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The proper balancing of information from experiment and theory is a long-standing problem in the analysis of noisy and incomplete data. Viewed as a Pareto optimization problem, improved agreement with the experimental data comes at the expense of growing inconsistencies with the theoretical reference model. Here, we propose how to set the exchange rate a priori to properly balance this trade-off. We focus on gentle ensemble refinement, where the difference between the potential energy surfaces of the reference and refined models is small on a thermal scale. By relating the variance of this energy difference to the Kullback–Leibler divergence between the respective Boltzmann distributions, one can encode prior knowledge about energy uncertainties, i.e., force-field errors, in the exchange rate. The energy uncertainty is defined in the space of observables and depends on their type and number and on the thermodynamic state. We highlight the relation of gentle refinement to free energy perturbation theory. A balanced encoding of prior knowledge increases the quality and transparency of ensemble refinement. Our findings extend to non-Boltzmann distributions, where the uncertainty in energy becomes an uncertainty in information. [ABSTRACT FROM AUTHOR]

The interior of living cells is densely filled with proteins and their complexes, which perform multitudes of biological functions. We use coarse-grained simulations to reach the system sizes and time scales needed to study protein complexes and their dense solutions and to interpret experiments. To take full advantage of coarse-graining, the models have to be efficiently implemented in simulation engines that are easy to use, modify, and extend. Here, we introduce the Complexes++ simulation software to simulate a residue-level coarse-grained model for proteins and their complexes, applying a Markov chain Monte Carlo engine to sample configurations. We designed a parallelization scheme for the energy evaluation capable of simulating both dilute and dense systems efficiently. Additionally, we designed the software toolbox pycomplexes to easily set up complex topologies of multi-protein complexes and their solutions in different thermodynamic ensembles and in replica-exchange simulations, to grow flexible polypeptide structures connecting ordered protein domains, and to automatically visualize structural ensembles. Complexes++ simulations can easily be modified and they can be used for efficient explorations of different simulation systems and settings. Thus, the Complexes++ software is well suited for the integration of experimental data and for method development. [ABSTRACT FROM AUTHOR]

Lipid membranes are integral building blocks of living cells and perform a multitude of biological functions. Currently, molecular simulations of cellular-scale membrane remodeling processes at atomic resolution are extremely difficult, due to their size, complexity, and the large times-scales on which these processes occur. Instead, elastic membrane models are used to simulate membrane shapes and transitions between them and to infer their properties and functions. Unfortunately, an efficiently parallelized open-source simulation code to do so has been lacking. Here, we present TriMem, a parallel hybrid Monte Carlo simulation engine for triangulated lipid membranes. The kernels are efficiently coded in C++ and wrapped with Python for ease-of-use. The parallel implementation of the energy and gradient calculations and of Monte Carlo flip moves of edges in the triangulated membrane enable us to simulate large and highly curved membrane structures. For validation, we reproduce phase diagrams of vesicles with varying surface-to-volume ratios and area difference. We also compute the density of states to verify correct Boltzmann sampling. The software can be used to tackle a range of large-scale membrane remodeling processes as a step toward cell-scale simulations. Additionally, extensive documentation make the software accessible to the broad biophysics and computational cell biology communities. [ABSTRACT FROM AUTHOR]

Among other improvements, the Martini 3 coarse-grained force field provides a more accurate description of the solvation of protein pockets and channels through the consistent use of various bead types and sizes. Here, we show that the representation of Na+ and Cl− ions as "tiny" (TQ5) beads limits the accessible time step to 25 fs. By contrast, with Martini 2, time steps of 30–40 fs were possible for lipid bilayer systems without proteins. This limitation is relevant for systems that require long equilibration times. We derive a quantitative kinetic model of time-integration instabilities in molecular dynamics (MD) as a function of the time step, ion concentration and mass, system size, and simulation time. We demonstrate that ion–water interactions are the main source of instability at physiological conditions, followed closely by ion–ion interactions. We show that increasing the ionic masses makes it possible to use time steps up to 40 fs with minimal impact on static equilibrium properties and dynamical quantities, such as lipid and solvent diffusion coefficients. Increasing the size of the bead representing the ions (and thus changing their hydration) also permits longer time steps. For a soluble protein, we find that increasing the mass of tiny beads also on the protein permits simulations with 30-fs time steps. The use of larger time steps in Martini 3 results in a more efficient exploration of configuration space. The kinetic model of MD simulation crashes can be used to determine the maximum allowed time step upfront for an efficient use of resources and whenever sampling efficiency is critical. [ABSTRACT FROM AUTHOR]

