5



0.5 ,
0 5 10 15 20 25
Number of Grafted Peptides

Figure 5-9. Rate of cell dispersion quantified by the random motility coefficient.
Random motility coefficient was found to be biphasically dependent on the degree of
RGD grafting to the collagen with a maximum at intermediate substratum adhesiveness.
It was not found to be dependent on the degree RGE grafting.

Estimates for characteristic time a cell persists in one direction, persistence time

are presented in Figure 5-9. A modal dependence of persistence time was also observed

as a function of degree of conjugation. For 8x gels, cells were found to persist in same

direction for longer time lengths compared to collagen cell tracks. However, for

conjugation greater than eight peptides, cell persistence time was found to be greater than

for collagen but less than that for 8X gels. This suggests that as the adhesive properties


are enhanced above the optimum level cell runs became shorter and characterized by

more frequent turns which leads to a more tortuous cell path. This supposition is further

supported by data on the persistence length (Figure 5-10), the characteristic length a cell

persist in one direction. Persistence length was also found to be modally dependent on

substratum adhesiveness with a maximum at intermediate adhesiveness. Both of these

results are contrary to results that other researchers have presented for two dimensional

cell migration.

J 16
I 14

Q. /
0 5 10 15 20 25
Number of RGD-Grafted Peptides

Figure 5-10. Characteristic time of directional persistence quantified by the directional
persistence time. Persistence time was found depend biphasically on the degree of RGD
grafting to the collagen with a maximum at intermediate adhesiveness.

Investigations of cell speed provide some insight into these differences. Cell

speed (Figure 5-11) was the only variable found to monotonically decrease as the amount

of RGD conjugation increased. This result is contrary to results that other researchers

have shown for two-dimensional cell migration[6, 8, 9]. Although two dimensional data

and the data for three dimensions both show that random motility coefficient has a modal


dependence on substratum adhesiveness, it seems that the two may be governed by

distinctly different mechanisms (i.e., two dimensional modal migration is governed by

the modal dependence on speed and three dimensional modal migration is governed by

the modal dependence on persistence time and persistence length).


12 -


-j 8

2 -
0 5 10 15 20 25
Number of RGD-Grafted Peptides

Figure 5-11. Tortuosity of the cell path quantified by the persistence length. Persistence
length was also found to depend biphasically on the degree of RGD grafting to the

5-3-4 Cell Migration in Spatial Gradients of Adhesiveness

Measurement of the net displacement of cells in the gradient direction indicate

that there was a small bias in the direction of the gradient. In three different gradients of

varying steepnesses both the drift velocity (Figure 5-12) and the orientation direction

(Figure 5-13) showed a small bias in the direction of the gradient. These data indicate

that that the drift velocity resulted in part from a bias in cell orientation toward the

gradient direction and in part from a differential in cell speed throughout the gradient.



E 0.7

8. 0.6-

0 0.5-

0 5 10 15 20 25
Number of RGD-Grafted Peptides

Figure 5-12. Rate of translational motion quantified by the root-mean-square cell speed.
Cell speed was found to decrease monotonically with increased degree of RGD grafting.

Drift Velocity

Collagen-8X Collagen-12X
[8.Tx1O-mol/cm4] I1.3x1O7mol/cm4]


Figure 5-13. Biased cell migration in gradient gels quantified by measuring the drift
velocity toward the gradient direction. The gradient steepnesses, dc/dz, are shown in
brackets. The haptotaxis coefficient, c [cm /mol-s], is defined by Vx = c dc/dz, and is
shown above the bars. Error bars represent standard errors in the mean.

Directional Orientation Bias

Collagen-8X Collagen-1 2X
[8.7x1Omol/cm4 [ 1.3xI07 mol/cm4]

[2.4x 10-mol/cm4]

Figure 5-14. The directional orientation bias is the mean angle of the displacements
relative to the gradient direction. Error bars represent standard errors in the mean.


6-1 Development of Model

Empirical observation of murine melanoma cell locomotion in three-dimensional

collagen matrices suggest that the ability ofpseudopods to transmit force to the collagen

matrix in an anisotropic fashion determines whether cells can efficiently migrate through

the collagen matrix. Cells that move most efficiently have several pseudopods extending

and retracting at the leading edge, but the retracting tail remains rounded and non-

adherent. However, cells that move less efficiently appear hyper-adherent with multiple

competing pseudopods extended in different directions unable to contract. Other cells

that cannot move effectively appear unable to form stable adhesions between the collagen

matrix and continually extend a retract pseudopods without cell displacement.

The goal of the model is to relate the adhesive properties of the matrix to the

ability of the cell to efficiently crawl through the matrix. This will ultimately serve to

interpret experimental results and to predict under what set of parameters random and

directional cell migration is optimal. In contrast to previous models for cell locomotion,

this model explicitly accounts for the extension and retraction ofpseudopods, which is

more relevant to the three-dimensional migration through tissue matrices. The model

consists of three parts: a) a model of the relationship between receptor-ligand binding and

pseudopod retraction rate; b) a model for the relationship ofpseudopod tractional forces

and cell displacement; and c) a phenomenological model for frequency and direction of

extension of new pseudopods.

The lifetime of a pseudopod is assumed to consist of three phases: i) extension of

the pseudopod ii) stabilization of the actin-myosin network in the pseudopod as it

undergoes gelation and receptor-binding occurs along the length of the pseudopod; iii)

retraction of the pseudopod as the actin-myosin network within the pseudopod contracts

creating a tractional force between the cell and the collagen matrix. Empirical

observation of crawling murine melanoma cells suggests that stabilization and extension

occur on a time scale much faster than retraction, thus are assumed instantaneous on the

time scale of interest.

