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The well-known phenomenon of phase separation in synthetic polymers and proteins has become a major topic in biophysics because it has been invoked as a mechanism of compartment formation in cells, without the need for membranes. Most of the coacervates (or condensates) are composed of Intrinsically Disordered Proteins (IDPs) or regions that are structureless, often in interaction with RNA and DNA. One of the more intriguing IDPs is the 526-residue RNA-binding protein, Fused in Sarcoma (FUS), whose monomer conformations and condensates exhibit unusual behavior that are sensitive to solution conditions. By focussing principally on the N-terminus low-complexity domain (FUS-LC comprising residues 1-214) and other truncations, we rationalize the findings of solid-state NMR experiments, which show that FUS-LC adopts a non-polymorphic fibril structure (core-1) involving residues 39-95, flanked by fuzzy coats on both the N- and C-terminal ends. An alternate structure (core-2), whose free energy is comparable to core-1, emerges only in the truncated construct (residues 110-214). Both core-1 and core-2 fibrils are stabilized by a Tyrosine ladder as well as hydrophilic interactions. The morphologies (gels, fibrils, and glass-like) adopted by FUS seem to vary greatly, depending on the experimental conditions. The effect of phosphorylation is site-specific. Simulations show that phosphorylation of residues within the fibril has a greater destabilization effect than residues that are outside the fibril region, which accords well with experiments. Many of the peculiarities associated with FUS may also be shared by other IDPs, such as TDP43 and hnRNPA2. We outline a number of problems for which there is no clear molecular explanation., (© 2023 Wiley Periodicals LLC.)

The spike protein of the SARS-CoV-2 virus (the causative agent of COVID-19) recognizes the host cell by binding to the peptidase domain (PD) of the extracellular receptor angiotensin-converting enzyme 2 (ACE2). A variety of carbohydrates could be attached to the six asparagines in the PD, resulting in a heterogeneous population of ACE2 glycoforms. Experiments have shown that the binding affinity of glycosylated and deglycosylated ACE2 to the virus is virtually identical. In most cases, the reduction in glycan size correlates with stronger binding, which suggests that volume exclusion, and hence entropic forces, determine the binding affinity. Here, we quantitatively test the entropy-based hypothesis by developing a lattice model for the complex between ACE2 and the SARS-CoV-2 spike protein receptor-binding domain (RBD). Glycans are treated as branched polymers with only volume exclusion, which we justify using all-atom molecular dynamics simulations in explicit water. We show that the experimentally measured changes in the ACE2-RBD dissociation constants for a variety of engineered ACE2 glycoforms are in reasonable agreement with our theory, thus supporting our hypothesis. However, a quantitative recovery of all the experimental data could require weak attractive interactions., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2023 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

SARS-CoV-2, the virus causing COVID-19, initiates cell invasion by deploying a receptor binding domain (RBD) to recognize the host transmembrane peptidase angiotensin-converting enzyme 2 (ACE2). Numerous experimental and theoretical studies have adopted high-throughput and structure-guided approaches to (i) understand how the RBD recognizes ACE2, (ii) rationalize, and (iii) predict the effect of viral mutations on the binding affinity. Here, we investigate the allosteric signal triggered by the dissociation of the ACE2-RBD complex. To this end, we construct an Elastic Network Model (ENM), and we use the Structural Perturbation Method (SPM). Our key result is that complex dissociation opens the ACE2 substrate-binding cleft located away from the interface and that fluctuations of the ACE2 binding cleft are facilitated by RBD binding. These and other observations provide a structural and dynamical basis for the influence of SARS-CoV-2 on ACE2 enzymatic activity. In addition, we identify a conserved glycine (G502 in SARS-CoV-2) as a key participant in complex disassembly., (© 2023 Author(s). Published under an exclusive license by AIP Publishing.)

Molecular motors, kinesin and myosin, are dimeric consisting of two linked identical monomeric globular proteins. Fueled by the free energy generated by ATP hydrolysis, they walk on polar tracks (microtubule or filamentous actin) processively, which means that only one head detaches and executes a mechanical step while the other stays bound to the track. One motor head must regulate the chemical state of the other, referred to as "gating", a concept that is still not fully understood. Inspired by experiments, showing that only a fraction of the energy from ATP hydrolysis is used to advance the kinesin motors against load, we demonstrate that the rest of the energy is associated with chemical transitions in the two heads. The coordinated chemical transitions involve communication between the two heads - a feature that characterizes gating. We develop a general framework, based on information theory and stochastic thermodynamics, and establish that gating could be quantified in terms of information flow between the motor heads. Applications to kinesin-1 and Myosin V show that information flow, with positive cooperativity, at external resistive loads less than a critical value, F c . When force exceeds F c , effective information flow ceases. Interestingly, F c , which is independent of the input energy generated through ATP hydrolysis, coincides with the force at which the probability of backward steps starts to increase. Our findings suggest that transport efficiency is optimal only at forces less than F c , which implies that these motors must operate at low loads under in vivo conditions.

