Molecular transport modulates the adaptive response of branched actin networks to an external force

Adaptive nonequilibrium design of actin-based metamaterials: Fundamental and practical limits of control

The adaptive and surprising emergent properties of biological materials self-assembled in far-from-equilibrium environments serve as an inspiration for efforts to design nanomaterials. In particular, controlling the conditions of self-assembly can modulate material properties, but there is no systematic understanding of either how to parameterize external control or how controllable a given material can be. Here, we demonstrate that branched actin networks can be encoded with metamaterial properties by dynamically controlling the applied force under which they grow and that the protocols can be selected using multi-task reinforcement learning. These actin networks have tunable responses over a large dynamic range depending on the chosen external protocol, providing a pathway to encoding "memory" within these structures. Interestingly, we obtain a bound that relates the dissipation rate and the rate of "encoding" that gives insight into the constraints on control-both physical and information theoretical. Taken together, these results emphasize the utility and necessity of nonequilibrium control for designing self-assembled nanostructures.

Forecasting Avalanches in Branched Actomyosin Networks with Network Science and Machine Learning

We explored the dynamic and structural effects of actin-related proteins 2/3 (Arp2/3) on actomyosin networks using mechanochemical simulations of active matter networks. On the nanoscale, the Arp2/3 complex alters the topology of actomyosin by nucleating a daughter filament at an angle with respect to a mother filament. At a subcellular scale, they orchestrate the formation of a branched actomyosin network. Using a coarse-grained approach, we sought to understand how an actomyosin network temporally and spatially reorganizes itself by varying the concentration of the Arp2/3 complexes. Driven by motor dynamics, the network stalls at a high concentration of Arp2/3 and contracts at a low Arp2/3 concentration. At an intermediate Arp2/3 concentration, however, the actomyosin network is formed by loosely connected clusters that may collapse suddenly when driven by motors. This physical phenomenon is called an "avalanche" largely due to the marginal instability inherent to the morphology of a branched actomyosin network when the Arp2/3 complex is present. While embracing the data science approaches, we unveiled the higher-order patterns in the branched actomyosin networks and discovered a sudden change in the "social" network topology of actomyosin, which is a new type of avalanche in addition to the two types of avalanches associated with a sudden change in the size or shape of the whole actomyosin network, as shown in a previous investigation. Our new finding promotes the importance of using network theory and machine learning models to forecast avalanches in actomyosin networks. The mechanisms of the Arp2/3 complexes in shaping the architecture of branched actomyosin networks obtained in this paper will help us better understand the emergent reorganization of the topology in dense actomyosin networks that are difficult to detect in experiments.

Discrete mechanical model of lamellipodial actin network implements molecular clutch mechanism and generates arcs and microspikes

Mechanical forces, actin filament turnover, and adhesion to the extracellular environment regulate lamellipodial protrusions. Computational and mathematical models at the continuum level have been used to investigate the molecular clutch mechanism, calculating the stress profile through the lamellipodium and around focal adhesions. However, the forces and deformations of individual actin filaments have not been considered while interactions between actin networks and actin bundles is not easily accounted with such methods. We develop a filament-level model of a lamellipodial actin network undergoing retrograde flow using 3D Brownian dynamics. Retrograde flow is promoted in simulations by pushing forces from the leading edge (due to actin polymerization), pulling forces (due to molecular motors), and opposed by viscous drag in cytoplasm and focal adhesions. Simulated networks have densities similar to measurements in prior electron micrographs. Connectivity between individual actin segments is maintained by permanent and dynamic crosslinkers. Remodeling of the network occurs via the addition of single actin filaments near the leading edge and via filament bond severing. We investigated how several parameters affect the stress distribution, network deformation and retrograde flow speed. The model captures the decrease in retrograde flow upon increase of focal adhesion strength. The stress profile changes from compression to extension across the leading edge, with regions of filament bending around focal adhesions. The model reproduces the observed reduction in retrograde flow speed upon exposure to cytochalasin D, which halts actin polymerization. Changes in crosslinker concentration and dynamics, as well as in the orientation pattern of newly added filaments demonstrate the model's ability to generate bundles of filaments perpendicular (actin arcs) or parallel (microspikes) to the protruding direction.

