Estimation of cell traction and migration in an isometric cell traction assay

Mathematical Modeling Can Advance Wound Healing Research

Significance: For over 30 years, there has been sustained interest in the development of mathematical models for investigating the complex mechanisms underlying each stage of the wound healing process. Despite the immense associated challenges, such models have helped usher in a paradigm shift in wound healing research. Recent Advances: In this article, we review contributions in the field that span epidermal, dermal, and corneal wound healing, and treatments of nonhealing wounds. The recent influence of mathematical models on biological experiments is detailed, with a focus on wound healing assays and fibroblast-populated collagen lattices. Critical Issues: We provide an overview of the field of mathematical modeling of wound healing, highlighting key advances made in recent decades, and discuss how such models have contributed to the development of improved treatment strategies and/or an enhanced understanding of the tightly regulated steps that comprise the healing process. Future Directions: We detail some of the open problems in the field that could be addressed through a combination of theoretical and/or experimental approaches. To move the field forward, we need to have a common language between scientists to facilitate cross-collaboration, which we hope this review can support by highlighting progress to date.

A model for one-dimensional morphoelasticity and its application to fibroblast-populated collagen lattices

The mechanical behaviour of solid biological tissues has long been described using models based on classical continuum mechanics. However, the classical continuum theories of elasticity and viscoelasticity cannot easily capture the continual remodelling and associated structural changes in biological tissues. Furthermore, models drawn from plasticity theory are difficult to apply and interpret in this context, where there is no equivalent of a yield stress or flow rule. In this work, we describe a novel one-dimensional mathematical model of tissue remodelling based on the multiplicative decomposition of the deformation gradient. We express the mechanical effects of remodelling as an evolution equation for the effective strain, a measure of the difference between the current state and a hypothetical mechanically relaxed state of the tissue. This morphoelastic model combines the simplicity and interpretability of classical viscoelastic models with the versatility of plasticity theory. A novel feature of our model is that while most models describe growth as a continuous quantity, here we begin with discrete cells and develop a continuum representation of lattice remodelling based on an appropriate limit of the behaviour of discrete cells. To demonstrate the utility of our approach, we use this framework to capture qualitative aspects of the continual remodelling observed in fibroblast-populated collagen lattices, in particular its contraction and its subsequent sudden re-expansion when remodelling is interrupted.

Remodeling by fibroblasts alters the rate-dependent mechanical properties of collagen

The ways that fibroblasts remodel their environment are central to wound healing, development of musculoskeletal tissues, and progression of pathologies such as fibrosis. However, the changes that fibroblasts make to the material around them and the mechanical consequences of these changes have proven difficult to quantify, especially in realistic, viscoelastic three-dimensional culture environments, leaving a critical need for quantitative data. Here, we observed the mechanisms and quantified the mechanical effects of fibroblast remodeling in engineered tissue constructs (ETCs) comprised of reconstituted rat tail (type I) collagen and human fibroblast cells. To study the effects of remodeling on tissue mechanics, stress-relaxation tests were performed on ETCs cultured for 24, 48, and 72h. ETCs were treated with deoxycholate and tested again to assess the ECM response. Viscoelastic relaxation spectra were obtained using the generalized Maxwell model. Cells exhibited viscoelastic damping at two finite time constants over which the ECM showed little damping, approximately 0.2s and 10-30s. Different finite time constants in the range of 1-7000s were attributed to ECM relaxation. Cells remodeled the ECM to produce a relaxation time constant on the order of 7000s, and to merge relaxation finite time constants in the 0.5-2s range into a single time content in the 1s range. Results shed light on hierarchical deformation mechanisms in tissues, and on pathologies related to collagen relaxation such as diastolic dysfunction.

STATEMENT OF SIGNIFICANCE

As fibroblasts proliferate within and remodel a tissue, they change the tissue mechanically. Quantifying these changes is critical for understanding wound healing and the development of pathologies such as cardiac fibrosis. Here, we characterize for the first time the spectrum of viscoelastic (rate-dependent) changes arising from the remodeling of reconstituted collagen by fibroblasts. The method also provides estimates of the viscoelastic spectra of fibroblasts within a three-dimensional culture environment. Results are of particular interest because of the ways that fibroblasts alter the mechanical response of collagen at loading frequencies associated with cardiac contraction in humans.

