Coarse-Graining Provides Insights on the Essential Nature of Heterogeneity in Actin Filaments

Experiments have shown that actin is structurally polymorphic, but knowledge of the details of molecular level heterogeneity in both the dynamics of a single subunit and the interactions between subunits is still lacking. Here, using atomistic molecular dynamics simulations of the actin filament, we identify domains of atoms that move in a correlated fashion, quantify interactions between these domains using coarse-grained (CG) analysis methods, and perform CG simulations to explore the importance of filament heterogeneity. The persistence length and torsional stiffness calculated from molecular dynamics simulation data agree with experimental values. We additionally observe that distinct actin conformations coexist in actin filaments. The filaments also exhibit random twist angles that are broadly distributed. CG analysis reveals that interactions between equivalent CG pairs vary from one subunit to another. To explore the importance of heterogeneity on filament dynamics, we perform CG simulations using different methods of parameterization to show that only by including heterogeneous interactions can we reproduce the twist angles and related properties. Free energy calculations further suggest that in general the actin filament is best represented as a set of subunits with differing CG sites and interactions, and the incorporating heterogeneity into the CG interactions is more important than including that in the CG sites. Our work therefore presents a systematic method to explore molecular level detail in this large and complex biopolymer.     

Effects of ATP and Actin-Filament Binding on the Dynamics of the Myosin II S1 Domain

Actin and myosin interact with one another to perform a variety of cellular functions. Central to understanding the processive motion of myosin on actin is the characterization of the individual states along the mechanochemical cycle. We present an all-atom molecular dynamics simulation of the myosin II S1 domain in the rigor state interacting with an actin filament. We also study actin-free myosin in both rigor and post-rigor conformations. Using all-atom level and coarse-grained analysis methods, we investigate the effects of myosin binding on actin, and of actin binding on myosin. In particular, we determine the domains of actin and myosin that interact strongly with one another at the actomyosin interface using a highly coarse-grained level of resolution, and we identify a number of salt bridges and hydrogen bonds at the interface of myosin and actin. Applying coarse-grained analysis, we identify differences in myosin states dependent on actin-binding, or ATP binding. Our simulations also indicate that the actin propeller twist-angle and nucleotide cleft-angles are influenced by myosin at the actomyosin interface. The torsional rigidity of the myosin-bound filament is also calculated, and is found to be increased compared to previous simulations of the free filament.     

Effects of ATP and Actin-Filament Binding on the Dynamics of the Myosin II S1 Domain

Actin and myosin interact with one another to perform a variety of cellular functions. Central to understanding the processive motion of myosin on actin is the characterization of the individual states along the mechanochemical cycle. We present an all-atom molecular dynamics simulation of the myosin II S1 domain in the rigor state interacting with an actin filament. We also study actin-free myosin in both rigor and post-rigor conformations. Using all-atom level and coarse-grained analysis methods, we investigate the effects of myosin binding on actin, and of actin binding on myosin. In particular, we determine the domains of actin and myosin that interact strongly with one another at the actomyosin interface using a highly coarse-grained level of resolution, and we identify a number of salt bridges and hydrogen bonds at the interface of myosin and actin. Applying coarse-grained analysis, we identify differences in myosin states dependent on actin-binding, or ATP binding. Our simulations also indicate that the actin propeller twist-angle and nucleotide cleft-angles are influenced by myosin at the actomyosin interface. The torsional rigidity of the myosin-bound filament is also calculated, and is found to be increased compared to previous simulations of the free filament.     

Do Skeletal Dynamics Mediate Sugar Uptake and Transport in Human Erythrocytes?

