Cations Stiffen Actin Filaments by Adhering a Key Structural Element to Adjacent Subunits

A direct computational assessment of vinculin-actin unbinding kinetics reveals catch-bonding behavior

Vinculin forms a catch bond with the cytoskeletal polymer actin, displaying an increased bond lifetime upon force application. Notably, this behavior depends on the direction of the applied force, which has significant implications for cellular mechanotransduction. In this work, we present a comprehensive molecular dynamics simulation study, employing enhanced sampling techniques to investigate the thermodynamic, kinetic, and mechanistic aspects of this phenomenon at physiologically relevant forces. We dissect a catch bond mechanism in which force shifts vinculin between either a weakly or strongly bound state. Our results demonstrate that models for these states have unbinding times consistent with those from single-molecule studies, and suggest that both have some intrinsic catch-bonding behavior. We provide atomistic insight into this behavior, and show how a directional pulling force can promote the strong or weak state. Crucially, our strategy can be extended to measure the difficult-to-capture effects of small mechanical forces on biomolecular systems in general, and those involved in mechanotransduction more specifically.

Histidine 73 methylation coordinates β-actin plasticity in response to key environmental factors

The functional importance of the methylation of histidine 73 (H73) in actin remains unclear. Focusing on cytoplasmic β-actin, present in all mammalian cells, we use molecular dynamics simulations with a polarizable force field and adaptive sampling to examine the effects of H73 methylation. Our results show that methylation enhances nucleotide binding cleft opening, alters allosteric pathways connecting subdomains 2 and 4 (SD2 and SD4) in G-actin, and affects backdoor openings and inorganic phosphate release in F-actin, as validated by biochemical assays. These effects depend on the nucleotide and ions interacting with the actin. Together, our findings reveal how H73 methylation regulates β-actin plasticity and integrates environmental cues.

Bending stiffness of Toxoplasma gondii actin filaments

Actin is essential for the survival and pathogenicity of the Apicomplexan parasite Toxoplasma gondii, where it plays essential functions in cargo transport, invasion, egress, and organelle inheritance. Recent work has shown that, unlike vertebrate skeletal muscle actin, purified T. gondii actin filaments (TgAct1) can undergo rapid treadmilling, due to large differences in the barbed- and pointed-end critical concentrations, rapid subunit dissociation from filament ends, and a rapid nucleotide exchange rate constant from free monomers. Previous structural analysis suggested that the unique assembly properties of TgAct1 filaments may be a functional consequence of reduced contacts between the DNAse-1-binding loop (D-loop) of a filament subunit and its adjacent, long-axis subunit neighbor. Because the D-loop makes stabilizing interactions between neighboring subunits, it has been implicated in regulating the mechanical properties of actin filaments. In this study, we measured the bending persistence length (LB) of TgAct1 filaments and the filament length distribution. We found that despite compromised intersubunit D-loop contacts, TgAct1 filaments have similar bending stiffness and thermodynamic stability as vertebrate actin filaments. Analysis of published cryo-EM image density maps indicates that TgAct1 filaments retain a stabilizing intersubunit salt bridge between E168 and K62 and reveals visible density between Y167 and S61 of adjacent filament subunits, consistent with a conserved cation binding site proximal to the D-loop, as initially identified in vertebrate skeletal muscle actin filaments. These results favor a mechanism in which weak D-loop interactions compromise TgAct1 subunit incorporation at filament ends, while minimally affecting overall subunit interactions within filaments.

High-resolution yeast actin structures indicate the molecular mechanism of actin filament stiffening by cations

Actin filament assembly and the regulation of its mechanical properties are fundamental processes essential for eukaryotic cell function. Residue E167 in vertebrate actins forms an inter-subunit salt bridge with residue K61 of the adjacent subunit. Saccharomyces cerevisiae actin filaments are more flexible than vertebrate filaments and have an alanine at this position (A167). Substitution of this alanine for a glutamic acid (A167E) confers Saccharomyces cerevisiae actin filaments with salt-dependent stiffness similar to vertebrate actins. We developed an optimized cryogenic electron microscopy workflow refining sample preparation and vitrification to obtain near-atomic resolution structures of wild-type and A167E mutant Saccharomyces cerevisiae actin filaments. The difference between these structures allowed us to pinpoint the potential binding site of a filament-associated cation that controls the stiffness of the filaments in vertebrate and A167E Saccharomyces cerevisiae actins. Through an analysis of previously published high-resolution reconstructions of vertebrate actin filaments, along with a newly determined high-resolution vertebrate actin structure in the absence of potassium, we identified a unique peak near residue 167 consistent with the binding of a magnesium ion. Our findings show how magnesium can contribute to filament stiffening by directly bridging actin subunits and allosterically affecting the orientation of the DNase-I binding loop of actin, which plays a regulatory role in modulating actin filament stiffness and interactions with regulatory proteins.

