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Sugar molecules play important roles as mediators of biomolecular interactions in cellular functions, disease, and infections. Molecular dynamics simulations are an indispensable tool to explore these interactions at the molecular level. The large time and length scales involved frequently necessitate the use of coarse-grained representations, which heavily depend on the parametrization of sugar-protein interactions. Here, we adjust the sugar-protein interactions in the widely used Martini 2.2 force field to reproduce the experimental osmotic second virial coefficients between sugars and proteins. In simulations of two model proteins in glucose solutions with adjusted force field parameters, we observe weak protein-sugar interactions. The sugar molecules are thus acting mainly as crowding agents, in agreement with experimental measurements. The procedure to fine-tune sugar-protein interactions is generally applicable and could also prove useful for atomistic force fields.

Intrinsically disordered regions (IDRs) play a pivotal role in organellar remodeling. They transduce signals across membranes, scaffold signaling complexes, and mediate vesicular traffic. Their functions are regulated by constraining conformational ensembles through specific intra- and intermolecular interactions, physical tethering, and posttranslational modifications. The endoplasmic reticulum (ER)-phagy receptor FAM134B/RETREG1, known for its reticulon homology domain (RHD), includes a substantial C-terminal IDR housing the LC3 interacting motif. Beyond engaging the autophagic machinery, the function of the FAM134B-IDR is unclear. Here, we investigate the characteristics of the FAM134B-IDR by extensive modeling and molecular dynamics simulations. We present detailed structural models for the IDR, mapping its conformational landscape in solution and membrane-anchored configurations. Our analysis reveals that depending on the membrane anchor, the IDRs collapse onto the membrane and induce positive membrane curvature to varying degrees. The charge patterns underlying this Janus-like behavior are conserved across other ER-phagy receptors. We found that IDRs alone are sufficient to sense curvature. When combined with RHDs, they intensify membrane remodeling and drive efficient protein clustering, leading to faster budding, thereby amplifying RHD remodeling functions. Our simulations provide a perspective on IDRs of FAM134B, their Janus-like membrane interactions, and the resulting modulatory functions during large-scale ER remodeling., Competing Interests: Competing interests statement:The authors declare no competing interest.

We used EPR spectroscopy to characterize the structure of RNA duplexes and their internal twist, stretch and bending motions. We prepared eight 20-base-pair-long RNA duplexes containing the rigid spin-label Çm, a cytidine analogue, at two positions and acquired orientation-selective PELDOR/DEER data. By using different frequency bands (X-, Q-, G-band), detailed information about the distance and orientation of the labels was obtained and provided insights into the global conformational dynamics of the RNA duplex. We used 19 F Mims ENDOR experiments on three singly Çm- and singly fluorine-labeled RNA duplexes to determine the exact position of the Çm spin label in the helix. In a quantitative comparison to MD simulations of RNA with and without Çm spin labels, we found that state-of-the-art force fields with explicit parameterization of the spin label were able to describe the conformational ensemble present in our experiments. The MD simulations further confirmed that the Çm spin labels are excellent mimics of cytidine inducing only small local changes in the RNA structure. Çm spin labels are thus ideally suited for high-precision EPR experiments to probe the structure and, in conjunction with MD simulations, motions of RNA., (© 2024 The Authors. Angewandte Chemie International Edition published by Wiley-VCH GmbH.)

Most membrane proteins are modified by covalent addition of complex sugars through N- and O-glycosylation. Unlike proteins, glycans do not typically adopt specific secondary structures and remain very mobile, shielding potentially large fractions of protein surface. High glycan conformational freedom hinders complete structural elucidation of glycoproteins. Computer simulations may be used to model glycosylated proteins but require hundreds of thousands of computing hours on supercomputers, thus limiting routine use. Here, we describe GlycoSHIELD, a reductionist method that can be implemented on personal computers to graft realistic ensembles of glycan conformers onto static protein structures in minutes. Using molecular dynamics simulation, small-angle X-ray scattering, cryoelectron microscopy, and mass spectrometry, we show that this open-access toolkit provides enhanced models of glycoprotein structures. Focusing on N-cadherin, human coronavirus spike proteins, and gamma-aminobutyric acid receptors, we show that GlycoSHIELD can shed light on the impact of glycans on the conformation and activity of complex glycoproteins., Competing Interests: Declaration of interests S.v.B., G.H., and M.S. have filed a patent application related to this work: European Patent Application No. 22203671.7 (2022). S.-T.D.H., C.H., and M.S. have filed a patent application related to this work: European Patent Application No. 23307151.3 (2023)., (Copyright © 2024 The Authors. Published by Elsevier Inc. All rights reserved.)

Cholesterol plays a crucial role in biomembranes by regulating various properties, such as fluidity, rigidity, permeability, and organization of lipid bilayers. The latest version of the Martini model, Martini 3, offers significant improvements in interaction balance, molecular packing, and inclusion of new bead types and sizes. However, the release of the new model resulted in the need to reparameterize many core molecules, including cholesterol. Here, we describe the development and validation of a Martini 3 cholesterol model, addressing issues related to its bonded setup, shape, volume, and hydrophobicity. The proposed model mitigates some limitations of its Martini 2 predecessor while maintaining or improving the overall behavior.

