Click chemistry functionalization of self-assembling peptide hydrogels.

Self-assembling peptide (SAP) hydrogels provide a fibrous microenvironment to cells while also giving users control of biochemical and mechanical cues. Previously, biochemical cues were introduced by physically mixing them with SAPs prior to hydrogel assembly, or by incorporating them into the SAP sequence during peptide synthesis, which limited flexibility and increased costs. To circumvent these limitations, we developed "Click SAPs," a novel formulation that can be easily functionalized via click chemistry thiol-ene reaction. Due to its high cytocompatibility, the thiol-ene click reaction is currently used to crosslink and functionalize other types of polymeric hydrogels. In this study, we developed a click chemistry compatible SAP platform by addition of a modified lysine (lysine-alloc) to the SAP sequence, enabling effective coupling of thiol-containing molecules to the SAP hydrogel network. We demonstrate the flexibility of this approach by incorporating a fluorescent dye, a cellular adhesion peptide, and a matrix metalloproteinase-sensitive biosensor using the thiol-ene reaction in 3D Click SAPs. Using atomic force microscopy, we demonstrate that Click SAPs retain the ability to self-assemble into fibers, similar to previous systems. Additionally, a range of physiologically relevant stiffnesses can be achieved by adjusting SAP concentration. Encapsulated cells maintain high viability in Click SAPs and can interact with adhesion peptides and a matrix metalloproteinase biosensor, demonstrating that incorporated molecules retain their biological activity. The Click SAP platform supports easier functionalization with a wider array of bioactive molecules and enables new investigations with temporal and spatial control of the cellular microenvironment.

A mechanistic motor-clutch model that explains cell shape dynamics to cyclic stretch.

Many cells in the body experience cyclic mechanical loading, which can impact cellular processes and morphology. In vitro studies often report that cells reorient in response to cyclic stretch of their substrate. To explore cellular mechanisms involved in this reorientation, a computational model was developed by adapting previous computational models of the actin-myosin-integrin motor-clutch system developed by others. The computational model predicts that under most conditions, actin bundles align perpendicular to the direction of applied cyclic stretch, but under specific conditions, such as low substrate stiffness, actin bundles align parallel to the direction of stretch. The model also predicts that stretch frequency impacts the rate of reorientation and that proper myosin function is critical in the reorientation response. These computational predictions are consistent with reports from the literature and new experimental results presented here. The model suggests that the impact of different stretching conditions (stretch type, amplitude, frequency, substrate stiffness, etc.) on the direction of cell alignment can largely be understood by considering their impact on cell-substrate detachment events, specifically whether detachments preferentially occur during stretching or relaxing of the substrate.

Decreased Substrate Stiffness Promotes a Hypofibrotic Phenotype in Cardiac Fibroblasts.

A hypofibrotic phenotype has been observed in cardiac fibroblasts (CFs) isolated from a volume overload heart failure model, aortocaval fistula (ACF). This paradoxical phenotype results in decreased ECM synthesis despite increased TGF-ß presence. Since ACF results in decreased tissue stiffness relative to control (sham) hearts, this study investigates whether the effects of substrate stiffness could account for the observed hypofibrotic phenotype in CFs isolated from ACF. CFs isolated from ACF and sham hearts were plated on polyacrylamide gels of a range of stiffness (2 kPa to 50 kPa). Markers related to cytoskeletal and fibrotic proteins were measured. Aspects of the hypofibrotic phenotype observed in ACF CFs were recapitulated by sham CFs on soft substrates. For instance, sham CFs on the softest gels compared to ACF CFs on the stiffest gels results in similar CTGF (0.80 vs. 0.76) and transgelin (0.44 vs. 0.57) mRNA expression. The changes due to stiffness may be explained by the observed decreased nuclear translocation of transcriptional regulators, MRTF-A and YAP. ACF CFs appear to have a mechanical memory of a softer environment, supported by a hypofibrotic phenotype overall compared to sham with less YAP detected in the nucleus, and less CTGF and transgelin on all stiffnesses.

