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We have recently reported that glycation can be exploited to increase the circumferential tensile stiffness and ultimate tensile strength of media-equivalents (MEs) and increase their resistance to collagenolytic degradation, all without loss of cell viability (Girton et al., 1999). The glycated MEs were fabricated by entrapping high passage adult rat aorta SMCs in collagen gel made from pepsin-digested bovine dermal collagen, and incubated for up to 10 weeks in complete medium with 30 mM ribose added. We report here on experiments showing that ME compaction due to traction exerted by the SMCs with consequent alignment of collagen fibrils was necessary to realize the glycation-mediated stiffening and strengthening, but that synthesis of extracellular matrix constituents by these cells likely contributed little, even when 50 [micro]g/ml ascorbate was added to the medium. These glycated MEs exhibited a compliance similar to arteries, but possessed less tensile strength and much less burst strength. MEs fabricated with low rather than high passage adult rat aorta SMCs possessed almost ten times greater tensile strength, suggesting that alternative SMCs sources and biopolymer gels may yield sufficient strength by compositional remodeling prior to implantation in addition to the structural remodeling (i. e., circumferential alignment) already obtained. [S0148-0731(00)00203-X] Keywords: Media-Equivalent, Tissue-Equivalent, Tissue Engineering, Bioartificial Artery, Glycation, Smooth Muscle Cell Collagen

Rat dermal fibroblasts were dispersed initially in the outer shell of a fibrin gel sphere, while the inner core either was devoid of cells or contained peritoneal exudate cells (primarily macrophages), thereby mimicking the inflammatory phase of wound healing. The fibroblasts compacted floating fibrin microspheres over time. In the absence of macrophages, the initial distribution of fibroblasts (only in the shell) induced circumferential alignment of fibrin fibrils via compaction of the shell relative to the core. The aligned fibrils created a contact guidance field, which was manifested by strong circumferential alignment of the fibroblasts. However, in the presence of macrophages, the fibroblasts exhibited more radial alignment despite the simultaneous contact guidance field in the circumferential direction associated with compaction. This was attributed to a chemotactic gradient emanating from the core due to a putative factor(s) released by the macrophages. The presence of a radial chemotactic stimulus was supported by the finding of even greater radial alignment when fibrin microspheres were embedded in an agarose–fibrin gel that abolished compaction and consequently the contact guidance field. Our assay permits the simulation of tissue morphogenetic processes that involve cell guidance phenomena and tractional restructuring of the extracellular matrix. [Copyright &y& Elsevier]

A tissue growth and development process occurred in neonatal SMC-fibrin gel constructs when cultured in DMEM supplemented with TGF-beta1 and insulin over a 5 week period. These constructs may thus serve as the basis for cardiovascular tissue replacements and future models of cardiovascular tissue growth, repair and regeneration. Following fibrin gel contraction during week 1, peak rates of SMC proliferation, collagen production and tropoelastin production occurred between weeks 1-4. Organized, cross-linked collagen and elastic fibers replaced the degrading fibrin over weeks 3-5 and were manifested as increased mechanical strength. The peak rate of SMC proliferation (weeks 1-2) preceded that for maximum collagen production (weeks 2-4), which was consistent with the 3 week time point of maximum expression of collagen type I and III from qRT-PCR. Insoluble elastin quantification revealed that the majority of elastic fibers were produced by week 4, which was also consistent with the qRT-PCR data showing a dramatic down-regulation of tropoelastin expression by week 4, indicating elastogenesis occurred during the early stages of tissue growth and development. There was a strong up-regulation of lysyl oxidase expression during weeks 1-3 with a peak in expression at week 3, correlating with the phases of collagen and tropoelastin production. An increase in MMP-2 expression over weeks 1-5 suggested an increase in ECM remodeling as the tissue developed. Mechanical strength doubled over weeks 4-5 when production of collagen and elastic fibers and expression of lysyl oxidase were subsiding. This may have been due in part to the more organized collagen fibrils evident from the histological sections in weeks 3-5.