Single-molecule localization microscopy allows practitioners to locate and track labeled molecules in biological systems. When extracting diffusion coefficients from the resulting trajectories, it is common practice to perform a linear fit on mean-squared-displacement curves. However, this strategy is suboptimal and prone to errors. Recently, it was shown that the increments between the observed positions provide a good estimate for the diffusion coefficient, and their statistics are well-suited for likelihood-based analysis methods. Here, we revisit the problem of extracting diffusion coefficients from single-particle tracking experiments subject to static noise and dynamic motion blur using the principle of maximum likelihood. Taking advantage of an efficient real-space formulation, we extend the model to mixtures of subpopulations differing in their diffusion coefficients, which we estimate with the help of the expectation–maximization algorithm. This formulation naturally leads to a probabilistic assignment of trajectories to subpopulations. We employ the theory to analyze experimental tracking data that cannot be explained with a single diffusion coefficient. We test how well a dataset conforms to the assumptions of a diffusion model and determine the optimal number of subpopulations with the help of a quality factor of known analytical distribution. To facilitate use by practitioners, we provide a fast open-source implementation of the theory for the efficient analysis of multiple trajectories in arbitrary dimensions simultaneously. [ABSTRACT FROM AUTHOR]

Despite the impending flattening of Moore's law, the system size, complexity, and length of molecular dynamics (MD) simulations keep on increasing, thanks to effective code parallelization and optimization combined with algorithmic developments. Going forward, exascale computing poses new challenges to the efficient execution and management of MD simulations. The diversity and rapid developments of hardware architectures, software environments, and MD engines make it necessary that users can easily run benchmarks to optimally set up simulations, both with respect to time-to-solution and overall efficiency. To this end, we have developed the software MDBenchmark to streamline the setup, submission, and analysis of simulation benchmarks and scaling studies. The software design is open and as such not restricted to any specific MD engine or job queuing system. To illustrate the necessity and benefits of running benchmarks and the capabilities of MDBenchmark, we measure the performance of a diverse set of 23 MD simulation systems using GROMACS 2018. We compare the scaling of simulations with the number of nodes for central processing unit (CPU)-only and mixed CPU–graphics processing unit (GPU) nodes and study the performance that can be achieved when running multiple simulations on a single node. In all these cases, we optimize the numbers of message passing interface (MPI) ranks and open multi-processing (OpenMP) threads, which is crucial to maximizing performance. Our results demonstrate the importance of benchmarking for finding the optimal system and hardware specific simulation parameters. Running MD simulations with optimized settings leads to a significant performance increase that reduces the monetary, energetic, and environmental costs of MD simulations. [ABSTRACT FROM AUTHOR]

In molecular dynamics simulations under periodic boundary conditions, particle positions are typically wrapped into a reference box. For diffusion coefficient calculations using the Einstein relation, the particle positions need to be unwrapped. Here, we show that a widely used heuristic unwrapping scheme is not suitable for long simulations at constant pressure. Improper accounting for box-volume fluctuations creates, at long times, unphysical trajectories and, in turn, grossly exaggerated diffusion coefficients. We propose an alternative unwrapping scheme that resolves this issue. At each time step, we add the minimal displacement vector according to periodic boundary conditions for the instantaneous box geometry. Here and in another paper [J. T. Bullerjahn, S. von Bülow, and G. Hummer, J. Chem. Phys. 153, 024116 (2020)], we apply the new unwrapping scheme to extensive molecular dynamics and Brownian dynamics simulation data. We provide practitioners with a formula to assess if and by how much earlier results might have been affected by the widely used heuristic unwrapping scheme. [ABSTRACT FROM AUTHOR]

