Nucleotide regulation of the structure and dynamics of G-actin

Quantifying Unbiased Conformational Ensembles from Biased Simulations Using ShapeGMM

Quantifying the conformational ensembles of biomolecules is fundamental to describing mechanisms of processes such as protein folding, interconversion between folded states, ligand binding, and allosteric regulation. Accurate quantification of these ensembles remains a challenge for conventional molecular simulations of all but the simplest molecules due to insufficient sampling. Enhanced sampling approaches, such as metadynamics, were designed to overcome this challenge; however, the nonuniform frame weights that result from many of these approaches present an additional challenge to ensemble quantification techniques such as Markov State Modeling or structural clustering. Here, we present rigorous inclusion of nonuniform frame weights into a structural clustering method entitled shapeGMM. The result of frame-weighted shapeGMM is a high dimensional probability density and generative model for the unbiased system from which we can compute important thermodynamic properties such as relative free energies and configurational entropy. The accuracy of this approach is demonstrated by the quantitative agreement between GMMs computed by Hamiltonian reweighting and direct simulation of a coarse-grained helix model system. Furthermore, the relative free energy computed from a shapeGMM probability density of alanine dipeptide reweighted from a metadynamics simulation quantitatively reproduces the underlying free energy in the basins. Finally, the method identifies hidden structures along the actin globular to filamentous-like structural transition from a metadynamics simulation on a linear discriminant analysis coordinate trained on GMM states, illustrating how structural clustering of biased data can lead to biophysical insight. Combined, these results demonstrate that frame-weighted shapeGMM is a powerful approach to quantifying biomolecular ensembles from biased simulations.

Comparative study of aluminum speciation on brain-type creatine kinase: Enzyme kinetic, molecular docking, cellular experiment, and mouse model study

Brain-type Creatine kinase (CK-BB), which has a high affinity for Aluminum (Al), and its abnormality is closely related to neurodegenerative diseases. In this study, the comparative effect of Al speciation on the bioactivity of CK-BB has been studied by the inhibition kinetics method, molecular docking, cellular experiment, and mouse model study. Results showed that the half-inhibitory concentration of AlCl₃ was 0.67 mM, while Al(mal)₃ was 3.81 mM. Fluorescence spectra showed that Al(mal)₃ had a more substantial effect on the endogenous fluorescence of CK-BB than AlCl₃. Molecular docking showed that AlCl₃ was closer to the active site of CK-BB. C6 cells were used to explore the enzyme activity and intracellular distribution of CK-BB by AlCl₃ or Al(mal)₃. AlCl₃ treatment may directly affect CK-BB activity and cause insufficient local ATP supply in cells which affected the formation of F-actin and cell morphology. The change in the hydrophobicity of CK-BB induced by Al(mal)₃ affected the movement of CK-BB, which subsequently activated thecytochrome C (Cyt C)/Caspase 9/Caspase 3 pathway. Similar results have been found in vivo experiments. This study demonstrated that interaction between Al and CK-BB might be related to the process of Al-induced energy metabolism disorders, in which the Al speciation revealed differentiated toxicity mechanisms.

Compressive and Tensile Deformations Alter ATP Hydrolysis and Phosphate Release Rates in Actin Filaments

Actin filament networks in eukaryotic cells are constantly remodeled through nucleotide state controlled interactions with actin binding proteins, leading to macroscopic structures such as bundled filaments, branched filaments, and so on. The nucleotide (ATP) hydrolysis, phosphate release, and polymerization/depolymerization reactions that lead to the formation of these structures are correlated with the conformational fluctuations of the actin subunits at the molecular scale. The resulting structures generate and experience varying levels of force and impart cells with several functionalities such as their ability to move, divide, transport cargo, etc. Models that explicitly connect the structure to reactions are essential to elucidate a fundamental level of understanding of these processes. In this regard, a bottom-up Ultra-Coarse-Grained (UCG) model of actin filaments that can simulate ATP hydrolysis, inorganic phosphate release (Pi), and depolymerization reactions is presented in this work. In this model, actin subunits are represented using coarse-grained particles that evolve in time and undergo reactions depending on the conformations sampled. The reactions are represented through state transitions, with each state represented by a unique effective coarse-grained potential. Effects of compressive and tensile strains on the rates of reactions are then analyzed. Compressive strains tend to unflatten the actin subunits, reduce the rate of ATP hydrolysis, and increase the Pi release rate. On the other hand, tensile strain flattens subunits, increases the rate of ATP hydrolysis, and decrease the Pi release rate. Incorporating these predictions into a Markov State Model highlighted that strains alter the steady-state distribution of subunits with ADPPi and ADP nucleotide, thus identifying possible additional factors underlying the cooperative binding of regulatory proteins to actin filaments.

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.

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.

Foundations for a Realism-Based Ontology of Protein Aggregates

The objective of this paper is to propose formal definitions for the terms 'protein aggregate' and 'protein-containing complex' such that the descriptions and usages of these terms in biomedical literature are unified and that those portions of reality are correctly represented. To this end, we surveyed the literature to assess the need for a distinction between these entities, then compared the features of usages and definitions found in the literature to the definitions for those terms found in Bioportal ontologies. Based on the results of this comparison, we propose updated definitions for the terms 'protein aggregate' and 'protein-containing complex'. Thus far, we propose the following distinguishing factors: first, that one important difference lies in whether an entity is disposed to change type in response to certain structural alterations, such as dissociation of a continuant part, and second that an important difference lies in the ability of the entity to realize its function after such an event occurs. These distinctions are reflected in the proposed definitions.