Fascin - F-actin interaction studied by molecular dynamics simulation and protein network analysis

Actin bundles are an important component of cellular cytoskeleton and participate in the movement of cells. The formation of actin bundles requires the participation of many actin binding proteins (ABPs). Fascin is a member of ABPs, which plays a key role in bundling filamentous actin (F-actin) to bundles. However, the detailed interactions between fascin and F-actin are unclear. In this study, we construct an atomic-level structure of fascin - F-actin complex based on a rather poor cryo-EM data with resolution of 20 nm. We first optimized the geometries of the complex by molecular dynamics (MD) simulation and analyzed the binding site and pose of fascin which bundles two F-actin chains. Next, binding free energy of fascin was calculated by MM/GBSA method. Finally, protein structure network analysis (PSNs) was performed to analyze the key residues for fascin binding. Our results show that residues of K22, E27, E29, K41, K43, R110, R149, K358, R408 and K471 on fascin are important for its bundling, which are in good agreement with the experimental data. On the other hand, the consistent results indicate that the atomic-level model of fascin - F-actin complex is reliable. In short, this model can be used to understand the detailed interactions between fascin and F-actin, and to develop novel potential drugs targeting fascin.Communicated by Ramaswamy H. Sarma.

K-Means Clustering Coarse-Graining (KMC-CG): A Next Generation Methodology for Determining Optimal Coarse-Grained Mappings of Large Biomolecules

Coarse-grained (CG) molecular dynamics (MD) has become a method of choice for simulating various large scale biomolecular processes; therefore, the systematic definition of the CG mappings for biomolecules remains an important topic. Appropriate CG mappings can significantly enhance the representability of a CG model and improve its ability to capture critical features of large biomolecules. In this work, we present a systematic and more generalized method called K-means clustering coarse-graining (KMC-CG), which builds on the earlier approach of essential dynamics coarse-graining (ED-CG). KMC-CG removes the sequence-dependent constraints of ED-CG, allowing it to explore a more extensive space and thus enabling the discovery of more physically optimal CG mappings. Furthermore, the implementation of the K-means clustering algorithm can variationally optimize the CG mapping with efficiency and stability. This new method is tested in three cases: ATP-bound G-actin, the HIV-1 CA pentamer, and the Arp2/3 complex. In these examples, the CG models generated by KMC-CG are seen to better capture the structural, dynamic, and functional domains. KMC-CG therefore provides a robust and consistent approach to generating CG models of large biomolecules that can then be more accurately parametrized by either bottom-up or top-down CG force fields.

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.

The actin cytoskeleton in hair bundle development and hearing loss

Inner ear hair cells assemble mechanosensitive hair bundles on their apical surface that transduce sounds and accelerations. Each hair bundle is comprised of ∼ 100 individual stereocilia that are arranged into rows of increasing height and width; their specific and precise architecture being necessary for mechanoelectrical transduction (MET). The actin cytoskeleton is fundamental to establishing this architecture, not only by forming the structural scaffold shaping each stereocilium, but also by composing rootlets and the cuticular plate that together provide a stable foundation supporting each stereocilium. In concert with the actin cytoskeleton, a large assortment of actin-binding proteins (ABPs) function to cross-link actin filaments into specific topologies, as well as control actin filament growth, severing, and capping. These processes are individually critical for sensory transduction and are all disrupted in hereditary forms of human hearing loss. In this review, we provide an overview of actin-based structures in the hair bundle and the molecules contributing to their assembly and functional properties. We also highlight recent advances in mechanisms driving stereocilia elongation and how these processes are tuned by MET.

