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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.)

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.

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.)

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.

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.

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.