Paired Pressure-Volume Loop Analysis and Biaxial Mechanical Testing Characterize Differences in Left Ventricular Tissue Stiffness of Volume Overload and Angiotensin-Induced Pressure Overload Hearts.

Pressure overload (PO) and volume overload (VO) of the heart result in distinctive changes to geometry, due to compensatory structural remodeling. This remodeling potentially leads to changes in tissue mechanical properties. Understanding such changes is important, as tissue modulus has an impact on cardiac performance, disease progression, and influences on cell phenotype. Pressure-volume (PV) loop analysis, a clinically relevant method for measuring left ventricular (LV) chamber stiffness, was performed in vivo on control rat hearts and rats subjected to either chronic PO through Angiotensin-II infusion (4-weeks) or VO (8-weeks). Immediately following PV loops, biaxial testing was performed on LV free wall tissue to directly measure tissue mechanical properties. The ß coefficient, an index of chamber stiffness calculated from the PV loop analysis, increased 98% in PO (n = 4) and decreased 38% in VO (n = 5) compared to control (n = 6). Material constants of LV walls obtained from ex vivo biaxial testing (n = 9-10) were not changed in Angiotensin-II induced PO and decreased by about half in VO compared to control (47% in the circumferential and 57% the longitudinal direction). PV loop analysis showed the expected increase in chamber stiffness of PO and expected decrease in chamber stiffness of VO. Biaxial testing showed a decreased modulus of the myocardium of the VO model, but no changes in the PO model, this suggests the increased chamber stiffness in PO, as shown in the PV loop analysis, may be secondary to changes in tissue mass and/or geometry but not an increase in passive tissue mechanical properties.

ßIV-Spectrin/STAT3 complex regulates fibroblast phenotype, fibrosis, and cardiac function.

Increased fibrosis is a characteristic remodeling response to biomechanical and neurohumoral stress and a determinant of cardiac mechanical and electrical dysfunction in disease. Stress-induced activation of cardiac fibroblasts (CFs) is a critical step in the fibrotic response, although the precise sequence of events underlying activation of these critical cells in vivo remain unclear. Here, we tested the hypothesis that a ßIV-spectrin/STAT3 complex is essential for maintenance of a quiescent phenotype (basal nonactivated state) in CFs. We reported increased fibrosis, decreased cardiac function, and electrical impulse conduction defects in genetic and acquired mouse models of ßIV-spectrin deficiency. Loss of ßIV-spectrin function promoted STAT3 nuclear accumulation and transcriptional activity, and it altered gene expression and CF activation. Furthermore, we demonstrate that a quiescent phenotype may be restored in ßIV-spectrin-deficient fibroblasts by expressing a ßIV-spectrin fragment including the STAT3-binding domain or through pharmacological STAT3 inhibition. We found that in vivo STAT3 inhibition abrogates fibrosis and cardiac dysfunction in the setting of global ßIV-spectrin deficiency. Finally, we demonstrate that fibroblast-specific deletion of ßIV-spectrin is sufficient to induce fibrosis and decreased cardiac function. We propose that the ßIV-spectrin/STAT3 complex is a determinant of fibroblast phenotype and fibrosis, with implications for remodeling response in cardiovascular disease (CVD).

Role of the cytoskeleton in the development of a hypofibrotic cardiac fibroblast phenotype in volume overload heart failure.