We explore, herein, the hypothesis that transport of molecules or ions into erythrocytes may be affected and directly stimulated by the dynamics of the spectrin/actin skeleton. Skeleton/actin motions are driven by thermal fluctuations that may be influenced by ATP hydrolysis as well as by structural alterations of the junctional complexes that connect the skeleton to the cell’s lipid membrane. Specifically, we focus on the uptake of glucose into erythrocytes via glucose transporter 1 and on the kinetics of glucose disassociation at the endofacial side of glucose transporter 1. We argue that glucose disassociation is affected by both hydrodynamic forces induced by the actin/spectrin skeleton and by probable contact of the swinging 37-nm-long F-actin protofilament with glucose, an effect we dub the “stickball effect.” Our hypothesis and results are interpreted within the framework of the kinetic measurements and compartmental kinetic models of Carruthers and co-workers; these experimental results and models describe glucose disassociation as the “slow step” (i.e., rate-limiting step) in the uptake process. Our hypothesis is further supported by direct simulations of skeleton-enhanced transport using our molecular-based models for the actin/spectrin skeleton as well as by experimental measurements of glucose uptake into cells subject to shear deformations, which demonstrate the hydrodynamic effects of advection. Our simulations have, in fact, previously demonstrated enhanced skeletal dynamics in cells in shear deformations, as they occur naturally within the skeleton, which is an effect also supported by experimental observations.     

Quantitative Analysis of Approaches to Measure Cooperative Phosphate Release in Polymerized Actin

We use stochastic simulations that treat several experimental probes of actin dynamics to explore the extent to which phosphate dissociation in filamentous actin may be cooperative. Phosphate time-courses from polymerization and copolymerization experiments of ATP- and ADP-actin are studied, including the effects of variations in filament-number concentration as well as single-filament depolymerization time-courses. We find that highly cooperative models are consistent with the treated experimental data. We also find that some types of experiments that are believed to provide strong constraints on the cooperativity of actin hydrolysis models do not provide such constraints.     

A Combination of Actin Treadmilling and Cross-Linking Drives Contraction of Random Actomyosin Arrays

We investigate computationally the self-organization and contraction of an initially random actomyosin ring. In the framework of a detailed physical model for a ring of cross-linked actin filaments and myosin-II clusters, we derive the force balance equations and solve them numerically. We find that to contract, actin filaments have to treadmill and to be sufficiently cross linked, and myosin has to be processive. The simulations reveal how contraction scales with mechanochemical parameters. For example, they show that the ring made of longer filaments generates greater force but contracts slower. The model predicts that the ring contracts with a constant rate proportional to the initial ring radius if either myosin is released from the ring during contraction and actin filaments shorten, or if myosin is retained in the ring, while the actin filament number decreases. We demonstrate that a balance of actin nucleation and compression-dependent disassembly can also sustain contraction. Finally, the model demonstrates that with time pattern formation takes place in the ring, worsening the contractile process. The more random the actin dynamics are, the higher the contractility will be.     

Nucleotide effects on the structure and dynamics of actin

Adenosine 5'-triphosphate or ATP is the primary energy source within the cell, releasing its energy via hydrolysis into adenosine 5'-diphosphate or ADP. Actin is an important ATPase involved in many aspects of cellular function, and the binding and hydrolysis of ATP regulates its polymerization into actin filaments as well as its interaction with a host of actin-associated proteins. Here we study the dynamics of monomeric actin in ATP, ADP-Pi, and ADP states via molecular dynamics simulations. As observed in some crystal structures we see that the DNase-I loop is an alpha-helix in the ADP state but forms an unstructured coil domain in the ADP-Pi and ATP states. We also find that this secondary structure change is reversible, and by mimicking nucleotide exchange we can observe the transition between the helical and coil states. Apart from the DNase-I loop, we also see several key structural differences in the nucleotide binding cleft as well as in the hydrophobic cleft between subdomains 1 and 3 where WH2-containing proteins have been shown to interact. These differences provide a structural basis for understanding the observed differences between the various nucleotide states of actin and provide some insight into how ATP regulates the interaction of actin with itself and other proteins.     

