Structure and membrane remodeling activity of ESCRT-III helical polymers.

The endosomal sorting complexes required for transport (ESCRT) proteins mediate fundamental membrane remodeling events that require stabilizing negative membrane curvature. These include endosomal intralumenal vesicle formation, HIV budding, nuclear envelope closure, and cytokinetic abscission. ESCRT-III subunits perform key roles in these processes by changing conformation and polymerizing into membrane-remodeling filaments. Here, we report the 4 angstrom resolution cryogenic electron microscopy reconstruction of a one-start, double-stranded helical copolymer composed of two different human ESCRT-III subunits, charged multivesicular body protein 1B (CHMP1B) and increased sodium tolerance 1 (IST1). The inner strand comprises "open" CHMP1B subunits that interlock in an elaborate domain-swapped architecture and is encircled by an outer strand of "closed" IST1 subunits. Unlike other ESCRT-III proteins, CHMP1B and IST1 polymers form external coats on positively curved membranes in vitro and in vivo. Our analysis suggests how common ESCRT-III filament architectures could stabilize different degrees and directions of membrane curvature.

Unraveling the mystery of ATP hydrolysis in actin filaments.

Actin performs its myriad cellular functions by the growth and disassembly of its filamentous form. The hydrolysis of ATP in the actin filament has been shown to modulate properties of the filament, thus making it a pivotal regulator of the actin life cycle. Actin has evolved to selectively hydrolyze ATP in the filamentous form, F-actin, with an experimentally observed rate increase over the monomeric form, G-actin, of 4.3 × 10(4). The cause of this dramatic increase in rate is investigated in this paper using extensive QM/MM simulations of both G- and F-actin. To compute the free energy of hydrolysis in both systems, metadynamics is employed along two collective variables chosen to describe the reaction coordinates of hydrolysis. F-actin is modeled as a monomer with restraints applied to coarse-grained variables enforced to keep it in a filament-like conformation. The simulations reveal a barrier height reduction for ATP hydrolysis in F-actin as compared to G-actin of 8 ± 1 kcal/mol, in good agreement with the experimentally measured barrier height reduction of 7 ± 1 kcal/mol. The barrier height reduction is influenced by an enhanced rotational diffusion of water in F-actin as compared to G-actin and shorter water wires between Asp154 and the nucleophilic water in F-actin, leading to more rapid proton transport.

Using multiscale preconditioning to accelerate the convergence of iterative molecular calculations.

Iterative procedures for optimizing properties of molecular models often converge slowly owing to the computational cost of accurately representing features of interest. Here, we introduce a preconditioning scheme that allows one to use a less expensive model to guide exploration of the energy landscape of a more expensive model and thus speed the discovery of locally stable states of the latter. We illustrate our approach in the contexts of energy minimization and the string method for finding transition pathways. The relation of the method to other multilevel simulation techniques and possible extensions are discussed.

Nucleotide regulation of the structure and dynamics of G-actin.

Actin, a highly conserved cytoskeletal protein found in all eukaryotic cells, facilitates cell motility and membrane remodeling via a directional polymerization cycle referred to as treadmilling. The nucleotide bound at the core of each actin subunit regulates this process. Although the biochemical kinetics of treadmilling has been well characterized, the atomistic details of how the nucleotide affects polymerization remain to be definitively determined. There is increasing evidence that the nucleotide regulation (and other characteristics) of actin cannot be fully described from the minimum energy structure, but rather depends on a dynamic equilibrium between conformations. In this work we explore the conformational mobility of the actin monomer (G-actin) in a coarse-grained subspace using umbrella sampling to bias all-atom molecular-dynamics simulations along the variables of interest. The results reveal that ADP-bound actin subunits are more conformationally mobile than ATP-bound subunits. We used a multiscale analysis method involving coarse-grained and atomistic representations of these simulations to characterize how the nucleotide affects the low-energy states of these systems. The interface between subdomains SD2-SD4, which is important for polymerization, is stabilized in an actin filament-like (F-actin) conformation in ATP-bound G-actin. Additionally, the nucleotide modulates the conformation of the SD1-SD3 interface, a region involved in the binding of several actin-binding proteins.

Minimizing memory as an objective for coarse-graining.