The binding and dissociation of receptors to the binding sites in the collagen

matrix are assumed to obey simple mass-action kinetics. Let PR be the total density of

integrins (#/unit pseudopod length (cm)) on a pseudopod, Ps be the number of bound

receptors (#/unit pseudopod length), and PL be the density of available ligand binding

sites (#/volume). Based on mass-action kinetics, the differential balance equation for pB


d = kfPL(PR pB) k,pj (6-1)

where kf and kr are the forward and reverse rate constants, respectively, of the binding

reaction. If the rate of retraction is slow compared rates of receptor-ligand binding, then

the binding reaction can be assumed to be at equilibrium. At binding equilibrium,

dp1l /dt = 0, such that

PH= P- (6-2)
1 + Ki /P.

where K, = k- is the equilibrium dissociation constant of the binding reaction.
The contraction of the actin myosin network is assumed to occur along the length

of the pseudopod, such that the force retracting the pseudopod, Fc, can be assumed

proportional to the length of the pseudopod, L, such that Fc=ryL, where y is a constant.

Bound receptors along the length of the pseudopod resist the retraction in. A

reasonable assumption is that the force on each bound receptor is proportional to the

retraction speed, v. A one-dimensional force balance on a pseudopod then yields

yL = rqvpBL (6-3)

which implies

y" l+Ka/P,.
v = 1+K/PL (6-4)
77 PR

where rl represents the viscous drag force on a collagen fibril.

The model predicts that the retraction velocity increases as the equilibrium

number of bound receptors decreases, because the substratum adhesion is insufficient to

resist the retraction.

The contraction of each pseudopod creates a force on the cell body. At any

instant, several pseudopods pull on the cell body. The cell velocity, V, is determined by

the force balance between the pulling pseudopods and the drag force on the cell moving

through the matrix. This force balance yields

V = J ,J (6-5)

where /fl is the drag coefficient and *, is a unit vector in the extension direction of

pseudopod, j. Because of the retraction and the motion of the cell, j, and L are

functions of time, governed by the differential equations:

dt -v/ <) ,-V.t (6-6)
Jb, v
___V (6-7)
di R+Lj

where R is the radius of the cell body. The initial length of all pseudopods is assumed to

be the same at Lo, and a pseudopod is assumed 'destroyed' once it reaches length zero.

Tractional Force: Fr i

\ V

Drag Force: FD = -f/v

Figure 6-1. Force balance on the model cell. One-dimensional pseudopods pull on the
cell body. The drag force resisting the pull, with drag coefficient, /J.

An empirical model is used to describe the formation of new pseudopods. The

probability per unit time of extension of a new pseudopod, Q, is assumed to decrease

with the current number of pseudopods to account for the depletion of available actin in

the cell to form new pseudopods. A simple phenomenological relation to account for this


Q= Q0 exp -AIL, (6-8)

where Q0 is the maximum extension frequency, and A is a parameter that reflects the

effect of actin depletion on restricting new pseudopod extension. To account for the fact

that cells tend to extend pseudopods primarily in the direction of the leading edge, we

assume that the direction of new pseudopod extension, (I,ew, has a normal distribution

around the cell velocity direction. Let 9 be the angle between V and 0,,, with the range

[- oo >> C > oo], then

p(9)d19 = fexpL--o2 Jd,9 (6-9)
*V2-CT (- 2a' )
where the standard deviation, a, reflects the degree cell polarity with respect to new

extensions. The effect of this parameter on predicted cell morphology is illustrated in

Figure 6-2.

C=0.5 cu=3.0

Figure 6-2. Schematic showing the effects of the polarity parameter, a, the direction of
pseudopod extension. Larger values of a- correspond to more randomly directed
pseudopods. A value of 0.5 was chosen based on empirical observation of crawling
murine melanoma cells.

The equations are now made dimensionless to reduce the number of parameters.

The chosen characteristic length scale for scaling is Lo, and the chosen characteristic time

scale is / / y. The retraction velocity is

uj= -=a(l +K, c) (6-10)

where a The dimensionless cell velocity is

U -= (6-11)

where 2Aj Lj / L0. Dimensionless forms of Equations (6-6) and (6-7) are then
= -uj *,.j A- ,.( (6-12)

i4 (6-13)
dr R +L1

where r R/L. The initial conditions are 2 (r=0)=l, 4,(r=0)=|,,ew. The
dimensionless form of Equation (6-8) is

co= co exp- Z12. (6-14)

where co =- oo -- and A 9-
7 7 L0

Table 6-1 Parameter Estimates used in the Model
Parameter Range Sources
PR 100-1000 receptors/pgm [63, 64]

PL 5 90 X 1017 ligands/cm3 [65, 66]

KD 3 6 X 10-4 M [38]

Y 0.03 0.04 dyne/cm [67]

S1.2 X 105 dyne-s/cm [68]

3 107 10- dyne-s/cm [69]

Q 0.25 extensions/min Direct Observation

A 1 2 X 104 molecules/ptm [70, 71]

Lo 30 40 ptm Direct Observation

R 20 p.m Direct Observation

6-2 Model Predictions

6-2-1 Model Predictions for Uniform Conditions

The model predicts that retraction velocity depends strongly on ligand

concentration. In Figure 6-3, the dimensionless retraction velocity as a function of

dimensionless ligand density, K'-is shown for various values of matrix viscosity. Matrix

viscosity and increased ligand concentration (or bond affinity) serve to decrease the

retraction velocity.

The effect of ligand concentration on the resulting cell motion can be seen by

numerical integration of Equations (6-12) and (6-13) and simulation of pseudopod

extension with frequency and direction given by Equations (6-13) and (6-14),

respectively. For the results in Figure 6-4, cell paths were simulated to 400 time units,


for increasing values of the dimensionless ligand density. By tracking the simulated cells,

the speed, directional persistence time, and random motility coefficients could be

estimated. These results are qualitatively similar to the experimental observations in

Figures 5-12, 5-10, and 5-9.


0 7
> 6
C 5
0 Increasing Viscosity, q
M~ 3

0 2 4 6 8 10
Ligand Concentration
Figure 6- 3. Dimensionless retraction velocity is plotted as a function of dimensionless
ligand concentration, K p, / K,, for various values of matrix viscosity, 77.

