Cell differentiation, proliferation and migration are essential processes in tissue regeneration. Experimental evidence confirms that cell differentiation or proliferation can be regulated according to the extracellular matrix stiffness. For instance, mesenchymal stem cells (MSCs) can differentiate to neuroblast, chondrocyte or osteoblast within matrices mimicking the stiffness of their native substrate. However, the precise mechanisms by which the substrate stiffness governs cell differentiation or proliferation are not well known. Therefore, a mechano-sensing computational model is here developed to elucidate how substrate stiffness regulates cell differentiation and/or proliferation during cell migration. In agreement with experimental observations, it is assumed that internal deformation of the cell (a mechanical signal) together with the cell maturation state directly coordinates cell differentiation and/or proliferation. Our findings indicate that MSC differentiation to neurogenic, chondrogenic or osteogenic lineage specifications occurs within soft (0.1-1 kPa), intermediate (20-25 kPa) or hard (30-45 kPa) substrates, respectively. These results are consistent with well-known experimental observations. Remarkably, when a MSC differentiate to a compatible phenotype, the average net traction force depends on the substrate stiffness in such a way that it might increase in intermediate and hard substrates but it would reduce in a soft matrix. However, in all cases the average net traction force considerably increases at the instant of cell proliferation because of cell-cell interaction. Moreover cell differentiation and proliferation accelerate with increasing substrate stiffness due to the decrease in the cell maturation time. Thus, the model provides insights to explain the hypothesis that substrate stiffness plays a key role in regulating cell fate during mechanotaxis.

Between other parameters, cell migration is partially guided by the mechanical properties of its substrate. Although many experimental works have been developed to understand the effect of substrate mechanical properties on cell migration, accurate 3D cell locomotion models have not been presented yet. In this paper, we present a novel 3D model for cells migration. In the presented model, we assume that a cell follows two main processes: in the first process, it senses its interface with the substrate to determine the migration direction and in the second process, it exerts subsequent forces to move. In the presented model, cell traction forces are considered to depend on cell internal deformation during the sensing step. A random protrusion force is also considered which may change cell migration direction and/or speed. The presented model was applied for many cases of migration of the cells. The obtained results show high agreement with the available experimental and numerical data.

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Cell migration is a vital process in many biological phenomena ranging from wound healing to tissue regeneration. Over the past few years, it has been proven that in addition to cell-cell and cell-substrate mechanical interactions (mechanotaxis), cells can be driven by thermal, chemical and/or electrical stimuli. A numerical model was recently presented by the authors to analyse single cell migration in a multi-signalling substrate. That work is here extended to include multi-cell migration due to cell-cell interaction in a multi-signalling substrate under different conditions. This model is based on balancing the forces that act on the cell population in the presence of different guiding cues. Several numerical experiments are presented to illustrate the effect of different stimuli on the trajectory and final location of the cell population within a 3D heterogeneous multi-signalling substrate. Our findings indicate that although multi-cell migration is relatively similar to single cell migration in some aspects, the associated behaviour is very different. For instance, cell-cell interaction may delay single cell migration towards effective cues while increasing the magnitude of the average net cell traction force as well as the local velocity. Besides, the random movement of a cell within a cell population is slightly greater than that of single cell migration. Moreover, higher electrical field strength causes the cell slug to flatten near the cathode. On the other hand, as with single cell migration, the existence of electrotaxis dominates mechanotaxis, moving the cells to the cathode or anode pole located at the free surface. The numerical results here obtained are qualitatively consistent with related experimental works.

Cell morphology plays a critical role in many biological processes, such as cell migration, tissue development, wound healing and tumor growth. Recent investigations demonstrate that, among other stimuli, cells adapt their shapes according to their substrate stiffness. Until now, the development of this process has not been clear. Therefore, in this work, a new three-dimensional (3D) computational model for cell morphology has been developed. This model is based on a previous cell migration model presented by the same authors. The new model considers that during cell-substrate interaction, cell shape is governed by internal cell deformation, which leads to an accurate prediction of the cell shape according to the mechanical characteristic of its surrounding micro-environment. To study this phenomenon, the model has been applied to different numerical cases. The obtained results, which are qualitatively consistent with well-known related experimental works, indicate that cell morphology not only depends on substrate stiffness but also on the substrate boundary conditions. A cell located within an unconstrained soft substrate (several kPa) with uniform stiffness is unable to adhere to its substrate or to send out pseudopodia. When the substrate stiffness increases to tens of kPa (intermediate and rigid substrates), the cell can adequately adhere to its substrate. Subsequently, as the traction forces exerted by the cell increase, the cell elongates and its shape changes. Within very stiff (hard) substrates, the cell cannot penetrate into its substrate or send out pseudopodia. On the other hand, a cell is found to be more elongated within substrates with a constrained surface. However, this elongation decreases when the cell approaches it. It can be concluded that the higher the net traction force, the greater the cell elongation, the larger the cell membrane area, and the less random the cell alignment.