Actin's C-terminus coordinates actin structural changes and functions

Actin is essential to eukaryotic cellular processes. Actin's C-terminus appears to play a direct role in modulating actin's structure and properties, facilitating the binding and function of actin-binding proteins (ABPs). The structural and functional characterization of filamentous actin's C-terminus has been impeded by its inherent flexibility, as well as actin's resistance to crystallization for x-ray diffraction and the historical resolution constraints associated with electron microscopy. Many biochemical studies have established that actin's C-terminus must retain its flexibility and structural integrity to modulate actin's structure and functions. For example, C-terminal structural changes are known to affect nucleotide binding and exchange, as well as propagate actin structural changes throughout extensive allosteric networks, facilitating the binding and function of ABPs. Advances in electron microscopy have resulted in high-resolution structures of filamentous actin, providing insights into subtle structural changes that are mediated by actin's C-terminus. Here, we review existing knowledge establishing the importance of actin's C-terminus within actin structural changes and functions and discuss how modern structural characterization techniques provide the tools to understand the role of actin's C-terminus in cellular processes.

Variants in ACTC1 underlie distal arthrogryposis accompanied by congenital heart defects

Contraction of the human sarcomere is the result of interactions between myosin cross-bridges and actin filaments. Pathogenic variants in genes such as MYH7, TPM1, and TNNI3 that encode parts of the cardiac sarcomere cause muscle diseases that affect the heart, such as dilated cardiomyopathy and hypertrophic cardiomyopathy. In contrast, pathogenic variants in homologous genes such as MYH2, TPM2, and TNNI2 that encode parts of the skeletal muscle sarcomere cause muscle diseases affecting skeletal muscle, such as distal arthrogryposis (DA) syndromes and skeletal myopathies. To date, there have been few reports of genes (e.g., MYH7) encoding sarcomeric proteins in which the same pathogenic variant affects skeletal and cardiac muscle. Moreover, none of the known genes underlying DA have been found to contain pathogenic variants that also cause cardiac abnormalities. We report five families with DA because of heterozygous missense variants in the gene actin, alpha, cardiac muscle 1 (ACTC1). ACTC1 encodes a highly conserved actin that binds to myosin in cardiac and skeletal muscle. Pathogenic variants in ACTC1 have been found previously to underlie atrial septal defect, dilated cardiomyopathy, hypertrophic cardiomyopathy, and left ventricular noncompaction. Our discovery delineates a new DA condition because of variants in ACTC1 and suggests that some functions of ACTC1 are shared in cardiac and skeletal muscle.

Using classifiers to understand coarse-grained models and their fidelity with the underlying all-atom systems

Bottom-up coarse-grained (CG) molecular dynamics models are parameterized using complex effective Hamiltonians. These models are typically optimized to approximate high dimensional data from atomistic simulations. However, human validation of these models is often limited to low dimensional statistics that do not necessarily differentiate between the CG model and said atomistic simulations. We propose that classification can be used to variationally estimate high dimensional error and that explainable machine learning can help convey this information to scientists. This approach is demonstrated using Shapley additive explanations and two CG protein models. This framework may also be valuable for ascertaining whether allosteric effects at the atomistic level are accurately propagated to a CG model.

Variants in ACTC1 underlie distal arthrogryposis accompanied by congenital heart defects

Contraction of the human sarcomere is the result of interactions between myosin cross-bridges and actin filaments. Pathogenic variants in genes such as MYH7 , TPM1 , and TNNI3 that encode parts of the cardiac sarcomere cause muscle diseases that affect the heart, such as dilated cardiomyopathy and hypertrophic cardiomyopathy. In contrast, pathogenic variants in homologous genes MYH2 , TPM2 , and TNNI2 , that encode parts of the skeletal muscle sarcomere, cause muscle diseases affecting skeletal muscle, such as the distal arthrogryposis (DA) syndromes and skeletal myopathies. To date, there have been few reports of genes (e.g., MYH7 ) encoding sarcomeric proteins in which the same pathogenic variant affects both skeletal and cardiac muscle. Moreover, none of the known genes underlying DA have been found to contain mutations that also cause cardiac abnormalities. We report five families with DA due to heterozygous missense variants in the gene actin, alpha, cardiac muscle 1 ( ACTC1 ). ACTC1 encodes a highly conserved actin that binds to myosin in both cardiac and skeletal muscle. Mutations in ACTC1 have previously been found to underlie atrial septal defect, dilated cardiomyopathy, hypertrophic cardiomyopathy, and left ventricular noncompaction. Our discovery delineates a new DA condition due to mutations in ACTC1 and suggests that some functions of actin, alpha, cardiac muscle 1 are shared in cardiac and skeletal muscle.

