Simulations of the contractile cycle in cell migration using a bio-chemical–mechanical model

Myosin-independent stiffness sensing by fibroblasts is regulated by the viscoelasticity of flowing actin

The stiffness of the extracellular matrix induces differential tension within integrin-based adhesions, triggering differential mechanoresponses. However, it has been unclear if the stiffness-dependent differential tension is induced solely by myosin activity. Here, we report that in the absence of myosin contractility, 3T3 fibroblasts still transmit stiffness-dependent differential levels of traction. This myosin-independent differential traction is regulated by polymerizing actin assisted by actin nucleators Arp2/3 and formin where formin has a stronger contribution than Arp2/3 to both traction and actin flow. Intriguingly, despite only slight changes in F-actin flow speed observed in cells with the combined inhibition of Arp2/3 and myosin compared to cells with sole myosin inhibition, they show a 4-times reduction in traction than cells with myosin-only inhibition. Our analyses indicate that traditional models based on rigid F-actin are inadequate for capturing such dramatic force reduction with similar actin flow. Instead, incorporating the F-actin network's viscoelastic properties is crucial. Our new model including the F-actin viscoelasticity reveals that Arp2/3 and formin enhance stiffness sensitivity by mechanically reinforcing the F-actin network, thereby facilitating more effective transmission of flow-induced forces. This model is validated by cell stiffness measurement with atomic force microscopy and experimental observation of model-predicted stiffness-dependent actin flow fluctuation.

A DISCRETE MATHEMATICAL MODEL FOR SINGLE AND COLLECTIVE MOVEMENT IN AMOEBOID CELLS

In this paper, we develop a new discrete mathematical model for individual and collective cell motility. We introduce a mechanical model for the movement of a cell on a two-dimensional rigid surface to describe and investigate the cell–cell and cell–substrate interactions. The cell cytoskeleton is modeled as a series of springs and dashpots connected in parallel. The cell–substrate attachments and the cell protrusions are also included. In particular, this model is used to describe the directed movement of endothelial cells on a Matrigel plate. We compare the results from our model with experimental data. We show that cell density and substrate rigidity play an important role in network formation.

Simulation of actin distribution of osteoblasts on titanium pillar arrays using a bio-chemo-mechanical model

A numerical model for the adhesion of osteoblasts on titanium micropillar structures is suggested, and a function representing the concentration level of the adhesion on the pillars is constructed based on experimental observation. The introduction of this function helps a well-known bio-chemo-mechanical model to better predict the formation of actin in osteoblasts when they are laid on arrays of titanium micro-pillars of various size attached to silicon substrate. A parameter study suggests that each pillar is associated with a different pattern of adhesion. Our finding emphasises a capability of the bio-chemo-mechanical model that it can well explain the strong influence of the boundary condition on the formation of actin within the cells.

Semi-analytical representation of the activation level in stress fibre directions as alternative to the angular representation in the bio-chemo-mechanical model for cell contractility

The bio-chemo-mechanical model has many applications in modelling cell contractility. In simulations this model usually is coupled to the continuum mechanics of the cell by defining a large number of directions for stress fibres at each point. In this paper, another representation for coupling the biochemical processes in the bio-chemo-mechanical model is introduced. Using a quadratic form to represent the angular dependency of the activation level, the model's number of degrees of freedom is significantly reduced. Numerical results similar to the original representation are obtained while a significant improvement in computation time is achieved.

[Effects of long time different negative pressures on osteogenic differentiation of rabbit bone mesenchymal stem cells]

Objective

To investigate the effects of long time different negative pressures on osteogenic diffe-rentiation of rabbit bone mesenchymal stem cells (BMSCs).