The aim of this study was to better understand how to increase collagen content in and enhance mechanical properties of tissue-equivalents formed by entrapping tissue cells in fibrin gels, with the ultimate goal of developing mechanically robust artificial tissues. The two main areas of focus were cell culture medium composition and replacement frequency relative to a base case of incubating constructs in medium supplemented with just serum and replaced weekly. The optimal condition involved a combination of all three factors investigated-TGF-beta, insulin, plasmin-with medium replacement three times a week. Compared to a base case without these three factors, the combination case resulted in 20 times more collagen and a ten-fold increase in tensile strength. The high strain modulus and tensile strength were within an order of magnitude of cardiovascular tissues. This study indicates great potential for fibrin-based tissue-equivalents in soft connective tissue applications.

A methodology for generating polarized light retardation and alignment direction images is presented. A rotated quarter-wave plate changes the linear polarized light to a polarized probe with various degrees of ellipticity by which samples are imaged with the use of a circular analyzer. A harmonic representation of image intensity allows simple analysis, requiring only simple image operations and realizing four orders-of-magnitude computational savings for strongly aligned tissues, where linear birefringence is the dominant optical property. The method is demonstrated for a porcine heart valve leaflet.

An automated method for generating a fiber alignment map in tissues, tissue-equivalents, and other fibrillar materials exhibiting linear and circular optical properties and scattering is presented. This method consists of interrogating the sample with elliptically polarized light from a rotated quarter-wave plate and an effective circular analyzer, and implementing nonlinear regression techniques to estimate parameters defining the optical properties of the optic train and the sample. Thus, an account is made for imperfect and misaligned optic elements. The optic train was modeled using the Mueller matrix representation and the combined sample properties by an exponential matrix. Because a sample's Mueller matrix does not uniquely determine the linear, circular, or scattering properties, the circular properties and effective scattering are estimated for a matched isotropic sample to determine and correct for the linear birefringence of an aligned sample. The method's utility is demonstrated by generating an alignment map of an arterial media-equivalent, a relevant test case because of its circumferential alignment and thus showing the method's sample orientation independence.

The dose-response effects of platelet-derived growth factor BB (PDGF-BB) on rat dermal fibroblast (RDF) behavior in mechanically stressed and unstressed type I collagen and fibrin were investigated using quantitative assays developed in our laboratory. In chemotaxis experiments, RDFs responded optimally (P < 0.05) to a gradient of 10 ng/ml PDGF-BB in both collagen and fibrin. In separate experiments, the migration of RDFs and the traction exerted by RDFs in the presence of PDGF-BB (0, 0.1, 1, 10, or 100 ng/ml) were assessed simultaneously in the presence or absence of stress. RDF migration increased significantly (P < 0.05) at doses of 10 and 100 ng/ml PDGF-BB in collagen and fibrin in the presence and absence of stress. In contrast, the effects of PDGF-BB on RDF traction depended on the gel type and stress state. PDGF-BB decreased fibroblast traction in stressed collagen, but increased traction in unstressed collagen (P < 0.05). No statistical conclusion could be inferred for stressed fibrin, but increasing PDGF-BB decreased traction in unstressed fibrin (P < 0.05). These results demonstrate the complex response of fibroblasts to environmental cues and suggest that mechanical resistance to compaction may be a crucial element in dictating fibroblast behavior., (Copyright 2001 Academic Press.)

During wound healing, both chemotaxis and contact guidance can contribute to the migration of blood and tissue cells to the wound. In order to understand the wound healing process, we must thus understand how cells respond to both these simultaneous directional cues, which are not necessarily coaligned. Although chemotaxis and contact guidance have been studied individually, the interaction between them has not been addressed. We extend a stochastic cell movement model, developed by Dickinson and Tranquillo (1995) [6] for individual cues, for simultaneous chemotaxis and contact guidance by a two-parameter perturbation analysis in terms of the two associated cues, a chemotactic factor gradient and aligned tissue fibers. We present results from analysis of the first-order perturbation, which includes the cell flux expression heuristically proposed by others, but reveals paradoxical results for other indices of cell movement, such as the mean-squared displacement. We then present second-order perturbation results that resolve these paradoxical results. Finally, we relate these results to a continuum mechanical model developed by Barocas and Tranquillo (1997) [3] that predicts fiber alignment due to cell traction induced tissue contraction.

