Polysome collapse and RNA condensation fluidize the cytoplasm.

The cell interior is packed with macromolecules of mesoscale size, and this crowded milieu significantly influences cellular physiology. Cellular stress responses almost universally lead to inhibition of translation, resulting in polysome collapse and release of mRNA. The released mRNA molecules condense with RNA-binding proteins to form ribonucleoprotein (RNP) condensates known as processing bodies and stress granules. Here, we show that polysome collapse and condensation of RNA transiently fluidize the cytoplasm, and coarse-grained molecular dynamic simulations support this as a minimal mechanism for the observed biophysical changes. Increased mesoscale diffusivity correlates with the efficient formation of quality control bodies (Q-bodies), membraneless organelles that compartmentalize misfolded peptides during stress. Synthetic, light-induced RNA condensation also fluidizes the cytoplasm. Together, our study reveals a functional role for stress-induced translation inhibition and formation of RNP condensates in modulating the physical properties of the cytoplasm to enable efficient response of cells to stress conditions.

Ionic solids from common colloids.

From rock salt to nanoparticle superlattices, complex structure can emerge from simple building blocks that attract each other through Coulombic forces1-4. On the micrometre scale, however, colloids in water defy the intuitively simple idea of forming crystals from oppositely charged partners, instead forming non-equilibrium structures such as clusters and gels5-7. Although various systems have been engineered to grow binary crystals8-11, native surface charge in aqueous conditions has not been used to assemble crystalline materials. Here we form ionic colloidal crystals in water through an approach that we refer to as polymer-attenuated Coulombic self-assembly. The key to crystallization is the use of a neutral polymer to keep particles separated by well defined distances, allowing us to tune the attractive overlap of electrical double layers, directing particles to disperse, crystallize or become permanently fixed on demand. The nucleation and growth of macroscopic single crystals is demonstrated by using the Debye screening length to fine-tune assembly. Using a variety of colloidal particles and commercial polymers, ionic colloidal crystals isostructural to caesium chloride, sodium chloride, aluminium diboride and K4C60 are selected according to particle size ratios. Once fixed by simply diluting out solution salts, crystals are pulled out of the water for further manipulation, demonstrating an accurate translation from solution-phase assembly to dried solid structures. In contrast to other assembly approaches, in which particles must be carefully engineered to encode binding information12-18, polymer-attenuated Coulombic self-assembly enables conventional colloids to be used as model colloidal ions, primed for crystallization.

Enabling three-dimensional real-space analysis of ionic colloidal crystallization.

Structures of molecular crystals are identified using scattering techniques because we cannot see inside them. Micrometre-sized colloidal particles enable the real-time observation of crystallization with optical microscopy, but in practice this is still hampered by a lack of 'X-ray vision'. Here we introduce a system of index-matched fluorescently labelled colloidal particles and demonstrate the robust formation of ionic crystals in aqueous solution, with structures that can be controlled by size ratio and salt concentration. Full three-dimensional coordinates of particles are distinguished through in situ confocal microscopy, and the crystal structures are identified via comparison of their simulated scattering pattern with known atomic arrangements. Finally, we leverage our ability to look inside colloidal crystals to observe the motion of defects and crystal melting in time and space and to reveal the origin of crystal twinning. Using this platform, the path to real-time analysis of ionic colloidal crystallization is now 'crystal clear'.

Structure of Arp2/3 complex at a branched actin filament junction resolved by single-particle cryo-electron microscopy.

