PhD candidate, Technical University of Eindhoven
Predicting and understanding cellular forces and (re)orientation in response to different stimuli
Our body is populated by trillions of cells that constantly remodel and respond to the stimuli of their surroundings. For example, cells are known to change their orientation in response to the mechanical stimuli caused by blood flow and the topographical stimuli provided by collagen fibers, the most abundant protein in our bodies. Mostly along their main direction, cells exert traction forces that can influence the biomechanics and functionality of tissues in our bodies. For instance, excessive cellular forces can lead to unwanted retraction and opening of heart valves, fundamental structures that ensure the unidirectionality of the blood circulation. Predicting and understanding cellular forces and (re)orientation is therefore of paramount importance.
In this context, computational simulations are very useful because of their predictive potential and versatility in testing different hypotheses. During my PhD I have developed unique computational models for the prediction and explanation of the remodeling and (re)orientation of cells in response to a wide range of mechanical and topographical stimuli. For the first time, these computational models could predict cellular forces and (re)orientation both in two- and three-dimensional environments. Overall, the computational simulations suggest that many feedback mechanisms contribute to the responses of cells to the stimuli coming from their surroundings.
In a subsequent study, I have coupled the models for cellular (re)orientation with a mathematical model for collagen remodeling. These coupled computational models were adopted to investigate cellular and collagen remodeling in native heart valves. Investigating collagen remodeling in such tissues is particularly important, because collagen fibers are their main load-bearing constituent, and collagen fiber organization strongly influences the heart valve functionality.
Strikingly, the computational simulations could successfully predict and explain the fundamental contribution of cells for the organization of collagen fibers in native heart valves. This computational approach is not only useful to understand native heart valves, but it also provides useful information for the improvement of current therapies for heart valve diseases, and the advancement of the growing field of regenerative medicine. Furthermore, it is also applicable to a wide range of other tissues, such as arteries and tendons.
Abstract: A kinetic model based on constrained mixture theory was developed to describe the reorganization of actin stress fibers in adherent cells in response to diverse patterns of mechanical stretch. The model was based on reports that stress fibers are pre-extended at a "homeostatic" level under normal, non-perturbed conditions, and that perturbations in stress fiber length destabilize stress fibers. In response to a step change in matrix stretch, the model predicts that stress fibers are initially stretched in registry with the matrix, but that these overly stretched fibers are gradually replaced by new fibers assembled with the homeostatic level of stretch in the new configuration of the matrix. In contrast, average fiber stretch is chronically perturbed from the homeostatic level when the cells are subjected to cyclic equibiaxial stretch. The model was able to describe experimentally measured time courses of stress fiber reorientation perpendicular to the direction of cyclic uniaxial stretch, as well as the lack of alignment in response to equibiaxial stretch. The model also accurately described the relationship between stretch magnitude and the extent of stress fiber alignment in endothelial cells subjected to cyclic uniaxial stretch. Further, in the case of cyclic simple elongation with transverse matrix contraction, stress fibers orient in the direction of least perturbation in stretch. In summary, the model predicts that the rate of stretch-induced stress fiber disassembly determines the rate of alignment, and that stress fibers tend to orient toward the direction of minimum matrix stretch where the rate of stress fiber turnover is a minimum.
Pub.: 26 Dec '08, Pinned: 29 Oct '17
Abstract: Preclinical studies of tissue-engineered heart valves (TEHVs) showed retraction of the heart valve leaflets as major failure of function mechanism. This retraction is caused by both passive and active cell stress and passive matrix stress. Cell-mediated retraction induces leaflet shortening that may be counteracted by the hemodynamic loading of the leaflets during diastole. To get insight into this stress balance, the amount and duration of stress generation in engineered heart valve tissue and the stress imposed by physiological hemodynamic loading are quantified via an experimental and a computational approach, respectively. Stress generation by cells was measured using an earlier described in vitro model system, mimicking the culture process of TEHVs. The stress imposed by the blood pressure during diastole on a valve leaflet was determined using finite element modeling. Results show that for both pulmonary and systemic pressure, the stress imposed on the TEHV leaflets is comparable to the stress generated in the leaflets. As the stresses are of similar magnitude, it is likely that the imposed stress cannot counteract the generated stress, in particular when taking into account that hemodynamic loading is only imposed during diastole. This study provides a rational explanation for the retraction found in preclinical studies of TEHVs and represents an important step towards understanding the retraction process seen in TEHVs by a combined experimental and computational approach.