Tissue constructs: platforms for basic research and drug discovery

The functions, form and mechanical properties of cells are inextricably linked to their extracellular environment. Cells from solid tissues change fundamentally when, isolated from this environment, they are cultured on rigid two-dimensional substrata. These changes limit the significance of mechanical measurements on cells in two-dimensional culture and motivate the development of constructs with cells embedded in three-dimensional matrices that mimic the natural tissue. While measurements of cell mechanics are difficult in natural tissues, they have proven effective in engineered tissue constructs, especially constructs that emphasize specific cell types and their functions, e.g. engineered heart tissues. Tissue constructs developed as models of disease also have been useful as platforms for drug discovery. Underlying the use of tissue constructs as platforms for basic research and drug discovery is integration of multiscale biomaterials measurement and computational modelling to dissect the distinguishable mechanical responses separately of cells and extracellular matrix from measurements on tissue constructs and to quantify the effects of drug treatment on these responses. These methods and their application are the main subjects of this review.

Analysis of individual cell trajectories in lattice-gas cellular automaton models for migrating cell populations

Collective dynamics of migrating cell populations drive key processes in tissue formation and maintenance under normal and diseased conditions. Collective cell behavior at the tissue level is typically characterized by considering cell density patterns such as clusters and moving cell fronts. However, there are also important observables of collective dynamics related to individual cell behavior. In particular, individual cell trajectories are footprints of emergent behavior in populations of migrating cells. Lattice-gas cellular automata (LGCA) have proven successful to model and analyze collective behavior arising from interactions of migrating cells. There are well-established methods to analyze cell density patterns in LGCA models. Although LGCA dynamics are defined by cell-based rules, individual cells are not distinguished. Therefore, individual cell trajectories cannot be analyzed in LGCA so far. Here, we extend the classical LGCA framework to allow labeling and tracking of individual cells. We consider cell number conserving LGCA models of migrating cell populations where cell interactions are regulated by local cell density and derive stochastic differential equations approximating individual cell trajectories in LGCA. This result allows the prediction of complex individual cell trajectories emerging in LGCA models and is a basis for model-experiment comparisons at the individual cell level.

Regulating tension in three-dimensional culture environments

The processes of development, repair, and remodeling of virtually all tissues and organs, are dependent upon mechanical signals including external loading, cell-generated tension, and tissue stiffness. Over the past few decades, much has been learned about mechanotransduction pathways in specialized two-dimensional culture systems; however, it has also become clear that cells behave very differently in two- and three-dimensional (3D) environments. Three-dimensional in vitro models bring the ability to simulate the in vivo matrix environment and the complexity of cell-matrix interactions together. In this review, we describe the role of tension in regulating cell behavior in three-dimensional collagen and fibrin matrices with a focus on the effective use of global boundary conditions to modulate the tension generated by populations of cells acting in concert. The ability to control and measure the tension in these 3D culture systems has the potential to increase our understanding of mechanobiology and facilitate development of new ways to treat diseased tissues and to direct cell fate in regenerative medicine and tissue engineering applications.

Poly (3-hydroxybutyrate-co-3-hydroxyhexanoate)/collagen hybrid scaffolds for tissue engineering applications

