Session A36: Physics of the Cytoskeleton I

Trainable control of active nematic defect dynamics using imperfect feedback and artificial intelligence

Learning how to control active matter systems is a key step to understanding how living systems regulate their own active components and how we might engineer new functional materials. Top-down approaches to this task which require full knowledge of the system’s physics, such as optimal control, cannot plausibly be implemented by biological feedback loops.  This motivates searching for new training protocols that do not require perfect system specification.  Inspired by advances in training neural networks using imperfect error signal propagation, we introduce an imperfect, thermodynamically-motivated learning algorithm for controlling non-equilibrium systems. In a supervised learning setup, our algorithm uses only local comparisons between the system’s free energy and that of a target trajectory to provide increments in a control parameter guiding the system. Surprisingly for these driven systems, these equilibrium free energy comparisons can provide sufficient information for convergence.  We characterize the conditions under which convergence happens, and we demonstrate this learning rule on the non-trivial control task of pulling defects in active nematic systems along desired trajectories.  This illustrates how a coarse projection of the full system state can allow iterative improvement of a non-equilibrium control process, which can guide future investigations into biologically plausible learning routines.  In addition to imperfect feedback, we also explore controlling active nematic defects using reinforcement learning – a “trial and error”-based machine learning technique that eschews any knowledge of the system’s physics.  This practical method can be useful for developing refined experimental control over living and engineered active matter systems.   

Dynamic remodeling biopolymer networks achieve mechanical homeostasis

The actin cortex is a biopolymer network consisting of actin filaments and actin binding proteins, along with molecular motors that actively stress the network. This network is known to undergo rapid turnover, where filaments are disassembled and polymerized dynamically while maintaining rigid mechanical properties. The fundamental processes that regulate the remodeling process (such as polymerization and depolymerization) are known, but the precise mechanisms that connect the physics of remodeling to the maintenance of mechanical properties during turnover remain elusive. Here, we perform simulations of prestressed disordered central-force spring networks that undergo successive edge pruning and insertion events that alter the network topology while preserving certain characteristics such as total filament mass and filament length distribution. The networks undergo substantial remodeling and achieve mechanical homeostasis for reasonable values of prestress when pruning is performed with a tension-based criterion. Our work offers important insight into how the interplay between polymerization and depolymerization during turnover contributes to the rigidity of the cytoskeleton.   

Residue-specific coarse-grained model of actin filaments

A challenge in understanding the molecular regulation of actin cytoskeleton is the development of computationally efficient and accurate models. We developed a coarse grained molecular dynamics model of actin filaments that incorporates residue-specific interactions through the C-alpha implicitsolvent model of Kim and Hummer (KH), modified to account for experimentally-determined actinactin interactions. While the KH model correctly predicts the broad features of actin-actin interactions, it does not consistently maintain all long- and short-pitch contacts required for a right handed helix of actin subunits. We show the latter can be achieved by specifying additional specific interactions between subdomains 3 and 4, two pairs between the D-loop and the cleft of subdomains 1 and 3, and one pair for short-pitch interaction. We also give the actin subunits flexibility to tilt/open to mimic the transition between G- and F- actin forms. The modified KH model is able to capture the critical contacts in actin filament formation and stabilization and should be useful to understand interactions of actin filaments to side binding proteins.   

Cytoskeletal response to external forces: Contractile to extensile transition

Cellular cytoskeleton is a highly complex material composed of various filaments, crosslinkers and molecular motors which drive the system out-of-equilibrium (i.e., active) via imparting forces at microscopic scale. Due to it's architechtural complexity and activity, the cytoskeletal structures may exhibit non-trivial response to external purturbations. Here we employ a simplified and coarse-grained agent-based description of the actin cytoskeleton using polar filaments and motors to understand it's response to the external forces. Interestingly, we find the actomyosin self-assembly to undergo a morphological transition from an aster to a bundle in response to the external forces. Based on the microscopic dynamics, we build a mesoscopic theorectical description to show that underlying the mentioned morphological transition, there is a transition of the active stress from being contractile in aster to become extensile in the bundles. We show this transition in local active stress arises due to the broken detailed balance at the microscopic scale. The emerging response to external force seen in our work may help in understanding the underlying physical principle of the physiologically important phenomenon of cellular mechanosensing.   