A substantial increase in the temporal resolution of the stepping of dimeric molecular motors is possible by tracking the position of a large gold nanoparticle (GNP) attached to a labeled site on one of the heads. This technique was employed to measure the stepping trajectories of conventional kinesin (Kin1) using the time-dependent position of the GNP as a proxy. The trajectories revealed that the detached head always passes to the right of the head that is tightly bound to the microtubule (MT) during a step. In interpreting the results of such experiments, it is assumed that the GNP does not significantly alter the diffusive motion of the detached head. We used coarse-grained simulations of a system consisting of the MT-Kin1 complex with and without attached GNP to investigate how the stepping trajectories are affected. The two significant findings are: (1) The GNP does not faithfully track the position of the stepping head, and (2) the rightward bias is typically exaggerated by the GNP. Both these findings depend on the precise residue position to which the GNP is attached. Surprisingly, the stepping trajectories of kinesin are not significantly affected if, in addition to the GNP, a 1 μm diameter cargo is attached to the coiled coil. Our simulations suggest the effects of the large probe have to be considered when inferring the stepping mechanisms using GNP tracking experiments.

Residues spanning distinct regions of the low-complexity domain of the RNA-binding protein, Fused in Sarcoma (FUS-LC), form fibril structures with different core morphologies. Solid-state NMR experiments show that the 214-residue FUS-LC forms a fibril with an S-bend (core-1, residues 39-95), while the rest of the protein is disordered. In contrast, the fibrils of the C-terminal variant (FUS-LC-C; residues 111-214) have a U-bend topology (core-2, residues 112-150). Absence of the U-bend in FUS-LC implies that the two fibril cores do not coexist. Computer simulations show that these perplexing findings could be understood in terms of the population of sparsely populated fibril-like excited states in the monomer. The propensity to form core-1 is higher compared to core-2. We predict that core-2 forms only in truncated variants that do not contain the core-1 sequence. At the monomer level, sequence-dependent enthalpic effects determine the relative stabilities of the core-1 and core-2 topologies.

We present a theoretical method to study how changes in pH shape the heterogeneous conformational ensemble explored by intrinsically disordered proteins (IDPs). The theory is developed in the context of coarse-grained models, which enable a fast, accurate, and extensive exploration of conformational space at a given protonation state. In order to account for pH effects, we generalize the molecular transfer model (MTM), in which conformations are re-weighted using the transfer free energy, which is the free energy necessary for bringing to equilibrium in a new environment a "frozen" conformation of the system. Using the semi-grand ensemble, we derive an exact expression of the transfer free energy, which amounts to the appropriate summation over all the protonation states. Because the exact result is computationally too demanding to be useful for large polyelectrolytes or IDPs, we introduce a mean-field (MF) approximation of the transfer free energy. Using a lattice model, we compare the exact and MF results for the transfer free energy and a variety of observables associated with the model IDP. We find that the precise location of the charged groups (the sequence), and not merely the net charge, determines the structural properties. We demonstrate that some of the limitations previously noted for MF theory in the context of globular proteins are mitigated when disordered polymers are studied. The excellent agreement between the exact and MF results poises us to use the method presented here as a computational tool to study the properties of IDPs and other biological systems as a function of pH.

Molecular motors, such as myosin, kinesin, and dynein, convert the energy released by the hydrolysis of ATP into mechanical work, thus allowing them to undergo directional motion on cytoskeletal tracks. A pivotal step in the chemomechanical transduction in myosin motors occurs after they bind to the actin filament, which triggers the release of phosphate (P i , product of ATP hydrolysis) and the rotation of the lever arm. Here, we investigate the mechanism of phosphate release in myosin VI using extensive molecular dynamics simulations involving multiple trajectories of several μs. Because the escape of phosphate is expected to occur on time-scales on the order of milliseconds or more in myosin VI, we observed P i release only if the trajectories were initiated with a rotated phosphate inside the nucleotide binding pocket. We discovered that although P i populates the traditional "back door" route, phosphate exits through various other gateways, thus establishing the heterogeneity in the escape routes. Remarkably, we observed that the release of phosphate is preceded by a stepwise hydration of the ADP-bound magnesium ion. The release of the anion occurred only after four water molecules hydrated the cation (Mg 2+ ). By performing comparative structural analyses, we show that hydration of magnesium is the key step in the phosphate release in a number of ATPases and GTPases. Nature may have evolved hydration of Mg 2+ as a general molecular switch for P i release, which is a universal step in the catalytic cycle of many machines that share little sequence or structural similarity.