Cellular force-sensing through actin filaments

The actin cytoskeleton orchestrates cell mechanics and facilitates the physical integration of cells into tissues, while tissue-scale forces and extracellular rigidity in turn govern cell behaviour. Here, we discuss recent evidence that actin filaments (F-actin), the core building blocks of the actin cytoskeleton, also serve as molecular force sensors. We delineate two classes of proteins, which interpret forces applied to F-actin through enhanced binding interactions: 'mechanically tuned' canonical actin-binding proteins, whose constitutive F-actin affinity is increased by force, and 'mechanically switched' proteins, which bind F-actin only in the presence of force. We speculate mechanically tuned and mechanically switched actin-binding proteins are biophysically suitable for coordinating cytoskeletal force-feedback and mechanical signalling processes, respectively. Finally, we discuss potential mechanisms mediating force-activated actin binding, which likely occurs both through the structural remodelling of F-actin itself and geometric rearrangements of higher-order actin networks. Understanding the interplay of these mechanisms will enable the dissection of force-activated actin binding's specific biological functions.

Specialization of actin isoforms derived from the loss of key interactions with regulatory factors

A paradox of eukaryotic cells is that while some species assemble a complex actin cytoskeleton from a single ortholog, other species utilize a greater diversity of actin isoforms. The physiological consequences of using different actin isoforms, and the molecular mechanisms by which highly conserved actin isoforms are segregated into distinct networks, are poorly known. Here, we sought to understand how a simple biological system, composed of a unique actin and a limited set of actin‐binding proteins, reacts to a switch to heterologous actin expression. Using yeast as a model system and biomimetic assays, we show that such perturbation causes drastic reorganization of the actin cytoskeleton. Our results indicate that defective interaction of a heterologous actin for important regulators of actin assembly limits certain actin assembly pathways while reinforcing others. Expression of two heterologous actin variants, each specialized in assembling a different network, rescues cytoskeletal organization and confers resistance to external perturbation. Hence, while species using a unique actin have homeostatic actin networks, actin assembly pathways in species using several actin isoforms may act more independently.

Cholate Conjugated Cationic Polymers for Regulation of Actin Dynamics

Cytoskeletal movement is a compulsory necessity for proper cell functioning and is largely controlled by actin filament dynamics. The actin dynamics can be finetuned by various natural and artificial materials...

Regulation of Actin Bundle Mechanics and Structure by Intracellular Environmental Factors

The mechanical and structural properties of actin cytoskeleton drive various cellular processes, including structural support of the plasma membrane and cellular motility. Actin monomers assemble into double-stranded helical filaments as well as higher-ordered structures such as bundles and networks. Cells incorporate macromolecular crowding, cation interactions, and actin-crosslinking proteins to regulate the organization of actin bundles. Although the roles of each of these factors in actin bundling have been well-known individually, how combined factors contribute to actin bundle assembly, organization, and mechanics is not fully understood. Here, we describe recent studies that have investigated the mechanisms of how intracellular environmental factors influence actin bundling. This review highlights the effects of macromolecular crowding, cation interactions, and actin-crosslinking proteins on actin bundle organization, structure, and mechanics. Understanding these mechanisms is important in determining in vivo actin biophysics and providing insights into cell physiology.

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.

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.

Effects of Nucleotide and End-Dependent Actin Conformations on Polymerization

The regulation of actin is key for controlled cellular function. Filaments are regulated by actin-binding proteins, but the nucleotide state of actin is also an important factor. From extended molecular dynamics simulations, we find that both nucleotide states of the actin monomer have significantly less twist than their crystal structures and that the ATP monomer is flatter than the ADP form. We also find that the filament's pointed end is flatter than the remainder of the filament and has a conformation distinct from G-actin, meaning that incoming monomers would need to undergo isomerization that would weaken the affinity and slow polymerization. Conversely, the barbed end of the filament takes on a conformation nearly identical to the ATP monomer, enhancing ATP G-actin's ability to polymerize as compared with ADP G-actin. The thermodynamic penalty imposed by differences in isomerization for the ATP and ADP growth at the barbed end exactly matches experimental results.

