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The present work examines the hypothesis that cochlear outer hair cell (OHC) properties vary in precise proportions along the tonotopic map to optimize electro-mechanical power conversion. We tested this hypothesis using a very simple model of a single isolated OHC driving a mechanical load. Results identify three nondimensional ratios that are predicted to optimize power conversion: the ratio of the resistive-capacitive (RC) corner to the characteristic frequency (CF), the ratio of nonlinear to linear capacitance, and the ratio of OHC stiffness to cochlear load stiffness. Optimum efficiency requires all three ratios to be universal constants, independent of CF and species. The same ratios are cardinal control parameters that maximize power output by positioning the OHC operating point on the edge of a dynamic instability. Results support the hypothesis that OHC properties evolved to optimize electro-mechanical power conversion. Identification of the RC corner frequency as a control parameter reveals a powerful mechanism used by medial olivocochlear efferent system to control OHC power output. Results indicate the upper frequency limit of OHC power output is not constrained by the speed of the motor itself, but instead is likely limited by the size of the nucleus and membrane surface area available for ion-channel expression.

The platelet integrin α

Cell migration is essential to physiological and pathological biology. Migration is driven by the motion of a leading edge, in which actin polymerization pushes against the edge and adhesions transmit traction to the substrate while membrane tension increases. How the actin and adhesions synergistically control edge protrusion remains elusive. We addressed this question by developing a computational model in which the Brownian ratchet mechanism governs actin filament polymerization against the membrane and the molecular clutch mechanism governs adhesion to the substrate (BR-MC model). Our model predicted that actin polymerization is the most significant driver of protrusion, as actin had a greater effect on protrusion than adhesion assembly. Increasing the lifetime of nascent adhesions also enhanced velocity, but decreased the protrusion’s motional persistence, because filaments maintained against the cell edge ceased polymerizing as membrane tension increased. We confirmed the model predictions with measurement of adhesion lifetime and edge motion in migrating cells. Adhesions with longer lifetime were associated with faster protrusion velocity and shorter persistence. Experimentally increasing adhesion lifetime increased velocity but decreased persistence. We propose a mechanism for actin polymerization-driven, adhesion-dependent protrusion in which balanced nascent adhesion assembly and lifetime generates protrusions with the power and persistence to drive migration.

Conversion of integrins from low to high affinity states, termed activation, is important in biological processes, including immunity, hemostasis, angiogenesis, and embryonic development. Integrin activation is regulated by large-scale conformational transitions from closed, low affinity states to open, high affinity states. Although it has been suggested that substrate stiffness shifts the conformational equilibrium of integrin and governs its unbinding, here, we address the role of integrin conformational activation in cellular mechanosensing. Comparison of wild-type versus activating mutants of integrin αVβ3 show that activating mutants shift cell spreading, focal adhesion kinase activation, traction stress, and force on talin toward high stiffness values at lower stiffness. Although all activated integrin mutants showed equivalent binding affinity for soluble ligands, the β3 S243E mutant showed the strongest shift in mechanical responses. To understand this behavior, we used coarse-grained computational models derived from molecular level information. The models predicted that wild-type integrin αVβ3 displaces under force and that activating mutations shift the required force toward lower values, with S243E showing the strongest effect. Cellular stiffness sensing thus correlates with computed effects of force on integrin conformation. Together, these data identify a role for force-induced integrin conformational deformation in cellular mechanosensing.

Chromosome segregation is mediated by spindle microtubules that attach to the kinetochore via dynamic protein complexes, such as Ndc80, Ska, Cdt1 and ch-TOG during mitotic metaphase. While experimental studies have previously shown that these proteins and protein complexes are all essential for maintaining a stable kinetochore-microtubule (kMT) interface, their exact roles in this mitotic metaphase remains elusive. In this study, we employed experimental and computational methods in order to characterize how these proteins can strengthen kMT attachments in both nonload-bearing and load-bearing conditions, typical of prometaphase and metaphase, respectively. Immunofluorescence staining of HeLa cells showed that the levels of Ska and Cdt1 significantly increased from prometaphase to metaphase, while levels of the Ndc80 complex remained unchanged. Our new computational model showed that by incorporating binding and unbinding of each protein complex coupled with a biased diffusion mechanism, the displacement of a possible complex formed by Ndc80-Ska-Cdt1 is significantly higher than that of Ndc80 alone or Ndc80-Ska. In addition, when we incorporate Ndc80/ch-TOG in the model, rupture force and time of attachment of the kMT interface increases. These results support the hypothesis that Ndc80-associated proteins strengthen kMT attachments, and that the interplay between kMT protein complexes in metaphase ensures stable attachments.