The benefits associated with polyhydroxyalkanoates (PHA) in tissue engineering include high immunotolerance, low toxicity, and biodegradability. Poly(3-hydroxybutyrate-co-3-hydroxyhexanoate) (PHBHHx), a molecule from the PHA family of biopolymers, shares these features. In this study, the applicability of human embryonic stem cells (hESCs), spontaneously differentiated hESCs (SDhESCs), and mesenchymal stem cells (hMSCs) in conjunction with PHBHHx and collagen as a biocompatible replacement strategy for damaged tissues was exploited. Collagen gel contraction was monitored by seeding cells at controlled densities (0, 10(3), 10(4), and 10(5) cells/mL) and measuring length and diameter at regular time intervals thereafter when cultured in a complete medium. Cell viability was measured by trypan blue exclusion assay. Porous PHBHHx tube scaffolds were prepared using a dipping method followed by salt leaching. PHBHHx/collagen composites were generated via syringe injection of collagen/cell mixtures into sterile PHBHHx porous tubes. Reverse transcription polymerase chain reaction was used to determine the fate of cells within PHBHHx/collagen scaffolds with tendon, bone, cartilage, and fat-linked transcript expression being explored at days 0, 5 10, and 20. The capacity of PHBHHx/collagen scaffolds to support differentiation was explored using a medium specific for osteogenic, chondrogenic, and adipogenic lineage generation. Collagen gel tube contraction required initial seeding densities of ≥10(5) hMSCs or SDhESCs in 1.5 mg/mL collagen gel tubes. Gels with a collagen concentration of 3 mg/mL did not display contraction across the examined cell seeding densities. Cell viability was ∼50% for SDhESC and 90% for hMSCs at all cell densities tested in porous PHBHHx tube/3 mg/mL collagen hybrid scaffolds after 20 days in vitro culture. Undifferentiated hESCs did not contract collagen gel tubes and were unviable after 20 days culture. In the absence of additional stimuli, SOX9 was sporadically found, while RUNX2 was not present in both hMSC and SDhESC. Hybrid scaffolds were shown to promote retention of osteogenic, chondrogenic, and adipogenic differentiation by expression of RUNX2, SOX9, and PPARγ genes, respectively, following exposure to the appropriate induction medium. PHBHHx/collagen scaffolds have been successfully used to culture hMSC and SDhESC over an extended period supporting the potential of this scaffold combination in future tissue engineering applications.

Tissue deformation spatially modulates VEGF signaling and angiogenesis

Physical forces play a major role in the organization of developing tissues. During vascular development, physical forces originating from a fluid phase or from cells pulling on their environment can alter cellular signaling and the behavior of cells. Here, we observe how tissue deformation spatially modulates angiogenic signals and angiogenesis. Using soft lithographic templates, we assemble three-dimensional, geometric tissues. The tissues contract autonomously, change shape stereotypically and form patterns of vascular structures in regions of high deformations. We show that this emergence correlates with the formation of a long-range gradient of Vascular Endothelial Growth Factor (VEGF) in interstitial cells, the local overexpression of the corresponding receptor VEGF receptor 2 (VEGFR-2) and local differences in endothelial cells proliferation. We suggest that tissue contractility and deformation can induce the formation of gradients of angiogenic microenvironments which could contribute to the long-range patterning of the vascular system.

Boundary stiffness regulates fibroblast behavior in collagen gels

Recent studies have illustrated the profound dependence of cellular behavior on the stiffness of 2D culture substrates. The goal of this study was to develop a method to alter the stiffness cells experience in a standard 3D collagen gel model without affecting the physiochemical properties of the extracellular matrix. A device was developed utilizing compliant anchors (0.048-0.64 N m(-1)) to tune the boundary stiffness of suspended collagen gels in between the commonly utilized free and fixed conditions (zero and infinite stiffness boundary stiffness). We demonstrate the principle of operation with finite element analyses and a wide range of experimental studies. In all cases, boundary stiffness has a strong influence on cell behavior, most notably eliciting higher basal tension and activated force (in response to KCl) and more pronounced remodeling of the collagen matrix at higher boundary stiffness levels. Measured equibiaxial forces for gels seeded with 3 million human foreskin fibroblasts range from 0.05 to 1 mN increasing monotonically with boundary stiffness. Estimated force per cell ranges from 17 to 100 nN utilizing representative volume element analysis. This device provides a valuable tool to independently study the effect of the mechanical environment of the cell in a 3D collagen matrix.