/P S P

0 00 00 00 7G 0 O0
%4 0 B A 0 0

4 0 B A 0 0 B
;~ 0
0 B 0 B
0 wP60
R 0 0O o 0
A o C
2( o sC "0 es
0 ..4 0 C
00000 0 00000
0---------.-- o.__________C__________
0.50. .3( 2 ):

05 5 2 05 1 1.5 2 0.5 1 1.5 2
Dimensionless Ligand Density Dimensionless Ligand Density Dimensionless Ligand Density

Figure 6-4. Simulation results of dimensionless random motility coefficient, speed, and
directional persistence time plotted vs. dimensionless ligand density. Values of other
dimensionless parameters were o=O0.5, coo=l0., X=2.0, and r=.25.

These results suggest that there may be an optimal adhesiveness for efficient

migration. If the ligand density too low, the pseudopods extend and retract too quickly

for efficient movement. If the ligand density too high, multiple slowly-retracting,

pseudopods end up extending in various directions, resulting in a spindly morphology.

6-2-2 Model Predictions for Spatial Gradients

The model predicts that biased migration is dependent on both the strength of

adhesion and the steepness of the spatial gradient applied. It also predicts that this bias

results not only from the gradient of adhesiveness present but also from an orientation

bias expressed by the cell.

The model predicts a minimum in adhesiveness for biased migration to occur. At

even very high values of gradient steepness the model predicts that there is a threshold of

adhesiveness that must be met before biased migration will occur (Figure 6-5). At the

lowest level of adhesion (Figure 6-5a) there is no observed bias in the simulated cell

paths. This result is not surprising as there is a minimum of adhesiveness for efficient

migration to occur even in the uniform adhesiveness case. Figure 6-5 also shows that the

most effective biased migration (Figure 6-5c) happens at the median level of adhesion,

which corresponds to the most efficient movement of the cell in the uniform adhesiveness


The model also predicts a minimum in gradient steepness (difference of adhesion

over the length of the cell expressed as a percent gradient) that must be met before biased

migration can occur. Figure 6-6 shows two representative levels of adhesiveness. As

seen in the figure, this minimum gradient for biased migration was also a function of the

initial adhesiveness of the matrix since at the low level of adhesiveness (Figure 6-6 a and

4 0


ti I. b E

*3 C -1 46 ^ 5 V VC C


Figure 6-5. Simulated cell paths for high gradients of adhesion at various strengths of
adhesion, a) Cell path for a high gradient at very low adhesion, b) Cell path for a high
gradient at low adhesion, c) Cell path for a high gradient at medium adhesion, d) Cell
path for a high gradient at high adhesion, e) Cell path for a high gradient at very high

X) 6 X)

-*s e


*310 -6

b) the percent gradient needed to produce a bias was smaller than that at the medium

level of adhesiveness (Figure 6-6 c and d). Also, Figure 6-6 b and d show that the

magnitude of the biased produced is a function of the initial level of adhesiveness. The

medium level of adhesiveness prompts cells to move nearly 3 or 4 times the distance they

move at the low level of adhesion. This is manifest in calculations of the drift velocity.

Drift velocity was seen to increase as both the percent of gradient increased and the initial

adhesiveness of the matrix increased (Figure 6-7). These results correspond well with the

experimental observations. In all gradient steepnesses tested a significant bias was

observed. However, even as the steepness of the gradient increased the overall bias did

not increase. The effective drift velocity or haptotaxis coefficient was approximately the

same in all cases with the value at the median level of adhesion slightly higher,

suggesting that as the initial adhesion level increased the steepness of the gradient also

needed to increase to create a biased migration. For the values of gradient steepness

tested in the experimental cell tracking studies (2.5%, 4%, and 6.8%), the model

predicted that bias migration should occur showing that the model can be used as a

predictive tool for when haptotaxis could be expected.

Lastly, it predicts that the orientation of the cell contributes more significantly to

the creation of a biased migration than the speed of the migration (Figure 6-8). Figure

6-8a was created by removing the dependence of migration on the speed of the cell,

thereby magnifying any effect that cell orientation would have in creating the biased

migration. Figure 6-8b was created by removing the dependence of migration on the

orientation of the cell to magnify any effect that cell speed would have on the biased

migration. The cell paths show that when the cell is not allowed to respond to orientation

there is much less movement and it is more random motion than when the cell can sense

pseudopod orientation in the gradient.

1. 15 20 20 5 1

Figure 6-6. Simulated cell paths for low and medium levels of adhesiveness showing the
minimum gradient necessary to produce a bias. a) Cell path for a 1% gradient at low
adhesion, b) Cell path for a 3% gradient at low adhesion, c) Cell path for a 9% gradient at
medium adhesion, d) Cell path for an 11% gradient at medium adhesion.


0.00 -


-nf i,


0 1 2 3 4 5 6 7
Percent Gradient


0 2 4 6 8 10
Percent Gradient

Figure 6-7. Drift velocities for low and medium levels of adhesiveness showing the
minimum gradient necessary to produce a bias. a) Drift velocities for gradients at low
adhesion, b) Drift velocities for gradients at medium adhesion. Open circles represent
drift in the y-direction. Filled circles represent drift in the x-direction (direction of the


a b

Figure 6-8. Simulated cell paths for medium levels of adhesiveness showing the relative
contributions of orientation bias and kinesis, a) Cell path for orientation bias. b) Cell
path for kinesis.

Therefore, it would seem that to create a biased path of migration the cell must be

expressing an orientation bias in the direction of the gradient. Data obtained from

experimental observation of cell migration confirm that the cells do exhibit this type of

biased behavior (Figure 5-14).


In this work, type I collagen and BSA were conjugated with GRGDSPC and

GRGESPC peptides. The reaction of collagen with GRGDSPC or GRGESPC peptides

did not inhibit the fibrillogenesis of the collagen monomers. The collagen gel structure,

as examined by SEM, did not reveal any qualitative or quantitative differences between

unconjugated and conjugated collagen gels. Additionally, the structure is similar to other

SEM micrographs of collagen presented in the literature [16]. One might expect there to

be a threshold in the percentage of amino acids, and in particular lysine residues, that

could be modified by the conjugation and/or in the percentage of amino acids added

through conjugation before the gel structure would be compromised. The slight

anomalies that are present in the highest conjugation level could suggest that these

thresholds could be 0.7% of total amino acids (13.8% of lysine residues) safely modified

by conjugation and/or 5.1% of amino acids safely added by conjugation.

