Dynamic Mechanisms of Cell Rigidity Sensing: Insights from a Computational Model of Actomyosin Networks

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

Computational model of kinetochore-microtubule attachments

The ability of cells to separate chromosomes during mitosis is critical to several phases of their physiology. Chromosome segregation is mediated by spindle microtubules that attach to mitotic kinetochores via a dynamic protein interface, which includes Ndc80 and its accessory proteins, Ska, Cdt1 and ch-TOG [1-3]. The Ndc80 complex forms the core component of the attachment sites while Ska, Cdt1 and ch-TOG binds kinetochores via the Ndc80 complex. From prometaphase to metaphase, the kinetochore levels of Ska and Cdt1 increase in Hela cells, while that of Ndc80 remains constant. This suggests a correlation between concentration of proteins at the kinetochore-microtubule (kMT) interface and increasing amounts of load during mitosis. Interestingly, while being dynamic, the kMT interface ensures stability of the connection between chromosomes and kinetochore microtubules. How the various interface proteins interplay to ensure a dynamic yet stable connection is not known because their exact roles in this process are still elusive. An interesting hypothesis is that the Ndc80-accessory proteins Ska, Cdt1 and ch-TOG directly strengthen the kinetochore-microtubule interface by forming additional connections between kinetochore-bound Ndc80 and spindle microtubules. However, since Ska, Cdt1 and ch-TOG dynamically form and break their connections with microtubules, a synergy between them is likely to exist. Here, in order to characterize the synergy between Ska, Cdt1 and ch-TOG, we developed a new computational model, based on a kinetic Monte Carlo approach. The model allowed us to explicitly incorporate Ndc80, Ska1, Cdt1 and ch-TOG, isolate their contributions, and characterize their synergistic effects on the stability of the interface. Each protein is defined by a position along a tubulin protofilament, and exists in two states, bound or unbound, while undergoing biased diffusion, as observed in experiments. The model also incorporates tension-dependent unbinding rates for each protein, including catch bond kinetics for ch-TOG, as detected experimentally [2]. As for the output, the model evaluates: (i) displacement of the kMT interface along the tubulin protofilament; (ii) time of kMT attachment under tension; and (iii) kMT attachment rupture force, corresponding to the force that detaches all proteins. We find that combining Ndc80, Ska and Cdt1 enhances kMT attachment strength with respect to individual components. Ch-TOG further strengthens the complex because of its catch bond kinetics. In addition, the model shows that the rupture force, corresponding to the load under which no protein is bound, increases in proportion to the number of simulated microtubules. Taken together, our results provide important mechanistic insights into how kMT proteins coordinate with each other to withstand tension and ensure accurate chromosome segregation. [1] D. Varma, and E. D. Salmon. J. Cell. Sci., 2013. [2] M. P. Miller, C.L. Asbury, and S. Biggins. Cell, 2016. [3] S. Agarwal, K.P. Smith, Y. Zhou, A. Suzuki, R.J. McKenney, and D. Varma. J. Cell Biol., 2018Non UBCUnreviewedAuthor affiliation: University of UtahResearche

Computational Study of Actin: Mechanics of Actin Filaments, Rheology of Actin Networks and Build up of Force in Contractile Actin Assemblies