Methods

The rabbit BMSCs were isolated and cultured by density gradient centrifugation. Flow cytometry was used to analyze expression of surface markers. The third passage cells cultured under condition of osteogenic induction and under different negative pressure of 0 mm Hg (control group), 75 mm Hg (low negative pressure group), and 150 mm Hg (high negative pressure group) (1 mm Hg=0.133 kPa), and the negative pressure time was 30 min/h. Cell growth was observed under phase contrast microscopy, and the growth curve was drawn; alkaline phosphatase (ALP) activity was detected by ELISA after induced for 3, 7, and 14 days. The mRNA and protein expressions of collagen type I (COL-I) and osteocalcin (OC) in BMSCs were analyzed by real-time fluorescence quantitative PCR and Western blot.

Results

The cultured cells were identified as BMSCs by flow cytometry. The third passage BMSCs exhibited typical long shuttle and irregular shape. Cell proliferation was inhibited with the increase of negative pressure. After induced for 4 days, the cell number of high negative pressure group was significantly less than that in control group and low negative pressure group ( P<0.05), but there was no significant difference between the low negative pressure group and the control group ( P>0.05); at 5-7 days, the cell number showed significant difference between 3 groups ( P<0.05). The greater the negative pressure was, the greater the inhibition of cell proliferation was. There was no significant difference in ALP activity between groups at 3 days after induction ( P>0.05); the ALP activity showed significant difference ( P<0.05) between the high negative pressure group and the control group at 7 days after induction; and significant difference was found in the ALP activity between 3 groups at 14 days after induction ( P<0.05). The greater the negative pressure was, the higher the ALP activity was. Real-time fluorescence quantitative PCR and Western blot detection showed that the mRNA and protein expressions of COL-I and OC protein were significantly higher in low negative pressure group and high negative pressure group than control group ( P<0.05), and in the high negative pressure group than the low negative pressure group ( P<0.05).

Conclusion

With the increase of the negative pressure, the osteogenic differentiation ability of BMSCs increases gradually, but the cell proliferation is inhibited.

Spatial and temporal coordination of traction forces in one-dimensional cell migration

Migration of a fibroblast along a collagen fiber can be regarded as cell locomotion in one-dimension (1D). In this process, a cell protrudes forward, forms a new adhesion, produces traction forces, and releases its rear adhesion in order to advance itself along a path. However, how a cell coordinates its adhesion formation, traction forces, and rear release in 1D migration is unclear. Here, we studied fibroblasts migrating along a line of microposts. We found that when the front of a cell protruded onto a new micropost, the traction force produced at its front increased steadily, but did so without a temporal correlation in the force at its rear. Instead, the force at the front coordinated with a decrease in force at the micropost behind the front. A similar correlation in traction forces also occurred at the rear of a cell, where a decrease in force due to adhesion detachment corresponded to an increase in force at the micropost ahead of the rear. Analysis with a bio-chemo-mechanical model for traction forces and adhesion dynamics indicated that the observed relationship between traction forces at the front and back of a cell is possible only when cellular elasticity is lower than the elasticity of the cellular environment.

Computational Tension Mapping of Adherent Cells Based on Actin Imaging

Forces transiting through the cytoskeleton are known to play a role in adherent cell activity. Up to now few approaches haves been able to determine theses intracellular forces. We thus developed a computational mechanical model based on a reconstruction of the cytoskeleton of an adherent cell from fluorescence staining of the actin network and focal adhesions (FA). Our custom made algorithm converted the 2D image of an actin network into a map of contractile interactions inside a 2D node grid, each node representing a group of pixels. We assumed that actin filaments observed under fluorescence microscopy, appear brighter when thicker, we thus presumed that nodes corresponding to pixels with higher actin density were linked by stiffer interactions. This enabled us to create a system of heterogeneous interactions which represent the spatial organization of the contractile actin network. The contractility of this interaction system was then adapted to match the level of force the cell truly exerted on focal adhesions; forces on focal adhesions were estimated from their vinculin expressed size. This enabled the model to compute consistent mechanical forces transiting throughout the cell. After computation, we applied a graphical approach on the original actin image, which enabled us to calculate tension forces throughout the cell, or in a particular region or even in single stress fibers. It also enabled us to study different scenarios which may indicate the mechanical role of other cytoskeletal components such as microtubules. For instance, our results stated that the ratio between intra and extra cellular compression is inversely proportional to intracellular tension.