Actin dynamics rapidly reset chemoattractant receptor sensitivity following adaptation in neutrophils

Neutrophils are cells of the innate immune system that hunt and kill pathogens using directed migration. This process, known as chemotaxis, requires the regulation of actin polymerization downstream of chemoattractant receptors. Reciprocal interactions between actin and intracellular signals are thought to underlie many of the sophisticated signal processing capabilities of the chemotactic cascade including adaptation, amplification and long-range inhibition. However, with existing tools, it has been difficult to discern actin''s role in these processes. Most studies investigating the role of the actin cytoskeleton have primarily relied on actin-depolymerizing agents, which not only block new actin polymerization but also destroy the existing cytoskeleton. We recently developed a combination of pharmacological inhibitors that stabilizes the existing actin cytoskeleton by inhibiting actin polymerization, depolymerization and myosin-based rearrangements; we refer to these processes collectively as actin dynamics. Here, we investigated how actin dynamics influence multiple signalling responses (PI3K lipid products, calcium and Pak phosphorylation) following acute agonist addition or during desensitization. We find that stabilized actin polymer extends the period of receptor desensitization following agonist binding and that actin dynamics rapidly reset receptors from this desensitized state. Spatial differences in actin dynamics may underlie front/back differences in agonist sensitivity in neutrophils.     

Molecular dynamics simulation of tropomyosin bound to actins/myosin in the closed and open states

Tropomyosin (Tpm) is a dimeric coiled-coil protein that binds to filamentous actin, and regulates actin-myosin interaction by moving between three positions corresponding to the blocked, closed, and open states. To elucidate how Tpm undergoes transitions between these functional states, we have built structural models and conducted extensive molecular dynamics simulations of the Tpm-actins/myosin complex in the closed and open states (total simulation time >1.4 μs). Based on the simulation trajectories, we have analyzed the dynamics and energetics of a truncated Tpm interacting with actins/myosin under the physiological conditions. Our simulations have shown distinct dynamics of four Tpm periods (P3-P6), featuring pronounced biased fluctuations of P4 and P5 toward the open position in the closed state, which is consistent with a conformational selection mechanism for Tpm-regulated myosin binding. Additionally, we have identified key residues of Tpm specifically binding to actins/myosin in the closed and open state. Some of them were validated as functionally important in comparison with past functional/clinical studies, and the rest will make promising targets for future mutational experiments.     

Mapping the cofilin binding site on yeast G-actin by chemical cross-linking

Cofilin is a major cytoskeletal protein that binds to both monomeric actin (G-actin) and polymeric actin (F-actin) and is involved in microfilament dynamics. Although an atomic structure of the G-actin-cofilin complex does not exist, models of the complex have been built using molecular dynamics simulations, structural homology considerations, and synchrotron radiolytic footprinting data. The hydrophobic cleft between actin subdomains 1 and 3 and, alternatively, the cleft between actin subdomains 1 and 2 have been proposed as possible high-affinity cofilin binding sites. In this study, the proposed binding of cofilin to the subdomain 1/subdomain 3 region on G-actin has been probed using site-directed mutagenesis, fluorescence labeling, and chemical cross-linking, with yeast actin mutants containing single reactive cysteines in the actin hydrophobic cleft and with cofilin mutants carrying reactive cysteines in the regions predicted to bind to G-actin. Mass spectrometry analysis of the cross-linked complex revealed that cysteine 345 in subdomain 1 of mutant G-actin was cross-linked to native cysteine 62 on cofilin. A cofilin mutant that carried a cysteine substitution in the α3-helix (residue 95) formed a cross-link with residue 144 in actin subdomain 3. Distance constraints imposed by these cross-links provide experimental evidence for cofilin binding between actin subdomains 1 and 3 and fit a corresponding docking-based structure of the complex. The cross-linking of the N-terminal region of recombinant yeast cofilin to actin residues 346 and 374 with dithio-bis-maleimidoethane (12.4 Å) and via disulfide bond formation was also documented. This set of cross-linking data confirms the important role of the N-terminal segment of cofilin in interactions with G-actin.     

Molecular dynamics simulation of a myosin subfragment-1 docking with an actin filament