Coarse-graining a molecular model is the process of integrating over degrees of freedom to obtain a reduced representation. This process typically involves two separate but related steps, selection of the coordinates comprising the reduced system and modeling their interactions. Both the coordinate selection and the modeling procedure present challenges. Here, we focus on the former. Typically, one seeks to integrate over the fast degrees of freedom and retain the slow degrees of freedom. Failure to separate timescales results in memory. With this motivation, we introduce a heuristic measure of memory and show that it can be used to compare competing coordinate selections for a given modeling procedure. We numerically explore the utility of this heuristic for three systems of increasing complexity. The first example is a four-particle linear model, which is exactly solvable. The second example is a sixteen-particle nonlinear model; this system has interactions that are characteristic of molecular force fields but is still sufficiently simple to permit exhaustive numerical treatment. The third example is an atomic-resolution representation of a protein, the class of models most often treated by relevant coarse-graining approaches; we specifically study an actin monomer. In all three cases, we find that the heuristic suggests coordinate selections that are physically intuitive and reflect molecular structure. The memory heuristic can thus serve as an objective codification of expert knowledge and a guide to sites within a model that requires further attention.

Coarse-graining methods for computational biology.

Connecting the molecular world to biology requires understanding how molecular-scale dynamics propagate upward in scale to define the function of biological structures. To address this challenge, multiscale approaches, including coarse-graining methods, become necessary. We discuss here the theoretical underpinnings and history of coarse-graining and summarize the state of the field, organizing key methodologies based on an emerging paradigm for multiscale theory and modeling of biomolecular systems. This framework involves an integrated, iterative approach to couple information from different scales. The primary steps, which coincide with key areas of method development, include developing first-pass coarse-grained models guided by experimental results, performing numerous large-scale coarse-grained simulations, identifying important interactions that drive emergent behaviors, and finally reconnecting to the molecular scale by performing all-atom molecular dynamics simulations guided by the coarse-grained results. The coarse-grained modeling can then be extended and refined, with the entire loop repeated iteratively if necessary.

Molecular origins of cofilin-linked changes in actin filament mechanics.

The actin regulatory protein cofilin plays a central role in actin assembly dynamics by severing filaments and increasing the concentration of ends from which subunits add and dissociate. Cofilin binding modifies the average structure and mechanical properties of actin filaments, thereby promoting fragmentation of partially decorated filaments at boundaries of bare and cofilin-decorated segments. Despite extensive evidence for cofilin-dependent changes in filament structure and mechanics, it is unclear how the two processes are linked at the molecular level. Here, we use molecular dynamics simulations and coarse-grained analyses to evaluate the molecular origins of the changes in filament compliance due to cofilin binding. Filament subunits with bound cofilin are less flat and maintain a significantly more open nucleotide cleft than bare filament subunits. Decorated filament segments are less twisted, thinner (considering only actin), and less connected than their bare counterparts, which lowers the filament bending persistence length and torsional stiffness. Using coarse-graining as an analysis method reveals that cofilin binding increases the average distance between the adjacent long-axis filament subunit, thereby weakening their interaction. In contrast, a fraction of lateral filament subunit contacts are closer and presumably stronger with cofilin binding. A cofilactin interface contact identified by cryo-electron microscopy is unstable during simulations carried out at 310K, suggesting that this particular interaction may be short lived at ambient temperatures. These results reveal the molecular origins of cofilin-dependent changes in actin filament mechanics that may promote filament severing.

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.

Comparison between actin filament models: coarse-graining reveals essential differences.

The interconversion of actin between monomeric and polymeric forms is a fundamental process in cell biology that is incompletely understood, in part because there is no high-resolution structure for filamentous actin. Several models have been proposed recently; identifying structural and dynamic differences between them is an essential step toward understanding actin dynamics. We compare three of these models, using coarse-grained analysis of molecular dynamics simulations to analyze the differences between them and evaluate their relative stability. Based on this analysis, we identify key motions that may be associated with polymerization, including a potential energetic barrier in the process. We also find that actin subunits are polymorphic; during simulations they assume a range of configurations remarkably similar to those seen in recent cryoEM images.

Optimal number of coarse-grained sites in different components of large biomolecular complexes.