Formins generate unbranched actin filaments by a conserved, processive actin assembly mechanism. Most organisms express multiple formin isoforms that mediate distinct cellular processes and facilitate actin filament polymerization by significantly different rates, but how these actin assembly differences correlate to cellular activity is unclear. We used a computational model of fission yeast cytokinetic ring assembly to test the hypothesis that particular actin assembly properties help tailor formins for specific cellular roles. Simulations run in different actin filament nucleation and elongation conditions revealed that variations in formin's nucleation efficiency critically impact both the probability and timing of contractile ring formation. To probe the physiological importance of nucleation efficiency, we engineered fission yeast formin chimera strains in which the FH1-FH2 actin assembly domains of full-length cytokinesis formin Cdc12 were replaced with the FH1-FH2 domains from functionally and evolutionarily diverse formins with significantly different actin assembly properties. Although Cdc12 chimeras generally support life in fission yeast, quantitative live-cell imaging revealed a range of cytokinesis defects from mild to severe. In agreement with the computational model, chimeras whose nucleation efficiencies are least similar to Cdc12 exhibit more severe cytokinesis defects, specifically in the rate of contractile ring assembly. Together, our computational and experimental results suggest that fission yeast cytokinesis is ideally mediated by a formin with properly tailored actin assembly parameters.

The ability of adherent cells to sense changes in the mechanical properties of their extracellular environments is critical to numerous aspects of their physiology. It has been well documented that cell attachment and spreading are sensitive to substrate stiffness. Here, we demonstrate that this behavior is actually biphasic, with a transition that occurs around a Young's modulus of ∼7 kPa. Furthermore, we demonstrate that, contrary to established assumptions, this property is independent of myosin II activity. Rather, we find that cell spreading on soft substrates is inhibited due to reduced myosin-II independent nascent adhesion formation within the lamellipodium. Cells on soft substrates display normal leading-edge protrusion activity, but these protrusions are not stabilized due to impaired adhesion assembly. Enhancing integrin-ECM affinity through addition of Mn2+ recovers nascent adhesion assembly and cell spreading on soft substrates. Using a computational model to simulate nascent adhesion assembly, we find that biophysical properties of the integrin-ECM bond are optimized to stabilize interactions above a threshold matrix stiffness that is consistent with the experimental observations. Together, these results suggest that myosin II-independent forces in the lamellipodium are responsible for mechanosensation by regulating new adhesion assembly, which, in turn, directly controls cell spreading. This myosin II-independent mechanism of substrate stiffness sensing could potentially regulate a number of other stiffness-sensitive processes.

Integrin conformational dynamics are critical to their receptor and signaling functions in many cellular processes, including spreading, adhesion, and migration. However, assessing integrin conformations is both experimentally and computationally challenging because of limitations in resolution and dynamic sampling. Thus, structural changes that underlie transitions between conformations are largely unknown. Here, focusing on integrin αvβ(3), we developed a modified form of the coarse-grained heterogeneous elastic network model (hENM), which allows sampling conformations at the onset of activation by formally separating local fluctuations from global motions. Both local fluctuations and global motions are extracted from all-atom molecular dynamics simulations of the full-length αvβ(3) bent integrin conformer, but whereas the former are incorporated in the hENM as effective harmonic interactions between groups of residues, the latter emerge by systematically identifying and treating weak interactions between long-distance domains with flexible and anharmonic connections. The new hENM model allows integrins and single-point mutant integrins to explore various conformational states, including the initiation of separation between α- and β-subunit cytoplasmic regions, headpiece extension, and legs opening.