Integrated Bioinformatics Analysis Reveals Potential Pathway Biomarkers and Their Interactions for Clubfoot

Background

Congenital talipes equinovarus (clubfoot), one of the most regular pediatric congenital skeletal anomalies, seriously affects the normal growth and development of about 1 in 1000 newborns. Although it has been investigated widely, the etiology and pathogenesis of clubfoot are still controversial.

Material/Methods

g: Profiler, NetworkAnalyst and WebGestalt were used to probe the enriched signaling pathways by using the Gene Ontology (GO), Human Phenotype Ontology (HP), Kyoto Encyclopedia of Genes and Genomes (KEGG), Reactome (REAC), and WikiPathways (WP) databases. Large numbers of enriched signaling pathways were identified using the integrated bioinformatics enrichment analyses.

Results

Apoptosis or programmed cell death (PCD), disease, muscle contraction, metabolism, and immune system were the top functions. Embryo or organ morphogenesis and development, cell or muscle contraction, and apoptosis were the top biological processes, and cell/muscle contraction and apoptosis were the top molecular functions using enriched GO terms analysis. There were a large number of complex interactions in the genes, enriched pathways, and transcription factor (TF)-miRNA co-regulatory networks. Transcription factors such as FOXN3, GLI3, HOX, and NCOR2 family regulated the gene expression of APAF1, BCL2, BID, CASP, MTHFR, and TPM family.

Conclusions

The results of bioinformatics enrichment analysis not only supported the previously proposed hypotheses, e.g., extracellular matrix (ECM) abnormality, fetal movement reducing, genetic abnormality, muscle abnormality, neurological abnormality, skeletal abnormality and vascular abnormality, but also indicated that cellular or immune responses to external stimulus, molecular transport and metabolism may be new etiological mechanisms in clubfoot.

Tensile force-induced cytoskeletal remodeling: Mechanics before chemistry

Understanding cellular remodeling in response to mechanical stimuli is a critical step in elucidating mechanical activation of biochemical signaling pathways. Experimental evidence indicates that external stress-induced subcellular adaptation is accomplished through dynamic cytoskeletal reorganization. To study the interactions between subcellular structures involved in transducing mechanical signals, we combined experimental data and computational simulations to evaluate real-time mechanical adaptation of the actin cytoskeletal network. Actin cytoskeleton was imaged at the same time as an external tensile force was applied to live vascular smooth muscle cells using a fibronectin-functionalized atomic force microscope probe. Moreover, we performed computational simulations of active cytoskeletal networks under an external tensile force. The experimental data and simulation results suggest that mechanical structural adaptation occurs before chemical adaptation during filament bundle formation: actin filaments first align in the direction of the external force by initializing anisotropic filament orientations, then the chemical evolution of the network follows the anisotropic structures to further develop the bundle-like geometry. Our findings present an alternative two-step explanation for the formation of actin bundles due to mechanical stimulation and provide new insights into the mechanism of mechanotransduction.

Remodeling the cytoskeletal network in response to external force is key to cellular mechanotransduction. Despite much focus on cytoskeletal remodeling in recent years, a comprehensive understanding of actin remodeling in real-time in cells under mechanical stimuli is still lacking. We integrated tensile stress-induced 3D actin remodeling and 3D computational simulations of actin cytoskeleton to study how the actin cytoskeleton form bundles and how these bundles evolve over time upon external tensile stress. We found that actin network remodels through a two-step process in which rapid alignment of actin filaments is followed by slower actin bundling. Based on these results, we propose a “mechanics before chemistry” model of actin cytoskeleton remodeling under external tensile force.

The role of the Arp2/3 complex in shaping the dynamics and structures of branched actomyosin networks

Actomyosin networks give cells the ability to move and divide. These networks contract and expand while being driven by active energy-consuming processes such as motor protein walking and actin polymerization. Actin dynamics is also regulated by actin-binding proteins, such as the actin-related protein 2/3 (Arp2/3) complex. This complex generates branched filaments, thereby changing the overall organization of the network. In this work, the spatiotemporal patterns of dynamical actin assembly accompanying the branching-induced reorganization caused by Arp2/3 were studied using a computational model (mechanochemical dynamics of active networks [MEDYAN]); this model simulates actomyosin network dynamics as a result of chemical reactions whose rates are modulated by rapid mechanical equilibration. We show that branched actomyosin networks relax significantly more slowly than do unbranched networks. Also, branched networks undergo rare convulsive movements, "avalanches," that release strain in the network. These avalanches are associated with the more heterogeneous distribution of mechanically linked filaments displayed by branched networks. These far-from-equilibrium events arising from the marginal stability of growing actomyosin networks provide a possible mechanism of the "cytoquakes" recently seen in experiments.