Processive molecular motors enable cargo transportation by assembling into dimers capable of taking several consecutive steps along a cytoskeletal filament. In the well-accepted hand-over-hand stepping mechanism, the trailing motor detaches from the track and binds the filament again in the leading position. This requires fuel consumption in the form of ATP hydrolysis and coordination of the catalytic cycles between the leading and the trailing heads. Alternate stepping pathways also exist, including inchworm-like movements, backward steps, and foot stomps. Whether all the pathways are coupled to ATP hydrolysis remains to be determined. Here, to establish the principles governing the dynamics of processive movement, we present a theoretical framework that includes all of the alternative stepping mechanisms. Our theory bridges the gap between the elemental rates describing the biochemical and structural transitions in each head and the experimentally measurable quantities such as velocity, processivity, and probability of backward stepping. Our results, obtained under the assumption that the track is periodic and infinite, provide expressions that hold regardless of the topology of the network connecting the intermediate states, and are therefore capable of describing the function of any molecular motor. We apply the theory to myosin VI, a motor that takes frequent backward steps and moves forward with a combination of hand-over-hand and inchworm-like steps. Our model quantitatively reproduces various observables of myosin VI motility reported by four experimental groups. The theory is used to predict the gating mechanism, the pathway for backward stepping, and the energy consumption as a function of ATP concentration., (Copyright © 2020 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Colloidal particles, which are ubiquitous, have become ideal testing grounds for the structural glass transition theories. In these systems glassy behavior arises as the density of the particles is increased. Thus, soft colloidal particles with varying degree of softness capture diverse glass-forming properties, observed normally in molecular glasses. Brownian dynamics simulations for a binary mixture of micron-sized charged colloidal suspensions show that tuning the softness of the interaction potential, achievable by changing the monovalent salt concentration results in a continuous transition from fragile to strong behavior. Remarkably, this is found in a system where the well characterized interaction potential between the colloidal particles is isotropic. We also show that the predictions of the random first-order transition (RFOT) theory quantitatively describes the universal features such as the growing correlation length, ξ∼(ϕ_{K}/ϕ-1)^{-ν} with ν=2/3 where ϕ_{K}, the analog of the Kauzmann temperature, depends on the salt concentration. As anticipated by the RFOT predictions, we establish a causal relationship between the growing correlation length and a steep increase in the relaxation time and dynamic heterogeneity as the system is compressed. The broad range of fragility observed in Wigner glasses is used to draw analogies with molecular and polymer glasses. The large variations in the fragility are normally found only when the temperature dependence of the viscosity is examined for a large class of diverse glass-forming materials. In sharp contrast, this is vividly illustrated in a single system that can be experimentally probed. Our work also shows that the RFOT predictions are accurate in describing the dynamics over the entire density range, regardless of the fragility of the glasses.

Conventional kinesin, responsible for directional transport of cellular vesicles, takes multiple nearly uniform 8.2-nm steps by consuming one ATP molecule per step as it walks toward the plus end of the microtubule (MT). Despite decades of intensive experimental and theoretical studies, there are gaps in the elucidation of key steps in the catalytic cycle of kinesin. How the motor waits for ATP to bind to the leading head is controversial. Two experiments using a similar protocol have arrived at different conclusions. One asserts that kinesin waits for ATP in a state with both the heads bound to the MT, whereas the other shows that ATP binds to the leading head after the trailing head detaches. To discriminate between the 2 scenarios, we developed a minimal model, which analytically predicts the outcomes of a number of experimental observable quantities (the distribution of run length, the distribution of velocity [[Formula: see text]], and the randomness parameter) as a function of an external resistive force (F) and ATP concentration ([T]). The differences in the predicted bimodality in [Formula: see text] as a function of F between the 2 models may be amenable to experimental testing. Most importantly, we predict that the F and [T] dependence of the randomness parameters differ qualitatively depending on the waiting states. The randomness parameters as a function of F and [T] can be quantitatively measured from stepping trajectories with very little prejudice in data analysis. Therefore, an accurate measurement of the randomness parameter and the velocity distribution as a function of load and nucleotide concentration could resolve the apparent controversy., Competing Interests: The authors declare no competing interest.