Bioresorbable collagen nerve guides filled with either magnetically aligned type I collagen gel or control collagen gel were implanted into 4- or 6-mm surgical gaps created in the sciatic nerve of mice and explanted 30 and 60 days postoperation (dpo) for histological and immunohistochemical evaluation. The hypothesis was that contact guidance of regenerating axons and/or invading nonneuronal cells to the longitudinally aligned collagen fibrils would improve nerve regeneration. The criterion for regeneration was observation of regenerating myelinated fibers distal to the nerve guide. Consistent with previous studies showing poor regeneration in 6-mm gaps at 60 dpo with entubulation repair, only one of six mice exhibited regeneration with control collagen gel. In contrast, four of four mice exhibited regeneration with magnetically aligned collagen gel, including the appearance of nerve fascicle formation. The numbers of myelinated fibers were less than the uninjured nerve in all groups, however, which may have been due to rapid resorption of the nerve guides. An attempt to increase the stability of the collagen gel, and thereby the directional information presented by the aligned collagen fibrils, by crosslinking the collagen with ribose before implantation proved detrimental for regeneration., (Copyright 1999 Academic Press.)

High-strength magnetic fields were used to align collagen gel formed into 4-mm-diameter rods during the self-assembly of type I collagen monomers into fibrils. We developed an in vitro assay to study neurite elongation into the magnetically aligned collagen gel rods from dorsal root ganglia (DRG) explants placed onto one end of the rods. The depth of neurite elongation from chick embryo DRG neurons into these rods was found to be substantially greater than that observed in controls and increased with an increase in magnetic field strength, as did the collagen gel rod birefringence, indicative of collagen fibril alignment along the rod axis. Moreover, the axial bias of neurite elongation became more pronounced with an increase in magnetic field strength, presumably due to a contact guidance response of growth cones at the neurite tips. Coinvasion of Schwann cells from neonatal rat DRG was also studied in these assays using double immunolabeling. In the absence of serum, Schwann cells were highly associated with, and often trailed, elongating neurites. In the presence of serum, Schwann cells showed significantly higher rates of invasion and formed axially aligned chords reminiscent of bands of Büngner. These results may translate into an improved method of entubulation repair of transected peripheral nerves by directing and stimulating axonal growth through a tube filled with magnetically aligned collagen gel., (Copyright 1999 Academic Press.)

Fibroblast chemotaxis is implicated in many physiological processes, including wound healing and morphogenesis. We present a novel assay for chemotaxis of fibroblasts (and other slow-moving tissue cells) in a direct-viewing chamber containing a physiologically relevant three-dimensional fibrin or collagen gel in which long-lasting, spatially continuous gradients have been sustained for at least 24 h, long enough for significant fibroblast migration. This combination of features is not available in any alternative assay of comparable setup simplicity. Using a putative fibroblast chemotactic factor, the fibronectin peptide GRGDSP, we measured human foreskin fibroblast alignment in the direction along the gradient, which followed a biphasic dependence on GRGDSP concentration with an optimal concentration of about 10 nM. Time-lapse video microscopy revealed that cell migration was up the soluble GRGDSP gradient, confirming positive chemotaxis to GRGDSP and rejecting the possibility of dominant haptotaxis down the soluble GRGDSP gradient, that is, up a putative gradient of integrin-mediated adhesion induced by the soluble GRGDSP gradient., (Copyright 1999 Academic Press.)

The use of reconstituted type I collagen gel as a scaffold for engineered soft tissues is a highly attractive prospect, given that collagen is the principal component of the extracellular matrix (ECM) in vivo, providing a mechanically suitable and information-rich scaffold for cell-ECM interactions. It has the advantage that cells can be directly entrapped within the comprising collagen fibrils as they grow into an entangled network from a cell containing solution of monomeric type I collagen. These tissue equivalents have the further advantage that the collagen fibrils can be aligned by applying a magnetic field during fibrillogenesis. Then, through a process termed "contact guidance," the cells align with the fibrils by directing their motility. Such alignment is characteristic of many tissues, and may provide microstructural and mechanical cues for regulation of cell phenotype and function, as well as influence the gross mechanical properties of the tissues. Recent research in our laboratory has used magnetic-induced alignment in the fabrication of tissue-equivalents, notably circumferential alignment in tubes, and longitudinal alignment in rods (patent pending). The former is aimed at reproducing the architecture of the arterial media; the latter is aimed at providing a bridge that promotes directed axonal growth between severed nerve ends. These tissue engineering applications exploit the finding of Torbet and Ronziere (1) in their cell-free studies that forming fibrils tend to align in the plane normal to the direction of the field (because of the negative diamagnetic anisotropy of collagen) and parallel to the mold surfaces (because of an uncharacterized interfacial effect).