Positively and negatively modulating cell adhesion to type I collagen via peptide grafting

The biophysical interactions between cells and type I collagen are controlled by the level of cell adhesion, which is dictated primarily by the density of ligands on collagen and the density of integrin receptors on cells. The native adhesivity of collagen was modulated by covalently grafting glycine-arginine-glycine-aspartic acid-serine (GRGDS), which includes the bioactive RGD sequence, or glycine-arginine-aspartic acid-glycine-serine (GRDGS), which includes the scrambled RDG sequence, to collagen with the hetero-bifunctional coupling agent 1-ethyl-3-(3-dimethylaminopropyl) carbodiimide. The peptide-grafted collagen self-assembled into a fibrillar gel with negligible changes in gel structure and rheology. Rat dermal fibroblasts (RDFs) and human smooth muscle cells demonstrated increased levels of adhesion on gels prepared from RGD-grafted collagen, and decreased levels of adhesion on RDG-grafted collagen. Both cell types demonstrated an increased ability to compact free-floating RGD-grafted collagen gels, and an impaired ability to compact RDG-grafted gels. RDF migration on and within collagen was increased with RDG-grafted collagen and decreased with RGD-grafted collagen, and dose-response experiments indicated a biphasic response of RDF migration to adhesion. Smooth muscle cells demonstrated similar, though not statistically significant, trends. The ability to both positively and negatively modulate cell adhesion to collagen increases the versatility of this natural biomaterial for regenerative therapies.

The Stiffness of Three-dimensional Ionic Self-assembling Peptide Gels Affects the Extent of Capillary-like Network Formation

Improving our ability to control capillary morphogenesis has implications for not only better understanding of basic biology, but also for applications in tissue engineering and in vitro testing. Numerous biomaterials have been investigated as cellular supports for these applications and the biophysical environment biomaterials provide to cells has been increasingly recognized as an important factor in directing cell function. Here, the ability of ionic self-assembling peptide gels to support capillary morphogenesis and the effect of their mechanical properties is investigated. When placed in a physiological salt solution, these oligopeptides spontaneously self-assemble into gels with an extracellular matrix (ECM)-like microarchitecture. To evaluate the ability of three-dimensional (3D) self-assembled peptide gels to support capillary-like network formation, human umbilical vein endothelial cells (HUVECs) were embedded within RAD16-I ((RADA)4) or RAD16-II ((RARADADA)2) peptide gels with various stiffness values. As peptide stiffness is decreased cells show increased elongation and are increasingly able to contract gels. The observation that capillary morphogenesis is favored in more malleable substrates is consistent with previous reports using natural biomaterials. The structural properties of peptide gels and their ability to support capillary morphogenesis in vitro make them promising biomaterials to investigate for numerous biomedical applications.

Cellular and matrix contributions to tissue construct stiffness increase with cellular concentration

The mechanics of bio-artificial tissue constructs result from active and passive contributions of cells and extracellular matrix (ECM). We delineated these for a fibroblast-populated matrix (FPM) consisting of chick embryo fibroblast cells in a type I collagen ECM through mechanical testing, mechanical modeling, and selective biochemical elimination of tissue components. From a series of relaxation tests, we found that contributions to overall tissue mechanics from both cells and ECM increase exponentially with the cell concentration. The force responses in these relaxation tests exhibited a logarithmic decay over the 3600 second test duration. The amplitudes of these responses were nearly linear with the amplitude of the applied stretch. The active component of cellular forces rose dramatically for FPMs containing higher cell concentrations.

Mechanobiology in the third dimension

Cells are mechanically coupled to their extracellular environments, which play critical roles in both communicating the state of the mechanical environment to the cell as well as in mediating cellular response to a variety of stimuli. Along with the molecular composition and mechanical properties of the extracellular matrix (ECM), recent work has demonstrated the importance of dimensionality in cell-ECM associations for controlling the sensitive communication between cells and the ECM. Matrix forces are generally transmitted to cells differently when the cells are on two-dimensional (2D) vs. within three-dimensional (3D) matrices, and cells in 3D environments may experience mechanical signaling that is unique vis-à-vis cells in 2D environments, such as the recently described 3D-matrix adhesion assemblies. This review examines how the dimensionality of the extracellular environment can affect in vitro cell mechanobiology, focusing on collagen and fibrin systems.