K1735 M4 murine melanoma cells were found to adhere to conjugated BSA in a

dose dependent manner suggesting specific integrin binding to the coupled GRGDSPC

peptide, which is not unexpected as it has been previously shown that the K 1735 cell line

expresses the integrins that bind specifically to the RGDS sequence[58]. Collagen that

was conjugated with GRGDSPC peptides was also found to have a similar effect on cell

adhesion. This dose-dependent response suggests that cell adhesion was enhanced by the

GRGDSPC even in the presence of the adhesive collagen substrate. Others have shown

that RGDS peptides affect both cell attachment to and detachment from various

substrates in a dose-dependent manner for a variety of cell types[38, 59]. Of interest

here, however, is the relative adhesion to the conjugated GRGDSPC peptide versus other

adhesive binding sites in the type I collagen. It has been shown that a recognition

sequence for collagen attachment is RGDT peptide, a ligand that is specific for a different

integrin than the RGDS peptide sequence[60, 72]. It has also been shown that RGDS in

solution is ineffective at removing attached cells from collagen[55]. Specifically,

Chelberg et al. have shown that RGDT peptide, when presented in solution, reduces the

ability of K1735 M4 melanoma cells to adhere to both type I and type IV collagen in a

concentration dependent manner, whereas, RGDS peptide has no effect on K1735 M4

melanoma cell adhesion to type I or IV collagen[72]. Therefore, in our experiments it is

possible that both the collagen-specific integrins and the RGDS-specific integrins bound

to the conjugated matrices, thus are involved in increasing the overall adhesiveness.

Also of interest is that the adhesion response does not differ when the same total

amount of peptide is presented clustered around a few highly conjugated collagen

molecules or more evenly distributed through medium conjugated collagen molecules.

This is not surprising based on an analysis of the size of the collagen molecule compared

to the size of an integrin. Collagen is a rod shaped molecule about 2600 A in length and

15 A in diameter[73] while the typical integrin is an ellipsoidal shape with radii of

approximately 80 A and 120 A[74]. The maximum conjugation level of 22 peptides per

monomer presents an additional 22 integrin binding sites. This number of integrins could

easily crowd around one collagen monomer as well as be shared by two adjacent collagen


Surfaces coated with collagen that was conjugated to GRGESPC peptide were

found to have no effect on cell adhesion. As the amount of GRGESPC conjugated to

collagen increased, no significant change in the adhesion as compared to a surface coated

with unconjugated collagen was observed. This was not unexpected because the RGE

sequence is a well-documented nonadhesive control peptide[40, 59]. The lack of either a

positive or negative response in cell adhesion to the GRGESPC-conjugated collagen

suggests that none of the normal mechanisms of cell adhesion to collagen have been

disrupted by conjugation with GRGESPC peptide. It can be inferred that these

mechanisms are likewise not disrupted by conjugation with GRGDSPC peptide. Further,

this strongly suggests that the conjugation procedure itself did not increase the

adhesiveness of the collagen substrate through the introduction of a charge differential or

change in the conformation of the collagen fibrils. This is also supported by the unaltered

microstructures of unconjugated and conjugated collagen gels as seen with SEM and the

measurement of similar fibril size and fibril spacing. Therefore, the increase in adhesion

found for collagen linked with GRGDSPC peptide is likely due to the direct presence of

the GRGDSPC peptide rather than indirect effects on the collagen structure due to the

binding reaction.

Together, these experimental results indicate that GRGDSPC and GRGESPC

peptides can be covalently linked to type I collagen monomers and modify adhesion

without seriously disrupting the structural properties of the resulting collagen matrix.

It has also been shown that the migration of K 1735 M4 cells in three dimensional

collagen matrices has a biphasic dependence on conjugation level with maximal

migration occurring at a median value of adhesiveness, which suggests that the difference

in adhesiveness extends to the case when collagen is cast in a three-dimensional gel.

Others have shown similar dependencies for adhesion-mediated migration of mammalian

cells across two-dimensional substrata that have been coated with various ECM

proteins[6, 8, 9].

Migration of melanoma cells is integrin-dependent, likely involving multiple cell-

surface receptors. As previously reported, melanoma cells express both ap 01 (VLA-1) and

cU2Ai (VLA-2), both which have a high affinity for collagen[75]. Although the Type I

collagen sequence contains multiple RGD amino acid sequences, the a,01 and acp1

receptors have previously been shown to be RGD-concentration independent for native

collagen[76]. This suggests, at least a third cell surface integrin receptor is likely involved

in the adhesion of these cells to the grafted RGD peptides. Based on a literature review,

the most likely integrin responsible for binding to the grafted-RGD in a concentration

dependent manner, is the Xvp3 integrin expressed by melanoma cells[75, 77]. Other

integrins expressed by melanoma cells have previously been reported[ 18, 78]. The

involvement of these integrins in cell migration for Type I collagen has been addressed

previously[78]. However, the extent and involvement of these integrins in the migration

through the conjugated and unconjugated collagen gels was not investigated here and

could be the subject of future work. It should be pointed out that, the involvement of

multiple integrins could activate multiple signaling pathways affecting the motile

processes of the cell and thus could be potentially responsible for some of the motile

behavior observed in this study compared to others.

In contrast to a biphasic dependence for cell speed as a function of increasing cell-

substratum adhesiveness as reported for several two-dimensional migration studies[6, 8,

9, 10, 79], our studies suggest the migration of melanoma cells within collagen gels was a

monotonically decreasing function of increasing adhesiveness. Possible reasons for such

discrepancies reported between this study and others previously referred to could be

attributed to the different cell types used between these studies. Other significant

differences between these studies and the current one should also be mentioned.

