Stochastic Ratcheting on a Funneled Energy Landscape is Necessary for Highly Efficient Contractility of Actomyosin Force Dipoles

Current understanding of how contractility emerges in disordered actomyosin networks of non-muscle cells is still largely based on the intuition derived from earlier works on muscle contractility. This view, however, largely overlooks the free energy gain following passive cross-linker binding, which, even in the absence of active fluctuations, provides a thermodynamic drive towards highly overlapping filamentous states. In this work, we shed light on this phenomenon, showing that passive cross-linkers, when considered in the context of two anti-parallel filaments, generate noticeable contractile forces. However, as binding free energy of cross-linkers is increased, a sharp onset of kinetic arrest follows, greatly diminishing effectiveness of this contractility mechanism, allowing the network to contract only with weakly resisting tensions at its boundary. We have carried out stochastic simulations elucidating this mechanism, followed by a mean-field treatment that predicts how contractile forces asymptotically scale at small and large binding energies, respectively. Furthermore, when considering an active contractile filament pair, based on non-muscle myosin II, we found that the non-processive nature of these motors leads to highly inefficient force generation, due to recoil slippage of the overlap during periods when the motor is dissociated. However, we discovered that passive cross-linkers can serve as a structural ratchet during these unbound motor time spans, resulting in vast force amplification. Our results shed light on the non-equilibrium effects of transiently binding proteins in biological active matter, as observed in the non-muscle actin cytoskeleton, showing that highly efficient contractile force dipoles result from synergy of passive cross-linker and active motor dynamics, via a ratcheting mechanism on a funneled energy landscape.Comment: 13 pages, 6 figure

UNCOVERING FUNDAMENTAL MECHANISMS OF ACTOMYOSIN CONTRACTILITY USING ANALYTICAL THEORY AND COMPUTER SIMULATION

Actomyosin contractility is a ubiquitous force-generating function of almost all eukaryotic organisms. While more understanding of its dynamic non-equilibrium be- havior has been uncovered in recent years, little is known regarding its self-emergent structures and phase transitions that are observed in vivo. With this in mind, this thesis aims to develop a state-of-the-art computational model for the simulation of actomyosin assemblies, containing detailed cytosolic reaction-diffusion processes such as actin filament treadmilling, cross-linker (un)binding, and molecular motor walking. This is explicitly coupled with novel mechanical potentials for semi-flexible actin filaments. Then, using this simulation framework combined with other ana- lytical approaches, we propose a novel mechanism of contractility in a fundamental actomyosin structural element, derived from a thermodynamic free energy gradi- ent favoring overlapped actin filament states when passive cross-linkers are present. With this spontaneous cross-linking, transient motors such as non-muscle myosin II can generate robust network contractility in a collective myosin II-cross-linker ratcheting mechanism. Finally, we map the phases of contractile behavior of disor- dered actomyosin using this theory, showing explicitly the cross-linking, motor and boundary conditions required for geometric collapse or tension generation in a net- work comprised of those elements. In this theory, we move away from the sarcomeric contractility mechanism typically reconciled in disordered non-muscle structures. It is our hope that this study adds theoretical knowledge as well as computational tools to study the diverse contractile assemblies found in non-muscle actomyosin networks

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

A cytoskeletal network in the MEDYAN model.

<p>A complex cytoskeletal network can be simulated with MEDYAN’s stochastic reaction-diffusion scheme. Chemical interactions will cause complex network evolution, such as the process of actin filament bundling. See Section A in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004877#pcbi.1004877.s001" target="_blank">S1 Text</a> for a more detailed description of all chemical reactions that can be included in a simulation.</p

MSD analysis of actin filaments in simulation.

<p>(A) MSD over time for various values of <i>χ</i>. Error bars represent the standard error of the MSD, for each set of trajectories, are smaller than the data points. (B) Diffusion exponent <i>ν</i> acquired from a log-log linear fit of (A). Error bars represent the standard linear regression error in <i>ν</i>.</p

A single trajectory snapshot of a 3 × 3 × 3 <i>μ</i>m³ actomyosin system simulation at R_α:a = 0.1 and R_m:a = 0.02 after 500 s of network evolution.

<p>Actin filament cylinders are colored by their angle with respect to the x-y plane.</p

Actomyosin network R_g,f / R_g,i and S for various <i>χ</i>.

<p>(A) <i>R</i>_g,f/<i>R</i>_g,i over the 2000 <i>s</i> network evolution for varying values of <i>χ</i>. Contractile behavior increases with decreasing <i>χ</i>. Standard deviations of the <i>R</i>_g,f/<i>R</i>_g,i values over all trajectories are shaded. (B) <i>S</i> after 2000 <i>s</i> of network evolution for varying values of <i>χ</i>. Global alignment peaks around <i>χ</i> = 0.5 to 2, and decreases for values outside of this range. Error bars represent standard deviation of <i>S</i> values over all trajectories.</p

A heat map of actomyosin network S as a function of R_m:a and R_α:a after 2000 s of network evolution.

<p>As NMIIA and <i>α</i>-actinin concentrations are increased, a correlation in alignment results in a similar fashion to <i>R</i>_g in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004877#pcbi.1004877.g006" target="_blank">Fig 6</a>.</p

A single trajectory snapshot of a 1 × 1 × 1 <i>μ</i>m³ actomyosin system simulation at R_α:a = 0.1 and R_m:a = 0.01 after 2000 s of network evolution.

<p>Actin filaments are represented as red connected cylinders, <i>α</i>-actinin are represented as green cylinders, and NMIIA mini-filaments are represented as blue cylinders. The corresponding diffusing species are also shown in the same colors. The system is bounded by a cubic, hard-wall potential.</p

A flow diagram of a MEDYAN simulation.

<p>(1) After the chemical stochastic simulation evolves the network in time and (2) local deformations are formed, (3) a mechanical equilibration is performed and (4) reaction rates are updated according to chosen functional forms <i>f</i>(<i>F</i>_{<i>current</i>}) where <i>F</i>_{<i>current</i>} is the force on that reacting molecule after equilibration.</p