Thermodynamically consistent treatment of the growth of a biopolymer in the presence of a smooth obstacle interaction potential

We investigate the effect of filament-obstacle interactions on the force-velocity relation of growing biopolymers, via calculations explicitly treating obstacle diffusion and stochastic addition and subtraction of subunits. We first show that the instantaneous subunit on- and off-rates satisfy a rigorous thermodynamic relationship determined by the filament-obstacle interaction potential, which has been violated by several calculations in the literature. The instantaneous rates depend not only on the average force on the obstacle but also on the shape of the potential on the nanometer length scale. Basing obstacle-induced reduction of the on-rate entirely on the force, as previous work has often done, is thermodynamically inconsistent and can overestimate the stall force, sometimes by more than a factor of two. We perform simulations and analytic calculations of the force-velocity relation satisfying the thermodynamic relationship. The force-velocity relation can deviate strongly from the Brownian-Ratchet predictions. For shallow potential wells of depth ∼5k_{B}T, which might correspond to transient filament-membrane attachments, the velocity drops more rapidly than predicted by the Brownian-Ratchet model, in some cases by as much as a factor of 50 at an opposing force of only 1 pN. On the other hand, the zero-force velocity is much less affected than would be expected from naive use of the Boltzmann factor. Furthermore, the growth velocity has a surprisingly strong dependence on the obstacle diffusion coefficient even when the dimensionless diffusion coefficient is large. For deep potential wells, as might result from strong filament-membrane links, both the on- and off-rates are reduced significantly, slowing polymerization. Such potentials can sustain pulling forces while polymerizing but only if the attractive well is relatively flat over a region comparable to or greater than the monomer size. For double-well potentials, which have such a flat region, the slowing of polymerization by external pushing force is almost linear up to the stall force in some parameter ranges.

Integrated bioinformatics analysis of potential pathway biomarkers using abnormal proteins in clubfoot

Background

As one of the most common major congenital distal skeletal abnormalities, congenital talipes equinovarus (clubfoot) affects approximately one in one thousandth newborns. Although several etiologies of clubfoot have been proposed and several genes have been identified as susceptible genes, previous studies did not further explore signaling pathways and potential upstream and downstream regulatory networks. Therefore, the aim of the present investigation is to explore abnormal pathways and their interactions in clubfoot using integrated bioinformatics analyses.

Methods

KEGG, gene ontology (GO), Reactome (REAC), WikiPathways (WP) or human phenotype ontology (HP) enrichment analysis were performed using WebGestalt, g:Profiler and NetworkAnalyst.

Results

A large number of signaling pathways were enriched e.g. signal transduction, disease, metabolism, gene expression (transcription), immune system, developmental biology, cell cycle, and ECM. Protein-protein interactions (PPIs) and gene regulatory networks (GRNs) analysis results indicated that extensive and complex interactions occur in these proteins, enrichment pathways, and TF-miRNA coregulatory networks. Transcription factors such as SOX9, CTNNB1, GLI3, FHL2, TGFBI and HOXD13, regulated these candidate proteins.

Conclusion

The results of the present study supported previously proposed hypotheses, such as ECM, genetic, muscle, neurological, skeletal, and vascular abnormalities. More importantly, the enrichment results also indicated cellular or immune responses to external stimuli, and abnormal molecular transport or metabolism may be new potential etiological mechanisms of clubfoot.