Arp2/3 complex nucleates branched actin filaments that provide pushing forces to drive cellular processes such as lamellipodial protrusion and endocytosis. Arp2/3 complex is intrinsically inactive, and multiple classes of nucleation promoting factors (NPFs) stimulate its nucleation activity. When activated by WASP family NPFs, the complex must bind to the side of a preexisting (mother) filament of actin to complete the nucleation process, ensuring that WASP-mediated activation creates branched rather than linear actin filaments. How actin filaments contribute to activation is currently not understood, largely due to the lack of high-resolution structures of activated Arp2/3 complex bound to the side of a filament. Here, we present the 3.9-Å cryo-electron microscopy structure of the Arp2/3 complex at a branch junction. The structure reveals contacts between Arp2/3 complex and the side of the mother actin filament that likely stimulate subunit flattening, a conformational change that allows the actin-related protein subunits in the complex (Arp2 and Arp3) to mimic filamentous actin subunits. In contrast, limited contact between the bottom half of the complex and the mother filament suggests that clamp twisting, a second major conformational change observed in the active state, is not stimulated by actin filaments, potentially explaining why actin filaments are required but insufficient to trigger nucleation during WASP-mediated activation. Along with biochemical and live-cell imaging data and molecular dynamics simulations, the structure reveals features critical for the interaction of Arp2/3 complex with actin filaments and regulated assembly of branched actin filament networks in cells.

Molecular dynamics simulations support a multistep pathway for activation of branched actin filament nucleation by Arp2/3 complex.

Actin-related protein 2/3 complex (Arp2/3 complex) catalyzes the nucleation of branched actin filaments that push against membranes in processes like cellular motility and endocytosis. During activation by WASP proteins, the complex must bind WASP and engage the side of a pre-existing (mother) filament before a branched filament is nucleated. Recent high-resolution structures of activated Arp2/3 complex revealed two major sets of activating conformational changes. How these activating conformational changes are triggered by interactions of Arp2/3 complex with actin filaments and WASP remains unclear. Here we use a recent high-resolution structure of Arp2/3 complex at a branch junction to design all-atom molecular dynamics simulations that elucidate the pathway between the active and inactive states. We ran a total of ∼4.6 microseconds of both unbiased and steered all-atom molecular dynamics simulations starting from three different binding states, including Arp2/3 complex within a branch junction, bound only to a mother filament, and alone in solution. These simulations indicate that the contacts with the mother filament are mostly insensitive to the massive rigid body motion that moves Arp2 and Arp3 into a short pitch helical (filament-like) arrangement, suggesting actin filaments alone do not stimulate the short pitch conformational change. In contrast, contacts with the mother filament stabilize subunit flattening in Arp3, an intrasubunit change that converts Arp3 from a conformation that mimics an actin monomer to one that mimics a filamentous actin subunit. Our results support a multistep activation pathway that has important implications for understanding how WASP-mediated activation allows Arp2/3 complex to assemble force-producing actin networks.

Computing equilibrium free energies through a nonequilibrium quench.

Many methods to accelerate sampling of molecular configurations are based on the idea that temperature can be used to accelerate rare transitions. These methods typically compute equilibrium properties at a target temperature using reweighting or through Monte Carlo exchanges between replicas at higher temperatures. A recent paper [G. M. Rotskoff and E. Vanden-Eijnden, Phys. Rev. Lett. 122, 150602 (2019)] demonstrated that accurate equilibrium densities of states can also be computed through a nonequilibrium "quench" process, where sampling is performed at a higher temperature to encourage rapid mixing and then quenched to lower energy states with dissipative dynamics. Here, we provide an implementation of the quench dynamics in LAMMPS and evaluate a new formulation of nonequilibrium estimators for the computation of partition functions or free energy surfaces (FESs) of molecular systems. We show that the method is exact for a minimal model of N-independent harmonic springs and use these analytical results to develop heuristics for the amount of quenching required to obtain accurate sampling. We then test the quench approach on alanine dipeptide, where we show that it gives an FES that is accurate near the most stable configurations using the quench approach but disagrees with a reference umbrella sampling calculation in high FE regions. We then show that combining quenching with umbrella sampling allows the efficient calculation of the free energy in all regions. Moreover, by using this combined scheme, we obtain the FES across a range of temperatures at no additional cost, making it much more efficient than standard umbrella sampling if this information is required. Finally, we discuss how this approach can be extended to solute tempering and demonstrate that it is highly accurate for the case of solvated alanine dipeptide without any additional modifications.

A strong nonequilibrium bound for sorting of cross-linkers on growing biopolymers.