Hemodynamic load regulates cardiac remodeling. In contrast to pressure overload (increased afterload), hearts subjected to volume overload (VO; preload) undergo a distinct pattern of eccentric remodeling, chamber dilation, and decreased extracellular matrix content. Critical profibrotic roles of cardiac fibroblasts (CFs) in postinfarct remodeling and in response to pressure overload have been well established. Little is known about the CF phenotype in response to VO. The present study characterized the phenotype of primary cultures of CFs isolated from hearts subjected to 4 wk of VO induced by an aortocaval fistula. Compared with CFs isolated from sham hearts, VO CFs displayed a "hypofibrotic" phenotype, characterized by a ~50% decrease in the profibrotic phenotypic markers α-smooth muscle actin, connective tissue growth factor, and collagen type I, despite increased levels of profibrotic transforming growth factor-ß1 and an intact canonical transforming growth factor-ß signaling pathway. Actin filament dynamics were characterized, which regulate the CF phenotype in response to biomechanical signals. Actin polymerization was determined by the relative amounts of G-actin monomers versus F-actin. Compared with sham CFs, VO CFs displayed ~78% less F-actin and an increased G-actin-to-F-actin ratio (G/F ratio). In sham CFs, treatment with the Rho kinase inhibitor Y-27632 to increase the G/F ratio resulted in recapitulation of the hypofibrotic CF phenotype observed in VO CFs. Conversely, treatment of VO CFs with jasplakinolide to decrease the G/F ratio restored a more profibrotic response (>2.5-fold increase in α-smooth muscle actin, connective tissue growth factor, and collagen type I). NEW & NOTEWORTHY The present study is the first to describe a "hypofibrotic" phenotype of cardiac fibroblasts isolated from a volume overload model. Our results suggest that biomechanical regulation of actin microfilament stability and assembly is a critical mediator of cardiac fibroblast phenotypic modulation.

Labeling of endothelial cells with magnetic microbeads by angiophagy.

OBJECTIVES: Attachment of magnetic particles to cells is needed for a variety of applications but is not always possible or efficient. Simpler and more convenient methods are thus desirable. In this study, we tested the hypothesis that endothelial cells (EC) can be loaded with micron-size magnetic beads by the phagocytosis-like mechanism 'angiophagy'. To this end, human umbilical vein EC (HUVEC) were incubated with magnetic beads conjugated or not (control) with an anti-VEGF receptor 2 antibody, either in suspension, or in culture followed by re-suspension using trypsinization. RESULTS: In all conditions tested, HUVEC incubation with beads induced their uptake by angiophagy, which was confirmed by (i) increased cell granularity assessed by flow cytometry, and (ii) the presence of an F-actin rich layer around many of the intracellular beads, visualized by confocal microscopy. For confluent cultures, the average number of beads per cell was 4.4 and 4.2, with and without the presence of the anti-VEGFR2 antibody, respectively. However, while the actively dividing cells took up 2.9 unconjugated beads on average, this number increased to 5.2 if binding was mediated by the antibody. Magnetic pulldown increased the cell density of beads-loaded cells in porous electrospun poly-capro-lactone scaffolds by a factor of 4.5 after 5 min, as compared to gravitational settling (p < 0.0001). CONCLUSION: We demonstrated that EC can be readily loaded by angiophagy with micron-sized beads while attached in monolayer culture, then dispersed in single-cell suspensions for pulldown in porous scaffolds and for other applications.

Independent control of matrix adhesiveness and stiffness within a 3D self-assembling peptide hydrogel.

A cell's insoluble microenvironment has increasingly been shown to exert influence on its function. In particular, matrix stiffness and adhesiveness strongly impact behaviors such as cell spreading and differentiation, but materials that allow for independent control of these parameters within a fibrous, stromal-like microenvironment are very limited. In the current work, we devise a self-assembling peptide (SAP) system that facilitates user-friendly control of matrix stiffness and RGD (Arg-Gly-Asp) concentration within a hydrogel possessing a microarchitecture similar to stromal extracellular matrix. In this system, the RGD-modified SAP sequence KFE-RGD and the scrambled sequence KFE-RDG can be directly swapped for one another to change RGD concentration at a given matrix stiffness and total peptide concentration. Stiffness is controlled by altering total peptide concentration, and the unmodified base peptide KFE-8 can be included to further increase this stiffness range due to its higher modulus. With this tunable system, we demonstrate that human mesenchymal stem cell morphology and differentiation are influenced by both gel stiffness and the presence of functional cell binding sites in 3D culture. Specifically, cells 24 hours after encapsulation were only able to spread out in stiffer matrices containing KFE-RGD. Upon addition of soluble adipogenic factors, soft gels facilitated the greatest adipogenesis as determined by the presence of lipid vacuoles and PPARγ-2 expression, while increasing KFE-RGD concentration at a given stiffness had a negative effect on adipogenesis. This three-component hydrogel system thus allows for systematic investigation of matrix stiffness and RGD concentration on cell behavior within a fibrous, three-dimensional matrix. STATEMENT OF SIGNIFICANCE: Physical cues from a cell's surrounding environment-such as the density of cell binding sites and the stiffness of the surrounding material-are increasingly being recognized as key regulators of cell function. Currently, most synthetic biomaterials used to independently tune these parameters lack the fibrous structure characteristic of stromal extracellular matrix, which can be important to cells naturally residing within stromal tissues. In this manuscript, we describe a 3D hydrogel encapsulation system that provides user-friendly control over matrix stiffness and binding site concentration within the context of a stromal-like microarchitecture. Binding site concentration and gel stiffness both influenced cell spreading and differentiation, highlighting the utility of this system to study the independent effects of these material properties on cell function.

