Computational model of integrin adhesion elongation under an actin fiber.

Cells create physical connections with the extracellular environment through adhesions. Nascent adhesions form at the leading edge of migrating cells and either undergo cycles of disassembly and reassembly, or elongate and stabilize at the end of actin fibers. How adhesions assemble has been addressed in several studies, but the exact role of actin fibers in the elongation and stabilization of nascent adhesions remains largely elusive. To address this question, here we extended our computational model of adhesion assembly by incorporating an actin fiber that locally promotes integrin activation. The model revealed that an actin fiber promotes adhesion stabilization and elongation. Actomyosin contractility from the fiber also promotes adhesion stabilization and elongation, by strengthening integrin-ligand interactions, but only up to a force threshold. Above this force threshold, most integrin-ligand bonds fail, and the adhesion disassembles. In the absence of contraction, actin fibers still support adhesions stabilization. Collectively, our results provide a picture in which myosin activity is dispensable for adhesion stabilization and elongation under an actin fiber, offering a framework for interpreting several previous experimental observations.

Application of Funnel Metadynamics to the Platelet Integrin αIIbß3 in Complex with an RGD Peptide.

Integrin αIIbß3 mediates platelet aggregation by binding the Arginyl-Glycyl-Aspartic acid (RGD) sequence of fibrinogen. RGD binding occurs at a site topographically proximal to the αIIb and ß3 subunits, promoting the conformational activation of the receptor from bent to extended states. While several experimental approaches have characterized RGD binding to αIIbß3 integrin, applying computational methods has been significantly more challenging due to limited sampling and the need for a priori information regarding the interactions between the RGD peptide and integrin. In this study, we employed all-atom simulations using funnel metadynamics (FM) to evaluate the interactions of an RGD peptide with the αIIb and ß3 subunits of integrin. FM incorporates an external history-dependent potential on selected degrees of freedom while applying a funnel-shaped restraint potential to limit RGD exploration of the unbound state. Furthermore, it does not require a priori information about the interactions, enhancing the sampling at a low computational cost. Our FM simulations reveal significant molecular changes in the ß3 subunit of integrin upon RGD binding and provide a free-energy landscape with a low-energy binding mode surrounded by higher-energy prebinding states. The strong agreement between previous experimental and computational data and our results highlights the reliability of FM as a method for studying dynamic interactions of complex systems such as integrin.

Data-driven prediction of αIIbß3 integrin activation paths using manifold learning and deep generative modeling.

The integrin heterodimer is a transmembrane protein critical for driving cellular process and is a therapeutic target in the treatment of multiple diseases linked to its malfunction. Activation of integrin involves conformational transitions between bent and extended states. Some of the conformations that are intermediate between bent and extended states of the heterodimer have been experimentally characterized, but the full activation pathways remain unresolved both experimentally due to their transient nature and computationally due to the challenges in simulating rare barrier crossing events in these large molecular systems. An understanding of the activation pathways can provide new fundamental understanding of the biophysical processes associated with the dynamic interconversions between bent and extended states and can unveil new putative therapeutic targets. In this work, we apply nonlinear manifold learning to coarse-grained molecular dynamics simulations of bent, extended, and two intermediate states of αIIbß3 integrin to learn a low-dimensional embedding of the configurational phase space. We then train deep generative models to learn an inverse mapping between the low-dimensional embedding and high-dimensional molecular space and use these models to interpolate the molecular configurations constituting the activation pathways between the experimentally characterized states. This work furnishes plausible predictions of integrin activation pathways and reports a generic and transferable multiscale technique to predict transition pathways for biomolecular systems.

Integrin αIIbß3 intermediates: From molecular dynamics to adhesion assembly.