The actin cytoskeleton is the scaffolding structure of eukaryotic cells, providing them with structural integrity, resistance to deformation and remodeling. It is mostly composed of: actin filaments (F-actin), cross-linking proteins, and molecular motors. The actin filament is a semiflexible polymer with the geometry of a right-handed double helix and whose mechanical performance depends on the bound ligands (i.e., ATP/ADP nucleotides and Ca2+/Mg2+ cations); cross-linking proteins comprise a family of actin binding proteins with molecular weight from 20 to 300 kDa that mediate the organization of F-actins into orthogonal networks or parallel bundles; myosin II molecular motors are ATP-dependent motor proteins comprising multiple myosin heads that collectively generate force dipoles on pairs of actin filaments with opposite polarities leading to organization of the actin network into various contractile assemblies, including stress fibers, random polarity bundles and the contractile ring. The characteristics of the various elements of the cytoskeleton, including the mechanics and length of F-actin, the density of molecular motors and the concentration of crosslinking proteins, have a direct effect on the morphology and rheology of the actin cytoskeleton and on the dynamics and steady state properties of its assemblies. Although various experimental and computational studies have been conducted, the interplay between the various elements in the actin cytoskeleton is still poorly understood and the use of one single technique is not sufficient to elucidate phenomena at different scales of complexity. In this thesis, we employed different computational methods, spanning temporal and spatial scales from nanoseconds to seconds and from angstroms to micrometers, in order to investigate the effects of various ligands on the mechanics of the actin filaments, the origin of the rheology of passively crosslinked actin networks in different conditions of filament and crosslinks mechanical properties, and the dynamics and steady state properties of contractile arc-shaped actin bundles. After reviewing the state of art in studying actin filaments, actin networks and contractile assemblies (Chapter 1), we captured the effects of nucleotides and cations on the mechanics of the single filaments (Chapter 2) using a combination of molecular dynamics (MD) simulations, elastic network modeling (ENM) and normal mode analysis (NMA). We found that specific groups of residues on the external surface of the actin monomers are responsible for strengthening (or weakening) longitudinal and lateral interactions and lead to enhanced (or reduced) filament rigidity. We incorporated our data regarding the mechanical properties of the filaments in the different conditions of bound cations and/or nucleotides into a 3D minimal model system mimicking an actin network composed of actin filaments and static crosslinking proteins (Chapter 3). While the network was passive, with no molecular motors, it was thermally activated. We investigated the regime of strain-stiffening, focusing on the interplay between the bending/stretching stiffness of the filaments and the bending/stretching rigidity of the crosslinking proteins (Chapter 4). Strain-stiffening was characterized by a first linear regime, followed by a nonlinear phase. We found that in the first linear regime, the deformation was mostly accommodated by crosslinking proteins, while the actin filaments deformed by bending, while in the nonlinear phase, actin filaments stretched out and the contribution from cross-linkers decreased proportionally with increasing deformation. Thermal fluctuations were manifested only at low deformation. By varying the actin concentration and the average length of the actin filaments (Chapter 5), the elastic shear modulus changed exponentially and reflected the degree of network percolation. We also characterized the contraction of the crosslinked actin network introducing into the passive network elements mimicking molecular motors and varying the rigidity of the surrounding boundaries (Chapter 6). We elucidated the relation between motor kinetics and level of contractile force. On soft substrates, motors stalled owing to occupancy of available binding, generating low contractile force and dense networks; on rigid substrates, motors stopped walking due to reaching of the stalling force, generating high contraction and sparse networks. Furthermore, we simulated the condensation of a homogeneous actin filament network into a contractile bundle resembling the dimensions and the level of axial force of an actin arc, typically found in the lamellipodium/lamella region of migrating cells (Chapter 7). We characterized the morphology of the arc-shaped bundle at the steady state and its build up of force along the longitudinal axis at different filament lengths, densities of motors and crosslinkers. We identified combinations of crosslinks/motors concentrations determining the transitions between a contractile network and an arc and between formation of an arc and a contractile sheet. By systematically varying the average length of the actin filaments, we also identified a threshold length of the filaments equal to 2 µm, below which the contraction of the network into a compact contractile assembly could not occur. Last, we discuss the future developments of this study (Chapter 8) and possible extensions of the computational approach adopted

Computational Study of Actin: Mechanics of Actin Filaments, Rheology of Actin Networks and Build up of Force in Contractile Actin Assemblies