An Agent-Based Discrete Collagen Fiber Network Model of Dynamic Traction Force-Induced Remodeling.

Microstructural properties of extracellular matrix (ECM) promote cell and tissue homeostasis as well as contribute to the formation and progression of disease. In order to understand how microstructural properties influence the mechanical properties and traction force-induced remodeling of ECM, we developed an agent-based model that incorporates repetitively applied traction force within a discrete fiber network. An important difference between our model and similar finite element models is that by implementing more biologically realistic dynamic traction, we can explore a greater range of matrix remodeling. Here, we validated our model by reproducing qualitative trends observed in three sets of experimental data reported by others: tensile and shear testing of cell-free collagen gels, collagen remodeling around a single isolated cell, and collagen remodeling between pairs of cells. In response to tensile and shear strain, simulated acellular networks with straight fibrils exhibited biphasic stress-strain curves indicative of strain-stiffening. When fibril curvature was introduced, stress-strain curves shifted to the right, delaying the onset of strain-stiffening. Our data support the notion that strain-stiffening might occur as individual fibrils successively align along the axis of strain and become engaged in tension. In simulations with a single, contractile cell, peak collagen displacement occurred closest to the cell and decreased with increasing distance. In simulations with two cells, compaction of collagen between cells appeared inversely related to the initial distance between cells. These results for cell-populated collagen networks match in vitro findings. A demonstrable benefit of modeling is that it allows for further analysis not feasible with experimentation. Within two-cell simulations, strain energy within the collagen network measured from the final state was relatively uniform around the outer surface of cells separated by 250 µm, but became increasingly nonuniform as the distance between cells decreased. For cells separated by 75 and 100 µm, strain energy peaked in the direction toward the other cell in the region in which fibrils become highly aligned and reached a minimum adjacent to this region, not on the opposite side of the cell as might be expected. This pattern of strain energy was partly attributable to the pattern of collagen compaction, but was still present when mapping strain energy divided by collagen density. Findings like these are of interest because fibril alignment, density, and strain energy may each contribute to contact guidance during tissue morphogenesis.

Biomechanics and Mechanobiology of Saphenous Vein Grafts.

Within several weeks of use as coronary artery bypass grafts (CABG), saphenous veins (SV) exhibit significant intimal hyperplasia (IH). IH predisposes vessels to thrombosis and atherosclerosis, the two major modes of vein graft failure. The fact that SV do not develop significant IH in their native venous environment coupled with the rapidity with which they develop IH following grafting into the arterial circulation suggests that factors associated with the isolation and preparation of SV and/or differences between the venous and arterial environments contribute to disease progression. There is strong evidence suggesting that mechanical trauma associated with traditional techniques of SV preparation can significantly damage the vessel and might potentially reduce graft patency though modern surgical techniques reduces these injuries. In contrast, it seems possible that modern surgical technique, specifically endoscopic vein harvest, might introduce other mechanical trauma that could subtly injure the vein and perhaps contribute to the reduced patency observed in veins harvested using endoscopic techniques. Aspects of the arterial mechanical environment influence remodeling of SV grafted into the arterial circulation. Increased pressure likely leads to thickening of the medial wall but its role in IH is less clear. Changes in fluid flow, including increased average wall shear stress, may reduce IH while disturbed flow likely increase IH. Nonmechanical stimuli, such as exposure to arterial levels of oxygen, may also have a significant but not widely recognized role in IH. Several potentially promising approaches to alter the mechanical environment to improve graft patency are including extravascular supports or altered graft geometries are covered.