The morphology and behaviour of tissue cells when surrounded by a network of protein fibres, such as for a tissue-equivalent comprising cells entrapped in a type I collagen gel, is distinct from that when cells are cultured on a rigid surface, and physiologically relevant. The highly elongated and apparently bipolar morphology leads to a 'reversing' type of cell movement in gels, as opposed to a directionally persistent movement characteristic of highly spread, polar cells on surfaces. However, the hallmark of a tissue-equivalent is consolidation of the fibrillar network, or gel compaction, resulting from traction exerted by the cells. When the gel is mechanically constrained from compacting, alignment of the fibrils occurs, inducing cell alignment through a contact guidance response. In order to understand this 'self-organization' of tissue-equivalents, some relevant structural and mechanical properties of collagen gel are considered first, followed by a review of seminal studies of cell traction and tissue-equivalent compaction. Random cell migration in an isotropic gel is then discussed, including a modification of the persistent random walk model used to analyse cell migration on surfaces, followed by a review of contact guidance studies in gels with fibrils having defined alignment. With this background, observations of self-organization of mechanically constrained compacting tissue-equivalents are summarized and explained using a mechanical theory that relates traction-induced compaction to fibre alignment and consequent contact guidance, i.e. a strain-based rather than stress-based cell response to gel compaction. Data in support of this theory obtained from studies involving the controlled applied compression of tissue-equivalents are then presented. Finally, possible mechanisms of contact guidance are discussed.

The proposed mathematical model investigates the simplified cytomechanics of cell shape change driven by stochastic stimulation from chemosensory receptors. The cytomechanical component of our model describes the dynamical distribution of F-actin and associated forces in an idealized cortical actin network around the cell periphery. The chemosensory component describes the distribution of chemotactic receptors in the cell membrane surrounding the cortex, where bound receptors give rise to an intracellular signal which modulates some property of the cortical network. As in our earlier models, an account is made for (1) the reactive, contractive properties of cortical actin, but here also for a stress induced by curvature of the cortex-membrane complex which carries an effective surface tension, and (2) statistical fluctuations in receptor binding, but generalized here to include statistical fluctuations in the spatial distribution of receptors, entirely determined by the additional prescription of membrane diffusion coefficients along with total receptor number, receptor binding rate constants and the local concentration field of chemotactic factor. We simplify the analysis by restricting the model to a prototype in which viscous stresses in the cortical network are negligible and the radial extension of the cell cortex is a prescribed function of the cortical actin concentration. We assume in particular that the assembly rate of cortical actin depends on the local density of bound receptors. These assumptions lead to a 4th-order parabolic differential equation on the unit circle coupled to a system of stochastic differential equations. We characterize via bifurcation analysis, stochastic simulations, and analytical correlation functions the spatial-temporal pattern of cell morphology under the influence of fluctuations in the bound receptor distribution for the case of a uniform concentration field of chemotactic factor. In addition to addressing the biological significance of our model, we remark on its relevance to the generic problem of the influence of correlated stochastic perturbations on spatial patterns in morphogenetic media.

The signal that governs the chemotactic response of mammalian white blood cells and tissue cells arises from membrane-localized binding events involving chemotactic factor ligands and receptors and G proteins. Fluctuations in this signal have been traditionally attributed to significant "noise" in receptor-ligand binding owing to a limited number of receptors. This paper examines the validity and consequences of a new hypothesis which states that the noise could be associated with a limited number of G proteins as well as receptors. This work characterizes via stochastic analysis and simulation the effects of the relative sizes of G protein and receptor populations on the variance of fluctuations of receptor states and consequently on the directional persistence behavior of cells in uniform chemotactic factor concentrations under the assumptions of the model used to link a G protein-mediated receptor signal to cell turning. Our results suggest that there may exist an optimal number of G proteins through which chemotactic receptors can signal that maximizes cell orientation accuracy in a chemotactic factor gradient.