Charge-dependent interactions of monomeric and filamentous actin with lipid bilayers

The cytoskeletal protein actin polymerizes into filaments that are essential for the mechanical stability of mammalian cells. In vitro experiments showed that direct interactions between actin filaments and lipid bilayers are possible and that the net charge of the bilayer as well as the presence of divalent ions in the buffer play an important role. In vivo, colocalization of actin filaments and divalent ions are suppressed, and cells rely on linker proteins to connect the plasma membrane to the actin network. Little is known, however, about why this is the case and what microscopic interactions are important. A deeper understanding is highly beneficial, first, to obtain understanding in the biological design of cells and, second, as a possible basis for the building of artificial cortices for the stabilization of synthetic cells. Here, we report the results of coarse-grained molecular dynamics simulations of monomeric and filamentous actin in the vicinity of differently charged lipid bilayers. We observe that charges on the lipid head groups strongly determine the ability of actin to adsorb to the bilayer. The inclusion of divalent ions leads to a reversal of the binding affinity. Our in silico results are validated experimentally by reconstitution assays with actin on lipid bilayer membranes and provide a molecular-level understanding of the actin-membrane interaction.

Molecular dynamics study of interactions between polymorphic actin filaments and gelsolin segment-1

The assembly of protein actin into double-helical filaments promotes many eukaryotic cellular processes that are regulated by actin-binding proteins (ABPs). Actin filaments can adopt multiple conformations, known as structural polymorphism, which possibly influences the interaction between filaments and ABPs. Gelsolin is a Ca²⁺ -regulated ABP that severs and caps actin filaments. Gelsolin binding modulates filament structure; however, it is not known how polymorphic actin filament structures influence an interaction of gelsolin S1 with the barbed-end of filament. Herein, we investigated how polymorphic structures of actin filaments affect the interactions near interfaces between the gelsolin segment 1 (S1) domain and the filament barbed-end. Using all-atom molecular dynamics simulations, we demonstrate that different tilted states of subunits modulate gelsolin S1 interactions with the barbed-end of polymorphic filaments. Hydrogen bonding and interaction energy at the filament-gelsolin S1 interface indicate distinct conformations of filament barbed ends, resulting in different interactions of gelsolin S1. This study demonstrates that filament's structural multiplicity plays important roles in the interactions of actin with ABPs.

Steered molecular dynamics simulations reveal the role of Ca2+ in regulating mechanostability of cellulose-binding proteins

The conversion of cellulosic biomass into biofuels requires degradation of the biomass into fermentable sugars. The most efficient natural cellulase system for carrying out this conversion is an extracellular multi-enzymatic complex named the cellulosome. In addition to temperature and pH stability, mechanical stability is important for functioning of cellulosome domains, and experimental techniques such as Single Molecule Force Spectroscopy (SMFS) have been used to measure the mechanical strength of several cellulosomal proteins. Molecular dynamics computer simulations provide complementary atomic-resolution quantitative maps of domain mechanical stability for identification of experimental leads for protein stabilization. In this study, we used multi-scale steered molecular dynamics computer simulations, benchmarked against new SMFS measurements, to measure the intermolecular contacts that confer high mechanical stability to a family 3 Carbohydrate Binding Module protein (CBM3) derived from the archetypal Clostridium thermocellum cellulosome. Our data predicts that electrostatic interactions in the calcium binding pocket modulate the mechanostability of the cellulose-binding module, which provides an additional design rule for the rational re-engineering of designer cellulosomes for biotechnology. Our data offers new molecular insights into the origins of mechanostability in cellulose binding domains and gives leads for synthesis of more robust cellulose-binding protein modules. On the other hand, simulations predict that insertion of a flexible strand can promote alternative unfolding pathways and dramatically reduce the mechanostability of the carbohydrate binding module, which gives routes to rational design of tailormade fingerprint complexes for force spectroscopy experiments.

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.

Actin Filament Mechanics and Structure in Crowded Environments

The cellular environment is crowded with high concentrations of macromolecules that significantly reduce accessible volume for biomolecular interactions. Reductions in cellular volume can generate depletion forces that affect protein assembly and stability. The mechanical and structural properties of actin filaments play critical roles in various cellular functions, including structural support, cell movement, division, and intracellular transport. Although the effects of molecular crowding on actin polymerization have been shown, how crowded environments affect filament mechanics and structure is unknown. In this study, we investigate the effects of solution crowding on the modulations of actin filament bending stiffness and conformations both in vitro and in silico. Direct visualization of thermally fluctuating filaments in the presence of crowding agents is achieved by fluorescence microscopy imaging. Biophysical analysis indicates that molecular crowding enhances filament's effective bending stiffness and reduces average filament lengths. Utilizing the all-atom molecular dynamics simulations, we demonstrate that molecular crowding alters filament conformations and intersubunit contacts that are directly coupled to the mechanical properties of filaments. Taken together, our study suggests that the interplay between excluded volume effects and nonspecific interactions raised from molecular crowding may modulate actin filament mechanics and structure.