Myosins are typical molecular motor proteins, which convert the chemical energy of ATP into mechanical work. The fundamental mechanism of this energy conversion is still unknown. To explain the experimental results observed in molecular motors, Masuda has proposed a theory called the “Driven by Detachment (DbD)” mechanism for the working principle of myosins. Based on this theory, the energy used during the power stroke of the myosins originates from the attractive force between a detached myosin head and an actin filament, and does not directly arise from the energy of ATP. According to this theory, every step in the myosin working process may be reproduced by molecular dynamics (MD) simulations, except for the ATP hydrolysis step. Therefore, MD simulations were conducted to reproduce the docking process of a myosin subfragment-1 (S1) against an actin filament. A myosin S1 directed toward the barbed end of an actin filament was placed at three different positions by shifting it away from the filament axis. After 30 ns of MD simulations, in three cases out of ten trials on average, the myosin made a close contact with two actin monomers by changing the positions and the orientation of both the myosin and the actin as predicted in previous studies. Once the docking was achieved, the distance between the myosin and the actin showed smaller fluctuations, indicating that the docking is stable over time. If the docking was not achieved, the myosin moved randomly around the initial position or moved away from the actin filament. MD simulations thus successfully reproduced the docking of a myosin S1 with an actin filament. By extending the similar MD simulations to the other steps of the myosin working process, the validity of the DbD theory may be computationally demonstrated.     

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

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

Stochastic simulation of actin dynamics reveals the role of annealing and fragmentation

Recent observations of F-actin dynamics call for theoretical models to interpret and understand the quantitative data. A number of existing models rely on simplifications and do not take into account F-actin fragmentation and annealing. We use Gillespie's algorithm for stochastic simulations of the F-actin dynamics including fragmentation and annealing. The simulations vividly illustrate that fragmentation and annealing have little influence on the shape of the polymerization curve and on nucleotide profiles within filaments but drastically affect the F-actin length distribution, making it exponential. We find that recent surprising measurements of high length diffusivity at the critical concentration cannot be explained by fragmentation and annealing events unless both fragmentation rates and frequency of undetected fragmentation and annealing events are greater than previously thought. The simulations compare well with experimentally measured actin polymerization data and lend additional support to a number of existing theoretical models.     

A theoretical analysis of filament length fluctuations in actin and other polymers

Control of the structure and dynamics of the actin cytoskeleton is essential for cell motility and for maintaining the structural integrity of cells. Central to understanding the control of these features is an understanding of the dynamics of actin filaments, first as isolated filaments, then as integrated networks, and finally as networks containing higher-order structures such as bundles, stress fibers and acto-myosin complexes. It is known experimentally that single filaments can exhibit large fluctuations, but a detailed understanding of the transient dynamics involved is still lacking. Here we first study stochastic models of a general system involving two-monomer types that can be analyzed completely, and then we report stochastic simulations on the complete actin model with three monomer types. We systematically examine the transient behavior of filament length dynamics so as to gain a better understanding of the time scales involved in reaching a steady state. We predict the lifetime of a cap of one monomer type and obtain the mean and variance of the survival time of a cap at the filament end, which together determine the filament length fluctuations.     

Key structural features of the actin filament Arp2/3 complex branch junction revealed by molecular simulation

We investigated the structure, properties and dynamics of the actin filament branch junction formed by actin-related protein (Arp) 2/3 complex using all-atom molecular dynamics (MD) simulations based on a model fit to a reconstruction from electron tomograms. Simulations of the entire structure consisting of 31 protein subunits together with solvent molecules containing ～3 million atoms were performed for an aggregate time of 175 ns. One 75-ns simulation of the original reconstruction was compared to two 50-ns simulations of alternate structures, showing that the hypothesized branch junction structure is very stable. Our simulations revealed that the interface between Arp2/3 complex and the mother actin filament features a large number of salt bridges and hydrophobic contacts, many of which are dynamic and formed/broken on the timescale of the simulation. The simulations suggest that the DNase binding loops in Arp3, and possibly Arp2, form stabilizing contacts with the mother filament. Unbiased comparison of models sampled from the MD simulation trajectory with the primary experimental electron tomography data identified regions were snapshots from the simulation provide atomic details of the model structures and also pinpoints regions where the initial modeling based on the electron tomogram reconstruction may be suboptimal.     