We develop a theory to probe the effect of nonequilibrium fluctuation-induced forces on the size of a polymer confined between two horizontal, thermally conductive plates subject to a constant temperature gradient, ∇ T. We assume that (a) the solvent is good and (b) the distance between the plates is large so that in the absence of a thermal gradient the polymer is a coil, whose size scales with the number of monomers as N ν , with ν ≈ 0.6. We find that above a critical temperature gradient, ∇ T c ≈ N -5/4 , a favorable attractive monomer-monomer interaction due to the giant Casimir force (GCF) overcomes the chain conformational entropy, resulting in a coil-globule transition. Our predictions can be verified using light-scattering experiments with polymers, such as polystyrene or polyisoprene in organic solvents in which the GCF is attractive.

Intrinsically disordered proteins (IDPs) lack well-defined three-dimensional structures, thus challenging the archetypal notion of structure-function relationships. Determining the ensemble of conformations that IDPs explore under physiological conditions is the first step toward understanding their diverse cellular functions. Here, we quantitatively characterize the structural features of IDPs as a function of sequence and length using coarse-grained simulations. For diverse IDP sequences, with the number of residues ( N T ) ranging from 20 to 441, our simulations not only reproduce the radii of gyration ( R g ) obtained from experiments, but also predict the full scattering intensity profiles in excellent agreement with small-angle X-ray scattering experiments. The R g values are well-described by the standard Flory scaling law, R g = R g 0 N T ν , with ν ≈ 0.588, making it tempting to assert that IDPs behave as polymers in a good solvent. However, clustering analysis reveals that the menagerie of structures explored by IDPs is diverse, with the extent of heterogeneity being highly sequence-dependent, even though ensemble-averaged properties, such as the dependence of R g on chain length, may suggest synthetic polymer-like behavior in a good solvent. For example, we show that for the highly charged Prothymosin-α, a substantial fraction of conformations is highly compact. Even if the sequence compositions are similar, as is the case for α-Synuclein and a truncated construct from the Tau protein, there are substantial differences in the conformational heterogeneity. Taken together, these observations imply that metrics based on net charge or related quantities alone cannot be used to anticipate the phases of IDPs, either in isolation or in complex with partner IDPs or RNA. Our work sets the stage for probing the interactions of IDPs with each other, with folded protein domains, or with partner RNAs, which are critical for describing the structures of stress granules and biomolecular condensates with important cellular functions.

Cytoplasmic dynein, whose motor domain belongs to the AAA+ family, walks on microtubules toward the minus end. Using the available structures in different nucleotide states, we performed simulations of a coarse-grained model to elucidate the dynamics of allosteric transitions. Binding of ATP closes the cleft between the AAA1 and AAA2 domains, triggering conformational changes in the rest of the motor domain, thus forming the pre-power stroke state. Interactions with the microtubule, modeled implicitly, enhance ADP release rate, and the formation of the post-power stroke state. The dynamics of the linker (LN), which reversibly changes from a straight to a bent state, is heterogeneous. Persistent interactions between the LN and the insert loops in the AAA2 domain prevent the formation of pre-power stroke state when ATP is bound to AAA3, thus locking dynein in a repressed non-functional state. Application of mechanical force to the LN restores motility in the repressed state., (Copyright © 2018 Elsevier Ltd. All rights reserved.)

Myosin VI (MVI) is the only known member of the myosin superfamily that, upon dimerization, walks processively toward the pointed end of the actin filament. The leading head of the dimer directs the trailing head forward with a power stroke, a conformational change of the motor domain exaggerated by the lever arm. Using a unique coarse-grained model for the power stroke of a single MVI, we provide the molecular basis for its motility. We show that the power stroke occurs in two major steps. First, the motor domain attains the poststroke conformation without directing the lever arm forward; and second, the lever arm reaches the poststroke orientation by undergoing a rotational diffusion. From the analysis of the trajectories, we discover that the potential that directs the rotating lever arm toward the poststroke conformation is almost flat, implying that the lever arm rotation is mostly uncoupled from the motor domain. Because a backward load comparable to the largest interhead tension in a MVI dimer prevents the rotation of the lever arm, our model suggests that the leading-head lever arm of a MVI dimer is uncoupled, in accord with the inference drawn from polarized total internal reflection fluorescence (polTIRF) experiments. Without any adjustable parameter, our simulations lead to quantitative agreement with polTIRF experiments, which validates the structural insights. Finally, in addition to making testable predictions, we also discuss the implications of our model in explaining the broad step-size distribution of the MVI stepping pattern., Competing Interests: The authors declare no conflict of interest.

