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The preponderance of Intrinsically Disordered Proteins (IDPs) in the eukaryotic proteome, and their ability to interact with each other, proteins, RNA, and DNA for functional purposes have made it important to quantitatively characterize their biophysical properties. Towards this end, we developed the transferable Self-Organized Polymer (SOP-IDP) model in order to calculate the properties of a number of IDPs. The calculated and measured radius of gyration values (Rgs) are in excellent agreement, with a correlation coefficient of 0.96. For AP180 and Epsin, the predicted and values obtained using Fluorescence Correlation Spectroscopy for the hydrodynamic radii (Rhs) are also in quantitative agreement. Strikingly, the calculated SAXS profiles for thirty six IDPs also nearly match the experiments. The dependence ofRg, the mean end-to-end distance (Re), andRhobey the Flory scaling law,Rα≈aαN0.59(α=g, e, andh), suggesting that globally IDPs behave as polymers in a good solvent. The values ofag,ae, andahare 0.21 nm, 0.53 nm, and 0.16 nm, respectively. Surprisingly, finite size corrections to scaling, expected on theoretical grounds, for all the three quantities are negligible. Sequence dependencies, masked in ensemble properties, emerge through a fine structure analyses of the conformational ensembles using a hierarchical clustering method. Typically, the ensemble of conformations partition into three distinct clusters, with differing extent of population and structural properties. The subpopulations could dictate phase separation tendencies and association with ligands. Without any adjustments to the three parameters in the SOP-IDP model, we obtained excellent agreement with paramagnetic relaxation enhancement (PRE) measurements forα-synuclein. The transferable SOP-IDP model sets the stage for a number of promising applications, including the study of phase separation in IDPs and interactions with nucleic acids.

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.

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. 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) has 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.TOC graphic

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 Nν, with ν ≈ 0.6. We find that above a critical temperature gradient, ∇ Tc ≈ 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.

The beautiful structures of single- and multi-domain proteins are clearly ordered in some fashion but cannot be readily classified using group theory methods that are successfully used to describe periodic crystals. For this reason, protein structures are considered to be aperiodic, and may have evolved this way for functional purposes, especially in instances that require a combination of softness and rigidity within the same molecule. By analyzing the solved protein structures, we show that orientational symmetry is broken in the aperiodic arrangement of the secondary structure elements (SSEs), which we deduce by calculating the nematic order parameter, P2. We find that the folded structures are nematic droplets with a broad distribution of P2. We argue that a non-zero value of P2, leads to an arrangement of the SSEs that can resist external forces, which is a requirement for allosteric proteins. Such proteins, which resist mechanical forces in some regions while being flexible in others, transmit signals from one region of the protein to another (action at a distance) in response to binding of ligands (oxygen, ATP, or other small molecules).

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.

Severe acute respiratory syndrome (SARS) and novel coronavirus disease (COVID-19) are caused by two closely related beta-coronaviruses, SARS-CoV and SARS-CoV-2, respectively. The envelopes surrounding these viruses are decorated with spike proteins, whose receptor binding domains (RBDs) initiate invasion by binding to the human angiotensin-converting enzyme 2 (ACE2). Subtle changes at the interface with ACE2 seem to be responsible for the enhanced affinity for the receptor of the SARS-CoV-2 RBD compared to SARS-CoV RBD. Here, we use Elastic Network Models (ENMs) to study the response of the viral RBDs and ACE2 upon dissassembly of the complexes. We identify a dominant detachment mode, in which the RBD rotates away from the surface of ACE2, while the receptor undergoes a conformational transition which stretches the active-site cleft. Using the Structural Perturbation Method, we determine the network of residues, referred to as the Allostery Wiring Diagram (AWD), which drives the large-scale motion activated by the detachment of the complex. The AWD for SARS-CoV and SARS-CoV-2 are remarkably similar, showing a network that spans the interface of the complex and reaches the active site of ACE2, thus establishing an allosteric connection between RBD binding and receptor catalytic function. Informed in part by the AWD, we used Molecular Dynamics simulations to probe the effect of interfacial mutations in which SARS-CoV-2 residues are replaced by their SARS-CoV counterparts. We focused on a conserved glycine (G502 in SARS-CoV-2, G488 in SARS-CoV) because it belongs to a region that initiates the dissociation of the complex along the dominant detachment mode, and is prominent in the AWD. Molecular Dynamics simulations of SARS-CoV-2 wild-type and G502P mutant show that the affinity for the human receptor of the mutant is drastically diminished. Our results suggest that in addition to residues that are in direct contact with the interface those involved in long range allosteric communication are also a determinant of the stability of the RBD-ACE2 complex.

