Motor force homeostasis in skeletal muscle contraction

Effects of Contact Surface Shape on Dynamic Lifetime and Strength of Molecular Bond Clusters under Displacement- and Force-Controlled Loading Conditions

Many experimental and theoretical studies have shown that the mechanical properties of cells and the extracellular matrix can significantly affect the lifetime and strength of the adhesion clusters of molecular bonds. However, there are few studies on how the shape of the contact surface affects the lifetime and strength of the adhesion clusters of molecular bonds, especially theoretical studies in this area. An idealized model of focal adhesion is adopted, in which two rigid media are bonded together by an array of receptor-ligand bonds modeled as Hookean springs on a complex surface topography, which is described by three parameters: the surface shape factor β, the length of a single identical surface shape L, and the amplitude of surface shapes w. In this study, systematic Monte Carlo simulations of this model are conducted to study the lifetime of the molecular bond cluster under linear incremental force loading and the strength of the molecular bond cluster under linear incremental displacement loading. We find that both small surface shape amplitudes and large surface shape factors will increase the lifetime and strength of the adhesion cluster, whereas the length of a single surface shape causes oscillations in the lifetime and strength of the cluster, and this oscillation amplitude is affected by the surface shape amplitude and the factor. At the same time, we also find that the pretension in the cluster will play a dominant role in the adhesion strength under large amplitudes and small factors of surface shapes. The physical mechanisms behind these phenomena are that the changes of the length of a single surface shape, the amplitude of surface shapes, and the surface shape factor cause the changes of stress concentration in the adhesion region, bond affinity, and the number of similar affinity bonds.

Force-mediated cellular anisotropy and plasticity dictate the elongation dynamics of embryos

We developed a unified dynamic model to explain how cellular anisotropy and plasticity, induced by alignment and severing/rebundling of actin filaments, dictate the elongation dynamics of Caenorhabditis elegans embryos. It was found that the gradual alignment of F-actins must be synchronized with the development of intracellular forces for the embryo to elongate, which is then further sustained by muscle contraction-triggered plastic deformation of cells. In addition, we showed that preestablished anisotropy is essential for the proper onset of the process while defects in the integrity or bundling kinetics of actin bundles result in abnormal embryo elongation, all in good agreement with experimental observations.

Standard Loading Profile in Matrix Rigidity Sensing

It is important to learn features of locally applied forces by cells during matrix rigidity sensing, since the function of mechanosensing proteins would be affected by force magnitude, loading velocity, or even loading history. Here, we investigate a rigidity-sensing apparatus consisting of a contractile unit on matrices. Strikingly, our analysis indicates that the matrix rigidity is not only sensed with a fixed step size in displacement but also with a fixed apparent loading velocity. The fixed step size is shown to be correlated with the monomer size of actin filament. This work suggests that the loading profile during rigidity sensing is regulated by various aspects of the contractile unit, which then serves as the standard in sensing varied rigidity of the matrix.

Antagonistic Behaviors of NMY-1 and NMY-2 Maintain Ring Channels in the C. elegans Gonad

Contractile rings play critical roles in a number of biological processes, including oogenesis, wound healing, and cytokinesis. In many cases, the activity of motor proteins such as nonmuscle myosins is required for appropriate constriction of these contractile rings. In the gonad of the nematode worm Caenorhabditis elegans, ring channels are a specialized form of contractile ring that are maintained at a constant diameter before oogenesis. We propose a model of ring channel maintenance that explicitly incorporates force generation by motor proteins that can act normally or tangentially to the ring channel opening. We find that both modes of force generation are needed to maintain the ring channels. We demonstrate experimentally that the type II myosins NMY-1 and NMY-2 antagonize each other in the ring channels by producing force in perpendicular directions: the experimental depletion of NMY-1/theoretical decrease in orthogonal force allows premature ring constriction and cellularization, whereas the experimental depletion of NMY-2/theoretical decrease in tangential force opens the ring channels and prevents cellularization. Together, our experimental and theoretical results show that both forces, mediated by NMY-1 and NMY-2, are crucial for maintaining the appropriate ring channel diameter and dynamics throughout the gonad.

A viscoelastic-stochastic model of the effects of cytoskeleton remodelling on cell adhesion

Cells can adapt their mechanical properties through cytoskeleton remodelling in response to external stimuli when the cells adhere to the extracellular matrix (ECM). Many studies have investigated the effects of cell and ECM elasticity on cell adhesion. However, experiments determined that cells are viscoelastic and exhibiting stress relaxation, and the mechanism behind the effect of cellular viscoelasticity on the cell adhesion behaviour remains unclear. Therefore, we propose a theoretical model of a cluster of ligand-receptor bonds between two dissimilar viscoelastic media subjected to an applied tensile load. In this model, the distribution of interfacial traction is assumed to follow classical continuum viscoelastic equations, whereas the rupture and rebinding of individual molecular bonds are governed by stochastic equations. On the basis of this model, we determined that viscosity can significantly increase the lifetime, stability and dynamic strength of the adhesion cluster of molecular bonds, because deformation relaxation attributed to the viscoelastic property can increase the rebinding probability of each open bond and reduce the stress concentration in the adhesion area.

Statistical mechanics of the Huxley-Simmons model

The chemomechanical model of Huxley and Simmons (HS) [A. F. Huxley and R. M. Simmons, Nature 233, 533 (1971)NATUAS0028-083610.1038/233533a0] provides a paradigmatic description of mechanically induced collective conformational changes relevant in a variety of biological contexts, from muscles power stroke and hair cell gating to integrin binding and hairpin unzipping. We develop a statistical mechanical perspective on the HS model by exploiting a formal analogy with a paramagnetic Ising model. We first study the equilibrium HS model with a finite number of elements and compute explicitly its mechanical and thermal properties. To model kinetics, we derive a master equation and solve it for several loading protocols. The developed formalism is applicable to a broad range of allosteric systems with mean-field interactions.