Review of cellular mechanotransduction on micropost substrates

As physical entities, living cells can sense and respond to various stimulations within and outside the body through cellular mechanotransduction. Any deviation in cellular mechanotransduction will not only undermine the orchestrated regulation of mechanical responses, but also lead to the breakdown of their physiological function. Therefore, a quantitative study of cellular mechanotransduction needs to be conducted both in experiments and in computational simulations to investigate the underlying mechanisms of cellular mechanotransduction. In this review, we present an overview of the current knowledge and significant progress in cellular mechanotransduction via micropost substrates. In the aspect of experimental studies, we summarize significant experimental progress and place an emphasis on the coupled relationship among cellular spreading, focal adhesion and contractility as well as the influence of substrate properties on force-involved cellular behaviors. In the other aspect of computational investigations, we outline a coupled framework including the biochemically motivated stress fiber model and thermodynamically motivated adhesion model and present their predicted biomechanical responses and then compare predicted simulation results with experimental observations to further explore the mechanisms of cellular mechanotransduction. At last, we discuss the future perspectives both in experimental technologies and in computational models, as well as facing challenges in the area of cellular mechanotransduction.

Three-dimensional numerical model of cell morphology during migration in multi-signaling substrates

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.

Unidirectional cell crawling model guided by extracellular cues

Cell migration is a highly regulated and complex cellular process to maintain proper homeostasis for various biological processes. Extracellular environment was identified as the main affecting factors determining the direction of cell crawling. It was observed experimentally that the cell prefers migrating to the area with denser or stiffer array of microposts. In this article, an integrated unidirectional cell crawling model was developed to investigate the spatiotemporal dynamics of unidirectional cell migration, which incorporates the dominating intracellular biochemical processes, biomechanical processes and the properties of extracellular micropost arrays. The interpost spacing and the stiffness of microposts are taken into account, respectively, to study the mechanism of unidirectional cell locomotion and the guidance of extracellular influence cues on the direction of unidirectional cell crawling. The model can explain adequately the unidirectional crawling phenomena observed in experiments such as "spatiotaxis" and "durotaxis," which allows us to obtain further insights into cell migration.

Cytoskeletal Mechanics Regulating Amoeboid Cell Locomotion

Migrating cells exert traction forces when moving. Amoeboid cell migration is a common type of cell migration that appears in many physiological and pathological processes and is performed by a wide variety of cell types. Understanding the coupling of the biochemistry and mechanics underlying the process of migration has the potential to guide the development of pharmacological treatment or genetic manipulations to treat a wide range of diseases. The measurement of the spatiotemporal evolution of the traction forces that produce the movement is an important aspect for the characterization of the locomotion mechanics. There are several methods to calculate the traction forces exerted by the cells. Currently the most commonly used ones are traction force microscopy methods based on the measurement of the deformation induced by the cells on elastic substrate on which they are moving. Amoeboid cells migrate by implementing a motility cycle based on the sequential repetition of four phases. In this paper we review the role that specific cytoskeletal components play in the regulation of the cell migration mechanics. We investigate the role of specific cytoskeletal components regarding the ability of the cells to perform the motility cycle effectively and the generation of traction forces. The actin nucleation in the leading edge of the cell, carried by the ARP2/3 complex activated through the SCAR/WAVE complex, has shown to be fundamental to the execution of the cyclic movement and to the generation of the traction forces. The protein PIR121, a member of the SCAR/WAVE complex, is essential to the proper regulation of the periodic movement and the protein SCAR, also included in the SCAR/WAVE complex, is necessary for the generation of the traction forces during migration. The protein Myosin II, an important F-actin cross-linker and motor protein, is essential to cytoskeletal contractility and to the generation and proper organization of the traction forces during migration.