Substantial increase in the temporal resolution of the stepping of dimeric molec- ular 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 used 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 implicitly 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. (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, we predict that 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.

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 ([Formula: see text]) and ATP concentration ([T]). The differences in the predicted bimodality in [Formula: see text] as a function of [Formula: see text] between the 2 models may be amenable to experimental testing. Most importantly, we predict that the [Formula: see text] and [T] dependence of the randomness parameters differ qualitatively depending on the waiting states. The randomness parameters as a function of [Formula: see text] 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.

Molecular motors, such as myosin, kinesin, and dynein, convert the energy released by the hydrolysis of ATP into mechanical work, which allows them to undergo directional motion on cytoskeletal tracks. This process is achieved through synchronization between the catalytic activity of the motor and the associated changes in its conformation. A pivotal step in the chemomechanical transduction in myosin motors occurs after they bind to the actin filament, which triggers the release of phosphate (Pi, product of ATP hydrolysis) and the rotation of the lever arm. Here, we investigate the mechanism of phosphate release in myosin VI, which has been debated for over two decades, using extensive molecular dynamics simulations involving multiple trajectories each severalμslong. Because the escape of phosphate is expected to occur on time-scales on the order of milliseconds in myosin VI, we observed Pirelease only if the trajectories were initiated with a rotated phosphate inside the nucleotide binding pocket. The rotation provided the needed perturbation that enabled successful expulsions of Piin several trajectories. Analyses of these trajectories lead to a robust mechanism of Pirelease in the class of motors belonging to the myosin super family. We discovered that although Pipopulates the traditional “back door” route, phosphate exits through various other gateways, thus establishing the heterogeneity in the escape routes. Remarkably, we observe that the release of phosphate is preceded by a step-wise hydration of the ADP-bound magnesium ion. In particular, the release of the anion occurredonly after four water moleculeshydrate the cation (Mg2+). By performing comparative structural analyses, we suggest that the hydration of magnesium is the key step in the phosphate release in a number of ATPases and GTPases that share a similar structure in the nucleotide binding pocket. Thus, nature may have evolved hydration of Mg2+by discrete water molecules as a general molecular switch for Pirelease, which is a universal step in the catalytic cycle of many machines which share little sequence or structural similarity.

Colloidal particles, which are ubiquitous, have become ideal testing grounds for the structural glass transition (SGT) theories. In these systems glassy behavior is manifested 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. By performing Brownian dynamics simulations for a binary mixture of micron-sized charged colloidal suspensions, known to form Wigner glasses, we show that by tuning the softness of the potential, achievable by changing the monovalent salt concentration, there is a continuous transition between fragile to strong behavior. Remarkably, this is found in a system where the well characterized 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, $\xi\sim (\phi_K/\phi - 1)^{-\nu}$ with $\nu = 2/3$ where $\phi_K$, the analogue 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. The broad range of fragility observed in Wigner glasses is used to draw analogies with molecular glasses. The large variations in the fragility is 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, implying that the physics describing the SGT is universal.

Many biological functions are executed by molecular machines, which consume energy and convert it into mechanical work. Biological machines have evolved to transport cargo, facilitate folding of proteins and RNA, remodel chromatin and replicate DNA. A common aspect of these machines is that their functions are driven out of equilibrium. It is a challenge to provide a general framework for understanding the functions of biological machines, such as molecular motors, molecular chaperones, and helicases. Using these machines as prototypical examples, we describe a few general theoretical methods providing insights into their functions. Although the theories rely on coarse-graining of these complex systems they have proven useful in not only accounting for many in vitro experiments but also addressing questions such as how the trade-off between precision, energetic costs and optimal performances are balanced. However, many complexities associated with biological machines will require one to go beyond current theoretical methods. Simple point mutations in the enzyme could drastically alter functions, making the motors bi-directional or result in unexpected diseases or dramatically restrict the capacity of molecular chaperones to help proteins fold. These examples are reminders that while the search for principles of generality in biology is intellectually stimulating, one also ought to keep in mind that molecular details must be accounted for to develop a deeper understanding of processes driven by biological machines. Going beyond generic descriptions of in vitro behavior to making genuine understanding of in vivo functions will likely remain a major challenge for some time to come. The combination of careful experiments and the use of physical principles will be useful in elucidating the rules governing the workings of biological machines.