Mammalian white blood cells are known to bias the direction of their movement along concentration gradients of specific chemical stimuli, a phenomenon called chemotaxis. Chemotaxis of leukocyte cells is central to the acute inflammatory response in living organisms and other critical physiological functions. On a molecular level, these cells sense the stimuli termed chemotactic factor (CF) through specific cell surface receptors that bind CF molecules. This triggers a complex signal transduction process involving intracellular biochemical pathways and biophysical events, eventually leading to the observable chemotactic response. Several investigators have shown theoretically that statistical fluctuations in receptor binding lead to "noisy" intracellular signals, which may explain the observed imperfect chemotactic response to a CF gradient. The most recent dynamic model (Tranquillo and Lauffenburger, J. Math. Biol. 25, 229-262. 1987) couples a scheme for intracellular signal transduction and cell motility response with fluctuations in receptor binding. However, this model employs several assumptions regarding receptor dynamics that are now known to be oversimplifications. We extend the earlier model by accounting for several known and speculated chemotactic receptor dynamics, namely, transient G-protein signaling, cytoskeletal association, and receptor internalization and recycling, including statistical fluctuations in the numbers of receptors among the various states. Published studies are used to estimate associated constants and ensure the predicted receptor distribution is accurate. Model analysis indicates that directional persistence in uniform CF concentrations is enhanced by increasing rate constants for receptor cytoskeletal inactivation, ternary complex dissociation, and binary complex dissociation, and by decreasing rate constants for receptor internalization and recycling. For most rate constants, we have detected an optimal range that maximizes orientation bias in CF gradients. We have also examined different desensitization and receptor recycling mechanisms that yield experimentally documented orientation behavior. These yield novel insights into the relationship between receptor dynamics and leukocyte chemosensory movement behavior.

We present here the first quantitative correlation for cell contact guidance in an oriented fibrillar network in terms of biased cell migration. The correlation is between the anisotropic cell diffusion parameter, DA = Dx/Dy, and the collagen gel birefringence, delta n, a measure of axially biased collagen fibril orientation in the x-direction. The cell diffusion coefficients, Dx and Dy, measure the dispersal of cells in the directions coincident with and normal to the axis of fibril orientation, respectively. Three essential methodological components are involved: (i) exploiting the orienting effect of a magnetic field on collagen fibrils during fibrillogenesis to systematically prepare uniform axially oriented collagen gels; (ii) using a microscope/image analysis workstation with precise, computer-controlled rotating and translating stages to automate birefringence measurement and, along with rapid "coarse optical sectioning" via digital image processing, to enable 3-D cell tracking of many cells in multiple samples simultaneously; and (iii) employing a rigorous statistical analysis of the cell tracks to estimate the magnitude and precision of the direction-dependent cell diffusion coefficients, Dx and Dy, that define DA. We find that this measure of biased migration in contact guidance (DA) increases with increasing collagen fibril orientation (delta n) due mainly to a rapid enhancement of migration along the axis of fibril orientation at low levels of fibril orientation, and to a continued suppression of migration normal to the axis of fibril orientation at high levels of fibril orientation.

An in vitro assay proposed to systematically characterize and compare cell invasion under different conditions is the collagen gel invasion assay where cells, initially seeded onto the surface of a type I collagen gel, penetrate the surface and migrate within the gel over time. Using simplifying assumptions about cell transport across the gel surface and migration within the gel, we formulate and solve a mathematical model of this assay which predicts the resulting cell distribution based on three phenomenological parameters characterizing the ability of cells to penetrate the gel surface interface, migrate randomly within the gel, and return to the gel surface. An index of cell invasiveness is defined based on these parameters that reflects the overall ability of cells to transport across the gel surface interface, that is, invade the gel. Cell concentration profiles predicted by the model correspond well to measured profiles for murine melanoma cells invading gels supplemented with extracellular matrix proteins fibronectin and type IV collagen as well as unsupplemented gels, allowing these parameters to be estimated by a nonlinear regression fit of the model solution to the measured profiles. Our analysis suggests that type IV collagen and fibronectin primarily modulate cell transport across the gel surface interface rather than migration within the gel. Further, we validate the key model assumptions and obtain independent, direct estimates of model parameters by time-lapse video microscopy and digital image analysis of cell penetration of the gel surface and migration within the gel during the assay.