Understanding the role of nonequilibrium driving in self-organization is crucial for developing a predictive description of biological systems, yet it is impeded by their complexity. The actin cytoskeleton serves as a paradigm for how equilibrium and nonequilibrium forces combine to give rise to self-organization. Motivated by recent experiments that show that actin filament growth rates can tune the morphology of a growing actin bundle cross-linked by two competing types of actin-binding proteins [S. L. Freedman et al., Proc. Natl. Acad. Sci. U.S.A. 116, 16192-16197 (2019)], we construct a minimal model for such a system and show that the dynamics of a growing actin bundle are subject to a set of thermodynamic constraints that relate its nonequilibrium driving, morphology, and molecular fluxes. The thermodynamic constraints reveal the importance of correlations between these molecular fluxes and offer a route to estimating microscopic driving forces from microscopy experiments.

A coarse-grained simulation model for colloidal self-assembly via explicit mobile binders.

Colloidal particles with mobile binding molecules constitute a powerful platform for probing the physics of self-assembly. Binding molecules are free to diffuse and rearrange on the surface, giving rise to spontaneous control over the number of droplet-droplet bonds, i.e., valence, as a function of the concentration of binders. This type of valence control has been realized experimentally by tuning the interaction strength between DNA-coated emulsion droplets. Optimizing for valence two yields droplet polymer chains, termed 'colloidomers', which have recently been used to probe the physics of folding. To understand the underlying self-assembly mechanisms, here we present a coarse-grained molecular dynamics (CGMD) model to study the self-assembly of this class of systems using explicit representations of mobile binding sites. We explore how valence of assembled structures can be tuned through kinetic control in the strong binding limit. More specifically, we optimize experimental control parameters to obtain the highest yield of long linear colloidomer chains. Subsequently tuning the dynamics of binding and unbinding via a temperature-dependent model allows us to observe a heptamer chain collapse into all possible rigid structures, in good agreement with recent folding experiments. Our CGMD platform and dynamic bonding model (implemented as an open-source custom plugin to HOOMD-Blue) reveal the molecular features governing the binding patch size and valence control, and opens the study of pathways in colloidomer folding. This model can therefore guide programmable design in experiments.

Neural potentials of proteins extrapolate beyond training data.

We evaluate neural network (NN) coarse-grained (CG) force fields compared to traditional CG molecular mechanics force fields. We conclude that NN force fields are able to extrapolate and sample from unseen regions of the free energy surface when trained with limited data. Our results come from 88 NN force fields trained on different combinations of clustered free energy surfaces from four protein mapped trajectories. We used a statistical measure named total variation similarity to assess the agreement between reference free energy surfaces from mapped atomistic simulations and CG simulations from trained NN force fields. Our conclusions support the hypothesis that NN CG force fields trained with samples from one region of the proteins' free energy surface can, indeed, extrapolate to unseen regions. Additionally, the force matching error was found to only be weakly correlated with a force field's ability to reconstruct the correct free energy surface.

Structural basis of fast- and slow-severing actin-cofilactin boundaries.

Members of the ADF/cofilin family of regulatory proteins bind actin filaments cooperatively, locally change actin subunit conformation and orientation, and sever filaments at "boundaries" between bare and cofilin-occupied segments. A cluster of bound cofilin introduces two distinct classes of boundaries due to the intrinsic polarity of actin filaments, one at the "pointed" end side and the other at the "barbed" end-side of the cluster; severing occurs more readily at the pointed end side of the cluster ("fast-severing" boundary) than the barbed end side ("slow-severing" boundary). A recent electron-cryomicroscopy (cryo-EM) model of the slow-severing boundary revealed structural "defects" at the interface that potentially contribute to severing. However, the structure of the fast-severing boundary remains uncertain. Here, we use extensive molecular dynamics simulations to produce atomic resolution models of both severing boundaries. Our equilibrated simulation model of the slow-severing boundary is consistent with the cryo-EM structural model. Simulations indicate that actin subunits at both boundaries adopt structures intermediate between those of bare and cofilin-bound actin subunits. These "intermediate" states have compromised intersubunit contacts, but those at the slow-severing boundary are stabilized by cofilin bridging interactions, accounting for its lower fragmentation probability. Simulations where cofilin proteins are removed from cofilactin filaments favor a mechanism in which a cluster of two contiguously bound cofilins is needed to fully stabilize the cofilactin conformation, promote cooperative binding interactions, and accelerate filament severing. Together, these studies provide a molecular-scale foundation for developing coarse-grained and theoretical descriptions of cofilin-mediated actin filament severing.