Pub.: 26 Nov '13, Pinned: 29 Oct '17
Abstract: Mechanical cues from the extracellular microenvironment play a central role in regulating the structure, function and fate of living cells. Nevertheless, the precise nature of the mechanisms and processes underlying this crucial cellular mechanosensitivity remains a fundamental open problem. Here we provide a novel framework for addressing cellular sensitivity and response to external forces by experimentally and theoretically studying one of its most striking manifestations--cell reorientation to a uniform angle in response to cyclic stretching of the underlying substrate. We first show that existing approaches are incompatible with our extensive measurements of cell reorientation. We then propose a fundamentally new theory that shows that dissipative relaxation of the cell's passively-stored, two-dimensional, elastic energy to its minimum actively drives the reorientation process. Our theory is in excellent quantitative agreement with the complete temporal reorientation dynamics of individual cells measured over a wide range of experimental conditions, thus elucidating a basic aspect of mechanosensitivity.
Pub.: 31 May '14, Pinned: 29 Oct '17
Abstract: Cells respond to their mechanical environment in different ways: while their response in terms of differentiation and proliferation has been widely studied, the question of the direction in which cells align when subject to a complex mechanical loading in a 3D environment is still widely open. In the present paper, we formulate the hypothesis that the cells orientate in the direction of unitary stretch computed from the right Cauchy-Green tensor in a given mechanical environment. The implications of this hypothesis are studied in different simple cases corresponding to either the available in vitro experimental data or physiological conditions, starting from finite element analysis results to computed preferential cellular orientation. The present contribution is a first step to the formulation of a deeper understanding of the orientation of cells within or at the surface of any 3D scaffold subject to any complex load. It is believed that these initial preferential directions have strong implications as far as the anisotropy of biological structures is concerned.
Pub.: 28 Sep '17, Pinned: 29 Oct '17
Abstract: Characterizing how cells in three-dimensional (3D) environments or natural tissues respond to biophysical stimuli is a longstanding challenge in biology and tissue engineering. We demonstrate a strategy to monitor morphological and mechanical responses of contractile fibroblasts in a 3D environment. Cells responded to stretch through specific, cell-wide mechanisms involving staged retraction and reinforcement. Retraction responses occurred for all orientations of stress fibers and cellular protrusions relative to the stretch direction, while reinforcement responses, including extension of cellular processes and stress fiber formation, occurred predominantly in the stretch direction. A previously unreported role of F-actin clumps was observed, with clumps possibly acting as F-actin reservoirs for retraction and reinforcement responses during stretch. Responses were consistent with a model of cellular sensitivity to local physical cues. These findings suggest mechanisms for global actin cytoskeleton remodeling in non-muscle cells and provide insight into cellular responses important in pathologies such as fibrosis and hypertension.
Pub.: 10 Jan '13, Pinned: 29 Oct '17
Abstract: Cells play an active role in the maintenance of mechanical homeostasis within tissues and their response to elastic forces is important for tissue engineering. We predict the collective response of an ensemble of contractile cells in a three-dimensional elastic medium to externally applied strain fields. Motivated by experiment, we model the cells as polarizable force dipoles that change their orientation in response to the local elastic strain. The analogy between the mechanical response of these systems and the dielectric response of polar molecules is used to calculate the elastic response function. We use this analogy to evaluate the average cell orientation, the mean polarization stress, and the effective elastic constants of the material, as a function of the cell concentration and matrix properties.