Translational diffusion coefficients are routinely estimated from molecular dynamics simulations. Linear fits to mean squared displacement (MSD) curves have become the de facto standard, from simple liquids to complex biomacromolecules. Nonlinearities in MSD curves at short times are handled with a wide variety of ad hoc practices, such as partial and piece-wise fitting of the data. Here, we present a rigorous framework to obtain reliable estimates of the self-diffusion coefficient and its statistical uncertainty. We also assess in a quantitative manner if the observed dynamics is, indeed, diffusive. By accounting for correlations between MSD values at different times, we reduce the statistical uncertainty of the estimator and, thereby, increase its efficiency. With a Kolmogorov–Smirnov test, we check for possible anomalous diffusion. We provide an easy-to-use Python data analysis script for the estimation of self-diffusion coefficients. As an illustration, we apply the formalism to molecular dynamics simulation data of pure TIP4P-D water and a single ubiquitin protein. In another paper [S. von Bülow, J. T. Bullerjahn, and G. Hummer, J. Chem. Phys. 153, 021101 (2020)], we demonstrate its ability to recognize deviations from regular diffusion caused by systematic errors in a common trajectory "unwrapping" scheme that is implemented in popular simulation and visualization software. [ABSTRACT FROM AUTHOR]

In single-molecule force spectroscopy experiments, a biomolecule is attached to a force probe via polymer linkers and the total extension of the molecule plus apparatus is monitored as a function of time. In a typical unfolding experiment at constant force, the total extension jumps between two values that correspond to the folded and unfolded states of the molecule. For several biomolecular systems, the committor, which is the probability to fold starting from a given extension, has been used to extract the molecular activation barrier (a technique known as "committor inversion"). In this work, we study the influence of the force probe, which is much larger than the molecule being measured, on the activation barrier obtained by committor inversion. We use a two-dimensional framework in which the diffusion coefficient of the molecule and of the pulling device can differ. We systematically study the free energy profile along the total extension obtained from the committor by numerically solving the Onsager equation and using Brownian dynamics simulations. We analyze the dependence of the extracted barrier on the linker stiffness, molecular barrier height, and diffusion anisotropy and, thus, establish the range of validity of committor inversion. Along the way, we showcase the committor of 2-dimensional diffusive models and illustrate how it is affected by barrier asymmetry and diffusion anisotropy. [ABSTRACT FROM AUTHOR]

We show how accurate rates of formation and dissociation of peptide dimers can be calculated using direct transition counting (DTC) from replica-exchange molecular dynamics (REMD) simulations. First, continuous trajectories corresponding to system replicas evolving at different temperatures are used to assign conformational states. Second, we analyze the entire REMD data to calculate the corresponding rates at each temperature directly from the number of transition counts. Finally, we compare the kinetics extracted directly, using the DTC method, with indirect estimations based on trajectory likelihood maximization using short-time propagators and on decay rates of state autocorrelation functions. For systems with relatively low-dimensional intrinsic conformational dynamics, the DTC method is simple to implement and leads to accurate temperature-dependent rates.We apply the DTC rate-extraction method to all-atom REMD simulations of dimerization of amyloid-forming NNQQ tetrapetides in explicit water. In an assessment of the REMD sampling efficiency with respect to standard MD, we find a gain of more than a factor of two at the lowest temperature. [ABSTRACT FROM AUTHOR]

Transition path sampling is a powerful tool in the study of rare events. Shooting trial trajectories from configurations along existing transition paths proved particularly efficient in the sampling of reactive trajectories. However, most shooting attempts tend not to result in transition paths, in particular in cases where the transition dynamics has diffusive character. To overcome the resulting efficiency problem, we developed an algorithm for "shooting from the top." We first define a shooting range through which all paths have to pass and then shoot off trial trajectories only from within this range. For a well chosen shooting range, nearly every shot is successful, resulting in an accepted transition path. To deal with multiple mechanisms, weighted shooting ranges can be used. To cope with the problem of unsuitably placed shooting ranges, we developed an algorithm that iteratively improves the location of the shooting range. The transition path sampling procedure is illustrated for models of diffusive and Langevin dynamics. The method should be particularly useful in cases where the transition paths are long so that only relatively few shots are possible, yet reasonable order parameters are known. [ABSTRACT FROM AUTHOR]

