How proteins open fusion pores: insights from molecular simulations

Fusion proteins can play a versatile and involved role during all stages of the fusion reaction. Their roles go far beyond forcing the opposing membranes into close proximity to drive stalk formation and fusion. Molecular simulations have played a central role in providing a molecular understanding of how fusion proteins actively overcome the free energy barriers of the fusion reaction up to the expansion of the fusion pore. Unexpectedly, molecular simulations have revealed a preference of the biological fusion reaction to proceed through asymmetric pathways resulting in the formation of, e.g., a stalk-hole complex, rim-pore, or vertex pore. Force-field based molecular simulations are now able to directly resolve the minimum free-energy path in protein-mediated fusion as well as quantifying the free energies of formed reaction intermediates. Ongoing developments in Graphics Processing Units (GPUs), free energy calculations, and coarse-grained force-fields will soon gain additional insights into the diverse roles of fusion proteins

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

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.

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

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

Effects of cryo-EM cooling on structural ensembles

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

Implementation of a Bayesian secondary structure estimation method for the SESCA circular dichroism analysis package

Circular dichroism spectroscopy is a structural biology technique frequently applied to determine the secondary structure composition of soluble proteins. Our recently introduced computational analysis package SESCA aids the interpretation of protein circular dichroism spectra and enables the validation of proposed corresponding structural models. To further these aims, we present the implementation and characterization of a new Bayesian secondary structure estimation method in SESCA, termed SESCA_bayes. SESCA_bayes samples possible secondary structures using a Monte Carlo scheme, driven by the likelihood of estimated scaling errors and non-secondary-structure contributions of the measured spectrum. SESCA_bayes provides an estimated secondary structure composition and separate uncertainties on the fraction of residues in each secondary structure class. It also assists efficient model validation by providing a posterior secondary structure probability distribution based on the measured spectrum. Our presented study indicates that SESCA_bayes estimates the secondary structure composition with a significantly smaller uncertainty than its predecessor, SESCA_deconv, which is based on spectrum deconvolution. Further, the mean accuracy of the two methods in our analysis is comparable, but SESCA_bayes provides more accurate estimates for circular dichroism spectra that contain considerable non-SS contributions

Variationally derived intermediates for correlated free-energy estimates between intermediate states

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 stepwise 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 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