Pub.: 10 Oct '06, Pinned: 29 Oct '17
Abstract: Adhering cells actively probe the mechanical properties of their environment and use the resulting information to position and orient themselves. We show that a large body of experimental observations can be consistently explained from one unifying principle, namely that cells strengthen contacts and cytoskeleton in the direction of large effective stiffness. Using linear elasticity theory to model the extracellular environment, we calculate optimal cell organization for several situations of interest and find excellent agreement with experiments for fibroblasts, both on elastic substrates and in collagen gels: cells orient in the direction of external tensile strain; they orient parallel and normal to free and clamped surfaces, respectively; and they interact elastically to form strings. Our method can be applied for rational design of tissue equivalents. Moreover, our results indicate that the concept of contact guidance has to be reevaluated. We also suggest that cell-matrix contacts are up-regulated by large effective stiffness in the environment because, in this way, build-up of force is more efficient.
Pub.: 29 Jul '03, Pinned: 29 Oct '17
Abstract: Collagen is the main load-bearing component of many soft tissues and has a large influence on the mechanical behavior of tissues when exposed to mechanical loading. Therefore, it is important to increase our understanding of collagen remodeling in soft tissues to understand the mechanisms behind pathologies and to control the development of the collagen network in engineered tissues. In the present study, a constitutive model was developed by coupling a recently developed model describing the orientation and contractile stresses exerted by cells in response to mechanical stimuli to physically motivated collagen remodeling laws. In addition, cell-mediated contraction of the collagen fibers was included as a mechanism for tissue compaction. The model appeared to be successful in predicting a range of experimental observations, which are (1) the change in transition stretch of periosteum after remodeling at different applied stretches, (2) the compaction and alignment of collagen fibers in tissue-engineered strips, (3) the fiber alignment in cruciform gels with different arm widths, and (4) the alignment of collagen fibers in engineered vascular grafts. Moreover, by changing the boundary conditions, the model was able to predict a helical architecture in the vascular graft without assuming the presence of two helical fiber families a priori. Ultimately, this model may help to increase our understanding of collagen remodeling in physiological and pathological conditions, and it may provide a tool for determining the optimal experimental conditions for obtaining native-like collagen architectures in engineered tissues.
Pub.: 29 Dec '13, Pinned: 29 Oct '17
Abstract: The orientation of cells and associated F-actin stress fibers is essential for proper tissue functioning. We have previously developed a computational model that qualitatively describes stress fiber orientation in response to a range of mechanical stimuli. In this paper, the aim is to quantitatively validate the model in a static, heterogeneous environment. The stress fiber orientation in uniaxially and biaxially constrained microscale tissues was investigated using a recently developed experimental system. Computed and experimental stress fiber orientations were compared, while accounting for changes in orientation with location in the tissue. This allowed for validation of the model, and additionally, it showed how sensitive the stress fiber orientation in the experimental system is to the location where it is measured, i.e., the heterogeneity of the stress fiber orientation. Computed and experimental stress fiber orientations showed good quantitative agreement in most regions. A strong local alignment near the locations where boundary conditions were enforced was observed for both uniaxially and biaxially constrained tissues. Excepting these regions, in biaxially constrained tissues, no preferred orientation was found and the distribution was independent of location. The stress fiber orientation in uniaxially constrained tissues was more heterogeneous, and stress fibers mainly oriented in the constrained direction or along the free edge. These results indicate that the stress fiber orientation in these constrained microtissues is mainly determined by the local mechanical environment, as hypothesized in our model, and also that the model is a valid tool to predict stress fiber orientation in heterogeneously loaded tissues.
Pub.: 25 Jan '14, Pinned: 29 Oct '17
Abstract: Cells in vivo reside within complex microenvironments composed of both biochemical and biophysical cues. The dynamic feedback between cells and their microenvironments hinges upon biophysical cues that regulate critical cellular behaviors. Understanding this regulation from sensing to reaction to feedback is therefore critical, and a large effort is afoot to identify and mathematically model the fundamental mechanobiological mechanisms underlying this regulation. This review provides a critical perspective on recent progress in mathematical models for the responses of cells to the biophysical cues in their microenvironments, including dynamic strain, osmotic shock, fluid shear stress, mechanical force, matrix rigidity, porosity, and matrix shape. The review highlights key successes and failings of existing models, and discusses future opportunities and challenges in the field.