The platelet integrin αIIbß3 undergoes long-range conformational transitions associated with its functional conversion from inactive (low-affinity) to active (high-affinity) during hemostasis. Although new conformations that are intermediate between the well-characterized bent and extended states have been identified, their molecular dynamic properties and functions in the assembly of adhesions remain largely unexplored. In this study, we evaluated the properties of intermediate conformations of integrin αIIbß3 and characterized their effects on the assembly of adhesions by combining all-atom simulations, principal component analysis, and mesoscale modeling. Our results show that in the low-affinity, bent conformation, the integrin ectodomain tends to pivot around the legs; in intermediate conformations, the headpiece becomes partially extended, away from the lower legs. In the fully open, active state, αIIbß3 is flexible, and the motions between headpiece and lower legs are accompanied by fluctuations of the transmembrane helices. At the mesoscale, bent integrins form only unstable adhesions, but intermediate or open conformations stabilize the adhesions. These studies reveal a mechanism by which small variations in ligand binding affinity and enhancement of the ligand-bound lifetime in the presence of actin retrograde flow stabilize αIIbß3 integrin adhesions.

Computational model of E-cadherin clustering under force.

E-cadherins play a critical role in the formation of cell-cell adhesions for several physiological functions, including tissue development, repair, and homeostasis. The formation of clusters of E-cadherins involves extracellular adhesive (trans-) and lateral (cis-) associations between E-cadherin ectodomains and stabilization through intracellular binding to the actomyosin cytoskeleton. This binding provides force to the adhesion and is required for mechanotransduction. However, the exact role of cytoskeletal force on the clustering of E-cadherins is not well understood. To gain insights into this mechanism, we developed a computational model based on Brownian dynamics. In the model, E-cadherins transit between structural and functional states; they are able to bind and unbind other E-cadherins on the same and/or opposite cell(s) through trans- and cis-interactions while also creating dynamic links with the actomyosin cytoskeleton. Our results show that actomyosin force governs the fraction of E-cadherins in clusters and the size and number of clusters. For low forces (below 10 pN), a large number of small E-cadherin clusters form with less than five E-cadherins each. At higher forces, the probability of forming fewer but larger clusters increases. These findings support the idea that force reinforces cell-cell adhesions, which is consistent with differences in cluster size previously observed between apical and lateral junctions of epithelial tissues.

Integrin-based mechanosensing through conformational deformation.

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 αVß3 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 ß3 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 αVß3 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.

Formin Cdc12's specific actin assembly properties are tailored for cytokinesis in fission yeast.

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.

Lamellipodium is a myosin-independent mechanosensor.

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.

Multiscale model of integrin adhesion assembly.

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 ß-1 and ß-3 integrins localize in nascent adhesions at the cell leading edge. In order to understand how different nanoscale parameters of ß-1 and ß-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.

Coarse-Grained Simulation of Full-Length Integrin Activation.

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 αvß3, 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 αvß3 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 ß-subunit cytoplasmic regions, headpiece extension, and legs opening.

Dynamic network morphology and tension buildup in a 3D model of cytokinetic ring assembly.

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.

Contributions of the individual domains of αIIbß3 integrin to its extension: Insights from multiscale modeling.

The platelet integrin αIIbß3 undergoes long-range conformational transitions between bent and extended conformations to regulate platelet aggregation during hemostasis and thrombosis. However, how exactly αIIbß3 transitions between conformations remains largely elusive. Here, we studied how transitions across bent and extended-closed conformations of αIIbß3 integrin are regulated by effective interactions between its functional domains. We first carried out µs-long equilibrium molecular dynamics (MD) simulations of full-length αIIbß3 integrins in bent and intermediate conformations, the latter characterized by an extended headpiece and closed legs. Then, we built heterogeneous elastic network models, perturbed inter-domain interactions, and evaluated their relative contributions to the energy barriers between conformations. Results showed that integrin extension emerges from: (i) changes in interfaces between functional domains; (ii) allosteric coupling of the head and upper leg domains with flexible lower leg domains. Collectively, these results provide new insights into integrin conformational activation based on short- and long-range interactions between its functional domains and highlight the importance of the lower legs in the regulation of integrin allostery.

Fascin structural plasticity mediates flexible actin bundle construction.