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.

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 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. However, alternative stepping mechanisms exist, including inchworm-like movements, backward steps, and foot stomps. Whether all of these pathways are coupled to ATP hydrolysis remains to be determined. Here, in order to establish the principles governing the dynamics of processive movement, we present a theoretical framework which 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 which 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 reproduces quantitatively various observables of myosin VI motility measured experimentally from two 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.Significance StatementMolecular motors harness the energy released by ATP hydrolysis to transport cargo along cytoskeletal filaments. The two identical heads in the motor step alternatively on the polar track by communicating with each other. Our goal is to elucidate how the coordination between the two heads emerges from the catalytic cycles. To do so, we created a theoretical framework that allows us to relate the measurable features of motility, such as motor velocity, with the biochemical rates in the leading and trailing heads, thereby connecting biochemical activity and motility. We illustrate the efficacy of the theory by analyzing experimental data for myosin VI, which takes frequent backward steps, and moves forward by a hand-over-hand and inchworm-like steps.

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 towards 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 (NT) ranging from 24 to 441, our simulations not only reproduce the radii of gyration (Rg) obtained from experiments, but also predict the full scattering intensity profiles in very good agreement with Small Angle X-ray Scattering experiments. The Rg values are well-described by the standard Flory scaling law, , with v ≈ 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 Rg 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.Graphical TOC Entry

1SummaryCytoplasmic Dynein, a motor with an unusual architecture made up of a motor domain belonging to the AAA+ family, walks on microtubule towards the minus end. Prompted by the availability of structures in different nucleotide states, we performed simulations based on a new coarse-grained model to illustrate the molecular details of the dynamics of allosteric transitions in the motor. The simulations show that binding of ATP results in the closure of the cleft between the AAA1 and AAA2, which in turn triggers conformational changes in the rest of the motor domain, thus poising dynein in the pre-power stroke state. Interactions with the microtubule, which are modeled implicitly, substantially enhances the rate of ADP release, and formation of the post-power stroke state. The dynamics associated with the key mechanical element, the linker (LN) domain, which changes from a straight to a bent state and vice versa, are highly heterogeneous suggestive of multiple routes in the pre power stroke to post power stroke transition. We show that 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 non-functional repressed state. Motility in such a state may be rescued by applying mechanical force to the LN domain. Taken together, these results show how the intricate signaling dynamics within the motor domain facilitate the stepping of dynein.

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.

Ketoreductases (KRs) from modular polyketide synthases (PKSs) can perform stereospecific catalysis, selecting a polyketide with a D-α or an 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 [Zheng, J. T. et al. (2010) Structure 18, 913–922], 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. T. et al. (2010) Structure 18, 913–922] in which a Q364H mutant was observed to lose stereospecificity.

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.

Alchemical transformations of chemical species into others provide a common numerical method to compute free energy differences. This method is particularly well suited to compute relative free energy differences formulated as thermodynamic cycles. Moreover, it allows us to compute experimentally measurable quantities, such as the relative binding free energy of small molecules to proteins.The drawback of the alchemical methods is that the annihilation/creation processes of mutated particles present sampling issues and singularities that reduce the accuracy of the calculation. It is therefore important to understand whether the process of annihilation can be simplified and perhaps even avoided.We report a rigorous proof that it is possible to find an alchemical pathway from the native to the mutant system, in which “self interactions” (bonded and non-bonded) are retained without affecting the relative free energy difference. We also provide a molecular dynamics illustrating of this proof in which a cycles of solvated side chains is considered.

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–Benard (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.

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.

We report on simulations of two-dimensional fluids subjected to a temperature gradient, with an orthogonal gravity field suddenly switched on. Short-time behavior is dominated by rapid oscillations for the temperature and density field variables: the latter are interpreted as compressibility effects accurately described by linearized hydrodynamic equations until convective transport establishes itself.