The interplay between cellular, biochemical, and biomechanical phenomena which result in wound contraction is examined with the aid of a mathematical model. The model accounts for fibroblasts repopulating the wound extracellular matrix (ECM) by a combination of migration and proliferation and, in the course of exerting traction forces associated with their motility, their deformation of the local ECM, which has a viscoelastic character. A base model, which assumes that cell and tissue properties are the same irrespective of position with respect to the wound center, is found to be inconsistent with wound contraction. Extensions of the base model which account for the possible influence of a concentration gradient of an inflammation-derived mediator on the traction, growth, or chemotactic properties of the fibroblasts do predict the qualitative features of a contracting wound. In particular, the case where traction is prescribed to increase as fibroblasts approach the wound center is shown to obey the commonly observed exponential rate contraction law and to be largely consistent with the findings of McGrath and Simon (Plast. Reconstr. Surg. 72, 66, 1983) concerning the independence of the contraction rate constant and final extent of contraction from initial wound size and geometry.

The active migration of blood and tissue cells is important in a number of physiological processes including inflammation, wound healing, embryogenesis, and tumor cell metastasis. These cells move by transmitting cytoplasmic force through membrane receptors which are bound specifically to adhesion ligands in the surrounding substratum. Recently, much research has focused on the influence of the composition of extracellular matrix and the distribution of its components on the speed and direction of cell migration. It is commonly believed that the magnitude of the adhesion influences cell speed and/or random turning behavior, whereas a gradient of adhesion may bias the net direction of the cell movement, a phenomenon known as haptotaxis. The mechanisms underlying these responses are presently not understood. A stochastic model is presented to provide a mechanistic understanding of how the magnitude and distribution of adhesion ligands in the substratum influence cell movement. The receptor-mediated cell migration is modeled as an interrelation of random processes on distinct time scales. Adhesion receptors undergo rapid binding and transport, resulting in a stochastic spatial distribution of bound receptors fluctuating about some mean distribution. This results in a fluctuating spatio-temporal pattern of forces on the cell, which in turn affects the speed and turning behavior on a longer time scale. The model equations are a system of nonlinear stochastic differential equations (SDE's) which govern the time evolution of the spatial distribution of bound and free receptors, and the orientation and position of the cell. These SDE's are integrated numerically to simulate the behavior of the model cell on both a uniform substratum, and on a gradient of adhesion ligand concentration. Furthermore, analysis of the governing SDE system and corresponding Fokker-Planck equation (FPE) yields analytical expressions for indices which characterize cell movement on multiple time scales in terms of cell cytomechanical, morphological, and receptor binding and transport parameters. For a uniform adhesion ligand concentration, this analysis provides expressions for traditional cell movement indices such as mean speed, directional persistence time, and random motility coefficient. In a small gradient of adhesion, a perturbation analysis of the FPE yields a constitutive cell flux expression which includes a drift term for haptotactic directional cell migration. The haptotactic drift contains terms identified as contributions from directional orientation bias (taxis), kinesis, and orthotaxis, of which taxis appears to be predominant given estimates of the model parameters.

We propose a mathematical model to aid the understanding of how events in wound healing are orchestrated to result in wound contraction. Ultimately, a validated model could provide a predictive means for enhancing or mitigating contraction as is appropriate for managing a particular wound. The complex nature of wound healing and the lack of a modeling framework which can account for both the relevant cell biology and biomechanics are major reasons for the absence of models to date. Here we adapt a model originally proposed by Murray and co-workers to show how cell traction forces can result in spatial patterns of cell aggregates since it offers a framework for understanding how traction exerted by wound fibroblasts drives wound contraction. Since it is a continuum model based on conservation laws which reflect assumed cell and tissue properties, it is readily extended to account for emerging understanding of the cell biology of wound healing and its relationship to inflammation. We consider various sets of assumed properties, based on current knowledge, within a base model of dermal wound healing and compare predictions of the rate and extent of wound contraction to published experimental results.