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Actin and myosin, which are key components of contractile machinery, are responsible for cell shape changes, movement, and tissue deformation during morphogenesis. To generate contractile forces, actin and myosin combine to form aggregates with functional structures. On the molecular scale, because the actin-myosin catch-bond behavior reinforces the actin-myosin bond when the force exerted on the bond increases, actin-myosin kinetics is likely modulated by the actomyosin-generated force as well as the external force. The catch-bond behavior is anticipated to couple the mechanical and kinetic aspects of actomyosin aggregate formation. In this study, to unveil new aspects of actomyosin aggregate formation, we employed two mathematical models based on coarse-grained particle dynamics that describe actomyosin dynamics with and without the catch bond. Comparing the computational simulation results obtained from two models, we observed that the catch-bond behavior assists in the assemblage of myosin in a random actomyosin network even at low myosin concentrations and accelerates the completion of aggregate formation at relatively higher concentrations. The actin-myosin catch bond is anticipated to support foci formation from a random actomyosin network at the cell cortex during morphogenesis. [ABSTRACT FROM AUTHOR]

The adaptive structure and functional changes of the actin cytoskeleton are induced by its mechanical behavior at various temporal and spatial scales. In particular, the mechanical behaviors at different scales play important roles in the mechanical functions of various cells, and these multiscale phenomena require clarification. To establish a milestone toward achieving multiscale modeling and simulation, this paper reviews mathematical analyses and simulation methods applied to the mechanics of the filamentous actin cytoskeleton. The actin cytoskeleton demonstrates characteristic behaviors at every temporal and spatial scale, and mathematical models and simulation methods can be applied to each level of actin cytoskeletal structure ranging from the molecular to the network level. This paper considers studies on mathematical models and simulation methods based on the molecular dynamics, coarse-graining, and continuum dynamics approaches. Every temporal and spatial scale of actin cytoskeletal structure is considered, and it is expected that discrete and continuum dynamics ranging from functional expression at the molecular level to macroscopic functional expression at the whole cell level will be developed and applied to multiscale modeling and simulation. [ABSTRACT FROM AUTHOR]

Actin polymerization-driven protrusion of the lamellipodia is a requisite initial step during actin-based cell migration, and is closely associated with attachment to the substrate. Although tremendous progress has been made in recent years toward elucidating the molecular details of focal adhesions, our understanding of the basic coordination of protrusion and adhesion, and how the two fundamental processes relate to actomyosin contractility is still inadequate. Therefore, to highlight the effect of cell-substrate interactions on the protrusive dynamics of the lamellipodia and to correlate protrusion with actomyosin activities, this study investigated the migration of fish epidermal keratocytes on fibronectin micropatterns intercalated with adhesion-suppressed gaps of varying widths. We show that insufficient adhesion associated with the gaps could limit lamellipodial protrusion such that the percentage of migrating cells decreases with an increase in gap width, and protrusion across the gaps is accompanied by ruffling. Moreover, our results suggest that up-regulating actomyosin contractility enhances the mechanical integrity of the actin cytoskeleton, leading to an increase in the width of the lamellipodia, and consequently, an increase in the percentage of cells migrating across the gaps. Thus, we demonstrate that the protrusion dynamics at the leading edge of migrating cells are functionally involved in the global mechanical regulation of actin cytoskeletal components that enable cell migration. [ABSTRACT FROM AUTHOR]