Fascin crosslinks actin filaments (F-actin) into bundles that support tubular membrane protrusions including filopodia and stereocilia. Fascin dysregulation drives aberrant cell migration during metastasis, and fascin inhibitors are under development as cancer therapeutics. Here, we use cryo-electron microscopy, cryo-electron tomography coupled with custom denoising, and computational modeling to probe fascin's F-actin crosslinking mechanisms across spatial scales. Our fascin crossbridge structure reveals an asymmetric F-actin binding conformation that is allosterically blocked by the inhibitor G2. Reconstructions of seven-filament hexagonal bundle elements, variability analysis, and simulations show how structural plasticity enables fascin to bridge varied inter-filament orientations, accommodating mismatches between F-actin's helical symmetry and bundle hexagonal packing. Tomography of many-filament bundles and modeling uncovers geometric rules underlying emergent fascin binding patterns, as well as the accumulation of unfavorable crosslinks that limit bundle size. Collectively, this work shows how fascin harnesses fine-tuned nanoscale structural dynamics to build and regulate micron-scale F-actin bundles.

A parametric blueprint for optimum cochlear outer hair cell design.

The present work examines the hypothesis that cochlear outer hair cell (OHC) properties vary in precise proportions along the tonotopic map to optimize electromechanical power conversion. We tested this hypothesis using a very simple model of a single isolated OHC driving a mechanical load. Results identify three non-dimensional 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 probably limited by the size of the nucleus and membrane surface area available for ion-channel expression.

Multiscale models of integrins and cellular adhesions.

Computational models of integrin-based adhesion complexes have revealed important insights into the mechanisms by which cells establish connections with their external environment. However, how changes in conformation and function of individual adhesion proteins regulate the dynamics of whole adhesion complexes remains largely elusive. This is because of the large separation in time and length scales between the dynamics of individual adhesion proteins (nanoseconds and nanometers) and the emergent dynamics of the whole adhesion complex (seconds and micrometers), and the limitations of molecular simulation approaches in extracting accurate free energies, conformational transitions, reaction mechanisms, and kinetic rates, that can inform mechanisms at the larger scales. In this review, we discuss models of integrin-based adhesion complexes and highlight their main findings regarding: (i) the conformational transitions of integrins at the molecular and macromolecular scales and (ii) the molecular clutch mechanism at the mesoscale. Lastly, we present unanswered questions in the field of modeling adhesions and propose new ideas for future exciting modeling opportunities.

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.

Nascent adhesions shorten the period of lamellipodium protrusion through the Brownian ratchet mechanism.

Directional cell migration is driven by the conversion of oscillating edge motion into lasting periods of leading edge protrusion. Actin polymerization against the membrane and adhesions control edge motion, but the exact mechanisms that determine protrusion period remain elusive. We addressed this by developing a computational model in which polymerization of actin filaments against a deformable membrane and variable adhesion dynamics support edge motion. Consistent with previous reports, our model showed that actin polymerization and adhesion lifetime power protrusion velocity. However, increasing adhesion lifetime decreased the protrusion period. Measurements of adhesion lifetime and edge motion in migrating cells confirmed that adhesion lifetime is associated with and promotes protrusion velocity, but decreased duration. Our model showed that adhesions' control of protrusion persistence originates from the Brownian ratchet mechanism for actin filament polymerization. With longer adhesion lifetime or increased-adhesion density, the proportion of actin filaments tethered to the substrate increased, maintaining filaments against the cell membrane. The reduced filament-membrane distance generated pushing force for high edge velocity, but limited further polymerization needed for protrusion duration. We propose a mechanism for cell edge protrusion in which adhesion strength regulates actin filament polymerization to control the periods of leading edge protrusion.

Multiscale modeling of cellular actin filaments: from atomistic molecular to coarse-grained dynamics.

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.

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.

Computational model demonstrates that Ndc80-associated proteins strengthen kinetochore-microtubule attachments in metaphase.

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 the 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.