Melanoma cells form strong stable adhesions to the collagen fibrils as exhibited by the

high degree of spreading and asymmetry. Further illustrating this, recently Friedl et al.

observed that for MV3 melanoma cells migrating within Type I collagen matrices a

substantial fraction of the a2 and p1i-integrins were released at the site of detachment

remaining associated with the substratum, correlating to a high cell-substratum

adhesiveness[35]. The grafting of additional adhesive RGD peptides to the collagen

fibrils is expected to further amplify the adhesiveness of the collagen substratum, thus

resulting in a limited range of adhesiveness we could explore. Consequently, the least

adhesive collagen matrices (unconjugated collagen) could compare to a substantially high

degree of adhesiveness compared to other studies and therefore result in a position on the

predicted biphasic cell speed diagram[8] beyond the maximal cell speed at which point

cell speed then becomes a decreasing function of increasing adhesiveness. Another

possible explanation for these differences could be that for a given level of adhesiveness,

the total effective adhesion a cell experiences within a three-dimensional matrix, coupled

with the biomechanical resistance of the fibril network imposed on the cell itself is

considerably greater than for two-dimensional substratum. Thus, points of lower

substratum adhesiveness could be functionally shifted to the right along on the biphasic

curve, resulting in consistent trends as seen in previous two-dimensional studies.

Cell persistence time and persistence length did exhibit a biphasic dependence on

increasing cell-substratum adhesion, suggesting cells migrated over longer distances

without significant directional changes at intermediate adhesiveness. Although most

previous studies for two-dimensional migration have reported instead a biphasic

dependence of cell speed as a function of cell-substratum adhesiveness, it is worth noting

Bergman and Zygourakis[80] recently observed that with increasing concentrations of

surfaces coated with fibronectin, using a lymphocyte cell line, enhanced cell migration

was correlated to increased persistence time with no significant changes in cell speed.

Friedl et al. reported that migration of MV3 melanoma cell migration within collagen

matrices resulted in a characteristic reorganization of the surrounding collagen matrix,

leading to the alignment of collagen fibers at binding sites, resulting in a contact

guidance-like mechanism[35]. As a result, cells migrated along a pre-existing pathway

with a high directional persistence. Another possibility is that increasing cell-substratum

adhesiveness resulted in the cell becoming hyper-adherent to the substrate with

competing psuedopods in multiple directions resulting in decreased persistence time.

The mathematical modeling of the cell by discretely modeling the extension and

retraction ofpseudopods in an adhesive gradient proved to be a tool for predicting the

biased behavior of cell migration. The model predicted that the biphasic dependence of

cell migration in three dimensions is related to the biphasic dependence of cell

persistence on cell-substratum adhesiveness. Additionally, it agreed quantitatively with

experiments in determining the magnitude of gradient steepness necessary to produce a

biased migration.

This study shows that cells can exhibit a biased response to a gradient of adhesion

bound ligands, that is, undergo haptotaxis. This study agrees with others in that it does

show a directed migration of cells toward higher adhesive strength. However, this study

is novel in that the migration of multiple individual cells was directly observed to allow

the calculation of individual cell speed, persistence and directional bias. This data was

also compared to a mechanistic model that predicted biased cell migration. This allowed

for a better elucidation of the possible mechanism underlying haptotaxis. The biased

resulted mainly from a preferential turning in the gradient direction, a result that is

consistent with the mode of topotaxis and the hypothesis put forth by Harris in 1973.


These results confirm that GRGDSPC peptide is covalently linked to both BSA

and collagen monomer and that the basic properties of collagen are not significantly

modified by this conjugation. They also show that the adhesive properties of both BSA

and collagen can be modified by this covalent linkage to provide a more adhesive

substrate. Data indicate that cell migration is modally dependent on the substratum

adhesiveness with a maximum migration at intermediate adhesiveness. This result is

similar to results presented for two-dimensional migration, however, our data indicated

that three dimensional migration is governed by a different mechanism than three

dimensional migration. Preliminary data also show that a biased migration can be

achieved by forming spatial gradients of substratum bound adhesion ligands (a direct

observation that haptotaxis exists). Additionally, the qualitative trend predictions from

the model correspond to the quantitative experimental data.

The modified adhesiveness of collagen due to grafting with GRGDSPC peptides

taken together with data showing its influence on cell motility suggest a potential strategy

for the use of covalently modified collagen or other biomaterials for the controlled

localization or redistribution of cells.



9-1 Conjugation to Alternative Matrices

Since collagen itself is adhesive to cells, the ability of the amplified adhesive

signal to stimulate biased migration may be dampened by this background signal.

Additional experiments should be completed where the adhesion ligands are grafted to a

naturally nonadhesive but still biologically relevant substrate. Agarose and poly-vinyl

alcohol (PVA) are both used in biomedical applications and are both nonadhesive to

cells. Both polymers also possess porous structures which would support the three

dimensional migration of cells. Agarose has been previously derivatized to a laminin

oligopeptide to promote cell adhesion and invasion[81 ]. PVA has also bee previously

photo-derivatized to RGD peptides to promote cell adhesion[82]. Although this has been

done previously, attempts to promote K1735 murine melanoma cell adhesion on both

agarose and PVA by derivatization with RGD peptides proved unsuccessful due to

limited knowledge of hydrogel matrices and casting protocols.

Agarose gels were derivatized with 1,1 carbonyldiimidazole (CDI) following the

procedure described by Bonzon et al[81 I]. Three to four milliliter gel blocks of 1%

agarose were dehydrated by repeated washes in acetone followed by dry acetone. A CDI

solution prepared in dry acetone (150 mg/25 ml) was added to the acetone washed gels (5

ml/3 g gel block). The activation reaction was allowed to proceed for 9 minutes with

gentle agitation. Gels were then washed 5 times with dry acetone for 6 minutes per wash

to remove unbound CDI. The activated gels were them exposed to RGD peptide

dissolved in 100 mM sodium bicarbonate buffer solution at pH 8.5 at a concentration of

0.6 mg/ml. The peptide coupling reaction was allowed to proceed for 36 hours under

gentle agitation. The gels were then washed thoroughly with PBS for 48 hours, further

quenched in sodium bicarbonate for 2 hours, dried and re-dissolved to the desired gel

concentration of 1%. Bonzon et al. showed that neurites cultured on grafted-agarose gels

exhibited enhanced neurite extension compared to those on plain agarose gels. However,

K1735 murine melanoma cells were not found to adhere to plain agarose or to grafted-

agarose gels.