The ability of adherent cells to form adhesions is critical to numerous phases of their physiology. The assembly of adhesions is mediated by several types of integrins. These integrins differ in physical properties, including rate of diffusion on the plasma membrane, rapidity of changing conformation from bent to extended, affinity for extracellular matrix ligands, and lifetimes of their ligand-bound states. However, the way in which nanoscale physical properties of integrins ensure proper adhesion assembly remains elusive. We observe experimentally that both β-1 and β-3 integrins localize in nascent adhesions at the cell leading edge. In order to understand how different nanoscale parameters of β-1 and β-3 integrins mediate proper adhesion assembly, we therefore develop a coarse-grained computational model. Results from the model demonstrate that morphology and distribution of nascent adhesions depend on ligand binding affinity and strength of pairwise interactions. Organization of nascent adhesions depends on the relative amounts of integrins with different bond kinetics. Moreover, the model shows that the architecture of an actin filament network does not perturb the total amount of integrin clustering and ligand binding; however, only bundled actin architectures favor adhesion stability and ultimately maturation. Together, our results support the view that cells can finely tune the expression of different integrin types to determine both structural and dynamic properties of adhesions., Author summary Integrin-mediated cell adhesions to the extracellular environment contribute to various cell activities and provide cells with vital environmental cues. Cell adhesions are complex structures that emerge from a number of molecular and macromolecular interactions between integrins and cytoplasmic proteins, between integrins and extracellular ligands, and between integrins themselves. How the combination of these interactions regulate adhesions formation remains poorly understood because of limitations in experimental approaches and numerical methods. Here, we develop a multiscale model of adhesion assembly that treats individual integrins and elements from both the cytoplasm and the extracellular environment as single coarse-grained (CG) point particles, thus simplifying the description of the main macromolecular components of adhesions. The CG model implements sequential interactions and dependencies between the components and ultimately allows one to characterize various regimes of adhesions formation based on experimentally detected parameters. The results reconcile a number of independent experimental observations and provide important insights into the molecular basis of adhesion assembly from various integrin types.

The budding yeast actin cables and contractile ring are important for polarized growth and division, revealing basic aspects of cytoskeletal function. To study these formin-nucleated structures, we built a three-dimensional (3D) computational model with actin filaments represented as beads connected by springs. Polymerization by formins at the bud tip and bud neck, crosslinking, severing, and myosin pulling, are included. Parameter values were estimated from prior experiments. The model generates actin cable structures and dynamics similar to those of wild type and formin deletion mutant cells. Simulations with increased polymerization rate result in long, wavy cables. Simulated pulling by type V myosin stretches actin cables. Increasing the affinity of actin filaments for the bud neck together with reduced myosin V pulling promotes the formation of a bundle of antiparallel filaments at the bud neck, which we suggest as a model for the assembly of actin filaments to the contractile ring.

Integrin binding to extracellular matrix proteins is regulated by conformational transitions from closed, low affinity states to open, high affinity states. However, the pathways of integrin conformational activation remain incompletely understood. Here, by combining all-atom molecular dynamics simulation, coarse-graining, heterogeneous elastic network modeling, and experimental ligand binding measurements, we test the effect of integrin β mutations that destabilize the closed conformation. Our results support a “deadbolt” model of integrin activation, where extension of the headpiece is not coupled to leg separation, consistent with recent cryo-EM reconstructions of integrin intermediates. Moreover, our results are inconsistent with a “switchblade-like” mechanism. The data show that locally correlated atomistic motions are likely responsible for extension of integrin headpiece before separation of transmembrane legs, without persistence of these correlations across the entire protein. By combining modeling and simulation with experiment, this study provides new insight into the structural basis of full-length integrin activation.