Stress Relaxation of Actin Networks and Solutions via Severing

Actin Filaments are maintained in the cytoskeleton along with the monomeric actin in dynamic self-assembly. These biopolymers form highly dynamic networks that contribute to force generation and mechanical stability in the cytoskeleton. They undergo reactions such as polymerization, depolymerization, and severing, which play a crucial role in self-assembly and affect the rheology of the networks. Recent experiments and theory have identified novel stress relaxation due to severing. Inspired by prior studies, we focus on the effects of severing and its rheological implications in both solution and network limits. We develop computational models to predict specific signatures in stress relaxation due to severing in both limits. By introducing mechano-chemical feedback of stress on severing, we study its implications on the network topology and the effects on the onset of floppy to rigid transition based on the network connectivity and the applied shear strain.   

Active deformation and self-organization in elastic fiber networks

Fibrous networks occur ubiquitously in living matter ranging from the cytoskeleton to the extracellular matrix. Due to their disordered structure and the propensity of slender fibers to bend and buckle,  these biomaterials exhibit unique mechanical properties such as elastic nonlinearity and rigidity transitions, non-affine deformation modes, and long-range but heterogeneous force transmission. These  properties emerge from the collective response of individual fibers to external stress as well as to intrinsic active stresses created by myosin motors. In this presentation, we consider how such actively generated forces are transmitted through the network and how this depends on fiber stiffness and connectivity. These mechanical forces can mediate long-range effects in the macroscopic deformation of the network as well as drive the self-organization of its structural components. We model the fibers as elastic bonds in a connected network which can stretch, bend, and buckle, while the contractile activity of myosin motors is represented by  force dipoles. We predict numerically that predominant fiber bending screens out force propagation, resulting in weaker macroscopic contractility and inter-dipole mechanical interactions. Further, we predict an atypical fiber buckling-induced softening regime under intermediate external shear, before the well-characterized stiffening regime. Both these predictions are supported by experiments on crosslinker-inhibited fibrin in platelet-contracted blood clots and has indirect support in in vitro actomyosin networks. Finally, we consider the 3D deformation of initially flat, contractile actomyosin gels to show how active motor-generated forces align and restructure the network, which in turn redirects the active forces. This feedback between force generating units and network elasticity provides insight into the spontaneous shape changes shown by cells and tissues during biological processes such as wound healing and morphogenesis.   

Role of fiber bending in the macroscopic active contraction of model cytoskeletal networks

Myosin motors in disordered actin networks produce contractile forces that drive cellular processes such as cell shape change and locomotion. The combined action of multiple myosin motors leads to macroscopic contraction of the actin gel, which typically occurs as a network of crosslinked elastic fibers. These fibers can undergo multiple deformation modes such as stretching, bending, and buckling, leading to a long-range and heterogeneous transmission of forces through the elastic network. We investigate the motor-driven macroscopic contraction of elastic fiber networks at different fiber bending rigidities. The network is modelled as a diluted triangular lattice with fixed boundaries, while the active stresses generated by myosin motors are modelled as isotropic contractile dipoles. We characterize the strain distribution and normal forces at the boundaries of the network for different configurations of dipoles. We find that networks with stiffer fibers show more force chains as well as higher normal forces at the boundaries, a measure of macroscopic network contraction. Thus, bending-dominated fiber networks under internal forces behave differently from conventional elastic materials under external compression. Our results may be compared to in vitro actomyosin network contraction, where the bending rigidity of actin bundles is varied by changing the concentration of bundling crosslinkers like fascin.   