Assessing models of force-dependent unbinding rates via infrequent metadynamics.

Protein-ligand interactions are crucial for a wide range of physiological processes. Many cellular functions result in these non-covalent "bonds" being mechanically strained, and this can be integral to proper cellular function. Broadly, two classes of force dependence have been observed-slip bonds, where the unbinding rate increases, and catch bonds, where the unbinding rate decreases. Despite much theoretical work, we cannot predict for which protein-ligand pairs, pulling coordinates, and forces a particular rate dependence will appear. Here, we assess the ability of MD simulations combined with enhanced sampling techniques to probe the force dependence of unbinding rates. We show that the infrequent metadynamics technique correctly produces both catch and slip bonding kinetics for model potentials. We then apply it to the well-studied case of a buckyball in a hydrophobic cavity, which appears to exhibit an ideal slip bond. Finally, we compute the force-dependent unbinding rate of biotin-streptavidin. Here, the complex nature of the unbinding process causes the infrequent metadynamics method to begin to break down due to the presence of unbinding intermediates, despite the use of a previously optimized sampling coordinate. Allowing for this limitation, a combination of kinetic and free energy computations predicts an overall slip bond for larger forces consistent with prior experimental results although there are substantial deviations at small forces that require further investigation. This work demonstrates the promise of predicting force-dependent unbinding rates using enhanced sampling MD techniques while also revealing the methodological barriers that must be overcome to tackle more complex targets in the future.

Mechanical and kinetic factors drive sorting of F-actin cross-linkers on bundles.

In cells, actin-binding proteins (ABPs) sort to different regions to establish F-actin networks with diverse functions, including filopodia used for cell migration and contractile rings required for cell division. Recent experimental work uncovered a competition-based mechanism that may facilitate spatial localization of ABPs: binding of a short cross-linker protein to 2 actin filaments promotes the binding of other short cross-linkers and inhibits the binding of longer cross-linkers (and vice versa). We hypothesize this sorting arises because F-actin is semiflexible and cannot bend over short distances. We develop a mathematical theory and lattice models encompassing the most important physical parameters for this process and use coarse-grained simulations with explicit cross-linkers to characterize and test our predictions. Our theory and data predict an explicit dependence of cross-linker separation on bundle polymerization rate. We perform experiments that confirm this dependence, but with an unexpected cross-over in dominance of one cross-linker at high growth rates to the other at slow growth rates, and we investigate the origin of this cross-over with further simulations. The nonequilibrium mechanism that we describe can allow cells to organize molecular material to drive biological processes, and our results can guide the choice and design of cross-linkers for engineered protein-based materials.

A Burst of Genetic Innovation in Drosophila Actin-Related Proteins for Testis-Specific Function.

Many cytoskeletal proteins perform fundamental biological processes and are evolutionarily ancient. For example, the superfamily of actin-related proteins (Arps) specialized early in eukaryotic evolution for diverse cellular roles in the cytoplasm and the nucleus. Despite its strict conservation across eukaryotes, we find that the Arp superfamily has undergone dramatic lineage-specific diversification in Drosophila. Our phylogenomic analyses reveal four independent Arp gene duplications that occurred in the common ancestor of the obscura group of Drosophila and have been mostly preserved in this lineage. All four obscura-specific Arp paralogs are predominantly expressed in the male germline and have evolved under positive selection. We focus our analyses on the divergent Arp2D paralog, which arose via a retroduplication event from Arp2, a component of the Arp2/3 complex that polymerizes branched actin networks. Computational modeling analyses suggest that Arp2D can replace Arp2 in the Arp2/3 complex and bind actin monomers. Together with the signature of positive selection, our findings suggest that Arp2D may augment Arp2's functions in the male germline. Indeed, we find that Arp2D is expressed during and following male meiosis, where it localizes to distinct locations such as actin cones-specialized cytoskeletal structures that separate bundled spermatids into individual mature sperm. We hypothesize that this unprecedented burst of genetic innovation in cytoskeletal proteins may have been driven by the evolution of sperm heteromorphism in the obscura group of Drosophila.