Cell Migration associated with cell shape changes are of central importance in many biological processes ranging from morphogenesis to metastatic cancer cells. Cell movement is a result of cyclic changes of cell morphology due to effective forces on cell body, leading to periodic fluctuations of the cell length and cell membrane area. It is well-known that the cell can be guided by different effective stimuli such as mechanotaxis, thermotaxis, chemotaxis and/or electrotaxis. Regulation of intracellular mechanics and cell’s physical interaction with its substrate rely on control of cell shape during cell migration. In this notion, it is essential to understand how each natural or external stimulus may affect the cell behavior. Therefore, a three-dimensional (3D) computational model is here developed to analyze a free mode of cell shape changes during migration in a multi-signaling micro-environment. This model is based on previous models that are presented by the same authors to study cell migration with a constant spherical cell shape in a multi-signaling substrates and mechanotaxis effect on cell morphology. Using the finite element discrete methodology, the cell is represented by a group of finite elements. The cell motion is modeled by equilibrium of effective forces on cell body such as traction, protrusion, electrostatic and drag forces, where the cell traction force is a function of the cell internal deformations. To study cell behavior in the presence of different stimuli, the model has been employed in different numerical cases. Our findings, which are qualitatively consistent with well-known related experimental observations, indicate that adding a new stimulus to the cell substrate pushes the cell to migrate more directionally in more elongated form towards the more effective stimuli. For instance, the presence of thermotaxis, chemotaxis and electrotaxis can further move the cell centroid towards the corresponding stimulus, respectively, diminishing the mechanotaxis effect. Besides, the stronger stimulus imposes a greater cell elongation and more cell membrane area. The present model not only provides new insights into cell morphology in a multi-signaling micro-environment but also enables us to investigate in more precise way the cell migration in the presence of different stimuli.

Cell migration, differentiation, proliferation and apoptosis are the main processes in tissue regeneration. Mesenchymal Stem Cells (MSCs) have the potential to differentiate into many cell phenotypes such as tissue-or organ-specific cells to perform special functions. Experimental observations illustrate that differentiation and proliferation of these cells can be regulated according to internal forces induced within their Extracellular matrix (ECM). The process of how exactly they interpret and transduce these signals is not well understood. Therefore, a previously developed three-dimensional (3D) computational model is here extended and employed to study how force-free substrates (FFS) and force-induced substrate (FIS) control cell differentiation and/or proliferation during the mechanosensing process. Consistent with experimental observations, it is assumed that cell internal deformation (a mechanical signal) in correlation with the cell maturation state directly triggers cell differentiation and/or proliferation. ECM is modeled as Neo-Hookean hyperelastic material assuming that cells are cultured within 3D nonlinear hydrogels. In agreement with wellknown experimental observations, the findings here indicate that within neurogenic (0.1-1 kPa), chondrogenic (20-25 kPa) and osteogenic (30-45 kPa) substrates, MSC differentiation and cell proliferation can be precipitated by inducing the substrate with an internal force. Therefore, cells require a longer time to grow and maturate within force-free substrates than withen force-induced substrates. In the instance of MSC differentiation into a compatible phenotype, the magnitude of the net traction force increases within chondrogenic and osteogenic substrates while it reduces within neurogenic substrates. This is consistent with experimental studies and numerical works recently published by the same authors. However, in all cases the magnitude of the net traction force considerably increases at the instant of cell proliferation because of cell-cell interaction. Consequently, the present model provides new perspectives to delineate the role of force-induced substrates in remotely controlling the cell fate during cell-matrix interaction, which open the door for new tissue regeneration methodologies.

Ruptures occurred at lower velocities in the PRK cornea model than in the corneal stromal bed of the LASIK model following blunt foreign body impact.