Ketoreductases (KRs) from modular polyketide synthases (PKSs) can perform stereospecific catalysis, selecting a polyketide with a D- or L-α-methyl substituent for NADPH-mediated reduction. In this report, molecular dynamics (MD) simulations were performed to investigate the interactions that control stereospecificity. We studied the A1-type KR from the second module of the amphotericin PKS (A1), which is known to be stereospecific for a D-α-methyl-substituted diketide substrate (dkD). MD simulations of two ternary complexes comprised of the enzyme, NADPH, and either the correct substrate, dkD, or its enantiomer (dkL) were performed. The coordinates for the A1/NADPH binary complex were obtained from a crystal structure (PDB entry 3MJS), and substrates were modeled in the binding pocket in conformations appropriate for reduction. Simulations were intended to reproduce the initial weak binding of the polyketide substrate to the enzyme. Long (tens of nanoseconds) MD simulations show that the correct substrate is retained in a conformation closer to the reactive configuration. Many short (up to a nanosecond) MD runs starting from the initial structures display evidence that Q364, three residues N-terminal to the catalytic tyrosine, forms a hydrogen bond to the incorrect dkL substrate to yield an unreactive conformation that is more favorable than the reactive configuration. This interaction is not as strong for dkD, as the D-α-methyl substituent is positioned between the glutamine and the reactive site. This result correlates with experimental findings [Zheng, J., et al. (2010) Structure 18, 913-922] in which a Q364H mutant was observed to lose stereospecificity.

A technology for optimization of potential parameters from condensed-phase simulations (POP) is discussed and illustrated. It is based on direct calculations of the derivatives of macroscopic observables with respect to the potential parameters. The derivatives are used in a local minimization scheme, comparing simulated and experimental data. In particular, we show that the Newton trust region protocol allows for more accurate and robust optimization. We apply the newly developed technology to study the liquid mixture of tert-butanol and water. We are able to obtain, after four iterations, the correct phase behavior and accurately predict the value of the Kirkwood Buff (KB) integrals. We further illustrate that a potential that is determined solely by KB information, or the pair correlation function, is not necessarily unique.

We propose an algorithm to extract the diffusion tensor from Molecular Dynamics simulations with Milestoning. A Kramers-Moyal expansion of a discrete master equation, which is the Markovian limit of the Milestoning theory, determines the diffusion tensor. To test the algorithm, we analyze overdamped Langevin trajectories and recover a multidimensional Fokker-Planck equation. The recovery process determines the flux through a mesh and estimates local kinetic parameters. Rate coefficients are converted to the derivatives of the potential of mean force and to coordinate dependent diffusion tensor. We illustrate the computation on simple models and on an atomically detailed system-the diffusion along the backbone torsions of a solvated alanine dipeptide.

The efficiency and accuracy of thermodynamic cycle calculations are considered. It is rigorously shown that the energy of the mutated part (MP) need not be scaled in a thermodynamic cycle computed with dual topology. Hence, there is no need to scale to zero any of the self-interactions (i.e. the interactions involving only particles of the same MP) regardless of whether the MP is bound or not to the main system. This observation carries a promise to lower computational resources and increase accuracy. A numerical test of a complete thermodynamic cycle illustrates cost and accuracy considerations.

We present a method based on dynamical nonequilibrium molecular dynamics (D-NEMD) that allows one to produce rigorous ensemble averages for the transient regimes. We illustrate the method by describing the formation of convective cells within a two-dimensional fluid system of soft disks in which a gravity field and a thermal gradient are present. We analyze two different physical settings, with the thermal gradient orthogonal or parallel to the gravity field. In both settings, we follow the formation of the convective flows from the initial time, when the perturbation is turned on, to the steady state. In the first setting (orthogonal fields) we investigate several different cases, varying the initial stationary ensemble and the perturbing field. We find that the final steady-state convective cell is independent of the specific sequence of perturbation fields, which only affects the transient behavior. In all cases, we find that the convective roll is formed through a sequence of damped oscillations of the local fields (density, temperature, and velocity), superimposed to an overall relaxation toward the local steady-state values. Then, we show how D-NEMD can be applied to the Rayleigh-Bénard (RB) setting (parallel fields). In these conditions, the convective flow only establishes above a threshold, without a preferred verse of rotation. We analyze only the response to the ignition of the gravity field in a stationary system under the action of a vertical thermal gradient. Also in this case we characterize the transient response by following the evolution of the density, temperature, and velocity fields until the steady-state RB convective cell is formed. The observed transients are similar to those observed in the case of orthogonal fields. However, the final steady states are quite different. Finally, we briefly discuss the conditions for the general applicability of the D-NEMD method.