Pub.: 10 Jul '17, Pinned: 29 Oct '17
Abstract: Numerical simulations that incorporate a biochemomechanical model for the contractility of the cytoskeleton have been used to rationalize the following observations. Uniaxial cyclic stretching of cells causes stress fibers to align perpendicular to the stretch direction, with degree of alignment dependent on the stretch strain magnitude, as well as the frequency and the transverse contraction of the substrate. Conversely, equibiaxial cyclic stretching induces a uniform distribution of stress fiber orientations. Demonstrations that the model successfully predicts the alignments experimentally found are followed by a parameter study to investigate the influence of a range of key variables including the stretch magnitude, the intrinsic rate sensitivity of the stress fibers, the straining frequency, and the transverse contraction of the substrate. The primary predictions are as follows. The rate sensitivity has a strong influence on alignment, equivalent to that attained by a few percent of additional stretch. The fiber alignment increases with increasing cycling frequency. Transverse contraction of the substrate causes the stress fibers to organize into two symmetrical orientations with respect to the primary stretch direction.
Pub.: 06 Jun '08, Pinned: 29 Oct '17
Abstract: A general model for the contractility of cells is presented that accounts for the dynamic reorganization of the cytoskeleton. The model is motivated by three key biochemical processes: (i) an activation signal that triggers actin polymerization and myosin phosphorylation, (ii) the tension-dependent assembly of the actin and myosin into stress fibers, and (iii) the cross-bridge cycling between the actin and myosin filaments that generates the tension. Simple relations are proposed to model these coupled phenomena and a continuum model developed for simulating cell contractility. The model is capable of predicting key experimentally established characteristics including: (i) the decrease in the forces generated by the cell with increasing substrate compliance, (ii) the influence of cell shape and boundary conditions on the development of structural anisotropy, and (iii) the high concentration of the stress fibers at the focal adhesions. We present numerical examples of a square cell on four supports to demonstrate these capabilities.
Pub.: 09 Sep '06, Pinned: 29 Oct '17
Abstract: Publication date: 15 November 2016 Source:Biophysical Journal, Volume 111, Issue 10 Author(s): Tommaso Ristori, Andrea Vigliotti, Frank P.T. Baaijens, Sandra Loerakker, Vikram S. Deshpande Cells respond to both mechanical and topographical stimuli by reorienting and reorganizing their cytoskeleton. Under certain conditions, such as for cells on cyclically stretched grooved substrates, the effects of these stimuli can be antagonistic. The biophysical processes that lead to the cellular reorientation resulting from such a competition are not clear yet. In this study, we hypothesized that mechanical cues and the diffusion of the intracellular signal produced by focal adhesions are determinants of the final cellular alignment. This hypothesis was investigated by means of a computational model, with the aim to simulate the (re)orientation of cells cultured on cyclically stretched grooved substrates. The computational results qualitatively agree with previous experimental studies, thereby supporting our hypothesis. Furthermore, cellular behavior resulting from experimental conditions different from the ones reported in the literature was simulated, which can contribute to the development of new experimental designs.
Pub.: 20 Nov '16, Pinned: 25 Oct '17
Abstract: Understanding collagen and stress fiber remodeling is essential for the development of engineered tissues with good functionality. These processes are complex, highly interrelated, and occur over different time scales. As a result, excessive computational costs are required to computationally predict the final organization of these fibers in response to dynamic mechanical conditions. In this study, an analytical approximation of a stress fiber remodeling evolution law was derived. A comparison of the developed technique with the direct numerical integration of the evolution law showed relatively small differences in results, and the proposed method is one to two orders of magnitude faster.
