945 research outputs found

    Determining Free Energy Differences Through Variational Morphing

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    Free energy calculations based on atomistic Hamiltonians and sampling are key to a first principles understanding of biomolecular processes, material properties, and macromolecular chemistry. Here, we generalize the Free Energy Perturbation method and derive non-linear Hamiltonian transformation sequences for optimal sampling accuracy that differ markedly from established linear transformations. We show that our sequences are also optimal for the Bennett Acceptance Ratio (BAR) method, and our unifying framework generalizes BAR to small sampling sizes and non-Gaussian error distributions. Simulations on a Lennard-Jones gas show that an order of magnitude less sampling is required compared to established methods.Comment: 7 pages, 5 figure

    Variationally Derived Intermediates for Correlated Free Energy Estimates between Intermediate States

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    Free energy difference calculations based on atomistic simulations generally improve in accuracy when sampling from a sequence of intermediate equilibrium thermodynamic states that bridge the configuration space between two states of interest. For reasons of efficiency, usually the same samples are used to calculate the step-wise difference of such an intermediate to both adjacent intermediates. However, this procedure violates the assumption of uncorrelated estimates that is necessary to derive both the optimal sequence of intermediate states and the widely used Bennett acceptance ratio (BAR) estimator. In this work, via a variational approach, we derive the sequence of intermediate states and the corresponding estimator with minimal mean squared error that account for these correlations and assess its accuracy

    Time-lagged independent component analysis of random walks and protein dynamics

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    Time-lagged independent component analysis (tICA) is a widely used dimension reduction method for the analysis of molecular dynamics (MD) trajectories and has proven particularly useful for the construction of protein dynamics Markov models. It identifies those ‘slow’ collective degrees of freedom onto which the projections of a given trajectory show maximal autocorrelation for a given lag time. Here we ask how much information on the actual protein dynamics and, in particular, the free energy landscape that governs these dynamics the tICA-projections of MD-trajectories contain, as opposed to noise due to the inherently stochastic nature of each trajectory. To answer this question, we have analyzed the tICA-projections of high dimensional random walks using a combination of analytical and numerical methods. We find that the projections resemble cosine functions and strongly depend on the lag time, exhibiting strikingly complex behaviour. In particular, and contrary to previous studies of principal component projections, the projections change non-continuously with increasing lag time. The tICA-projections of selected 1 μs protein trajectories and those of random walks are strikingly similar, particularly for larger proteins, suggesting that these trajectories contain only little information on the energy landscape that governs the actual protein dynamics. Further the tICA-projections of random walks show clusters very similar to those observed for the protein trajectories, suggesting that clusters in the tICA-projections of protein trajectories do not necessarily reflect local minima in the free energy landscape. We also conclude that, in addition to the previous finding that certain ensemble properties of non-converged protein trajectories resemble those of random walks, this is also true for their time correlations. Due to the higher complexity of the latter, this result also suggests tICA analyses as a more sensitive tool to test MD simulations for proper convergence

    do_x3dna: A tool to analyze structural fluctuations of dsDNA or dsRNA from molecular dynamics simulations.

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    The do_x3dna package has been developed to analyze the structural fluctuations of DNA or RNA during molecular dynamics simulations. It extends the capability of the 3DNA package to GROMACS MD trajectories and includes new methods to calculate the global-helical axis of DNA and bending fluctuations during simulations. The package also includes a Python module dnaMD to perform and visualize statistical analyses of complex data obtained from the trajectories

    Per|Mut: Spatially resolved hydration entropies from atomistic simulations

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    The hydrophobic effect is essential for many biophysical phenomena and processes. It is governed by a fine-tuned balance between enthalpy and entropy contributions from the hydration shell. Whereas enthalpies can in principle be calculated from an atomistic simulation trajectory, calculating solvation entropies by sampling the extremely large configuration space is challenging and often impossible. Furthermore, to qualitatively understand how the balance is affected by individual side chains, chemical groups, or the protein topology, a local description of the hydration entropy is required. In this study, we present and assess the new method “Per|Mut”, which uses a permutation reduction to alleviate the sampling problem by a factor of N! and employs a mutual information expansion to the third order to obtain spatially resolved hydration entropies. We tested the method on an argon system, a series of solvated n-alkanes, and solvated octanol

    Proteindynamik von Ligand/Rezeptor-Bindungen.

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    Effects of cryo-EM cooling on structural ensembles

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    Structure determination by cryo electron microscopy (cryo-EM) provides information on structural heterogeneity and ensembles at atomic resolution. To obtain cryo-EM images of macromolecules, the samples are first rapidly cooled down to cryogenic temperatures. To what extent the structural ensemble is perturbed during cooling is currently unknown. Here, to quantify the effects of cooling, we combined continuum model calculations of the temperature drop, molecular dynamics simulations of a ribosome complex before and during cooling with kinetic models. Our results suggest that three effects markedly contribute to the narrowing of the structural ensembles: thermal contraction, reduced thermal motion within local potential wells, and the equilibration into lower free-energy conformations by overcoming separating free-energy barriers. During cooling, barrier heights below 10 kJ/mol were found to be overcome, which is expected to reduce B-factors in ensembles imaged by cryo-EM. Our approach now enables the quantification of the heterogeneity of room-temperature ensembles from cryo-EM structures

    Molecular dynamics of conformational substates for a simplified protein model.

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    Extended molecular dynamics simulations covering a total of 0.232 μs have been carried out on a simplified protein model. Despite its simplified structure, that model exhibits properties similar to those of more realistic protein models. In particular, the model was found to undergo transitions between conformational substates at a time scale of several hundred picoseconds. The computed trajectories turned out to be sufficiently long as to permit a statistical analysis of that conformational dynamics. To check whether effective descriptions neglecting memory effects can reproduce the observed conformational dynamics, two stochastic models were studied. A one‐dimensional Langevin effective potential model derived by elimination of subpicosecond dynamical processes could not describe the observed conformational transition rates. In contrast, a simple Markov model describing the transitions between but neglecting dynamical processes within conformational substates reproduced the observed distribution of first passage times. These findings suggest, that protein dynamics generally does not exhibit memory effects at time scales above a few hundred picoseconds, but confirms the existence of memory effects at a picosecond time scale
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