Membrane protrusion is a mechanochemical process of active membrane deformation driven by actin polymerization. Previously, Brownian ratchet (BR) was modeled on the basis of the underlying molecular mechanism. However, because the BR requires a priori load that cannot be determined without information of the cell shape, it cannot be effective in studies in which resultant shapes are to be solved. Other cellular-scale models describing the protrusion have also been suggested for modeling a whole cell; however, these models were not developed on the basis of coarse-grained physics representing the underlying molecular mechanism. Therefore, to express the membrane protrusion on the cellular scale, we propose a novel mathematical model, the coarse-grained BR (CBR), which is derived on the basis of nonequilibrium thermodynamics theory. The CBR can reproduce the BR within the limit of the quasistatic process of membrane protrusion and can estimate the protrusion velocity consistently with an effective elastic constant that represents the state of the energy of the membrane. Finally, to demonstrate the applicability of the CBR, we attempt to perform a cellular-scale simulation of migrating keratocyte in which the proposed CBR is used for the membrane protrusion model on the cellular scale. The results show that the experimentally observed shapes of the leading edge are well reproduced by the simulation. In addition, The trend of dependences of the protrusion velocity on the curvature of the leading edge, the temperature, and the substrate stiffness also agreed with the other experimental results. Thus, the CBR can be considered an appropriate cellular-scale model to express the membrane protrusion on the basis of its underlying molecular mechanism. [ABSTRACT FROM AUTHOR]

Abstract: It is essential to investigate the mechanical behaviour of cytoskeletal actin filaments in order to understand their critical role as mechanical components in various cellular functional activities. These actin filaments consisting of monomeric molecules function in the thermal fluctuations. Hence, it is important to understand their mechanical behaviour on the microscopic scale by comparing the stiffness based on thermal fluctuations with the one experimentally measured on the macroscopic scale. In this study, we perform a large-scale molecular dynamics (MD) simulation for a half-turn structure of an actin filament. We analyse its longitudinal and twisting Brownian motions in equilibrium and evaluated its apparent extensional and torsional stiffness on the nanosecond scale. Upon increasing the sampling-window durations for analysis, the apparent stiffness gradually decreases and exhibits a trend to converge to a value that is close to the experimental value. This suggests that by extrapolating the data obtained in the MD analysis, we can estimate the experimentally determined stiffness on the microsecond to millisecond scales. For shorter temporal scales, the apparent stiffness is larger than experimental values, indicating that fast, local motions of the molecular structure are dominant. To quantify the local structural changes within the filament on the nanosecond scale and investigate the molecular mechanisms, such as the binding of the actin-regulatory proteins to the filaments, it is preferable to analyse the mechanical behaviour on the nanometre and nanosecond scales using MD simulation. [ABSTRACT FROM AUTHOR]

Abstract: Dynamic turnover and transport of actin filament network is essential for protrusive force generation and traction force development during cell migration. To elucidate the dynamic coupling between actin network flow and turnover, we focused on flow dynamics in the lamella of one of the simplest but elegant motility systems; crawling fragments derived from fish keratocytes. Interestingly, we show that actin network in the lamella of fragments is not stationary as earlier reported, but exhibits a flow dynamics that is strikingly similar to that reported for higher order cells, suggesting that network flow is an intrinsic property of the actin cytoskeleton that is fundamental to cell migration. We also demonstrate that whereas polymerization mediates network assembly at the front, surprisingly, network flow convergence modulates network disassembly toward the rear of the lamella, suggesting that flow and turnover are coupled during migration. These results obtained using simple motility systems are significant to the understanding of actin network dynamics in migrating cells, and they will be found useful for developing biophysical models for elucidating the fundamental mechanisms of cell migration. [Copyright &y& Elsevier]

Abstract: Coupling interactions among mechanical and biochemical factors are important for the realization of various cellular processes that determine cell migration. Although F-actin network dynamics has been the focus of many studies, it is not yet clear how mechanical forces generated by actomyosin contractility spatiotemporally regulate this fundamental aspect of cell migration. In this study, using a combination of fluorescent speckle microscopy and particle imaging velocimetry techniques, we perturbed the actomyosin system and examined quantitatively the consequence of actomyosin contractility on F-actin network flow and deformation in the lamellipodia of actively migrating fish keratocytes. F-actin flow fields were characterized by retrograde flow at the front and anterograde flow at the back of the lamellipodia, and the two flows merged to form a convergence zone of reduced flow intensity. Interestingly, activating or inhibiting actomyosin contractility altered network flow intensity and convergence, suggesting that network dynamics is directly regulated by actomyosin contractility. Moreover, quantitative analysis of F-actin network deformation revealed that the deformation was significantly negative and predominant in the direction of cell migration. Furthermore, perturbation experiments revealed that the deformation was a function of actomyosin contractility. Based on these results, we suggest that the actin cytoskeletal structure is a mechanically self-regulating system, and we propose an elaborate pathway for the spatiotemporal self-regulation of the actin cytoskeletal structure during cell migration. In the proposed pathway, mechanical forces generated by actomyosin interactions are considered central to the realization of the various mechanochemical processes that determine cell motility. [Copyright &y& Elsevier]