Interplay of actin, ADP and Mg2+ interactions with striated muscle myosin: Implications of their roles in ATPase

The effects of Mg²⁺ on the interaction between ADP, a product of the ATPase reaction, and striated muscle myosin-subfragment 1 (S1) were investigated with both functional and spectroscopic methods. Mg²⁺ inhibited striated muscle myosin ATPase in the presence of F-actin. Significant effects of Mg²⁺ were observed in both rate constants of NOE build-up and maximal intensities in WaterLOGSY NMR experiments as F-actin concentration increased. In the absence of F-actin, myosin S1 with Mg²⁺ bound to a fluorescent ADP analog about five-times tighter than without Mg²⁺. In the presence of F-actin, the affinity of myosin S1 toward the ADP analog significantly decreased both with and without Mg²⁺. The equilibrium titration of myosin-S1 into F-actin revealed that in the presence of ADP the apparent dissociation constant (K_d) without Mg²⁺ was more than five-fold smaller than with Mg²⁺. Further, we examined effects of F-actin, ADP and Mg²⁺ binding to myosin on the tertiary structure of myosin-S1 using near UV circular dichroism (CD) spectroscopy. Both in the presence and absence of ADP, there was a Mg²⁺-dependent difference in the near UV CD spectra of actomyosin. Our results show that Mg²⁺ affects myosin-ADP and actin-myosin interactions which may be reflected in myosin ATPase activity.

Multiscale simulation of actin filaments and actin-associated proteins

Actin is an important cytoskeletal protein that serves as a building block to form filament networks that span across the cell. These networks are orchestrated by a myriad of other cytoskeletal entities including the unbranched filament-forming protein formin and branched network-forming protein complex Arp2/3. Computational models have been able to provide insights into many important structural transitions that are involved in forming these networks, and into the nature of interactions essential for actin filament formation and for regulating the behavior of actin-associated proteins. In this review, we summarize a subset of such models that focus on the atomistic features and those that can integrate atomistic features into a larger picture in a multiscale fashion.

Perspective: Identification of collective variables and metastable states of protein dynamics

The statistical analysis of molecular dynamics simulations requires dimensionality reduction techniques, which yield a low-dimensional set of collective variables (CVs) {x _i } = x that in some sense describe the essential dynamics of the system. Considering the distribution P( x ) of the CVs, the primal goal of a statistical analysis is to detect the characteristic features of P( x ), in particular, its maxima and their connection paths. This is because these features characterize the low-energy regions and the energy barriers of the corresponding free energy landscape ΔG( x ) = -k _B T ln P( x ), and therefore amount to the metastable states and transition regions of the system. In this perspective, we outline a systematic strategy to identify CVs and metastable states, which subsequently can be employed to construct a Langevin or a Markov state model of the dynamics. In particular, we account for the still limited sampling typically achieved by molecular dynamics simulations, which in practice seriously limits the applicability of theories (e.g., assuming ergodicity) and black-box software tools (e.g., using redundant input coordinates). We show that it is essential to use internal (rather than Cartesian) input coordinates, employ dimensionality reduction methods that avoid rescaling errors (such as principal component analysis), and perform density based (rather than k-means-type) clustering. Finally, we briefly discuss a machine learning approach to dimensionality reduction, which highlights the essential internal coordinates of a system and may reveal hidden reaction mechanisms.

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.

Structural evidence for the roles of divalent cations in actin polymerization and activation of ATP hydrolysis

Actin polymerization is a divalent cation-dependent process. Here we identify a cation binding site on the surface of actin in a 2.0-Å resolution X-ray structure of actin and find evidence of three additional sites in published high-resolution structures. These cations are stable in molecular dynamics (MD) simulations of the filament, suggesting a functional role in polymerization or filament rigidity. Polymerization activates the ATPase activity of the incorporating actin protomers. Careful analysis of water molecules that approach the ATP in the MD simulations revealed Gln137-activated water to be in a suitable position in F-actin, to initiate attack for ATP hydrolysis, and its occupancy was dependent on bound cations.