The ability of adherent cells to sense changes in the mechanical properties of their extracellular environments is critical to numerous aspects of their physiology. It has been well documented that cell attachment and spreading are sensitive to substrate stiffness. Here we demonstrate that this behavior is actually biphasic, with a transition that occurs around a Young’s modulus of ∼7 kPa. Furthermore, we demonstrate that, contrary to established assumptions, this property is independent of myosin II activity. Rather, we find that cell spreading on soft substrates is inhibited due to reduced nascent adhesion formation within the lamellipodium. Cells on soft substrates display normal leading edge protrusion activity, but these protrusions are not stabilized due to impaired adhesion assembly. Enhancing integrin-ECM affinity through addition of Mn2+recovers nascent adhesion assembly and cell spreading on soft substrates. Using a computational model to simulate nascent adhesion assembly, we find that biophysical properties of the integrin-ECM bond are optimized to stabilize interactions above a threshold matrix stiffness that is consistent with the experimentally observations. Together these results suggest that myosin II-independent forces in the lamellipodium are responsible for mechanosensation by regulating new adhesion assembly, which in turn, directly controls cell spreading. This myosin II-independent mechanism of substrate stiffness sensing could potentially regulate a number of other stiffness sensitive processes.Significance StatementCell physiology can be regulated by the mechanics of the extracellular environment. Here, we demonstrate that cell spreading is a mechanosensitive process regulated by weak forces generated at the cell periphery and independent of motor activity. We show that stiffness sensing depends on the kinetics of the initial adhesion bonds that are subjected to forces driven by protein polymerization. This work demonstrates how the binding kinetics of adhesion molecules are sensitively tuned to a range of forces that enable mechanosensation.

Cells assemble numerous types of actomyosin bundles that generate contractile forces for biological processes, such as cytokinesis and cell migration. One example of contractile bundles is a transverse arc that forms via actomyosin-driven condensation of actin filaments in the lamellipodia of migrating cells and exerts significant forces on the surrounding environments. Structural reorganization of a network into a bundle facilitated by actomyosin contractility is a physiologically relevant and biophysically interesting process. Nevertheless, it remains elusive how actin filaments are reoriented, buckled, and bundled as well as undergo tension buildup during the structural reorganization. In this study, using an agent-based computational model, we demonstrated how the interplay between the density of myosin motors and cross-linking proteins and the rigidity, initial orientation, and turnover of actin filaments regulates the morphological transformation of a cross-linked actomyosin network into a bundle and the buildup of tension occurring during the transformation., Author Summary Contractile networks and bundles generate mechanical forces required for various cellular processes, particularly cell division and migration. In many of these processes, networks are structurally reorganized into bundles by the activity of molecular motors. During this morphological transformation, filaments constituting networks are reoriented and undergo deformation and turnover, and large tensile forces are generated and sustained in bundles. However, it remains inconclusive how the morphological transformation and force generation are regulated. Here, using a rigorous computational model, we quantitatively demonstrated that the interplay between several factors determines the characteristics of generated tensile force and regulates the transformation from networks to bundles. Thus, results in this study provide insights into the physical and mechanistic basis of the complex transition from networks to bundles observed in cells.

Recent research on biological materials and bioartificial systems has created one of the most dynamic field at the confluence of physical sciences, molecular engineering, cell biology, materials sciences, biotechnology and (nano) medicine. This field concerns better understanding of living systems, design of bio-inspired materials, synthesis of bioartificial technologies with new properties depending on their multi-scale architectures. Biological and man-made systems show the first level of organization at the nanoscale, where the fundamental properties and functions are settled (e.g., proteome and genome). The nanoscale properties reflect on larger scales: mesoscale, microscale, and continuum. Mechanisms by which phenomena at the different length and time scales are coupled and influence each other is the central issue in linking properties to functionalities, with a dramatic impact in designing and engineering biosystems. To get insights into the progressive trough-scales cascade effects-from molecular to macroscale level and from nanoseconds to life expectancy duration-multiscale/multiphysics models are required, dealing with inorganic, biological and hybrid matter. Thus, bioartificial systems technology depends upon our ability in assembling molecules into objects, hierarchically along several length scales, and in disassembling objects into molecules, in a tailored manner. As a peculiar feature, in bioartificial systems, the definition of the interactions between artificial and biological components needs to incorporate the “time” variable, in order to reproduce the evolution of the overall system, and to simulate complex phenomena as biodegradation and tissue remodeling. Herein, a number of paradigmatic multiscale models that attend the investigation of biological systems and the engineering of bioartificial systems is reviewed and discussed.