Microfluidics Enabled Bottom-Up Engineering of 3D Vascularized Tumor for Drug Discovery.

Development of high-fidelity three-dimensional (3D) models to recapitulate the tumor microenvironment is essential for studying tumor biology and discovering anticancer drugs. Here we report a method to engineer the 3D microenvironment of human tumors, by encapsulating cancer cells in the core of microcapsules with a hydrogel shell for miniaturized 3D culture to obtain avascular microtumors first. The microtumors are then used as the building blocks for assembling with endothelial cells and other stromal cells to create macroscale 3D vascularized tumor. Cells in the engineered 3D microenvironment can yield significantly larger tumors in vivo than 2D-cultured cancer cells. Furthermore, the 3D vascularized tumors are 4.7 and 139.5 times more resistant to doxorubicin hydrochloride (a commonly used chemotherapy drug) than avascular microtumors and 2D-cultured cancer cells, respectively. Moreover, this high drug resistance of the 3D vascularized tumors can be overcome by using nanoparticle-mediated drug delivery. The high-fidelity 3D tumor model may be valuable for studying the effect of microenvironment on tumor progression, invasion, and metastasis and for developing effective therapeutic strategy to fight against cancer.

Biomaterial microarchitecture: a potent regulator of individual cell behavior and multicellular organization.

Insoluble cues from a cell's surrounding microenvironment have increasingly been shown to be important regulators of cell behavior. The microarchitecture of biomaterials used for 3D cell encapsulation, however, is often underappreciated as an important insoluble factor guiding cell activity. In this review, we illustrate that the subcellular physical features of a scaffold influence a range of cell behaviors, including morphology, cytoskeletal organization, migration, matrix remodeling, and long-range force transmission. We emphasize that the microarchitecture of stromal extracellular matrix (ECM)-specifically the fact that it consists of a network of long interconnecting fibers with micron and nanometer-sized diameters-is an important determinant of how cells naturally interact with their surrounding matrix and each other. Synthetic biomaterials with a microarchitecture similar to stromal ECM can support analogous cellular responses, suggesting that this fibrous microarchitecture is a key regulator of these cell behaviors. Drawing upon examples from in vitro, in silico, and in vivo studies, we compare these behaviors in fibrous matrices to those of cells cultured within nanoporous matrices (e.g., alginate and PEG gels) as well as macroporous scaffolds to highlight key differences in the cellular response to each type of microarchitecture. Understanding how microarchitecture affects cell behavior can lead to more efficient biomaterial selection when designing tissue engineered scaffolds for therapeutic applications. © 2016 Wiley Periodicals, Inc. J Biomed Mater Res Part A: 105A: 640-661, 2017.

The effect of RGD peptide on 2D and miniaturized 3D culture of HEPM cells, MSCs, and ADSCs with alginate hydrogel.

Advancements in tissue engineering require the development of new technologies to study cell behavior in vitro. This study focuses on stem cell behavior within various miniaturized three-dimensional (3D) culture conditions of alginate biomaterials modified with the Arg-Gly-Asp (RGD) peptide known for its role in cell adhesion/attachment. Human embryonic palatal mesenchyme (HEPM) cells, bone marrow derived mesenchymal stem cells (MSCs), and human adipose derived stem cells (ADSCs) were cultured on a flat hydrogel of different concentrations of alginate-RGD, and in the miniaturized 3D core of microcapsules with either a 2% alginate or 2% alginate-RGD shell. The core was made of 0%, 0.5%, or 2% alginate-RGD. Cell spreading was observed in all systems containing the RGD peptide, and the cell morphology was quantified by measuring the cell surface area and circularity. In all types of stem cells, there was a significant increase in the cell surface area (p < 0.05) and a significant decrease in cell circularity (p < 0.01) in alginate-RGD conditions, indicating that cells spread much more readily in environments containing the peptide. This control over the cell spreading within a 3D microenvironment can help to create the ideal biomimetic condition in which to conduct further studies on cell behavior.