The Effect of Tropomyosin Mutations on Actin-Tropomyosin Binding: In Search of Lost Time

The initial binding of tropomyosin onto actin filaments and then its polymerization into continuous cables on the filament surface must be precisely tuned to overall thin-filament structure, function, and performance. Low-affinity interaction of tropomyosin with actin has to be sufficiently strong to localize the tropomyosin on actin, yet not so tight that regulatory movement on filaments is curtailed. Likewise, head-to-tail association of tropomyosin molecules must be favorable enough to promote tropomyosin cable formation but not so tenacious that polymerization precedes filament binding. Arguably, little molecular detail on early tropomyosin binding steps has been revealed since Wegner’s seminal studies on filament assembly almost 40 years ago. Thus, interpretation of mutation-based actin-tropomyosin binding anomalies leading to cardiomyopathies cannot be described fully. In vitro, tropomyosin binding is masked by explosive tropomyosin polymerization once cable formation is initiated on actin filaments. In contrast, in silico analysis, characterizing molecular dynamics simulations of single wild-type and mutant tropomyosin molecules on F-actin, is not complicated by tropomyosin polymerization at all. In fact, molecular dynamics performed here demonstrates that a midpiece tropomyosin domain is essential for normal actin-tropomyosin interaction and that this interaction is strictly conserved in a number of tropomyosin mutant species. Elsewhere along these mutant molecules, twisting and bending corrupts the tropomyosin superhelices as they “lose their grip” on F-actin. We propose that residual interactions displayed by these mutant tropomyosin structures with actin mimic ones that occur in early stages of thin-filament generation, as if the mutants are recapitulating the assembly process but in reverse. We conclude therefore that an initial binding step in tropomyosin assembly onto actin involves interaction of the essential centrally located domain.     

A Stochastic Tick-Borne Disease Model: Exploring the Probability of Pathogen Persistence

We formulate and analyse a stochastic epidemic model for the transmission dynamics of a tick-borne disease in a single population using a continuous-time Markov chain approach. The stochastic model is based on an existing deterministic metapopulation tick-borne disease model. We compare the disease dynamics of the deterministic and stochastic models in order to determine the effect of randomness in tick-borne disease dynamics. The probability of disease extinction and that of a major outbreak are computed and approximated using the multitype Galton–Watson branching process and numerical simulations, respectively. Analytical and numerical results show some significant differences in model predictions between the stochastic and deterministic models. In particular, we find that a disease outbreak is more likely if the disease is introduced by infected deer as opposed to infected ticks. These insights demonstrate the importance of host movement in the expansion of tick-borne diseases into new geographic areas.     

An Open Model of Actin Dendritic Nucleation

The availability of quantitative experimental data on the kinetics of actin assembly has enabled the construction of many mathematical models focused on explaining specific behaviors of this complex system. However these ad hoc models are generally not reusable or accessible by the large community of actin biologists. In this work, we present a comprehensive model that integrates and unifies much of the in vitro data on the components of the dendritic nucleation mechanism for actin dynamics. More than 300 simulations have been run based on compartmental and three-dimensional spatial versions of this model. Several key findings are highlighted, including an explanation for the sharp boundary between actin assembly and disassembly in the lamellipodia of migrating cells. Because this model, with the simulation results, is “open source”, in the sense that it is publicly available and editable through the Virtual Cell database (http://vcell.org), it can be accessed, analyzed, modified, and extended.     

Structural modeling and molecular dynamics simulation of the actin filament

Actin is a major structural protein of the eukaryotic cytoskeleton and enables cell motility. Here, we present a model of the actin filament (F-actin) that not only incorporates the global structure of the recently published model by Oda et al. but also conserves internal stereochemistry. A comparison is made using molecular dynamics simulation of the model with other recent F-actin models. A number of structural determents such as the protomer propeller angle, the number of hydrogen bonds, and the structural variation among the protomers are analyzed. The MD comparison is found to reflect the evolution in quality of actin models over the last 6 years. In addition, simulations of the model are carried out in states with both ADP or ATP bound and local hydrogen-bonding differences characterized.     

Models for the length distributions of actin filaments: II. Polymerization and fragmentation by gelsolin acting together

In a previous paper, we studied elementary models for polymerization, depolymerization, and fragmentation of actin filaments (Edelstein-Keshet and Ermentrout, 1998, Bull. Math. Biol. 60, 449–475). When these processes act together, more complicated dynamics occur. We concentrate on a particular case study, using the actin-fragmenting protein gelsolin. A set of biological parameter values (drawn from the experimental literature) is used in computer simulations of the kinetics of gelsolin-mediated actin filament fragmentation.