The actin cytoskeleton is the scaffolding structure of eukaryotic cells, providing them with structural integrity, resistance to deformation and remodeling. It is mostly composed of: actin filaments (F-actin), cross-linking proteins, and molecular motors. The actin filament is a semiflexible polymer with the geometry of a right-handed double helix and whose mechanical performance depends on the bound ligands (i.e., ATP/ADP nucleotides and Ca2+/Mg2+ cations); cross-linking proteins comprise a family of actin binding proteins with molecular weight from 20 to 300 kDa that mediate the organization of F-actins into orthogonal networks or parallel bundles; myosin II molecular motors are ATP-dependent motor proteins comprising multiple myosin heads that collectively generate force dipoles on pairs of actin filaments with opposite polarities leading to organization of the actin network into various contractile assemblies, including stress fibers, random polarity bundles and the contractile ring. The characteristics of the various elements of the cytoskeleton, including the mechanics and length of F-actin, the density of molecular motors and the concentration of crosslinking proteins, have a direct effect on the morphology and rheology of the actin cytoskeleton and on the dynamics and steady state properties of its assemblies. Although various experimental and computational studies have been conducted, the interplay between the various elements in the actin cytoskeleton is still poorly understood and the use of one single technique is not sufficient to elucidate phenomena at different scales of complexity. In this thesis, we employed different computational methods, spanning temporal and spatial scales from nanoseconds to seconds and from angstroms to micrometers, in order to investigate the effects of various ligands on the mechanics of the actin filaments, the origin of the rheology of passively crosslinked actin networks in different conditions of filament and crosslinks mechanical properties, and the dynamics and steady state properties of contractile arc-shaped actin bundles. After reviewing the state of art in studying actin filaments, actin networks and contractile assemblies (Chapter 1), we captured the effects of nucleotides and cations on the mechanics of the single filaments (Chapter 2) using a combination of molecular dynamics (MD) simulations, elastic network modeling (ENM) and normal mode analysis (NMA). We found that specific groups of residues on the external surface of the actin monomers are responsible for strengthening (or weakening) longitudinal and lateral interactions and lead to enhanced (or reduced) filament rigidity. We incorporated our data regarding the mechanical properties of the filaments in the different conditions of bound cations and/or nucleotides into a 3D minimal model system mimicking an actin network composed of actin filaments and static crosslinking proteins (Chapter 3). While the network was passive, with no molecular motors, it was thermally activated. We investigated the regime of strain-stiffening, focusing on the interplay between the bending/stretching stiffness of the filaments and the bending/stretching rigidity of the crosslinking proteins (Chapter 4). Strain-stiffening was characterized by a first linear regime, followed by a nonlinear phase. We found that in the first linear regime, the deformation was mostly accommodated by crosslinking proteins, while the actin filaments deformed by bending, while in the nonlinear phase, actin filaments stretched out and the contribution from cross-linkers decreased proportionally with increasing deformation. Thermal fluctuations were manifested only at low deformation. By varying the actin concentration and the average length of the actin filaments (Chapter 5), the elastic shear modulus changed exponentially and reflected the degree of network percolation. We also characterized the contraction of the crosslinked actin network introducing into the passive network elements mimicking molecular motors and varying the rigidity of the surrounding boundaries (Chapter 6). We elucidated the relation between motor kinetics and level of contractile force. On soft substrates, motors stalled owing to occupancy of available binding, generating low contractile force and dense networks; on rigid substrates, motors stopped walking due to reaching of the stalling force, generating high contraction and sparse networks. Furthermore, we simulated the condensation of a homogeneous actin filament network into a contractile bundle resembling the dimensions and the level of axial force of an actin arc, typically found in the lamellipodium/lamella region of migrating cells (Chapter 7). We characterized the morphology of the arc-shaped bundle at the steady state and its build up of force along the longitudinal axis at different filament lengths, densities of motors and crosslinkers. We identified combinations of crosslinks/motors concentrations determining the transitions between a contractile network and an arc and between formation of an arc and a contractile sheet. By systematically varying the average length of the actin filaments, we also identified a threshold length of the filaments equal to 2 µm, below which the contraction of the network into a compact contractile assembly could not occur. Last, we discuss the future developments of this study (Chapter 8) and possible extensions of the computational approach adopte

Integrin Conformational Dynamics and Mechanotransduction

The function of the integrin family of receptors as central mediators of cell-extracellular matrix (ECM) and cell–cell adhesion requires a remarkable convergence of interactions and influences. Integrins must be anchored to the cytoskeleton and bound to extracellular ligands in order to provide firm adhesion, with force transmission across this linkage conferring tissue integrity. Integrin affinity to ligands is highly regulated by cell signaling pathways, altering affinity constants by 1000-fold or more, via a series of long-range conformational transitions. In this review, we first summarize basic, well-known features of integrin conformational states and then focus on new information concerning the impact of mechanical forces on these states and interstate transitions. We also discuss how these effects may impact mechansensitive cell functions and identify unanswered questions for future studies

Extracellular matrix sensing via modulation of orientational order of integrins and F-actin in focal adhesions

Specificity of cellular responses to distinct cues from the ECM requires precise and sensitive decoding of physical information. However, how known mechanisms of mechanosensing like force-dependent catch bonds and conformational changes in FA proteins can confer that this sensitivity is not known. Using polarization microscopy and computational modeling, we identify dynamic changes in an orientational order of FA proteins as a molecular organizational mechanism that can fine-tune cell sensitivity to the ECM. We find that αV integrins and F-actin show precise changes in the orientational order in an ECM-mediated integrin activation-dependent manner. These changes are sensitive to ECM density and are regulated independent of myosin-II activity though contractility can enhance this sensitivity. A molecular-clutch model demonstrates that the orientational order of integrin-ECM binding coupled to directional catch bonds can capture cellular responses to changes in ECM density. This mechanism also captures decoupling of ECM density sensing from stiffness sensing thus elucidating specificity. Taken together, our results suggest relative geometric organization of FA molecules as an important molecular architectural feature and regulator of mechanotransduction