Turnover versus treadmilling in actin network assembly and remodeling

Actin networks are highly dynamic cytoskeletal structures that continuously undergo structural remodeling. One prominent way to probe these processes is via Fluorescence Recovery After Photobleaching (FRAP), which can be used to estimate the rate of turnover for filamentous actin monomers. It is thought that head-to-tail treadmilling and de novo filament nucleation constitute two primary mechanisms underlying turnover kinetics. More generally, these self-assembly activities are responsible for many important cellular functions such as force generation, cellular shape dynamics, and cellular motility. In what relative proportions filament treadmilling and de novo filament nucleation contribute to actin network turnover is still not fully understood. We used an advanced stochastic reaction-diffusion model in three dimensions, MEDYAN, to study turnover dynamics of actin networks containing Arp2/3, formin and capping protein at experimentally meaningful length- and time-scales. Our results reveal that, most commonly, treadmilling of older filaments is the main contributor to actin network turnover. On the other hand, although turnover and treadmilling are often used interchangeably, we show clear instances where this assumption would not be justified, for example, finding that rapid turnover is accompanied by slow treadmilling in highly dendritic Arp2/3 networks.

Quantifying dissipation in actomyosin networks

Quantifying entropy production in various active matter phases will open new avenues for probing self-organization principles in these far-from-equilibrium systems. It has been hypothesized that the dissipation of free energy by active matter systems may be optimized, leading to system trajectories with histories of large dissipation and an accompanying emergence of ordered dynamical states. This interesting idea has not been widely tested. In particular, it is not clear whether emergent states of actomyosin networks, which represent a salient example of biological active matter, self-organize following the principle of dissipation optimization. In order to start addressing this question using detailed computational modelling, we rely on the MEDYAN simulation platform, which allows simulating active matter networks from fundamental molecular principles. We have extended the capabilities of MEDYAN to allow quantification of the rates of dissipation resulting from chemical reactions and relaxation of mechanical stresses during simulation trajectories. This is done by computing precise changes in Gibbs free energy accompanying chemical reactions using a novel formula and through detailed calculations of instantaneous values of the system's mechanical energy. We validate our approach with a mean-field model that estimates the rates of dissipation from filament treadmilling. Applying this methodology to the self-organization of small disordered actomyosin networks, we find that compact and highly cross-linked networks tend to allow more efficient transduction of chemical free energy into mechanical energy. In these simple systems, we observe that spontaneous network reorganizations tend to result in a decrease in the total dissipation rate to a low steady-state value. Future studies might carefully test whether the dissipation-driven adaptation hypothesis applies in this instance, as well as in more complex cytoskeletal geometries.

Building a dendritic actin filament network branch by branch: models of filament orientation pattern and force generation in lamellipodia

We review mathematical and computational models of the structure, dynamics, and force generation properties of dendritic actin networks. These models have been motivated by the dendritic nucleation model, which provided a mechanistic picture of how the actin cytoskeleton system powers cell motility. We describe how they aimed to explain the self-organization of the branched network into a bimodal distribution of filament orientations peaked at 35° and - 35° with respect to the direction of membrane protrusion, as well as other patterns. Concave and convex force-velocity relationships were derived, depending on network organization, filament, and membrane elasticity and accounting for actin polymerization at the barbed end as a Brownian ratchet. This review also describes models that considered the kinetics and transport of actin and diffuse regulators and mechanical coupling to a substrate, together with explicit modeling of dendritic networks.

Polymerisation force of a rigid filament bundle: diffusive interaction leads to sublinear force-number scaling

Polymerising filaments generate force against an obstacle, as in, e.g., microtubule-kinetochore interactions in the eukaryotic cell. Earlier studies of this problem have not included explicit three-dimensional monomer diffusion, and consequently, missed out on two important aspects: (i) the barrier, even when it is far from the polymers, affects free diffusion of monomers and reduces their adsorption at the tips, while (ii) parallel filaments could interact through the monomer density field ("diffusive coupling"), leading to negative interference between them. In our study, both these effects are included and their consequences investigated in detail. A mathematical treatment based on a set of continuum Fokker-Planck equations for combined filament-wall dynamics suggests that the barrier-induced monomer depletion reduces the growth velocity and also the stall force, while the total force produced by many filaments remains additive. However, Brownian dynamics simulations show that the linear force-number scaling holds only when the filaments are far apart; when they are arranged close together, forming a bundle, sublinear scaling of force with number appears, which could be attributed to diffusive interaction between the growing polymer tips.