Infinite switch simulated tempering in force (FISST).

Many proteins in cells are capable of sensing and responding to piconewton-scale forces, a regime in which conformational changes are small but significant for biological processes. In order to efficiently and effectively sample the response of these proteins to small forces, enhanced sampling techniques will be required. In this work, we derive, implement, and evaluate an efficient method to simultaneously sample the result of applying any constant pulling force within a specified range to a molecular system of interest. We start from simulated tempering in force, whereby force is added as a linear bias on a collective variable to the system's Hamiltonian, and the coefficient is taken as a continuous auxiliary degree of freedom. We derive a formula for an average collective-variable-dependent force, which depends on a set of weights learned on-the-fly throughout a simulation, that reflect the limit where force varies infinitely quickly. Simulation data can then be used to retroactively compute averages of any observable at any force within the specified range. This technique is based on recent work deriving similar equations for infinite switch simulated tempering in temperature, which showed that the infinite switch limit is the most efficient for sampling. Here, we demonstrate that our method accurately samples molecular systems at all forces within a user defined force range simultaneously and show how it can serve as an enhanced sampling tool for cases where the pulling direction destabilizes states that have low free-energy at zero-force. This method is implemented in and freely distributed with the PLUMED open-source sampling library, and hence can be readily applied to problems using a wide range of molecular dynamics software packages.

Plastic Deformation and Fragmentation of Strained Actin Filaments.

The assembly of actin filaments and filament networks generate forces that drive cell and vesicle movement. These structures and the comprising actin filaments must be mechanically stable to sustain these forces and maintain their structural integrity. Filaments in these dynamic structures must also be disassembled to recycle and replenish the pool of actin monomers available for polymerization. Actin-severing proteins such as cofilin and contractile myosin motor proteins fragment these nominally stable structures. We developed a mesoscopic-length-scale actin filament model to investigate force-induced filament fragmentation. We show that fragmentation in our model occurs at curvatures similar to previous measurements of fragmentation within (cofil)actin and actin-cofilactin boundaries. Boundaries between bare and cofilin-decorated segments are brittle and fragment at small bending and twisting deformations. Extending filaments disperses strain uniformly over subunit interfaces, and filaments fragment with no detectable partial rupture or plastic deformation. In contrast, bending or twisting filaments imposes nonuniform interface strain and leads to partial interface rupture, accelerating filament fragmentation. As a result, the rupture force under compressive loads is an order of magnitude lower than under tensile loads. Partial interface rupture may be a primary mechanism of accelerating actin filament fragmentation by other actin-destabilizing proteins.

Insights into the Cooperative Nature of ATP Hydrolysis in Actin Filaments.

Actin filaments continually assemble and disassemble within a cell. Assembled filaments "age" as a bound nucleotide ATP within each actin subunit quickly hydrolyzes followed by a slower release of the phosphate Pi, leaving behind a bound ADP. This subtle change in nucleotide state of actin subunits affects filament rigidity as well as its interactions with binding partners. We present here a systematic multiscale ultra-coarse-graining approach that provides a computationally efficient way to simulate a long actin filament undergoing ATP hydrolysis and phosphate-release reactions while systematically taking into account available atomistic details. The slower conformational changes and their dependence on the chemical reactions are simulated with the ultra-coarse-graining model by assigning internal states to the coarse-grained sites. Each state is represented by a unique potential surface of a local heterogeneous elastic network. Internal states undergo stochastic transitions that are coupled to conformations of the underlying molecular system. The model reproduces mechanical properties of the filament and allows us to study whether conformational fluctuations in actin subunits produce cooperative filament aging. We find that the nucleotide states of neighboring subunits modulate the reaction kinetics, implying cooperativity in ATP hydrolysis and Pi release. We further systematically coarse grain the system into a Markov state model that incorporates assembly and disassembly, facilitating a direct comparison with previously published models. We find that cooperativity in ATP hydrolysis and Pi release significantly affects the filament growth dynamics only near the critical G-actin concentration, whereas far from it, both cooperative and random mechanisms show similar growth dynamics. In contrast, filament composition in terms of the bound nucleotide distribution varies significantly at all monomer concentrations studied. These results provide new insights, to our knowledge, into the cooperative nature of ATP hydrolysis and Pi release and the implications it has for actin filament properties, providing novel predictions for future experimental studies.