PVA was cross-linked to RGD peptides via a heterobifuntional cross-linker, PDP-

hydrazide. Labelling solution was made of 0.1 M sodium acetate buffer at pH 5.5. One

ml of labelling solution was added to 2 ml of a 1% PVA gel solution. Cold sodium meta-

periodate solution (0.3 ml of a 100 mM solution) was added to the PVA solution. The

oxidation reaction was allowed to proceed for 20 minutes at OC in the dark. To stop the

oxidation, 4.5 ul of glycerol were added and the mixture was incubated for 5 minutes at

OC. To remove excess iodizer the sample was separated on a 5 ml desalting column

(Sephadex G-25 Superfine) and eluted with labelling solution. The fractions containing

the PVA were pooled and concentrated. PDP-hydrazide was added to the desalted

sample to a final concentration of 5 mM and allowed to react with agitation for 2 hours at

room temperature in the dark. To remove excess cross-linker, the sample was again

applied to a desalting column and eluted with PBS buffer. The fractions containing PVA

were pooled and concentrated to 1.0 ml. RGD (3 mg) was added to the concentrate and

incubated overnight at room temperature. This mixture was separated by size exclusion

chromatography on Sephadex G-200 column eluted with PBS. The fractions containing

the conjugate were pooled and concentrated. K1735 murine melanoma cells were not

found to adhere to plain PVA or to grafted-PVA gels.

The expansion to alternative matrices would also allow for the testing of

medically relevant device applications. One such application could be the directed

reseeding of vascular grafts with endothelial cells.

9-2 Additional Gradient Work

The work up to now on spatially controlled gradients of adhesiveness has been

limited to linear steepnesses of various RGD-grafted collagens. Additional work needs to

be done to include more gradient steepnesses and perhaps concave, convex or

exponential gradients. Parallel experiments with an additional adhesion ligands such as

RGDT or YGIRS would also complement the work to date.

9-3 Study of Integrin Specificity

To more completely analyze the mechanisms involved in the adhesion-mediated

migration of cells an integrin specificity test should be done. The collagen gels could be

supplemented with antibodies specific for various integrin complexes or integrin subunits

to block their activity in the adhesion process. Therefore, the individual or group of

integrins involved could be isolated. This would aid in the determination of whether the

process is driven by different integrins than normal adhesion to collagen or whether it is

an additive effect of multiple integrins acting synergistically. The extent of each

integrins contribution to the overall motility of the cell could be gained by such


9-4 Cellular Labeling

It would be interesting to pursue the labeling of the intracellular components of the

actin myosin network, which form the contractile protein network and produce the

cellular motile force. In studies such as this markers could be injected to allow for the

visualization of the network and determine more readily some of the factors limiting the

network's polymerization and their effect on the cell motility.

9-5 Cellular Force Measurements

In combination with the total internal reflection microscope and three dimensional

optical trap, it would be interesting to determine the force a psuedopod can exert on the

environment. Additionally, it might be possible to study individual receptor ligand bond


9-6 Expansion of Modeling

In this work, the mathematical model allowed for pseudopod extension in only the x

and y directions. Future work should include expansion of the model to allow for

simultaneous pseudopod extension in all directions.


This appendix contains the image analysis and programs used to obtain cell count

data for adhesion experiments.

Following are the programs described above. They are written in the Analytical

Language for Images (ALI), which is used by the image analysis program, Optimas.

// Program Name Adhes.mac

RunMacro("C:/burgess/bcomm 1 .mac");
RunMacro ("C:/burgess/macros/bscini2.mac");
RunMacro ("C :/burgess/macros/bscinic.mac");
hLib = LoadMacroLibrary("surface.oml");

ymid=(m[l ]-m[3]);show(ymid);
show(xdist=abs(m[2] m[0]));
show(ydist=abs(m[3]-m[ 1l]));
freezeo;Delayms(1 000);
Th = SetArThresh(NGrid, 1);

Show("go to far left comer to start and press enter");

freezeo;delayms( 1500);
xdist= abs(roi[0] -roi[2]);
ydist=abs(m[ I ]-m[3]);show(xdist);show(ydist);
Show("The area of the ROI is ":totext(area):" microns squared");

/* Start Here to Restart Program */

//Integer Count(ij);
while (j {

While (i { delayms(1500);
//show("Now refocus and push enter when ready");
INTEGER iLumGrid=GetLuminanceGrid(ROI, NGrid);
ApplyLuminanceGrid( ROI, iLumGrid,
ArithmeticOp ("Subtract", "BUFFER");
SetExport(ArCentroid, 1, TRUE);
SetExport(PtPoints, 1, TRUE);
AutoExtract = TRUE;delayms(100);
m=CreateArea(, FALSE, TRUE);
// Count(i,j)=m;


row=row+ 1;
sheet="sheet 1";
spacing="R":totext(row): "C2";
hchan= DDEInitiate("Excel",sheet);
hchan2= DDEInitiate("Excel",sheet);
DDEPoke(hchan,spacing ,x);

if (j==4)



This appendix contains the image analysis programs used to obtain cell path data

in cell migration experiments.

Following are the programs described above. They are written in the Analytical

Language for Images (ALI), which is used by the image analysis program, Optimas.