Abstract: Cell motility is spatiotemporally regulated by interactions among mechanical and biochemical factors involved in the regulation of cytoskeletal actin structure reorganization. Although the molecular mechanisms underlying cell motility have been well investigated, the contributions of mechanical factors such as strain in the network reorganization remain unclear. In this study, we have quantitatively evaluated the strain field in the actin filament network forming the lamellipodia of migrating fish keratocytes to elucidate the mechanism by which actin filament network reorganization is regulated by biomechanical factors. The results highlight the existence of a negative (compressive) strain in the lamellipodia whose direction is parallel to that of cell movement. A close correlation was found between the distributions of the strain and the actin filament density in the lamellipodia, suggesting that negative strain may be involved in filament depolymerization. Based on this result, we propose a selective depolymerization model which suggests that negative strain may couple with biomechanical factors such as ADF/cofilin to promote selective depolymerization of filaments oriented in the direction of the deformation because such filaments experience relatively higher levels of the deformation. This model, in conjunction with others, may explain the observed reduction in filament density and the reorganization of actin filament network at the back of the lamellipodia of migrating fish keratocytes. Thus, we suggest that by coupling with biochemical factors, mechanical factors are involved in the regulation of actin filament depolymerization, thereby contributing to the regulation of cell motility. [Copyright &y& Elsevier]

Understanding in multicellular behaviors in three-dimensional (3D) culture models such as organoids is important to help us better comprehend the mechanisms of the morphogenesis and functions of diverse organs in vivo cellular environment. In this study, we elucidated the multicellular behaviors of the osteocytic spheroids in response to the chemically induced osteogenesis supplements (OS). Particularly, we conducted 1) size change measurement, 2) fusion experiment, and 3) collagen embedding experiment of spheroids, in response to the OS. We found out that the OS alters the multicellular behaviors of the spheroid by greater reduction in the size change measurement and slowing down the speed of fusion experiment and collagen embedding experiment of the spheroids. We also highlighted that the driving force of these changes was the tight actin filaments generated on the surface of the spheroids. Hence, the results altogether indicate that the spheroid model exerted the different multicellular behaviors against the differentiation capability. This study will contribute to understanding the multicellular behaviors of the 3D culture model reconstructed by the cells with greater cell-cell interaction force. • Chemical osteogenesis supplements modulated multicellular behavior of the spheroid. • Osteogenesis supplements enhanced actin filaments on the surface of the spheroid. • Tight actin filaments deformed the nuclei on the surface of the spheroid. [ABSTRACT FROM AUTHOR]

Abstract: Actin filaments have a double-helix structure consisting of globular actin molecules. In many mechanical cellular activities, such as cell movement, division, and shape control, modulation of the extensional and torsional dynamics of the filament has been linked to regulatory actin-binding protein functions. Therefore, it is important to quantitatively evaluate extension–torsion coupling of filament to better understand the actin filament dynamics. In the present study, the extension–torsion coupling was investigated using molecular dynamics simulations. We constructed a model for the actin filament consisting of 14 actin subunits in an ionic solvent as a minimal functional unit, and analyzed longitudinal and twisting Brownian motions of the filament. We then derived the expected value of energy associated with extension and torsion at equilibrium, and evaluated the extension–torsion stiffness of the filament from the thermal fluctuations obtained from the MD simulations. The results demonstrated that as the analyzed sampling-window duration was increased, the extension–torsion coupling stiffness evaluated on a nanosecond scale tended to converge to a value of 7.6×10−11 N. The results obtained from this study will contribute to the understanding of biomechanical events, under mechanical tension and torque, involving extension–torsion coupling of filaments. [Copyright &y& Elsevier]