We describe different Bayesian ensemble refinement methods, examine their interrelation, and discuss their practical application. With ensemble refinement, the properties of dynamic and partially disordered (bio)molecular structures can be characterized by integrating a wide range of experimental data, including measurements of ensemble-averaged observables. We start from a Bayesian formulation in which the posterior is a functional that ranks different configuration space distributions. By maximizing this posterior, we derive an optimal Bayesian ensemble distribution. For discrete configurations, this optimal distribution is identical to that obtained by the maximum entropy "ensemble refinement of SAXS" (EROS) formulation. Bayesian replica ensemble refinement enhances the sampling of relevant configurations by imposing restraints on averages of observables in coupled replica molecular dynamics simulations. We show that the strength of the restraints should scale linearly with the number of replicas to ensure convergence to the optimal Bayesian result in the limit of infinitely many replicas. In the "Bayesian inference of ensembles" method, we combine the replica and EROS approaches to accelerate the convergence. An adaptive algorithm can be used to sample directly from the optimal ensemble, without replicas. We discuss the incorporation of single-molecule measurements and dynamic observables such as relaxation parameters. The theoretical analysis of different Bayesian ensemble refinement approaches provides a basis for practical applications and a starting point for further investigations. [ABSTRACT FROM AUTHOR]

Using the helix-coil transitions of alanine pentapeptide as an illustrative example, we demonstrate the use of diffusion maps in the analysis of molecular dynamics simulation trajectories. Diffusion maps and other nonlinear data-mining techniques provide powerful tools to visualize the distribution of structures in conformation space. The resulting low-dimensional representations help in partitioning conformation space, and in constructing Markov state models that capture the conformational dynamics. In an initial step, we use diffusion maps to reduce the dimensionality of the conformational dynamics of Ala5. The resulting pretreated data are then used in a clustering step. The identified clusters show excellent overlap with clusters obtained previously by using the backbone dihedral angles as input, with small—but nontrivial—differences reflecting torsional degrees of freedom ignored in the earlier approach. We then construct a Markov state model describing the conformational dynamics in terms of a discrete-time random walk between the clusters. We show that by combining fuzzy C-means clustering with a transition-based assignment of states, we can construct robust Markov state models. This state-assignment procedure suppresses short-time memory effects that result from the non-Markovianity of the dynamics projected onto the space of clusters. In a comparison with previous work, we demonstrate how manifold learning techniques may complement and enhance informed intuition commonly used to construct reduced descriptions of the dynamics in molecular conformation space. [ABSTRACT FROM AUTHOR]

We derive simple analytical expressions for the error and computational efficiency of simulated tempering (ST) simulations. The theory applies to the important case of systems whose dynamics at long times is dominated by the slow interconversion between two metastable states. An extension to the multistate case is described. We show that the relative gain in efficiency of ST simulations over regular molecular dynamics (MD) or Monte Carlo (MC) simulations is given by the ratio of their reactive fluxes, i.e., the number of transitions between the two states summed over all ST temperatures divided by the number of transitions at the single temperature of the MD or MC simulation. This relation for the efficiency is derived for the limit in which changes in the ST temperature are fast compared to the two-state transitions. In this limit, ST is most efficient. Our expression for the maximum efficiency gain of ST simulations is essentially identical to the corresponding expression derived by us for replica exchange MD and MC simulations [E. Rosta and G. Hummer, J. Chem. Phys. 131, 165102 (2009)] on a different route. We find quantitative agreement between predicted and observed efficiency gains in a test against ST and replica exchange MC simulations of a two-dimensional Ising model. Based on the efficiency formula, we provide recommendations for the optimal choice of ST simulation parameters, in particular, the range and number of temperatures, and the frequency of attempted temperature changes. [ABSTRACT FROM AUTHOR]