Computational methods, as Molecular Dynamics (MD) simulations, have been used for years to gain insight into the properties of small fractions of microtubules (MTs) and actin filaments (F-actins). However, when considering an entire cytoskeleton filament, MD simulations lack of sufficient sampling of the phase space. In order to acquire adequate amount of data with statistical validity, a faster sampling technique is here developed and the bending stiffness of entire MTs and F-actins is computed. Our approach allows to propagate the information obtained at a fine-grained atomistic scale to a coarse grained (CG) scale. We perform MD simulations on representative units of the MT and F-actin. Then, we describe each monomer of these representative units with few interacting grains and employ them to build CG filaments: (1) entire MTs with lengths from ~300 nm to ~1.5 μm and (2) an entire actin filament of ~500 nm. The dynamics of these CG systems is analyzed using Brownian Dynamics (BD) simulations, allowing to achieve time and length scales hundreds of times higher than MD simulations. For our BD simulations an ad hoc force field is used, that matches MD atomistic fluctuations on the interaction potentials between pairs of CG beads. Results from the here proposed combination of atomistic MD simulations with coarse grained BD simulations are in agreement with experimental finding, providing more informative proofs of concept on how thermal fluctuations change interaction potentials among beads and on how the molecular rearrangements affect MT and F-actin rigidities.

Microtubules (MTs) are cellular supramolecular structures that, in combination with actin and intermediate filaments, form the cell cytoskeleton. Within cytoskeleton filaments, MTs exhibit the highest bending stiffness. Up today, experimental techniques have not been able to investigate the origin of MTs flexural rigidity, despite the many experimental efforts done to estimate MT mechanical properties. Molecular Dynamic (MD) and Normal mode Analysis (NMA) show the potentiality for getting insight into this topic. However, these standard molecular modelling techniques are not yet able to simulate large molecular structures as MTs. In this work we developed a multiscale Coarse Grain (CG) model of an entire MT up to 180 nm long, by integrating information from MD and NMA molecular modelling. In particular, MD models were used to obtain information about the molecular conformation and arrangement of the tubulin dimers inside the MT lattice structure and Normal Mode Analysis (NMA) was used in order to study the mechanical behaviour of a MT modelled as an elastic network. MT macroscopic properties, such as bending stiffness (kf), bending modulus (Yf), stretching modulus (Ys), and persistence length (lp) were calculated on the basis of the bending and stretching modes, and results were directly compared to experimental data. Starting from the stretching modes calculated for MTs with lengths up to 180 nm, we found a non-length dependent Ys of about 0.5 GPa, which is in the range of the experimental values (Ys~0.1-2.5 GPa), and a Yb in the range of 0.13-0.35 GPa depending on MT length. These results strongly confirm the anisotropy of the MT mechanical properties.

Summary The cortical endoplasmic reticulum (ER), an elaborate network of tubules and cisternae [1], establishes contact sites with the plasma membrane (PM) through tethering machinery involving a set of conserved integral ER proteins [2]. The physiological consequences of forming ER-PM contacts are not fully understood. Here, we reveal a kinetic restriction role of ER-PM contacts over ring compaction process for proper actomyosin ring assembly in Schizosaccharomyces pombe . We show that fission yeast cells deficient in ER-PM contacts exhibit aberrant equatorial clustering of actin cables during ring assembly and are particularly susceptible to compromised actin filament crosslinking activity. Using quantitative image analyses and computer simulation, we demonstrate that ER-PM contacts function to modulate the distribution of ring components and to constrain their compaction kinetics. We propose that ER-PM contacts have evolved as important physical modulators to ensure robust ring assembly.

The budding yeast actin cables and contractile ring are important for polarized growth and division, revealing basic aspects of cytoskeletal function. To study these formin-nucleated structures, we built a three-dimensional (3D) computational model with actin filaments represented as beads connected by springs. Polymerization by formins at the bud tip and bud neck, crosslinking, severing, and myosin pulling, are included. Parameter values were estimated from prior experiments. The model generates actin cable structures and dynamics similar to those of wild type and formin deletion mutant cells. Simulations with increased polymerization rate result in long, wavy cables. Simulated pulling by type V myosin stretches actin cables. Increasing the affinity of actin filaments for the bud neck together with reduced myosin V pulling promotes the formation of a bundle of antiparallel filaments at the bud neck, which we suggest as a model for the assembly of actin filaments to the contractile ring.