For cellular adaptation in mechanical environments, it is important to consider transmission of forces from the outside to the inside of cells via a focal molecular complex. The focal molecular complex, which consists of integrin, talin, vinculin and actin, is known to form in response to a force applied via the extra-cellular matrix (ECM). In the early formation process of the complex, the complex–actin connection is reinforced. These structural changes of the nascent complex result in an increase in its mechanical integrity and overall stiffness, possibly leading to the maturation of the nascent complex by enhancing force transmission. In this study, we hypothesized that the complex component talin is a crucial factor in increasing the stiffness of the nascent complex. To test the hypothesis, we used atomic force microscopy (AFM) to measure the stiffness of the nascent complex using a probe coated with fibronectin. Stiffness measurements were conducted for intact and talin knocked-down cells. Our results demonstrated that talin was required to increase the stiffness of the nascent complex, which could be caused by the reinforced connection between the complex and actin filaments mediated by talin. • In the cell adhesion region, forces are transmitted via focal molecular complex. • Talin could reinforce the connection between the nascent complex and actin filament. • AFM experiment revealed that talin is required to increase stiffness of the complex. [ABSTRACT FROM AUTHOR]

Abstract: Actomyosin contractility is a major force-generating mechanism that drives rearrangement of actomyosin networks; it is fundamental to cellular functions such as cellular reshaping and movement. Thus, to clarify the mechanochemical foundation of the emergence of cellular functions, understanding the relationship between actomyosin contractility and rearrangement of actomyosin networks is crucial. For this purpose, in this study, we present a new particulate-based model for simulating the motions of actin, non-muscle myosin II, and . To confirm the model''s validity, we successfully simulated sliding and bending motions of actomyosin filaments, which are observed as fundamental behaviors in dynamic rearrangement of actomyosin networks in migrating keratocytes. Next, we simulated the dynamic rearrangement of actomyosin networks. Our simulation results indicate that an increase in the density fraction of myosin induces a higher-order structural transition of actomyosin filaments from networks to bundles, in addition to increasing the force generated by actomyosin filaments in the network. We compare our simulation results with experimental results and confirm that actomyosin bundles bridging focal adhesions and the characteristics of myosin-dependent rearrangement of actomyosin networks agree qualitatively with those observed experimentally. [Copyright &y& Elsevier]

Abstract: Actin filaments are the most abundant components of the cellular cytoskeleton, and play critical roles in various cellular functions such as migration, division and shape control. In these activities, mechanical tension causes structural changes in the double-helical structure of the actin filament, which is a key modulator of cytoskeletal reorganization. This study performed large-scale molecular dynamics (MD) and steered MD simulations to quantitatively analyze the effects of tensile force on the mechanical behavior of actin filaments. The results revealed that when a tensile force of 200pN was applied to a filament consisting of 14 actin subunits, the twist angle of the filament decreased by approximately 20°, corresponding to a rotation of approximately −2° per subunit, representing a critical structural change in actin filaments. Based on these structural changes, the variance in filament length and twist angle was found to decrease, leading to increases in extensional and torsional stiffness. Torsional stiffness increased significantly under the tensile condition, and the ratio of filament stiffness under tensile force to that under no external force increased significantly on longer temporal scales. The results obtained from this study contribute to the understanding of mechano-chemical interactions concerning actin dynamics, showing that increased tensile force in the filament prevents actin regulatory proteins from binding to the filament. [Copyright &y& Elsevier]

Abstract: A mechanochemical relationship between intracellular flow fields of actin and remodeling of actin filaments is important to the realization of cell motility. In this study, to investigate this mechanochemical relationship, we present a mathematical model describing motions of actin filament and remodeling of the filaments in shear flows. We perform simulations of the dynamics of actin filaments remodeled by polymerization, depolymerization, and severing, and investigate contributions of these remodeling processes to effective shear viscosities of the system. [ABSTRACT FROM AUTHOR]