We derive simple analytical expressions for the error and computational efficiency of replica exchange molecular dynamics (REMD) simulations (and by analogy replica exchange Monte Carlo simulations). The theory applies to the important case of systems whose dynamics at long times is dominated by the slow interconversion between two metastable states. As a specific example, we consider the folding and unfolding of a protein. The efficiency is defined as the rate with which the error in an estimated equilibrium property, as measured by the variance of the estimator over repeated simulations, decreases with simulation time. For two-state systems, this rate is in general independent of the particular property. Our main result is that, with comparable computational resources used, the relative efficiency of REMD and molecular dynamics (MD) simulations is given by the ratio of the number of transitions between the two states averaged over all replicas at the different temperatures, and the number of transitions at the single temperature of the MD run. This formula applies if replica exchange is frequent, as compared to the transition times. High efficiency of REMD is thus achieved by including replica temperatures in which the frequency of transitions is higher than that at the temperature of interest. In tests of the expressions for the error in the estimator, computational efficiency, and the rate of equilibration we find quantitative agreement with the results both from kinetic models of REMD and from actual all-atom simulations of the folding of a peptide in water. [ABSTRACT FROM AUTHOR]

We describe a reverse integration approach for the exploration of low-dimensional effective potential landscapes. Coarse reverse integration initialized on a ring of coarse states enables efficient navigation on the landscape terrain: Escape from local effective potential wells, detection of saddle points, and identification of significant transition paths between wells. We consider several distinct ring evolution modes: Backward stepping in time, solution arc length, and effective potential. The performance of these approaches is illustrated for a deterministic problem where the energy landscape is known explicitly. Reverse ring integration is then applied to noisy problems where the ring integration routine serves as an outer wrapper around a forward-in-time inner simulator. Two versions of such inner simulators are considered: A Gillespie-type stochastic simulator and a molecular dynamics simulator. In these “equation-free” computational illustrations, estimation techniques are applied to the results of short bursts of inner simulation to obtain the unavailable (in closed-form) quantities (local drift and diffusion coefficient estimates) required for reverse ring integration; this naturally leads to approximations of the effective landscape. [ABSTRACT FROM AUTHOR]

The reactive flux between folded and unfolded states of a two-state protein, whose coarse-grained dynamics is described by a master equation, is expressed in terms of the commitment or splitting probabilities of the microstates in the bottleneck region. This allows one to determine how much each transition through a dividing surface contributes to the reactive flux. By repeating the analysis for a series of dividing surfaces or, alternatively, by partitioning the reactive flux into contributions of unidirectional pathways that connect reactants and products, insight can be gained into the mechanism of protein folding. Our results for the flux in a network with complex connectivity, obtained using the discrete counterpart of Kramers’ theory of activated rate processes, show that the number of reactive transitions is typically much smaller than the total number of transitions that cross a dividing surface at equilibrium. [ABSTRACT FROM AUTHOR]

We present a recently developed one-dimensional dipole lattice model that accurately captures the key properties of water in narrow nanopores. For this model, we derive three equivalent representations of the Hamiltonian that together yield a transparent physical picture of the energetics of the water chain and permit efficient computer simulations. In the charge representation, the Hamiltonian consists of nearest-neighbor interactions and Coulomb-like interactions of effective charges at the ends of dipole ordered segments. Approximations based on the charge picture shed light on the influence of the Coulomb-like interactions on the structure of nanopore water. We use Monte Carlo simulations to study the system behavior of the full Hamiltonian and its approximations as a function of chemical potential and system size and investigate the bimodal character of the density distribution occurring at small system sizes. [ABSTRACT FROM AUTHOR]