MEDYAN: Mechanochemical Simulations of Contraction and Polarity Alignment in Actomyosin Networks

Active matter systems, and in particular the cell cytoskeleton, exhibit complex mechanochemical dynamics that are still not well understood. While prior computational models of cytoskeletal dynamics have lead to many conceptual insights, an important niche still needs to be filled with a high-resolution structural modeling framework, which includes a minimally-complete set of cytoskeletal chemistries, stochastically treats reaction and diffusion processes in three spatial dimensions, accurately and efficiently describes mechanical deformations of the filamentous network under stresses generated by molecular motors, and deeply couples mechanics and chemistry at high spatial resolution. To address this need, we propose a novel reactive coarse-grained force field, as well as a publicly available software package, named the Mechanochemical Dynamics of Active Networks (MEDYAN), for simulating active network evolution and dynamics (available at www.medyan.org). This model can be used to study the non-linear, far from equilibrium processes in active matter systems, in particular, comprised of interacting semi-flexible polymers embedded in a solution with complex reaction-diffusion processes. In this work, we applied MEDYAN to investigate a contractile actomyosin network consisting of actin filaments, alpha-actinin cross-linking proteins, and non-muscle myosin IIA mini-filaments. We found that these systems undergo a switch-like transition in simulations from a random network to ordered, bundled structures when cross-linker concentration is increased above a threshold value, inducing contraction driven by myosin II mini-filaments. Our simulations also show how myosin II mini-filaments, in tandem with cross-linkers, can produce a range of actin filament polarity distributions and alignment, which is crucially dependent on the rate of actin filament turnover and the actin filament’s resulting super-diffusive behavior in the actomyosin-cross-linker system. We discuss the biological implications of these findings for the arc formation in lamellipodium-to-lamellum architectural remodeling. Lastly, our simulations produce force-dependent accumulation of myosin II, which is thought to be responsible for their mechanosensation ability, also spontaneously generating myosin II concentration gradients in the solution phase of the simulation volume.

Active matter systems have the distinct ability to convert energy from their surroundings into mechanical work, which gives rise to them having highly dynamic properties. Modeling active matter systems and capturing their complex behavior has been a great challenge in past years due to the many coupled interactions between their constituent parts, including not only distinct chemical and mechanical properties, but also feedback between them. One of the most intriguing biological active matter systems is the cell cytoskeleton, which can dynamically respond to chemical and mechanical cues to control cell structure and shape, playing a central role in many higher-order cellular processes. To model these systems and reproduce their behavior, we present a new modeling approach which combines the chemical, mechanical, and molecular transport aspects of active matter systems, all represented with equivalent complexity, while also allowing for various forms of mechanochemical feedback. This modeling approach, named MEDYAN, and software implementation is flexible so that a wide range of active matter systems can be simulated with a high level of detail, and ultimately can help to describe active matter phenomena, and in particular, the dynamics of the cell cytoskeleton. In this work, we have used MEDYAN to simulate a cytoskeletal network consisting of actin filaments, cross-linking proteins, and myosin II molecular motors. We found that these systems show rich dynamical behaviors, undergoing alignment and bundling transitions, with an emergent contractility, as the concentrations of myosin II and cross-linking proteins, as well as actin filament turnover rates, are varied.

How capping protein enhances actin filament growth and nucleation on biomimetic beads

Capping protein (CP), which caps the growing ends of actin filaments, accelerates actin-based motility. Recent experiments on biomimetic beads have shown that CP also enhances the rate of actin filament nucleation. Proposed explanations for these phenomena include (i) the actin funneling hypothesis (AFH), in which the presence of CP increases the free-actin concentration, and (ii) the monomer gating model, in which CP binding to actin filament barbed ends makes more monomers available for filament nucleation. To establish how CP increases the rates of filament elongation and nucleation on biomimetic beads, we perform a quantitative modeling analysis of actin polymerization, using rate equations that include actin filament nucleation, polymerization and capping, as modified by monomer depletion near the surface of the bead. With one adjustable parameter, our simulation results match previously measured time courses of polymerized actin and filament number. The results support a version of the AFH where CP increases the local actin monomer concentration at the bead surface, but leaves the global free-actin concentration nearly constant. Because the rate of filament nucleation increases with the monomer concentration, the increased local monomer concentration enhances actin filament nucleation. We derive a closed-form formula for the characteristic CP concentration where the local free-actin concentration reaches half the bulk value, and find it to be comparable to the global Arp2/3 complex concentration. We also propose an experimental protocol for distinguishing branching nucleation of filaments from spontaneous nucleation.