Schwann cell behavior in three-dimensional collagen gels: Evidence for differential mechano-transduction and the influence of TGF-beta 1 in morphological polarization and differentiation

Schwann cells (SCs) cultured on and within magnetically aligned collagen gels were examined for their abilities to spread and exhibit contact guidance, two functions that are relevant to their potential enhancement of neurite migration and regeneration in entubulation repair of transection-type nerve injuries. Cells seeded at or near the surfaces of gels abandoned their initially spherical shapes, adopting spread morphologies rapidly compared to cells within the gels. Those few cells within the gels that did spread exhibited marked contact guidance responses, aligning strongly with the aligned collagen fibrils. Spreading of cells in gels could not be induced by varied cell concentration, collagen density, mitogen presence, inclusion of soluble laminin, or use of fibrin gel in lieu of collagen. However, cells that settled at the interface between collagen gel layers during gellation of the top layer above a preformed bottom layer were highly spread. This suggests that a differential mechanical interaction across the cell at an interface, where at least one surface presents constituents of the basal lamina, permits the Schwann cell to rapidly revert to a spread, differentiated phenotype. Unlike other reagents, TGF-beta1 was able to induce significant SC spreading as early as 4 h post-seeding. Consistent with the differential-mechanical cue mechanism, TGF-beta1 appears to facilitate this response, at least in part, by upregulating beta1 integrin expression, thereby enabling the SC to more acutely detect these local cues in the mechanical environment.

Glioma expansion in collagen I matrices: analyzing collagen concentration-dependent growth and motility patterns

We study the growth and invasion of glioblastoma multiforme (GBM) in three-dimensional collagen I matrices of varying collagen concentration. Phase-contrast microscopy studies of the entire GBM system show that invasiveness at early times is limited by available collagen fibers. At early times, high collagen concentration correlates with more effective invasion. Conversely, high collagen concentration correlates with inhibition in the growth of the central portion of GBM, the multicellular tumor spheroid. Analysis of confocal reflectance images of the collagen matrices quantifies how the collagen matrices differ as a function of concentration. Studying invasion on the length scale of individual invading cells with a combination of confocal and coherent anti-Stokes Raman scattering microscopy reveals that the invasive GBM cells rely heavily on cell-matrix interactions during invasion and remodeling.

The relative magnitudes of endothelial force generation and matrix stiffness modulate capillary morphogenesis in vitro

When suspended in collagen gels, endothelial cells elongate and form capillary-like networks containing lumens. Human blood outgrowth endothelial cells (HBOEC) suspended in relatively rigid 3 mg/ml floating collagen gels, formed in vivo-like, thin, branched multi-cellular structures with small, thick-walled lumens, while human umbilical vein endothelial cells (HUVEC) formed fewer multi-cellular structures, had a spread appearance, and had larger lumens. HBOEC exert more traction on collagen gels than HUVEC as evidenced by greater contraction of floating gels. When the stiffness of floating gels was decreased by decreasing the collagen concentration from 3 to 1.5 mg/ml, HUVEC contracted gels more and formed thin, multi-cellular structures with small lumens, similar in appearance to HBOEC in floating 3 mg/ml gels. In contrast to floating gels, traction forces exerted by cells in mechanically constrained gels encounter considerable resistance. In constrained collagen gels (3 mg/ml), both cell types appeared spread, formed structures with fewer cells, had larger, thinner-walled lumens than in floating gels, and showed prominent actin stress fibers, not seen in floating gels. These results suggest that the relative magnitudes of cellular force generation and apparent matrix stiffness modulate capillary morphogenesis in vitro and that this balance may play a role in regulating angiogenesis in vivo.

Materials as morphogenetic guides in tissue engineering

Within native tissues cells are held within the extracellular matrix (ECM), which has a role in maintaining homeostasis, guiding development and directing regeneration. Efforts in tissue engineering have aimed to mimick the ECM to help guide morphogenesis and tissue repair. Studies have not only looked at ways to mimick the structure and characteristics of the ECM, but have also considered ways to reproduce its molecular properties including its bioadhesive character, proteolytic susceptibility and ability to bind growth factors.