Pub.: 30 Jan '16, Pinned: 25 Oct '17
Abstract: One of the most critical problems in heart valve tissue engineering is the progressive development of valvular insufficiency due to leaflet retraction. Understanding the underlying mechanisms of this process is crucial for developing tissue-engineered heart valves (TEHVs) that maintain their functionality in the long term. In the present study, we adopted a computational approach to predict the remodeling process in TEHVs subjected to dynamic pulmonary and aortic pressure conditions, and to assess the risk of valvular insufficiency. In addition, we investigated the importance of the intrinsic cell contractility on the final outcome of the remodeling process. For valves implanted in the aortic position, the model predictions suggest that valvular insufficiency is not likely to occur as the blood pressure is high enough to prevent the development of leaflet retraction. In addition, the collagen network was always predicted to remodel towards a circumferentially aligned network, which is corresponding to the native situation. In contrast, for valves implanted in the pulmonary position, our model predicted that there is a high risk for the development of valvular insufficiency, unless the cell contractility is very low. Conversely, the development of a circumferential collagen network was only predicted at these pressure conditions when cell contractility was high. Overall, these results, therefore, suggest that tissue remodeling at aortic pressure conditions is much more stable and favorable compared to tissue remodeling at pulmonary pressure conditions.
Pub.: 19 Oct '15, Pinned: 25 Oct '17
Abstract: In this study we present a steady-state adaptation of the thermodynamically motivated stress fiber (SF) model of Vigliotti et al. (2015). We implement this steady-state formulation in a non-local finite element setting where we also consider global conservation of the total number of cytoskeletal proteins within the cell, global conservation of the number of binding integrins on the cell membrane, and adhesion limiting ligand density on the substrate surface. We present a number of simulations of cell spreading in which we consider a limited subset of the possible deformed spread-states assumed by the cell in order to examine the hypothesis that free energy minimization drives the process of cell spreading. Simulations suggest that cell spreading can be viewed as a competition between (i) decreasing cytoskeletal free energy due to strain induced assembly of cytoskeletal proteins into contractile SFs, and (ii) increasing elastic free energy due to stretching of the mechanically passive components of the cell. The computed minimum free energy spread area is shown to be lower for a cell on a compliant substrate than on a rigid substrate. Furthermore, a low substrate ligand density is found to limit cell spreading. The predicted dependence of cell spread area on substrate stiffness and ligand density is in agreement with the experiments of Engler et al. (2003). We also simulate the experiments of Théry et al. (2006), whereby initially circular cells deform and adhere to "V-shaped" and "Y-shaped" ligand patches. Analysis of a number of different spread states reveals that deformed configurations with the lowest free energy exhibit a SF distribution that corresponds to experimental observations, i.e. a high concentration of highly aligned SFs occurs along free edges, with lower SF concentrations in the interior of the cell. In summary, the results of this study suggest that cell spreading is driven by free energy minimization based on a competition between decreasing cytoskeletal free energy and increasing passive elastic free energy.
Pub.: 25 Jun '17, Pinned: 25 Oct '17
Abstract: To build anisotropic, mechanically functioning tissue, it is essential to understand how cells orient in response to mechanical stimuli. Therefore, a computational model was developed which predicts cell orientation, based on the actin stress fiber distribution inside the cell. In the model, the stress fiber distribution evolves dynamically according to the following: (1) Stress fibers contain polymerized actin. The total amount of depolymerized plus polymerized actin is constant. (2) Stress fibers apply tension to their environment. This active tension is maximal when strain rate and absolute strain are zero and reduces with increasing shortening rate and absolute strain. (3) A high active fiber stress in a direction leads to a large amount of fibers in this direction. (4) The cell is attached to a substrate; all fiber stresses are homogenized into a total cell stress, which is in equilibrium with substrate stress. This model predicts that on a substrate of anisotropic stiffness, fibers align in the stiffest direction. Under cyclic strain when the cellular environment is so stiff that no compaction occurs (1 MPa), the model predicts strain avoidance, which is more pronounced with increasing strain frequency or amplitude. Under cyclic strain when the cellular environment is so soft that cells can compact it (10 kPa), the model predicts a preference for the cyclically strained compared to the compacting direction. These model predictions all agree with experimental evidence. For the first time, a computational model predicts cell orientation in response to this range of mechanical stimuli using a single set of parameters.
Pub.: 28 May '13, Pinned: 25 Oct '17
Join Sparrho today to stay on top of science
Discover, organise and share research that matters to you