Cells are able to respond to mechanical forces and deformations. The actin cytoskeleton, a highly dynamic scaffolding structure, plays an important role in cell mechano-sensing. Thus, understanding rheological behaviors of the actin cytoskeleton is critical for delineating mechanical behaviors of cells. The actin cytoskeleton consists of interconnected actin filaments (F-actin) that form via self-assembly of actin monomers. It has been shown that molecular changes of the monomer subunits impact the rigidity of F-actin. However, it remains inconclusive whether or not the molecular changes can propagate to the network level and thus alter the rheological properties of actin networks. Here, we focus on how cation binding and nucleotide state tune the molecular conformation and rigidity of F-actin and a representative rheological behavior of actin networks, strain-stiffening. We employ a multiscale approach by combining established computational techniques: molecular dynamics, normal mode analysis and Brownian dynamics. Our findings indicate that different combinations of nucleotide (ATP, ADP or ADP-Pi) and cation [Formula: see text] or [Formula: see text] at one or multiple sites) binding change the molecular conformation of F-actin by varying inter- and intra-strand interactions which bridge adjacent subunits between and within F-actin helical strands. This is reflected in the rigidity of actin filaments against bending and stretching. We found that differences in extension and bending rigidity of F-actin induced by cation binding to the low-, intermediate- and high-affinity sites vary the strain-stiffening response of actin networks crosslinked by rigid crosslinkers, such as scruin, whereas they minimally impact the strain-stiffening response when compliant crosslinkers, such as filamin A or [Formula: see text]-actinin, are used.

Cell spreading and polarization are morphogenetic responses to extracellular matrix adhesion. Cultured fibroblasts polarize when plated on rigid, but not compliant substrates. In this study, we demonstrate that fibroblasts have increased spread area on compliant substrates when integrins are directly activated via manganese (Mn2+), even upon inhibition of myosin motor activity. Integrin activation is primarily regulated by changes in tertiary and quaternary structure and Mn2+ treatments enhance the lifetime of integrin/ligand bonds. The decrease of integrin/ligand unbinding rate under tension suggests a mechanosensing role of activated integrins in regulating adhesion formation. Using a combination of atomistic molecular dynamics and coarse grain Brownian dynamics simulations, we identify integrin intermediates along the activation pathway and show that modulation of integrin catch bond kinetics upon Mn2+-activation promotes integrin binding on compliant substrates. Combining experiments with simulations, our results support the idea that different regimes of ligand binding and cell spreading result from variations in integrin catch bond kinetics. This suggests an alternative mechanosensing pathway based on integrin activity and independent of myosin activity.

During fission yeast cytokinesis, actin filaments are nucleated in random directions by cortical Cdc12 and captured by myosin-II motors from neighboring nodes, exerting forces that pull them together into a contractile ring. Contractile ring assembly has been previously described using a stochastic 2D computational model based on a “search, capture, pull and release” mechanism (SCPR). In this model, actin filaments are assumed to polymerize along the cell membrane, consistent with enhanced concentration of actin filaments near the cell membrane in experiments. Recent observations in mutant and wild-type cells have suggested that actin filaments nucleated in the cytoplasm and in non-medial locations can also participate into the assembly of the cytokinetic ring as well as in clump, star, and meshwork actomyosin morphologies. The relative contributions of the non-medially nucleated actin filaments has been debated. In order to examine these effects that involve 3D dynamics and to better understand the mechanisms that confine actin filaments along the cell surface, we extended the SCPR model to 3D. In this model semiflexible actin filaments (represented as beads connected by springs) grow from nodes and they can be captured by myosin in neighboring nodes. Cross-linking by alpha-actinin and fimbrin is represented by an attractive interaction between filament beads. We also implemented cytoplasmic formin nucleation and actin cable incorporation into the contractile ring. We quantified the resulting distribution and orientation of actin around the band of myosin nodes and studied the effects of varying model parameter values. We describe the conditions under which ring, clump, transient star and meshwork structures may form along the cell membrane and compare to prior experiments.