An aperture-shifting light-microscopic method for rapidly quantifying positions of cells in 3D matrices

BACKGROUND

Rapid measurements of large numbers of cells in 3D are often required for measurements of cell migration. A method is presented for quantifying the position of cells in three-dimensional gels using brightfield microscopy.

METHODS

Images were recorded using transmitted light with a closed condenser aperture diaphragm positioned off axis to produce oblique illumination. Two or more images, each at the same focal plane, were obtained with the aperture shifted equally to either side of the optical axis. All in-focus objects were at the same position in the two images, but out-of-focus objects were displaced parallel to the aperture movement.

RESULTS

The method was tested using gels containing 12-microm-diameter glass beads or cells that had migrated several hundred micrometers into the gel. The position in the image plane varied linearly with axial position, being reversed for objects above and below the focal plane. Beads and cells could be visualized up to a depth of >1 mm in gels.

CONCLUSIONS

The method facilitates measurements of positions of cells in 3D matrices by eliminating the need to perform optical sectioning and can be used with any brightfield microscope. Supplementary material for this article can be found at http://www.interscience.wiley.com/jpages/0196-4763/suppmat/54_2/v54.125.html

Temporal variations in cell migration and traction during fibroblast-mediated gel compaction

Current models used in our laboratory to assess the migration and traction of a population of cells within biopolymer gels are extended to investigate temporal changes in these parameters during compaction of mechanically constrained gels. The random cell migration coefficient, micro (t) is calculated using a windowing technique by regressing the mean-squared displacement of cells tracked at high magnification in three dimensions with a generalized least squares algorithm for a subset of experimental time intervals, and then shifting the window interval-by-interval until all time points are analyzed. The cell traction parameter, tau(0)(t), is determined by optimizing the solution of our anisotropic biphasic theory to tissue equivalent compaction. The windowing technique captured simulated sinusoidal and step changes in cell migration superposed on a persistent random walk in simulated cell movement. The optimization software captured simulated time dependence of compaction on cell spreading. Employment of these techniques on experimental data using rat dermal fibroblasts (RDFs) and human foreskin fibroblasts (HFFs) demonstrated that these cells exhibit different migration-traction relationships. Rat dermal fibroblast migration was negatively correlated to traction, suggesting migration was not the driving force for compaction with these cells, whereas human foreskin fibroblast migration was positively correlated to traction.

Confined compression of a tissue-equivalent: collagen fibril and cell alignment in response to anisotropic strain

A method to impose and measure a one dimensional strain field via confined compression of a tissue-equivalent and measure the resulting cell and collagen fibril alignment was developed Strain was determined locally by the displacement of polystyrene beads dispersed and entrapped within the network of collagen fibrils along with the cells, and it was correlated to the spatial variation of collagen network birefringence and concentration. Alignment of fibroblasts and smooth muscle cells was determined based on the long axis of elongated cells. Cell and collagen network alignment were observed normal to the direction of compression after a step strain and increased monotonically up to 50% strain. These results were independent of time after straining over 24 hr despite continued cell motility after responding instantly to the step strain with a change in alignment by deforming/convecting with the strained network. Since the time course of cell alignment followed that of strain and not stress which, due to the viscoelastic fluid-like nature of the network relaxes completely within the observation period, these results imply cell alignment in a compacting tissue-equivalent is due to fibril alignment associated with anisotropic network strain. Estimation of a contact guidance sensitivity parameter indicates that both cell types align to a greater extent than the surrounding fibrils.

A novel implantable collagen gel assay for fibroblast traction and proliferation during wound healing

BACKGROUND

A novel implantable assay for studying cellular behavior in the wound environment was developed. The assay is unique in that it combines the more quantitative nature of in vitro assays with the greater physiological relevance of in vivo wound healing models.

MATERIALS AND METHODS

Cells were seeded in a physiologically relevant biological matrix, a collagen gel, contained within a semipermeable tube, and then exposed to soluble factors of the wound environment at different stages of the wound healing response. Gels were harvested at prescribed time points, and cell proliferation rates and gel compaction were measured. These data were combined with our theory for cell-matrix mechanical interactions to estimate the cell traction exerted by the cells leading to gel compaction. Cell morphology and alpha-smooth muscle actin expression were also characterized.