The structure of the actin filament is known at a resolution that has allowed the architecture of protein components to be unambiguously assigned. However, fully understanding the chemistry of the system requires higher resolution to identify the ions and water molecules involved in polymerization and ATP hydrolysis. Here, we find experimental evidence for the association of cations with the surfaces of G-actin in a 2.0-Å resolution X-ray structure of actin bound to a Cordon-Bleu WH2 motif and in previously determined high-resolution X-ray structures. Three of four reoccurring divalent cation sites were stable during molecular dynamics (MD) simulations of the filament, suggesting that these sites may play a functional role in stabilizing the filament. We modeled the water coordination at the ATP-bound Mg²⁺, which also proved to be stable during the MD simulations. Using this model of the filament with a hydrated ATP-bound Mg²⁺, we compared the cumulative probability of an activated hydrolytic water molecule approaching the γ-phosphorous of ATP, in comparison with G-actin, in the MD simulations. The cumulative probability increased in F-actin in line with the activation of actin’s ATPase activity on polymerization. However, inclusion of the cations in the filament lowered cumulative probability, suggesting the rate of hydrolysis may be linked to filament flexibility. Together, these data extend the possible roles of Mg²⁺ in polymerization and the mechanism of polymerization-induced activation of actin’s ATPase activity.

Principal component analysis on a torus: Theory and application to protein dynamics

A dimensionality reduction method for high-dimensional circular data is developed, which is based on a principal component analysis (PCA) of data points on a torus. Adopting a geometrical view of PCA, various distance measures on a torus are introduced and the associated problem of projecting data onto the principal subspaces is discussed. The main idea is that the (periodicity-induced) projection error can be minimized by transforming the data such that the maximal gap of the sampling is shifted to the periodic boundary. In a second step, the covariance matrix and its eigendecomposition can be computed in a standard manner. Adopting molecular dynamics simulations of two well-established biomolecular systems (Aib₉ and villin headpiece), the potential of the method to analyze the dynamics of backbone dihedral angles is demonstrated. The new approach allows for a robust and well-defined construction of metastable states and provides low-dimensional reaction coordinates that accurately describe the free energy landscape. Moreover, it offers a direct interpretation of covariances and principal components in terms of the angular variables. Apart from its application to PCA, the method of maximal gap shifting is general and can be applied to any other dimensionality reduction method for circular data.

Cations Modulate Actin Bundle Mechanics, Assembly Dynamics, and Structure

Actin bundles are key factors in the mechanical support and dynamic reorganization of the cytoskeleton. High concentrations of multivalent counterions promote bundle formation through electrostatic attraction between actin filaments that are negatively charged polyelectrolytes. In this study, we evaluate how physiologically relevant divalent cations affect the mechanical, dynamic, and structural properties of actin bundles. Using a combination of total internal reflection fluorescence microscopy, transmission electron microscopy, and dynamic light scattering, we demonstrate that divalent cations modulate bundle stiffness, length distribution, and lateral growth. Molecular dynamics simulations of an all-atom model of the actin bundle reveal specific actin residues coordinate cation-binding sites that promote the bundle formation. Our work suggests that specific cation interactions may play a fundamental role in the assembly, structure, and mechanical properties of actin bundles.

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.

Coarse-Grained Directed Simulation

Many free-energy sampling and quantum mechanics/molecular mechanics (QM/MM) computations on protein complexes have been performed where, by necessity, a single component is studied isolated in solution while its overall configuration is kept in the complex-like state by either rigid restraints or harmonic constraints. A drawback in these studies is that the system's native fluctuations are lost, both due to the change of environment and the imposition of the extra potential. Yet, we know that having both accurate structure and fluctuations is likely crucial to achieving correct simulation estimates for the subsystem within its native larger protein complex context. In this work, we provide a new approach to this problem by drawing on ideas developed to incorporate experimental information into a molecular simulation by relative entropy minimization to a target system. We show that by using linear biases on coarse-grained (CG) observables (such as distances or angles between large subdomains within a protein), we can maintain the protein in a particular target conformation while also preserving the correct equilibrium fluctuations of the subsystem within its larger biomolecular complex. As an application, we demonstrate this algorithm by training a bias that causes an actin monomer (and trimer) in solution to sample the same average structure and fluctuations as if it were embedded within a much larger actin filament. Additionally, we have developed a number of algorithmic improvements that accelerate convergence of the on-the-fly relative entropy minimization algorithms for this type of application. Finally, we have contributed these methods to the PLUMED open source free energy sampling software library.