Cytokinetic ring assembly in model organism fission yeast is a dynamic process, involving condensation of a network of actin filaments and myosin motors bound to the cell membrane through cortical nodes. A 3D computational model of cytokinetic ring assembly based on the “search, capture, pull and release” mechanism illustrates how the combined activities of myosin motors, filament crosslinkers and actin filament turnover can lead to robust ring formation [Bidone et al. Biophys. J, 2014]. We extended the model to study the importance of the physical properties of node movement along the cell membrane and of myosin recruitment to nodes. Experiments by D. Zhang (Temasek Life Sciences) show that tethering of the cortical endoplasmic reticulum (ER) to the plasma membrane modulates the speed of node condensation and the degree of node clumping. We were able to capture the trend observed in these experiments by changes in the node drag coefficient and initial node distribution in simulations. The model predicted that reducing crosslinking activities in ER tethering mutants with faster node speed enhances the probability of actomyosin clumping. We developed a model of how tilted and/or misplaced rings assemble in cells that lack the node structural component anillin-like Mid1 and thus fail to recruit myosin II to nodes independently of actin. If actin-dependent binding of diffusive myosin to the cortex is incorporated into the model, it generates progressively elongating cortical actomyosin strands with fluctuating actin bundles at the tails. These stands often close into a ring, similar to observations by the group of J.Q. Wu (The Ohio State University).

In this article, we present a computational multiscale model for the characterization of subcellular proteins. The model is encoded inside a simulation tool that builds coarse-grained (CG) force fields from atomistic simulations. Equilibrium molecular dynamics simulations on an all-atom model of the actin filament are performed. Then, using the statistical distribution of the distances between pairs of selected groups of atoms at the output of the MD simulations, the force field is parameterized using the Boltzmann inversion approach. This CG force field is further used to characterize the dynamics of the protein via Brownian dynamics simulations. This combination of methods into a single computational tool flow enables the simulation of actin filaments with length up to 400 nm, extending the time and length scales compared to state-of-the-art approaches. Moreover, the proposed multiscale modeling approach allows to investigate the relationship between atomistic structure and changes on the overall dynamics and mechanics of the filament and can be easily (i) extended to the characterization of other subcellular structures and (ii) used to investigate the cellular effects of molecular alterations due to pathological conditions.

Cells modulate themselves in response to the surrounding environment like substrate elasticity, exhibiting structural reorganization driven by the contractility of cytoskeleton. The cytoskeleton is the scaffolding structure of eukaryotic cells, playing a central role in many mechanical and biological functions. It is composed of a network of actins, actin cross-linking proteins (ACPs), and molecular motors. The motors generate contractile forces by sliding couples of actin filaments in a polar fashion, and the contractile response of the cytoskeleton network is known to be modulated also by external stimuli, such as substrate stiffness. This implies an important role of actomyosin contractility in the cell mechano-sensing. However, how cells sense matrix stiffness via the contractility remains an open question. Here, we present a 3-D Brownian dynamics computational model of a cross-linked actin network including the dynamics of molecular motors and ACPs. The mechano-sensing properties of this active network are investigated by evaluating contraction and stress in response to different substrate stiffness. Results demonstrate two mechanisms that act to limit internal stress: (i) In stiff substrates, motors walk until they exert their maximum force, leading to a plateau stress that is independent of substrate stiffness, whereas (ii) in soft substrates, motors walk until they become blocked by other motors or ACPs, leading to submaximal stress levels. Therefore, this study provides new insights into the role of molecular motors in the contraction and rigidity sensing of cells.

Actin dynamics, which is at the basis of many fundamental cellular processes as cell migration [1], is governed by the self-assembly and disassembly of actin monomers (G-actin) that, in turn, are determined by the kinetics of ATP hydrolysis and by the local concentrations of Mg2+ and Ca2+ [2]. During cell migration, interactions of the actin filaments (F-actin) with different nucleotide-cation complexes induce local topological rearrangements, because the filament building G-actins undergo conformational shifts between multiple equilibrium states separated by low-energy barriers. For example, the structural rearrangements of the DNase-I binding loop (residues 38–52) in subdomain 2 are driven by ATP hydrolysis and the changes in the conformation of subdomain 4 are induced by the presence of a tightly-bound Mg2+ or Ca2+ ion (Figure 1a). These conformational shifts alter the cross-linking between monomers, varying the contact surfaces among adjacent inter- and intrasubdomains of G-actin, and reflect on the overall properties of F-actin.Copyright © 2011 by ASME