RESULTS

The proliferation of and traction exerted by fibroblasts exposed to the soluble wound environment were different from those in similar collagen gels maintained in culture in complete medium. Proliferation and traction also varied over the course of the wound healing response. Traction was higher and proliferation lower in day 1-5 wounds compared to day 7-11 wounds. Recovered cells no longer stained for alpha-smooth muscle actin, in contrast to cells maintained in culture.

CONCLUSIONS

Changes in the soluble wound environment that occur as the wound healing response proceeds alter fibroblast traction and migration. We have developed a new assay that employs a physiologically relevant biological matrix and allows the effects of the dynamic soluble wound environment on cellular traction, proliferation, and other phenomena such as protein expression to be quantified.

Macrophages influence a competition of contact guidance and chemotaxis for fibroblast alignment in a fibrin gel coculture assay

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.

Predicting local cell deformations in engineered tissue constructs: a multilevel finite element approach

A multilevel finite element approach is applied to predict local cell deformations in engineered tissue constructs. Cell deformations are predicted from detailed nonlinear FE analysis of the microstructure, consisting of an arrangement of cells embedded in matrix material. Effective macroscopic tissue behavior is derived by a computational homogenization procedure. To illustrate this approach, we simulated the compression of a skeletal muscle tissue construct and studied the influence of microstructural heterogeneity on local cell deformations. Results show that heterogeneity has a profound impact on local cell deformations, which highly exceed macroscopic deformations. Moreover, microstructural heterogeneity and the presence of neighboring cells leads to complex cell shapes and causes non-uniform deformations within a cell.

Epidermal growth factor induces acute matrix contraction and subsequent calpain-modulated relaxation

During wound healing, dermal fibroblasts switch from a migratory, repopulating phenotype to a contractile, matrix-reassembling phenotype. The mechanisms controlling this switch are unknown. A possible explanation is suggested by the finding that chemokines that appear late in wound repair prevent growth factor-induced cell-substratum de-adhesion by blocking calpain activation. In this study, we tested the specific hypothesis that fibroblast contraction of the matrix is promoted by a pro-repair growth factor, epidermal growth factor, and is modulated by calpain-mediated release of adhesions. We employed an isometric force transduction system designed to measure the contraction of a collagen matrix under tension by a population of NR6 fibroblasts transfected with the human epidermal growth factor receptor. By maintaining a fixed level of strain, we could monitor both the initial contraction and subsequent relaxation of the matrix. Epidermal growth factor stimulated a transient, dose-dependent increase in matrix contraction that peaked within 60 minutes and then decayed over the ensuing 3 to 6 hours. Calpain inhibitor I (ALLN) prevented epidermal growth factor-stimulated cell de-adhesion and resulted in a significantly slower decay of matrix contraction, with only a slight decrease of the peak magnitude of contraction. The mitogen-activated protein kinase kinase-1-selective inhibitor PD 98059 that blocks signaling through the extracellular signal-regulated kinase/mitogen-activated protein kinase pathway, required for epidermal growth factor receptor-mediated activation of calpain and de-adhesion, does not significantly affect the magnitude of matrix contraction within minutes of epidermal growth factor addition, but slows the decay similarly to calpain inhibition. Epidermal growth factor receptor signaling thus stimulates the complementary mechanisms of intracellular contractile force generation and calpain-mediated de-adhesion, which are known to coordinately facilitate cell migration. These findings suggest that calpain can act as a functional switch for transmission of intracellular contractile force to the surrounding matrix, with calpain-mediated de-adhesion reducing this transmission and corresponding matrix contraction. Countervailing processes that down-regulate calpain activation can, accordingly, direct the transition of cell function from locomotion to matrix contraction.

Alignment maps of tissues: I. Microscopic elliptical polarimetry

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.

Effects of pdgf-bb on rat dermal fibroblast behavior in mechanically stressed and unstressed collagen and fibrin gels

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.