D-loop Dynamics and Near-Atomic-Resolution Cryo-EM Structure of Phalloidin-Bound F-Actin

Detailed molecular information on G-actin assembly into filaments (F-actin), and their structure, dynamics, and interactions, is essential for understanding their cellular functions. Previous studies indicate that a flexible DNase I binding loop (D-loop, residues 40-50) plays a major role in actin's conformational dynamics. Phalloidin, a "gold standard" for actin filament staining, stabilizes them and affects the D-loop. Using disulfide crosslinking in yeast actin D-loop mutant Q41C/V45C, light-scattering measurements, and cryoelectron microscopy reconstructions, we probed the constraints of D-loop dynamics and its contribution to F-actin formation/stability. Our data support a model of residues 41-45 distances that facilitate G- to F-actin transition. We report also a 3.3-Å resolution structure of phalloidin-bound F-actin in the ADP-Pi-like (ADP-BeFx) state. This shows the phalloidin-binding site on F-actin and how the relative movement between its two protofilaments is restricted by it. Together, our results provide molecular details of F-actin structure and D-loop dynamics.

Structural Effects and Functional Implications of Phalloidin and Jasplakinolide Binding to Actin Filaments

Actin undergoes structural transitions during polymerization, ATP hydrolysis, and subsequent release of inorganic phosphate. Several actin-binding proteins sense specific states during this transition and can thus target different regions of the actin filament. Here, we show in atomic detail that phalloidin, a mushroom toxin that is routinely used to stabilize and label actin filaments, suspends the structural changes in actin, likely influencing its interaction with actin-binding proteins. Furthermore, high-resolution cryoelectron microscopy structures reveal structural rearrangements in F-actin upon inorganic phosphate release in phalloidin-stabilized filaments. We find that the effect of the sponge toxin jasplakinolide differs from the one of phalloidin, despite their overlapping binding site and similar interactions with the actin filament. Analysis of structural conformations of F-actin suggests that stabilizing agents trap states within the natural conformational space of actin.

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.

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 basis for cofilin binding and actin filament disassembly

Actin depolymerizing factor (ADF) and cofilin accelerate actin dynamics by severing and disassembling actin filaments. Here, we present the 3.8 Å resolution cryo-EM structure of cofilactin (cofilin-decorated actin filament). The actin subunit structure of cofilactin (C-form) is distinct from those of F-actin (F-form) and monomeric actin (G-form). During the transition between these three conformations, the inner domain of actin (subdomains 3 and 4) and the majority of subdomain 1 move as two separate rigid bodies. The cofilin–actin interface consists of three distinct parts. Based on the rigid body movements of actin and the three cofilin–actin interfaces, we propose models for the cooperative binding of cofilin to actin, preferential binding of cofilin to ADP-bound actin filaments and cofilin-mediated severing of actin filaments.

Cofilin is a small actin-binding protein that accelerates actin turnover by disassembling actin filaments. Here the authors present the 3.8 Å cryo-EM structure of a cofilin-decorated actin filament and discuss mechanistic implications.

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.

Characterization of the flexibility of the peripheral stalk of prokaryotic rotary A-ATPases by atomistic simulations

Rotary ATPases are involved in numerous physiological processes, with the three distinct types (F/A/V‐ATPases) sharing functional properties and structural features. The basic mechanism involves the counter rotation of two motors, a soluble ATP hydrolyzing/synthesizing domain and a membrane‐embedded ion pump connected through a central rotor axle and a stator complex. Within the A/V‐ATPase family conformational flexibility of the EG stators has been shown to accommodate catalytic cycling and is considered to be important to function. For the A‐ATPase three EG structures have been reported, thought to represent conformational states of the stator during different stages of rotary catalysis. Here we use long, detailed atomistic simulations to show that those structures are conformers explored through thermal fluctuations, but do not represent highly populated states of the EG stator in solution. We show that the coiled coil tail domain has a high persistence length (∼100 nm), but retains the ability to adapt to different conformational states through the presence of two hinge regions. Moreover, the stator network of the related V‐ATPase has been suggested to adapt to subunit interactions in the collar region in addition to the nucleotide occupancy of the catalytic domain. The MD simulations reported here, reinforce this observation showing that the EG stators have enough flexibility to adapt to significantly different structural re‐arrangements and accommodate structural changes in the catalytic domain whilst resisting the large torque generated by catalytic cycling. These results are important to understand the role the stators play in the rotary‐ATPase mechanism. Proteins 2016; 84:1203–1212. © 2016 The Authors. Proteins: Structure, Function, and Bioinformatics Published by Wiley Periodicals, Inc.

Exploring Valleys without Climbing Every Peak: More Efficient and Forgiving Metabasin Metadynamics via Robust On-the-Fly Bias Domain Restriction

Metadynamics is an enhanced sampling method designed to flatten free energy surfaces uniformly. However, the highest-energy regions are often irrelevant to study and dangerous to explore because systems often change irreversibly in unforeseen ways in response to driving forces in these regions, spoiling the sampling. Introducing an on-the-fly domain restriction allows metadynamics to flatten only up to a specified energy level and no further, improving efficiency and safety while decreasing the pressure on practitioners to design collective variables that are robust to otherwise irrelevant high energy driving. This paper describes a new method that achieves this using sequential on-the-fly estimation of energy wells and redefinition of the metadynamics hill shape, termed metabasin metadynamics. The energy level may be defined a priori or relative to unknown barrier energies estimated on-the-fly. Altering only the hill ensures that the method is compatible with many other advances in metadynamics methodology. The hill shape has a natural interpretation in terms of multiscale dynamics, and the computational overhead in simulation is minimal when studying systems of any reasonable size, for instance proteins or other macromolecules. Three example applications show that the formula is accurate and robust to complex dynamics, making metadynamics significantly more forgiving with respect to CV quality and thus more feasible to apply to the most challenging biomolecular systems.