Molecular dynamics simulations on quantum energy surfaces are carried out to study the effects of perturbing electric fields on proton transport (PT) in protonated water chains. As an idealized model of a hydrophobic cavity in the interior of a protein the water molecules are confined into a carbon nanotube (CNT). The water chain connects a hydrated hydronium ion (H3O+) at one end of the CNT and an imidazole molecule at the other end. Without perturbing electric fields PT from the hydronium proton donor to the imidazole acceptor occurs on a picosecond time scale. External perturbations to PT are created by electric fields of varying intensities, normal to the CNT axis, generated by a neutral pair of charges on the nanotube wall. For fields above ∼0.5 V/Å, the hydronium ion is effectively trapped at the CNT center, and PT blocked. Fields of comparable strength are generated inside proteins by nearby polar/charged amino acids. At lower fields the system displays a rich dynamic behavior, where the excess charge shuttles back and forth along the water chain before reaching the acceptor group on the picosecond time scale. The effects of the perturbing field on the proton movement are analyzed in terms of structural and dynamic properties of the water chain. The implications of these observations on PT in biomolecular systems and its control by external perturbing fields are discussed. [ABSTRACT FROM AUTHOR]

Carbon nanotubes can serve as simple nonpolar water channels. Here we report computer simulations exploring the relationship between the mechanical properties of such channels and their interaction with water. We show that on one hand, increasing the flexibility of the carbon nanotubes increases their apparent hydrophobic character, while on the other hand the presence of water inside the channel makes them more resistant to radial collapse. We quantify the effect of increasing flexibility on the hydrophobicity of the nanotube water channel. We also show that flexibility impedes water transport across the nanotube channel by increasing the free-energy barriers to such motion. Conversely, the presence of water inside the nanotube is shown to affect the energetics of radial collapse in a water nanotube, an ostensibly mechanical property. We quantify the magnitude of the effect and show that it arises from the formation of energetically favorable low-dimensional water structures inside the nanotube such as one-dimensional wires and two-dimensional sheets. [ABSTRACT FROM AUTHOR]

Water molecules in the narrow cylindrical pore of a (6,6) carbon nanotube form single-file chains with their dipoles collectively oriented either up or down along the tube axis. We study the interaction of such water chains with homogeneous electric fields for finite closed and infinite periodically replicated tubes. By evaluating the grand-canonical partition function term-by-term, we show that homogeneous electric fields favor the filling of previously empty nanotubes with water from the bulk phase. A two-state description of the collective water dipole orientation in the nanotube provides an excellent approximation for the dependence of the water-chain polarization and the filling equilibrium on the electric field. The energy and entropy contributions to the free energy of filling the nanotube were determined from the temperature dependence of the occupancy probabilities. We find that the energy of transfer depends sensitively on the water-tube interaction potential, and that the entropy of one-dimensionally ordered water chains is comparable to that of bulk water. We also discuss implications for proton transfer reactions in biology. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Transition states are defined as points in configuration space with the highest probability that trajectories passing through them are reactive (i.e., form transition paths between reactants and products). In the high-friction (diffusive) limit of Langevin dynamics, the resulting ensemble of transition states is shown to coincide with the separatrix formed by points of equal commitment (or splitting) probabilities for reaching the product and reactant regions. Transition states according to the new criterion can be identified directly from equilibrium trajectories, or indirectly by calculating probability densities in the equilibrium and transition-path ensembles using umbrella and transition-path sampling, respectively. An algorithm is proposed to calculate rate coefficients from the transition-path and equilibrium ensembles by estimating the frequency of transitions between reactants and products. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We present a “coarse molecular dynamics” approach and apply it to studying the kinetics and thermodynamics of a peptide fragment dissolved in water. Short bursts of appropriately initialized simulations are used to infer the deterministic and stochastic components of the peptide motion parametrized by an appropriate set of coarse variables. Techniques from traditional numerical analysis (Newton–Raphson, coarse projective integration) are thus enabled; these techniques help analyze important features of the free-energy landscape (coarse transition states, eigenvalues and eigenvectors, transition rates, etc.). Reverse integration of coarse variables backward in time can assist escape from free energy minima and trace low-dimensional free energy surfaces. To illustrate the coarse molecular dynamics approach, we combine multiple short (0.5 ps) replica simulations to map the free energy surface of the “alanine dipeptide” in water, and to determine the ∼1/(1000 ps) rate of interconversion between the two stable configurational basins corresponding to the α-helical and extended minima. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The kinetics of water filling and emptying the interior channel of carbon nanotubes is studied by molecular dynamics simulations. Filling and emptying occur predominantly by sequential addition of water to or removal from a single-file chain inside the nanotube. Advancing and receding water chains are orientationally ordered. This precludes simultaneous filling from both tube ends, and forces chain rupturing to occur at the tube end where a water molecule donates a hydrogen bond to the bulk fluid. We use transition path concepts and a Bayesian approach to identify a transition state ensemble that we characterize by its commitment probability distribution. At the transition state, the tube is filled with all but one water molecule. Filling thermodynamics and kinetics depend sensitively on the strength of the attractive nanotube-water interactions. This sensitivity increases with the length of the tubes. [ABSTRACT FROM AUTHOR]