The actin microfilament (F-actin) is a structural and functional component of the cell cytoskeleton. Notwithstanding the primary role it plays for the mechanics of the cell, the mechanical behaviour of F-actin is still not totally explored. In particular, the relationship between the mechanics of F-actin and its molecular architecture is not completely understood. In this study, the mechanical properties of F-actin were related to the molecular topology of its building monomers (G-actin) by employing a computational multi-level approach. F-actins with lengths up to 500 nm were modelled and characterized, using a combination of equilibrium molecular dynamics (MD) simulations and normal mode analysis (NMA). MD simulations were performed to analyze the molecular rearrangements of G-actin in physiological conditions; NMA was applied to compute the macroscopic properties of F-actin from its vibrational modes of motion. Results from this multi-level approach showed that bending stiffness, bending modulus and persistence length are independent from the length of F-actin. On the contrary, the orientations and motions of selected groups of residues of G-actin play a primary role in determining the filament flexibility. In conclusion, this study (i) demonstrated that a combined computational approach of MD and NMA allows to investigate the biomechanics of F-actin taking into account the molecular topology of the filament (i.e., the molecular conformations of G-actin) and (ii) that this can be done using only crystallographic G-actin, without the need of introducing experimental parameters nor of reducing the number of residues.

Cell mechanics depends on the mechanical properties of actin microfilaments (MFs), microtubules (MTs) and intermediate filaments (IFs), that build the cytoskeleton. Actin microfilaments are the most abundant components and play significant roles in various cellular processes [1]. Among them, the mechanical properties of MFs are essential for the functions of the cytoskeleton and are directly related to their molecular architecture.Copyright © 2010 by ASME

During fission yeast cytokinesis, actin filaments nucleated by cortical formin Cdc12 are captured by myosin motors bound to a band of cortical nodes and bundled by cross-linking proteins. The myosin motors exert forces on the actin filaments, resulting in a net pulling of the nodes into a contractile ring, while cross-linking interactions help align actin filaments and nodes into a single bundle. We used these mechanisms in a three-dimensional computational model of contractile ring assembly, with semiflexible actin filaments growing from formins at cortical nodes, capturing of filaments by neighboring nodes, and cross-linking among filaments through attractive interactions. The model was used to predict profiles of actin filament density at the cell cortex, morphologies of condensing node-filament networks, and regimes of cortical tension by varying the node pulling force and strength of cross-linking among actin filaments. Results show that cross-linking interactions can lead to confinement of actin filaments at the simulated cortical boundary. We show that the ring-formation region in parameter space lies close to regions leading to clumps, meshworks or double rings, and stars/cables. Since boundaries between regions are not sharp, transient structures that resemble clumps, stars, and meshworks can appear in the process of ring assembly. These results are consistent with prior experiments with mutations in actin-filament turnover regulators, myosin motor activity, and changes in the concentration of cross-linkers that alter the morphology of the condensing network. Transient star shapes appear in some simulations, and these morphologies offer an explanation for star structures observed in prior experimental images. Finally, we quantify tension along actin filaments and forces on nodes during ring assembly and show that the mechanisms describing ring assembly can also drive ring constriction once the ring is formed.

At the onset of cytokinesis in fission yeast (a model organism for studying mitosis), the locations of actin filament nucleation by formins shift from the cell tips to the cell middle. These actin filaments are captured by myosin motors bound to medial cortical nodes and bundled by crosslinking proteins, in order to form a ring. The myosin motors exert forces on the actin filaments, resulting in net pulling of nodes and filaments towards the cell equator, while cross-linking interactions help align actin filaments into a single bundle. We used these mechanisms in a 3D computational model of ring assembly, with semiflexible actin filaments growing from formins at the cell tips and at the medial cell cortex, capturing and pulling of filaments by nodes, and cross-linking among filaments through attractive interactions. The model was used to predict profiles of actin density at the cortex, morphologies of condensing node-filament networks, including the transition from actin cables to ring in different conditions of myosin activity and strength of crosslinking. Results show that cross-linking interactions can lead to confinement of actin filaments that grow from medial locations of the cell cortex. We show that the ring formation region in parameter space lies close to regions leading to clumps, meshworks or double rings, and stars/cables. Since boundaries between regions are not sharp, transient structures that resemble clumps, stars and meshworks can appear in the process of ring assembly. The presence of transient nonmedial cables linking the medial region to the cell tips can further modify these boundaries. These results are consistent with prior experiments with mutations in actin filament turnover regulators, myosin motor activity and changes in the concentration of cross linkers that alter the morphology of the condensing network.