Temperature effect on the chemomechanical regulation of substeps within the power stroke of a single Myosin II

Myosin IIs in the skeletal muscle are highly efficient nanoscale machines evolved in nature. Understanding how they function can not only bring insights into various biological processes but also provide guidelines to engineer synthetic nanoscale motors working in the vicinity of thermal noise. Though it was clearly demonstrated that the behavior of a skeletal muscle fiber, or that of a single myosin was strongly affected by the temperature, how exactly the temperature affects the kinetics of a single myosin is not fully understood. By adapting the newly developed transitional state model, which successfully explained the intriguing motor force regulation during skeletal muscle contraction, here we systematically explain how exactly the power stroke of a single myosin proceeds, with the consideration of the chemomechanical regulation of sub-steps within the stroke. The adapted theory is then utilized to investigate the temperature effect on various aspects of the power stroke. Our analysis suggests that, though swing rates, the isometric force, and the maximal stroke size all strongly vary with the temperature, the temperature can have a very small effect on the releasable elastic energy within the power stroke.

Modeling Active Mechanosensing in Cell-Matrix Interactions

Cells actively sense the mechanical properties of the extracellular matrix, such as its rigidity, morphology, and deformation. The cell-matrix interaction influences a range of cellular processes, including cell adhesion, migration, and differentiation, among others. This article aims to review some of the recent progress that has been made in modeling mechanosensing in cell-matrix interactions at different length scales. The issues discussed include specific interactions between proteins, the structure and mechanosensitivity of focal adhesions, the cluster effects of the specific binding, the structure and behavior of stress fibers, cells' sensing of substrate stiffness, and cell reorientation on cyclically stretched substrates. The review concludes by looking toward future opportunities in the field and at the challenges to understanding active cell-matrix interactions.

Catch-slip bonds can be dispensable for motor force regulation during skeletal muscle contraction

It is intriguing how multiple molecular motors can perform coordinated and synchronous functions, which is essential in various cellular processes. Recent studies on skeletal muscle might have shed light on this issue, where rather precise motor force regulation was partly attributed to the specific stochastic features of a single attached myosin motor. Though attached motors can randomly detach from actin filaments either through an adenosine triphosphate (ATP) hydrolysis cycle or through "catch-slip bond" breaking, their respective contribution in motor force regulation has not been clarified. Here, through simulating a mechanical model of sarcomere with a coupled Monte Carlo method and finite element method, we find that the stochastic features of an ATP hydrolysis cycle can be sufficient while those of catch-slip bonds can be dispensable for motor force regulation.

Self-Regulation of Motor Force Through Chemomechanical Coupling in Skeletal Muscle Contraction

It is intriguing how the mechanics of molecular motors is regulated to perform the mechanical work in living systems. In sharp contrast to the conventional wisdom, recent experiments indicated that motor force maintains ∼6 pN upon a wide range of filament loads during skeletal muscle contraction at the steady state. Here we find that this rather precise regulation which takes place in an essentially chaotic system, can be due to that a “working” motor is arrested in a transitional state when the motor force is ∼6 pN. Our analysis suggests that the motor force can be self-regulated through chemomechanical coupling, and motor force homeostasis is a built-in feature at the level of a single motor, which provides insights to understanding the coordinated function of multiple molecular motors existing in various physiological processes. With a coupled stochastic-elastic numerical framework, the kinetic model for a Actin-myosin-ATP cycle constructed in this work might pave the way to decently investigate the transient behaviors of the skeletal muscle or other actomyosin complex structures.

Muscle contraction and the elasticity-mediated crosstalk effect

Cooperative action of molecular motors is essential for many cellular processes. One possible regulator of motor coordination is the elasticity-mediated crosstalk (EMC) coupling between myosin II motors whose origin is the tensile stress that they collectively generate in actin filaments. Here, we use a statistical mechanical analysis to investigate the influence of the EMC effect on the sarcomere -- the basic contractile unit of skeletal muscles. We demonstrate that the EMC effect leads to an increase in the attachment probability of motors located near the end of the sarcomere while simultaneously decreasing the attachment probability of the motors in the central part. Such a polarized attachment probability would impair the motors' ability to cooperate efficiently. Interestingly, this undesired phenomenon becomes significant only when the system size exceeds that of the sarcomere in skeletal muscles, which provides an explanation for the remarkable lack of sarcomere variability in vertebrates. Another phenomenon that we investigate is the recently observed increase in the duty ratio of the motors with the tension in muscle. We reveal that the celebrated Hill's equation for muscle contraction is very closely related to this observation.

Cyclic stretch induces cell reorientation on substrates by destabilizing catch bonds in focal adhesions

A minimal model of cellular mechanosensing system that consists of a single stress fiber adhering on a substrate via two focal adhesions made of catch bonds is adopted to investigate the phenomena of cell reorientation on substrates induced by an applied uniaxial cyclic stretch. The model indicates that the catch bonds in the focal adhesions experience a periodically oscillating internal force with amplitude and frequency controlled by two intrinsic clocks of the stress fiber, one associated with localized activation and the other with homogeneous activation of sarcomere units along the stress fiber. It is shown that this oscillating force due to cyclic stretch tends to destabilize focal adhesions by reducing the lifetime of catch bonds. The resulting slide or relocation of focal adhesions then causes the associated stress fiber to shorten and rotate to configurations nearly perpendicular to the stretching direction. These predicted behaviors from our model are consistent with a wide range of experimental observations.