A class of simple expressions of increasing accuracy for the free-energy difference between two states is derived based on numerical thermodynamic integration. The implementation of these formulas requires simulations of the initial and final (and possibly a few intermediate) states. They involve higher free-energy derivatives at these states which are related to the moments of the probability distribution of the perturbation. Given a specified number of such derivatives, these integration formulas are optimal in the sense that they are exact to the highest possible order of free-energy perturbation theory. The utility of this approach is illustrated for the hydration free energy of water. This problem provides a quite stringent test because the free energy is a highly nonlinear function of the charge so that even fourth order perturbation theory gives a very poor estimate of the free-energy change. Our results should prove most useful for complex, computationally demanding problems where free-energy differences arise primarily from changes in the electrostatic interactions (e.g., electron transfer, charging of ions, protonation of amino acids in proteins). © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The pair and triplet correlations of a restricted primitive model (RPM) description of aqueous NaCl solutions have been computed in the concentration regime 0.5–4 M via Monte Carlo simulations, using both the method of configuration statistics and the particle insertion (chemical potential) method. Comparison of the triplet data to Kirkwood’s superposition approximation and the Abe and convolution approximations shows that deviations occur only for distances close to contact. The entropy computed via the entropy expansion including terms up to third order and the insertion method is dominated essentially by packing effects. The pair correlations and thermodynamic properties derived from the simulations were compared to the hypernetted chain (HNC) approximation which was found to be very good corroborating the conclusions drawn from earlier RPM studies. [ABSTRACT FROM AUTHOR]

Examines the use of Ewald summation in calculating electrostatic interactions in computer simulations of polar and charged substances. Derivation of formula to be implemented in standard molecular dynamics; Difference between virial and thermodynamic pressures; Model used in investigating the difference between virial and thermodynamic pressures.

Performs Monte Carlo simulations of the tetramethylammonium ion hydrated by simple charge water molecules. Relation of the derivatives of the free energy with the fluctuations in the ion-water interaction energies; Dependence of the calculated hydration free energies on system size and the method used in calculating electrostatic interactions.

Studies the free energies of ionic solvation calculated from computer simulations. System of size dependence exhibited by the free energies; Estimation of the Born ion size; Application of the finite-size correlation to systems.

In a typical single-molecule force spectroscopy experiment, the ends of the molecule of interest are connected by long polymer linkers to a pair of mesoscopic beads trapped in the focus of two laser beams. At constant force load, the total extension, i.e., the end-to-end distance of the molecule plus linkers, is measured as a function of time. In the simplest systems, the measured extension fluctuates about two values characteristic of folded and unfolded states, with occasional transitions between them. We have recently shown that molecular (un)folding rates can be recovered from such trajectories, with a small linker correction, as long as the characteristic time of the bead fluctuations is shorter than the residence time in the unfolded (folded) state. Here, we show that accurate measurements of the molecular transition path times require an even faster apparatus response. Transition paths, the trajectory segments in which the molecule (un)folds, are properly resolved only if the beads fluctuate more rapidly than the end-to-end distance of the molecule. Therefore, over a wide regime, the measured rates may be meaningful but not the transition path times. Analytic expressions for the measured mean transition path times are obtained for systems diffusing anisotropically on a two-dimensional free energy surface. The transition path times depend on the properties both of the molecule and of the pulling device. [ABSTRACT FROM AUTHOR]