Myosin-I enhances the force generation of Arp2/3-mediated branched actin assembly

Actin and myosin are molecular machineries that convert free energy released from ATP hydrolysis into mechanical force. Polymerizing actin filaments and myosin motor activity generate forces that power a variety of cellular processes. Myosin-I proteins, commonly found alongside branched actin networks stimulated by Arp2/3 complex, play a key role in force generation for membrane deformation and cell protrusion. Yet, the molecular mechanism of how myosin-I coordinates with branched actin assembly to generate force remains largely unknown. To investigate the role of myosin-Is in branched actin assembly, we reconstituted an in vitro actin-based bead motility system, where branched actin networks were nucleated by Arp2/3 complex on the surface of micron-sized beads coated with Arp2/3 activating factors. Actin filaments first formed a symmetric shell around the bead, which transitioned into a polarized comet tail that propelled the bead forward after symmetry breaking. We site-specifically coupled various densities of myosin-Is to the bead surface and assessed their effects on actin polymerization, network architecture, and symmetry breaking. We also developed filament-level dendritic network simulations to further mimic the effects of myosin-I on actin networks. Our findings suggest that myosin-I enhances the force generation of Arp2/3-mediated branched actin assembly by regulating the actin assembly kinetics and network architecture through its force-generating power stroke.   

Confined actin ring assembly through bundle coarsening prior to kinetic arrest

Controlled assembly of large cytoskeletal architectures in living or synthetic cells requires overcoming thermodynamic and kinetic barriers. Prototypical examples include the assembly of fission yeast cytokinetic rings, red blood cell marginal bands, and equatorial actin rings by passive cross-linkers when confined within a sphere. Recent in vitro experiments have demonstrated that actin rings form when the confining geometry is sufficiently small while complex bundled networks form for larger geometries. Exploring the determinants and pathways for forming cytoskeletal rings requires new computational methods that can systematically vary molecular interactions and concentrations over micron length and minute timescales. We used the high-performance, open-source software aLENS where a constraint method enforces hard-core repulsion between rigid spherocylinders and crosslinking forces in a unified implicit solver.  We simulate polymerization to correspond with a depleting monomer pool and varying distributions of nucleating actin seeds. Under typical in vitro polymerization conditions, we find that single elongating filaments merge into growing bundles, reaching an overlap threshold, which significantly slows down their diffusive dynamics. However, the topology of these bundle networks continues to evolve through filament merging, zippering, and cross-linker condensation, resulting in thicker bundles. Confinement aids network coarsening and loop formation with a ring or open bundle being the stable end state of this dynamical system if reached prior to kinetic arrest.  We explored the effects of viscosity, nucleation rate, and type of passive cross-linkers. Our study informs the structure and mechanics of both confined and bulk networks of semiflexible filaments.   

Lévy distributed fluctuations and cytoquakes in the actomyosin cortex

The mechanics of the actomyosin cortex, a thin sheet of active material that provides animal cells with a strong and flexible exterior, have long defied satisfactory explanation. Here we report low noise, high statistical power measurements of lateral fluctuations in the cortex of multiple cell types, using arrays of flexible microposts. Such fluctuations are found to be highly non-Gaussian and have previously been observed to contain occasional large rearrangements, termed cytoquakes. Analysis of the structure of the largest post displacements shows that they are indistinguishable from chance fluctuations of the superdiffusive random process describing the rest of the fluctuations. The full distribution of micropost displacements is well-described by an exponentially truncated Lévy alpha-stable distribution, further reinforcing the notion that cells' non-Gaussian fluctuations and cytoquakes are manifestations of a single phenomenon. The lag time dependence of these distributions is not captured by existing models, and we conjecture that the Lévy distributed fluctuations are caused by a heavy-tailed distribution of microscopic stresses on cytoskeletal elements. These findings will be used to inform and constrain future physical modeling of the cortex.