//File Name: Bscan2.mac

/*This macro is designed to scan any number of fields in 3-D and store the positions in an
excel file.
Brian Burgess Original Version: Feb 1996 */

hLib = LoadMacroLibrary'("surface.oml");
R=2;C=2; k=c; //represent row 1 and column I for sheet 1;
q=l;j=l; //represents row 1 and column 1 for sheet 2;
RunMacro ("C:/burgess/macros/bcomml.mac");
RunMacro ("C:/burgess/macros/bscini2.mac");
RunMacro ("C:/burgess/macros/bscinic.mac");
//RunMacro ("C:/optimas/macros/rich/comml.mac");



/*Cells is equal to the number of fields to scan*/

objective=Prompt("Which Objective Lens are You Using? 20 or 40?" integerER");
if (objective==20)
calibrate(cal20x); }

show("The select full screen command holds the values ":totext(roijj[0]),"
":totext(roijj [1 ])," ":totext(roijj [2])," ":totext(roijj [3]));

show("Move to test cell and hit ok");
Focus(l); Fwaito;


Th = SetArThresh(NGrid,l );

/*Send some general info about program to excell spreadsheet*/

Message="This is data Stored From Running C:/Burgess/Macros/BSCAN2";
sheet="sheet ";
hchan= DDEInitiate("Excel",sheet);
spacing ="RlC4:R I C8";
spacing2="RIC9:R1C25"; // r is the row for the different time step;
k=cell/column number
DDEPoke(hchan, spacing 1 ,gotime);

/* End general info */

/* Restart Here if Cell Positioning is Necessary */

CELLS=Prompt("How many Cells to Scan", "INTEGER");


/*Now I will Find the Fields Manually */
show(" Move to reference object");
Focus(3); FwaitO;
if (itest[0]=-0)
{ Acquire();
Show("Pick a New Reference Point. This one will not work. Hit Enter when
Found New Ref.");

starttime = dostimeO; //the first time increment will be off3 but thereafter
it should be fine
LONG time=dostimeo-starttime;


pos=FindingCells(cells); //show(pos);
R=R+ 1 ;k=c; //written all
positions,now move down a row

/*Now all initial positions are stored in an array*/
/*Stored Initial Positions in excel file*/
/* Restart Here if Cell Positioning is Unnecessary */

/*Redefine the Clock Timer so Do not Lose Time While Setting Up Cells in Fields*/
LONG time=dostime()-starttime;
/*Reposition routine*/
LONG timmax =72000L; show(time,timmax);show(starttime);
While (time { //movabs(0,0,0);here(0,0,0);
Acquireo;delayms(400); //was 1000

while (i<(CELLS))
// if(i/2*2==i)
// { Recenter(Th,ROIJJ,NGrid); } //recenters everyother cell
cfstep(1 00);
ny=pos[i, l];
nf=- pos[i,2];
movabs(nx,ny,nf); //absolute move
Wait(); FwaitO; //waits for motors to


// Focus(3);
// Fwait0;

if (itest[0]==0)

to original value for program



//change back on cfstep


if (itest[0]>0)
{ goto


if (itest[0]==0)


hchan= DDEInitiate("Excel",sheet);

/* sheet="sheet2";


spacing 1 ="R" :totext(q+2):"C" :totext(j);

spacing2="R":totext(q+2): "C ":totext(j+ I): ":R":totext(q+2): "C":totext(j+3);

spacing3="R":totext(q+2): "C":totext(j+2):":R":totext(q+2): "C":totext(j+4);
time=dostime0 -
DDEPoke(hchan,spacing 1,time);
DDEPoke(hchan,spacing2,"Cell ":totext(i+l));

*/ q=q+l;
goto LOST;
if (itest[0]>0)
ymid=(ROIJJ[ 1 ]-ROIJJ[3 ])/2;
CreatePoints(xymid=xmid:ymid); //
// show(marcentroid);
Real diff[itest[0],2];
//diff=xymid-marcentroid; //show(diff[,0]);
dist=difft,0]*diff[,0]+diff[, 1 ]*diffl, 1 ];
// can return value to spreadsheet as dist. traveled;
ii=0; lmin=TRUE;
while (Imin)
// NewCent=mArCentroid[ii- 1l,]; //show(newcent);
// CreatePoints(NewCent);

LONG mdist[2];
mdist[0]=l L*(10.*diff[ii-1,0]+.5); //
MovRel(mdist[0],mdist[ 1 ],0);
Wait(); Fwaito;
pos[i, ]=findposo;
//redefines the xyz pos coordinates
time=dostimeo starttime;


if( i==41) //this loop resets the column for sheet 2 back to 2nd column
for the 42nd cell which is on sheet 2
k=2; //this loop resets the column for
sheet 3 back to 2nd column for the 81nd cell which is on sheet 2
coordXYZ(pos,time,message,i,k); //writes the xyz pos to
spreadsheet w/ time increment
R=R+1 ;k=c;

//Warning Signal Program is Finished, Twinkle Twinkle Little Star!!!
while (t<2)
Beep(40,4); Beep(40,4); Beep(47,4); Beep(47,4); Beep(49,4); Beep(49,4);
Beep(47,2); delayms(200); Beep(45,4); Beep(45,4); Beep(44,4); Beep(44,4);
Beep(42,4); Beep(40,2);delayms( 100);
t=t+ 1;


This appendix contains the Matlab programs used to simulate cell paths from the

mechanistic model of adhesion mediated cell migration.

% Program Name: runh.m

clear all

nt=5000; % number of time increments
nplot=5; % number of time increments to skip before plotting
nrun=6; % number of conditions
nc=5; % number of cells/condition

par=[1 2.5.001 0 10];
bias0=0.05; dbias=.01;

% Parameters
% par(1l)=eta, par(2)=delta, par(3)=alpha, par(4)=mu,par(5)=a0
% 1: eta: Unstressed reverse rate constant = kr0*beta/Fc
% 2: Delta: matrix elasticity = NO*delta/Fc
% 3: alpha: Stress sensitivity of bond = gamma*Fc*LO/kT/NO
% 4: Mu: matrix viscosity = NO*mu*beta/LO0
% 5: aO: dimensionless ligand concentration = kf*A/kr0
% kr0 = unstressed reverse rate constant
% beta = drag coefficient
% Fc = contraction force per unit length
% gamma = bond sensitivity to stress
% NO = # receptors per pseudopod
% LO = initial pseudopod length
% kT = thermal temp (Boltzmann's constant X temp)
% kf = forward rate constant
% A = ligand density
% delta = matrix elasticity
% mu = matrix viscosity

trdat=[]; ddat=[]; uudat=[]; stdat=[]; rrt=[]; gvdat=[];

for ir=l:nrun
xxt=[]; yyt=[];
for ic=1 :nc
[tt, thavv,sthav,d2,rr,uu]=hapto(par,bias,nt,nplot,bopt);