Direct influence of culture dimensionality on human mesenchymal stem cell differentiation at various matrix stiffnesses using a fibrous self-assembling peptide hydrogel.

Much is unknown about the effects of culture dimensionality on cell behavior due to the lack of biomimetic substrates that are suitable for directly comparing cells grown on two-dimensional (2D) and encapsulated within three-dimensional (3D) matrices of the same stiffness and biochemistry. To overcome this limitation, we used a self-assembling peptide hydrogel system that has tunable stiffness and cell-binding site density as well as a fibrous microarchitecture resembling the structure of collagen. We investigated the effect of culture dimensionality on human mesenchymal stem cell differentiation at different values of matrix stiffness (G' = 0.25, 1.25, 5, and 10 kPa) and a constant RGD (Arg-Gly-Asp) binding site concentration. In the presence of the same soluble induction factors, culture on top of stiff gels facilitated the most efficient osteogenesis, while encapsulation within the same stiff gels resulted in a switch to predominantly terminal chondrogenesis. Adipogenesis dominated at soft conditions, and 3D culture induced better adipogenic differentiation than 2D culture at a given stiffness. Interestingly, initial matrix-induced cell morphology was predictive of these end phenotypes. Furthermore, optimal culture conditions corresponded to each cell type's natural niche within the body, highlighting the importance of incorporating native matrix dimensionality and stiffness into tissue engineering strategies. © 2016 Wiley Periodicals, Inc. J Biomed Mater Res Part A: 104A: 2356-2368, 2016.

Vascular Mechanics in Decellularized Aortas and Coronary Resistance Microvessels in Type 2 Diabetic db/db Mice.

We previously reported differences in stiffness between macro- and micro-vessels in type 2 diabetes (T2DM). The aim of this study was to define the mechanical properties of the ECM independent of vascular cells in coronary resistance micro-vessels (CRMs) and macro-vessels (aorta) in control Db/db and T2DM db/db mice. Passive vascular remodeling and mechanics were measured in both intact and decellularized CRMs and aortas from 0 to 125 mmHg. We observed no differences in intact control and diabetic aortic diameters, wall thicknesses, or stiffnesses (p > 0.05). Aortic decellularization caused a significant increase in internal and external diameters and incremental modulus over a range of pressures that occurred to a similar degree in T2DM. Differences in aortic diameters due to decellularization occurred at lower pressures (0-75 mmHg) and converged with intact aortas at higher, physiological pressures (100-125 mmHg). In contrast, CRM decellularization caused increased internal diameter and incremental modulus only in the db/db mice, but unlike the aorta, the intact and decellularized CRM curves were more parallel. These data suggest that (1) micro-vessels may be more sensitive to early adverse consequences of diabetes than macro-vessels and (2) the ECM is a structural limit in aortas, but not CRMs.

Arterial levels of oxygen stimulate intimal hyperplasia in human saphenous veins via a ROS-dependent mechanism.

Saphenous veins used as arterial grafts are exposed to arterial levels of oxygen partial pressure (pO2), which are much greater than what they experience in their native environment. The object of this study is to determine the impact of exposing human saphenous veins to arterial pO2. Saphenous veins and left internal mammary arteries from consenting patients undergoing coronary artery bypass grafting were cultured ex vivo for 2 weeks in the presence of arterial or venous pO2 using an established organ culture model. Saphenous veins cultured with arterial pO2 developed intimal hyperplasia as evidenced by 2.8-fold greater intimal area and 5.8-fold increase in cell proliferation compared to those freshly isolated. Saphenous veins cultured at venous pO2 or internal mammary arteries cultured at arterial pO2 did not develop intimal hyperplasia. Intimal hyperplasia was accompanied by two markers of elevated reactive oxygen species (ROS): increased dihydroethidium associated fluorescence (4-fold, p<0.05) and increased levels of the lipid peroxidation product, 4-hydroxynonenal (10-fold, p<0.05). A functional role of the increased ROS saphenous veins exposed to arterial pO2 is suggested by the observation that chronic exposure to tiron, a ROS scavenger, during the two-week culture period, blocked intimal hyperplasia. Electron paramagnetic resonance based oximetry revealed that the pO2 in the wall of the vessel tracked that of the atmosphere with a ~30 mmHg offset, thus the cells in the vessel wall were directly exposed to variations in pO2. Monolayer cultures of smooth muscle cells isolated from saphenous veins exhibited increased proliferation when exposed to arterial pO2 relative to those cultured at venous pO2. This increased proliferation was blocked by tiron. Taken together, these data suggest that exposure of human SV to arterial pO2 stimulates IH via a ROS-dependent pathway.