Phosphomimetic S3D cofilin binds but only weakly severs actin filaments.

Many biological processes, including cell division, growth, and motility, rely on rapid remodeling of the actin cytoskeleton and on actin filament severing by the regulatory protein cofilin. Phosphorylation of vertebrate cofilin at Ser-3 regulates both actin binding and severing. Substitution of serine with aspartate at position 3 (S3D) is widely used to mimic cofilin phosphorylation in cells and in vitro The S3D substitution weakens cofilin binding to filaments, and it is presumed that subsequent reduction in cofilin occupancy inhibits filament severing, but this hypothesis has remained untested. Here, using time-resolved phosphorescence anisotropy, electron cryomicroscopy, and all-atom molecular dynamics simulations, we show that S3D cofilin indeed binds filaments with lower affinity, but also with a higher cooperativity than wild-type cofilin, and severs actin weakly across a broad range of occupancies. We found that three factors contribute to the severing deficiency of S3D cofilin. First, the high cooperativity of S3D cofilin generates fewer boundaries between bare and decorated actin segments where severing occurs preferentially. Second, S3D cofilin only weakly alters filament bending and twisting dynamics and therefore does not introduce the mechanical discontinuities required for efficient filament severing at boundaries. Third, Ser-3 modification (i.e. substitution with Asp or phosphorylation) "undocks" and repositions the cofilin N terminus away from the filament axis, which compromises S3D cofilin's ability to weaken longitudinal filament subunit interactions. Collectively, our results demonstrate that, in addition to inhibiting actin binding, Ser-3 modification favors formation of a cofilin-binding mode that is unable to sufficiently alter filament mechanical properties and promote severing.

Nonequilibrium phase diagrams for actomyosin networks.

Living cells dynamically modulate the local morphologies of their actin networks to perform biological functions, including force transduction, intracellular transport, and cell division. A major challenge is to understand how diverse structures of the actin cytoskeleton are assembled from a limited set of molecular building blocks. Here we study the spontaneous self-assembly of a minimal model of cytoskeletal materials, consisting of semiflexible actin filaments, crosslinkers, and molecular motors. Using coarse-grained simulations, we demonstrate that by changing concentrations and kinetics of crosslinkers and motors, as well as filament lengths, we can generate three distinct structural phases of actomyosin assemblies: bundled, polarity-sorted, and contracted. We introduce new metrics to distinguish these structural phases and demonstrate their functional roles. We find that the binding kinetics of motors and crosslinkers can be tuned to optimize contractile force generation, motor transport, and mechanical response. By quantitatively characterizing the relationships between the modes of cytoskeletal self-assembly, the resulting structures, and their functional consequences, our work suggests new principles for the design of active materials.

A Versatile Framework for Simulating the Dynamic Mechanical Structure of Cytoskeletal Networks.

Computer simulations can aid in understanding how collective materials properties emerge from interactions between simple constituents. Here, we introduce a coarse-grained model that enables simulation of networks of actin filaments, myosin motors, and cross-linking proteins at biologically relevant time and length scales. We demonstrate that the model qualitatively and quantitatively captures a suite of trends observed experimentally, including the statistics of filament fluctuations, and mechanical responses to shear, motor motilities, and network rearrangements. We use the simulation to predict the viscoelastic scaling behavior of cross-linked actin networks, characterize the trajectories of actin in a myosin motility assay, and develop order parameters to measure contractility of a simulated actin network. The model can thus serve as a platform for interpretation and design of cytoskeletal materials experiments, as well as for further development of simulations incorporating active elements.