% tt: vector of time steps
% thavv: average orientation
% sthav: standard deviation of orientation
% d2: vector of all increments
%rr: path

if (ir*ic==l)
ddat=[ddat,d2']; % Tack on matrices
xxt=[xxt,rr(1l,:)']; yyt=[yyt,rr(2,:)'];
if (ir*ic==l)
sz=size(uu); nt=sz(2);
for i=0:nav-1;
gv(l,i+ 1) = uu(, I:nt-i)*uu(,1 +i:nt)'/(nt-i);
gv(2,i+l) = uu(2,1:nt-i)*uu(2,1+i:nt)'/(nt-i);

hold off;
plot(xxt,yyt,'o'); axis([-10 10-10 10]);
hold off


'dd2.dat' ddat -ascii -tabs
'tr.dat' trdat -ascii -tabs
'st.dat' stdat -ascii -tabs
'uudat.dat' uudat -ascii -tabs
'gvdat.dat' gvdat -ascii -tabs

% Program Name: hapto.m

function [tt, thavv,sthav,d2,rr,uu] = hapto(par,grad,nt,nplot,bopt)


lm=12.; sn = .5 ; sig=.5 ; om0=10 ; a=.25; % Pseudopod Parameters
test= 1 e5

% Note: probability per unit time of extending a new pseudopod
% is om0*exp(sn*(lm-ltot)) where Itot is total length
% of the existing pseudopods
% The direction of the new extension is normally distributed
% around the current velocity direction.

% im: most probable total length of all pseudopods
% sn: sensitive of extension to length
% sig: variance in direction of new pseudopod
% omO: frequency of extension
%a: cell radius

% Simulation Parameters ******************************
dt=2e-2 ; nm= 1000; nl=0; u=zeros(2, 1);
ninterp=50; nintx=bopt* 10+2; axlim=l0; xmax=50;

% nt: number of time steps
% dt: time increment
% nm: maximum number of pseudopods over simulation
% nl: current number of pseudopods
% ux: current x-velocity
% uy: current y-velocity
% nplot: number of time point to skip between plottin pts.
% nav: number of time intervals in calculating statistics
% ninterp: number of points on cell circumference to plot
% xmax: range of x values
%/ **************************+*******************************

% Variables
l=zeros(l,nm); phi=zeros(l,nm); theta=rand(l)*2*pi-pi; u=0.;
r=zeros(2,1); thav=zeros(1 ,nt); theta=0;

% 1: vector of pseudopod lengths
% phi: vector of pseudopod angles
% theta: orientation of cell
% u: cell speed
% x: x-position y: y-position
% thav: running average of cos(theta)

% Plot parameters
% plot(0,0,'.');
sc=.3; sp = .08; fopt=l;
lim=[-axlim axlim -axlim axlim];
% lim: axis limits
% sc: length of velocity vector for plotting
% sp: width of protrusion for plotting

% Interpolation Data
% This section calculates a data set for retraction velocity as
% a function of orientation angle for subsequent interpolation
% in the simulation routine

del0=par(2); mu0=par(4);
rint=(0*th'*xint)'; sizerint=size(rint); sizeth=size(th);
rint0=pseud(par); temp=l :ninterp+l;
for ii=l:nintx+l
for jj=l :ninterp+l
par(5)=max(.001 ,c0+grad*(xint(ii)+cos(th(jj))));
%Hapto w/ varying ligand conc. as cell moves
% par(5)=max(.001,c0+grad*(cos(th(jj))));
%Hapto w/o varying ligand conc. as cell moves
% par(5)=max(.001,c0+grad*(xint(ii)));
%Hapto w/o varying ligand conc. with orientation

[ii xint(ii) par(5)]

% Calculate Mean velocity
vmd= 1.+grad/c0*cos(th);
vmd0=l .+0*th;
% plot(th,rint(nintx/2,:)/rint0,th,vmd); drawnow; lim=[-pi pi 0 2]; axis(lim); pause;
hold off;



for i=l :nt % Begin Simulation

% Plot Current configuration at every nplot time increments
px=fopt*r( 1l)+l.*cos(phi);
fun=(a+(l(jIj)-a)*exp((cos(phi(jj)-th)-l 1)/spA2));
ff= [ff;fun];
pfx=fopt*r( 1 )+max(ff).*cos(th);

fopt*r( 1 )+sc*u( 1)], [fopt*r(2) fopt*r(2)+sc*u(2)],'m-',pfx,pfyw-')
hold on;
axis(lim); title('Bias'); drawnow

% Find new velocity, u, and orientation, theta
s=0. ; u=zeros(2,1); rt=zeros(1l,nl);
% keep angles between -pi and pi
while (phi(jj)>pi) % keep angles between -pi and pi
while (phi(jj)<-pi)
rt(jj)=interp2(xint,th',rint',r( 1 ),phi(jj));
%determine new retraction velocity
suml=suml+l(jj); % running sum of total length ofpseudopods

theta=--atan2(u(2),u(l1)); % Find new direction of velocity
thav(i)=sumlt/suml; % Find mean of cos2(theta)
s=sqrt(u'*u); % Find speed

% Update
phi(jj)= phi(jj)-s/l(jj)*sin(theta-phi(jj))*dt;
nr=nr+ 1;

% resort
lt=zeros(l ,nl-nr);
phit=zeros( 1 ,nl-nr);
if (nstop(jj)-=I);

% New protrusion
% om=om0*exp(sn*(lm-ltot)); % Probability per unit time of new protrusion
om=om0*(1 -ltot/lm);
if Randd( 1 ) nl=nl+ 1;
phi(nl) = sig*randn(1 )+theta; % New orientation wrapped normal distribution
l(nl)=l.; % New length = 1



for i=l :nav;
sumr=zeros(2, 1);
sumr( 1 )=sumr(l )+(rr(l ,i+jj)-rr( 1 jj))^2;
ct=ct+ 1;

sthav= 1 -thavv;


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