This special issue presents a series of papers that highlight a new and evolving view of water's molecular role in biological structure and dynamics. Increasingly water is appreciated for playing an active role in biological function rather than just serving as a spectator. The areas represented include molecular interfaces with water, biological self-assembly, conformational changes by macromolecules, and chemical reactivity [ABSTRACT FROM AUTHOR]

We used molecular dynamics simulations to investigate the thermodynamics of filling of a (6,6) open carbon nanotube (diameter D = 0.806 nm) solvated in TIP3P water over a temperature range from 280 K to 320 K at atmospheric pressure. In simulations of tubes with slightly weakened carbon-water attractive interactions, we observed multiple filling and emptying events. From the water occupancy statistics, we directly obtained the free energy of filling, and from its temperature dependence the entropy of filling. We found a negative entropy of about -1.3 kB per molecule for filling the nanotube with a hydrogen-bonded single-file chain of water molecules. The entropy of filling is nearly independent of the strength of the attractive carbon-water interactions over the range studied. In contrast, the energy of transfer depends strongly on the carbon-water attraction strength. These results are in good agreement with entropies of about -0.5 kB per water molecule obtained from grand-canonical Monte Carlo calculations of water in quasi-infinite tubes in vacuum under periodic boundary conditions. Overall, for realistic carbon-water interactions we expect that at ambient conditions filling of a (6,6) carbon nanotube open to a water reservoir is driven by a favorable decrease in energy, and opposed by a small loss of water entropy. [ABSTRACT FROM AUTHOR]

We calculate the pair diffusion coefficient D(r) as a function of the distance r between two hard sphere particles in a dense monodisperse fluid. The distance-dependent pair diffusion coefficient describes the hydrodynamic interactions between particles in a fluid that are central to theories of polymer and colloid dynamics. We determine D(r) from the propagators (Green's functions) of particle pairs obtained from molecular dynamics simulations. At distances exceeding ∼3 molecular diameters, the calculated pair diffusion coefficients are in excellent agreement with predictions from exact macroscopic hydrodynamic theory for large Brownian particles suspended in a solvent bath, as well as the Oseen approximation. However, the asymptotic 1/r distance dependence of D(r) associated with hydrodynamic effects emerges only after the pair distance dynamics has been followed for relatively long times, indicating non-negligible memory effects in the pair diffusion at short times. Deviations of the calculated D(r) from the hydrodynamic models at short distances r reflect the underlying many-body fluid structure, and are found to be correlated to differences in the local available volume. The procedure used here to determine the pair diffusion coefficients can also be used for single-particle diffusion in confinement with spherical symmetry. [ABSTRACT FROM AUTHOR]

Equilibrium free energy differences can be calculated accurately from repeated fast-growth thermodynamic integration (TI) based on Jarzynski's identity [Phys. Rev. Lett. 78, 2690 (1997)]. We derive expressions for the free energy differences. Error estimates allow us to quantify the relative efficiency of performing many fast-growth vs few slow-growth TIs for a given total computational cost. Fast-growth TI is illustrated through the calculation of the potential of mean force between two methane molecules and compared to umbrella sampling analyzed by using the weighted histogram analysis method. Fast-growth TI is well suited for parallel computer architectures, requiring only the simplest parallelism with repeated runs for different starting conditions. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The information theory approach is used to study molecular-scale density fluctuations and solvation of hard-core molecules in a condensed polymeric system, supported by extensive computer simulations. In contrast to simple liquids, it is found that the bond connectivity in polymers leads to non-Gaussian density fluctuations in molecular volumes. We define "renormalized" polymers with a reduced number of monomers of increased effective size. This reduces correlations between monomers and simplifies the effective density fluctuations. Chemical potentials of hard-core solutes in polyethylene can then be calculated accurately using information theory. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]