Actin Filament Strain Promotes Severing and Cofilin Dissociation

Computational and structural studies have been indispensable in investigating the molecular origins of actin filament mechanical properties and modulation by the regulatory severing protein cofilin. All-atom molecular dynamics simulations of cofilactin filament structures determined by electron cryomicroscopy reveal how cofilin enhances the bending and twisting compliance of actin filaments. Continuum mechanics models suggest that buckled cofilactin filaments localize elastic energy at boundaries between bare and cofilin-decorated segments because of their nonuniform elasticity, thereby accelerating filament severing. Here, we develop mesoscopic length-scale (cofil)actin filament models and evaluate the effects of compressive and twisting loads on strain energy distribution at specific interprotein interfaces. The models reliably capture the filament bending and torsional rigidities and intersubunit torsional flexibility measured experimentally with purified protein components. Buckling is predicted to enhance cofilactin filament severing with minimal effects on cofilin occupancy, whereas filament twisting enhances cofilin dissociation without compromising filament integrity. Preferential severing at actin-cofilactin boundaries of buckled filaments is more prominent than predicted by continuum models because of the enhanced spatial resolution. The models developed here will be valuable for evaluating the effects of filament shape deformations on filament stability and interactions with regulatory proteins, and analysis of single filament manipulation assays.

Tropomodulins and Leiomodins: Actin Pointed End Caps and Nucleators in Muscles

Cytoskeletal structures characterized by actin filaments with uniform lengths, including the thin filaments of striated muscles and the spectrin-based membrane skeleton, use barbed and pointed-end capping proteins to control subunit addition/dissociation at filament ends. While several proteins cap the barbed end, tropomodulins (Tmods), a family of four closely related isoforms in vertebrates, are the only proteins known to specifically cap the pointed end. Tmods are ∼350 amino acids in length, and comprise alternating tropomyosin- and actin-binding sites (TMBS1, ABS1, TMBS2, and ABS2). Leiomodins (Lmods) are related in sequence to Tmods, but display important differences, including most notably the lack of TMBS2 and the presence of a C-terminal extension featuring a proline-rich domain and an actin-binding WASP-Homology 2 domain. The Lmod subfamily comprises three somewhat divergent isoforms expressed predominantly in muscle cells. Biochemically, Lmods differ from Tmods, acting as powerful nucleators of actin polymerization, not capping proteins. Structurally, Lmods and Tmods display crucial differences that correlate well with their different biochemical activities. Physiologically, loss of Lmods in striated muscle results in cardiomyopathy or nemaline myopathy, whereas complete loss of Tmods leads to failure of myofibril assembly and developmental defects. Yet, interpretation of some of the in vivo data has led to the idea that Tmods and Lmods are interchangeable or, at best, different variants of two subfamilies of pointed-end capping proteins. Here, we review and contrast the existing literature on Tmods and Lmods, and propose a model of Lmod function that attempts to reconcile the in vitro and in vivo data, whereby Lmods nucleate actin filaments that are subsequently capped by Tmods during sarcomere assembly, turnover, and repair.

Structural Basis for pH-mediated Regulation of F-actin Severing by Gelsolin Domain 1

Six-domain gelsolin regulates actin structural dynamics through its abilities to sever, cap and uncap F-actin. These activities are modulated by various cellular parameters like Ca2+ and pH. Until now, only the molecular activation mechanism of gelsolin by Ca2+ has been understood relatively well. The fragment comprising the first domain and six residues from the linker region into the second domain has been shown to be similar to the full-length protein in F-actin severing activity in the absence of Ca2+ at pH 5. To understand how this gelsolin fragment is activated for F-actin severing by lowering pH, we solved its NMR structures at both pH 7.3 and 5 in the absence of Ca2+ and measured the pKa values of acidic amino acid residues and histidine residues. The overall structure and dynamics of the fragment are not affected significantly by pH. Nevertheless, local structural changes caused by protonation of His29 and Asp109 result in the activation on lowering the pH, and protonation of His151 directly effects filament binding since it resides in the gelsolin/actin interface. Mutagenesis studies support that His29, Asp109 and His151 play important roles in the pH-dependent severing activity of the gelsolin fragment.