Agent-based modeling traction force mediated compaction of cell-populated collagen gels using physically realistic fibril mechanics.

Agent-based modeling was used to model collagen fibrils, composed of a string of nodes serially connected by links that act as Hookean springs. Bending mechanics are implemented as torsional springs that act upon each set of three serially connected nodes as a linear function of angular deflection about the central node. These fibrils were evaluated under conditions that simulated axial extension, simple three-point bending and an end-loaded cantilever. The deformation of fibrils under axial loading varied <0.001% from the analytical solution for linearly elastic fibrils. For fibrils between 100 µm and 200 µm in length experiencing small deflections, differences between simulated deflections and their analytical solutions were <1% for fibrils experiencing three-point bending and <7% for fibrils experiencing cantilever bending. When these new rules for fibril mechanics were introduced into a model that allowed for cross-linking of fibrils to form a network and the application of cell traction force, the fibrous network underwent macroscopic compaction and aligned between cells. Further, fibril density increased between cells to a greater extent than that observed macroscopically and appeared similar to matrical tracks that have been observed experimentally in cell-populated collagen gels. This behavior is consistent with observations in previous versions of the model that did not allow for the physically realistic simulation of fibril mechanics. The significance of the torsional spring constant value was then explored to determine its impact on remodeling of the simulated fibrous network. Although a stronger torsional spring constant reduced the degree of quantitative remodeling that occurred, the inclusion of torsional springs in the model was not necessary for the model to reproduce key qualitative aspects of remodeling, indicating that the presence of Hookean springs is essential for this behavior. These results suggest that traction force mediated matrix remodeling may be a robust phenomenon not limited to fibrils with a precise set of material properties.

Complex matrix remodeling and durotaxis can emerge from simple rules for cell-matrix interaction in agent-based models.

Using a top-down approach, an agent-based model was developed within NetLogo where cells and extracellular matrix (ECM) fibers were composed of multiple agents to create deformable structures capable of exerting, reacting to, and transmitting mechanical force. At the beginning of the simulation, long fibers were randomly distributed and cross linked. Throughout the simulation, imposed rules allowed cells to exert traction forces by extending pseudopodia, binding to fibers and pulling them towards the cell. Simulated cells remodeled the fibrous matrix to change both the density and alignment of fibers and migrated within the matrix in ways that are consistent with previous experimental work. For example, cells compacted the matrix in their pericellular regions much more than the average compaction experienced for the entire matrix (696% versus 21%). Between pairs of cells, the matrix density increased (by 92%) and the fibers became more aligned (anisotropy index increased from 0.45 to 0.68) in the direction parallel to a line connecting the two cells, consistent with the "lines of tension" observed in experiments by others. Cells migrated towards one another at an average rate of ∼0.5 cell diameters per 10,000 arbitrary units (AU); faster migration occurred in simulations where the fiber density in the intercellular area was greater. To explore the potential contribution of matrix stiffness gradients in the observed migration (i.e., durotaxis), the model was altered to contain a regular lattice of fibers possessing a stiffness gradient and just a single cell. In these simulations cells migrated preferentially in the direction of increasing stiffness at a rate of ∼2 cell diameter per 10,000 AU. This work demonstrates that matrix remodeling and durotaxis, both complex phenomena, might be emergent behaviors based on just a few rules that control how a cell can interact with a fibrous ECM.