The computational study of large biomolecular complexes (molecular machines, cytoskeletal filaments, etc.) is a formidable challenge facing computational biophysics and biology. To achieve biologically relevant length and time scales, coarse-grained (CG) models of such complexes usually must be built and employed. One of the important early stages in this approach is to determine an optimal number of CG sites in different constituents of a complex. This work presents a systematic approach to this problem. First, a universal scaling law is derived and numerically corroborated for the intensity of the intrasite (intradomain) thermal fluctuations as a function of the number of CG sites. Second, this result is used for derivation of the criterion for the optimal number of CG sites in different parts of a large multibiomolecule complex. In the zeroth-order approximation, this approach validates the empirical rule of taking one CG site per fixed number of atoms or residues in each biomolecule, previously widely used for smaller systems (e.g., individual biomolecules). The first-order corrections to this rule are derived and numerically checked by the case studies of the Escherichia coli ribosome and Arp2/3 actin filament junction. In different ribosomal proteins, the optimal number of amino acids per CG site is shown to differ by a factor of 3.5, and an even wider spread may exist in other large biomolecular complexes. Therefore, the method proposed in this paper is valuable for the optimal construction of CG models of such complexes.

Coarse-graining of multiprotein assemblies.

Multiscale models are important tools to elucidate how small changes in local subunit conformations may propagate to affect the properties of macromolecular complexes. We review recent advances in coarse-graining methods for poly-protein assemblies, systems that are composed of many copies of relatively few components, with a particular focus on viral capsids and cytoskeletal filaments. These methods are grouped into two broad categories-mapping methods, which use information from one scale of representation to parameterize a lower resolution model, and bridging methods, which repeatedly connect different scales during simulation-and we provide examples of both classes at different levels of complexity. Collectively, these models illustrate the numerous approaches to information transfer between scales and demonstrate that the complexity required of the model depends in general on the nature of the information sought.

Water molecules in the nucleotide binding cleft of actin: effects on subunit conformation and implications for ATP hydrolysis.

In the monomeric actin crystal structure, the positions of a highly organized network of waters are clearly visible within the active site. However, the recently proposed models of filamentous actin (F-actin) did not extend to including these waters. Since the water network is important for ATP hydrolysis, information about water position is critical to understanding the increased rate of catalysis upon filament formation. Here, we show that waters in the active site are essential for intersubdomain rotational flexibility and that they organize the active-site structure. Including the crystal structure waters during simulation setup allows us to observe distinct changes in the active-site structure upon the flattening of the actin subunit, as proposed in the Oda model for F-actin. We identify changes in both protein position and water position relative to the phosphate tail that suggest a mechanism for accelerating the rate of nucleotide hydrolysis in F-actin by stabilizing charge on the ß-phosphate and by facilitating deprotonation of catalytic water.

Origins of enhanced proton transport in the Y7F mutant of human carbonic anhydrase II.

Human carbonic anhydrase II (HCA II), among the fastest enzymes known, catalyzes the reversible hydration of CO 2 to HCO 3 (-). The rate-limiting step of this reaction is believed to be the formation of an intramolecular water wire and transfer of a proton across the active site cavity from a zinc-bound solvent to a proton shuttling residue (His64). X-ray crystallographic studies have shown this intramolecular water wire to be directly stabilized through hydrogen bonds via a small well-defined set of amino acids, namely, Tyr7, Asn62, Asn67, Thr199, and Thr200. Furthermore, X-ray crystallographic and kinetic studies have shown that the mutation of tyrosine 7 to phenylalanine, Y7F HCA II, has the effect of increasing the proton transfer rate by 7-fold in the dehydration direction of the enzyme reaction compared to wild-type (WT). This increase in the proton transfer rate is postulated to be linked to the formation of a more directional, less branched, water wire. To evaluate this proposal, molecular dynamics simulations have been employed to study water wire formation in both the WT and Y7F HCA II mutant. These studies reveal that the Y7F mutant enhances the probability of forming small water wires and significantly extends the water wire lifetime, which may account for the elevated proton transfer seen in the Y7F mutant. Correlation analysis of the enzyme and intramolecular water wire indicates that the Y7F mutant significantly alters the interaction of the active site waters with the enzyme while occupancy data of the water oxygens reveals that the Y7F mutant stabilizes the intramolecular water wire in a manner that maximizes smaller water wire formation. This increase in the number of smaller water wires is likely to elevate the catalytic turnover of an already very efficient enzyme.