Disordered proteins and nucleic acids play key roles in cellular function and disease. Here, we review recent advances in the computational exploration of the conformational dynamics of flexible biomolecules. While atomistic molecular dynamics (MD) simulation has seen a lot of improvement in recent years, large-scale computing resources and careful validation are required to simulate full-length disordered biopolymers in solution. As a computationally efficient alternative, hierarchical chain growth (HCG) combines pre-sampled chain fragments in a statistically reproducible manner into ensembles of full-length atomically detailed biomolecular structures. Experimental data can be integrated during and after chain assembly. Applications to the neurodegeneration-linked proteins α-synuclein, tau, and TDP-43, including as condensate, illustrate the use of HCG. We conclude by highlighting the emerging connections to AI-based structural modeling including AlphaFold2., (Copyright © 2022 The Author(s). Published by Elsevier Ltd.. All rights reserved.)

Simulations with adaptive time-dependent bias enable an efficient exploration of the conformational space of a system. However, the dynamic information is altered by the bias. Infrequent metadynamics recovers the transition rate of crossing a barrier, if the collective variables are ideal and there is no bias deposition near the transition state. Unfortunately, these conditions are not always fulfilled. To overcome these limitations, and inspired by single-molecule force spectroscopy, we use Kramers' theory for calculating the barrier-crossing rate when a time-dependent bias is added to the system. We assess the efficiency of collective variables parameter by measuring how efficiently the bias accelerates the transitions. We present approximate analytical expressions of the survival probability, reproducing the barrier-crossing time statistics and enabling the extraction of the unbiased transition rate even for challenging cases. We explore the limits of our method and provide convergence criteria to assess its validity.

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.

The spike protein (S) of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is required for cell entry and is the primary focus for vaccine development. In this study, we combined cryo-electron tomography, subtomogram averaging, and molecular dynamics simulations to structurally analyze S in situ. Compared with the recombinant S, the viral S was more heavily glycosylated and occurred mostly in the closed prefusion conformation. We show that the stalk domain of S contains three hinges, giving the head unexpected orientational freedom. We propose that the hinges allow S to scan the host cell surface, shielded from antibodies by an extensive glycan coat. The structure of native S contributes to our understanding of SARS-CoV-2 infection and potentially to the development of safe vaccines., (Copyright © 2020 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.)

Interactions among proteins, nucleic acids, and other macromolecules are essential for their biological functions and shape the physicochemcial properties of the crowded environments inside living cells. Binding interactions are commonly quantified by dissociation constants K d , and both binding and nonbinding interactions are quantified by second osmotic virial coefficients B 2 . As a measure of nonspecific binding and stickiness, B 2 is receiving renewed attention in the context of so-called liquid-liquid phase separation in protein and nucleic acid solutions. We show that K d is fully determined by B 2 and the fraction of the dimer observed in molecular simulations of two proteins in a box. We derive two methods to calculate B 2 . From molecular dynamics or Monte Carlo simulations using implicit solvents, we can determine B 2 from insertion and removal energies by applying Bennett's acceptance ratio (BAR) method or the (binless) weighted histogram analysis method (WHAM). From simulations using implicit or explicit solvents, one can estimate B 2 from the probability that the two molecules are within a volume large enough to cover their range of interactions. We validate these methods for coarse-grained Monte Carlo simulations of three weakly binding proteins. Our estimates for K d and B 2 allow us to separate out the contributions of nonbinding interactions to B 2 . Comparison of calculated and measured values of K d and B 2 can be used to (re-)parameterize and improve molecular force fields by calibrating specific affinities, overall stickiness, and nonbinding interactions. The accuracy and efficiency of K d and B 2 calculations make them well suited for high-throughput studies of large interactomes.

Intrinsically disordered proteins (IDPs) constitute a large fraction of the human proteome and are critical in the regulation of cellular processes. A detailed understanding of the conformational dynamics of IDPs could help to elucidate their roles in health and disease. However, the inherent flexibility of IDPs makes structural studies and their interpretation challenging. Molecular dynamics (MD) simulations could address this challenge in principle, but inaccuracies in the simulation models and the need for long simulations have stymied progress. To overcome these limitations, we adopt a hierarchical approach that builds on the "flexible-meccano" model reported by Bernadó et al. ( J. Am. Chem. Soc. 2005, 127, 17968-17969). First, we exhaustively sample small IDP fragments in all-atom simulations to capture their local structures. Then, we assemble the fragments into full-length IDPs to explore the stereochemically possible global structures of IDPs. The resulting ensembles of three-dimensional structures of full-length IDPs are highly diverse, much more so than in standard MD simulation. For the paradigmatic IDP α-synuclein, our ensemble captures both the local structure, as probed by nuclear magnetic resonance spectroscopy, and its overall dimension, as obtained from small-angle X-ray scattering in solution. By generating representative and meaningful starting ensembles, we can begin to exploit the massive parallelism afforded by current and future high-performance computing resources for atomic-resolution characterization of IDPs.

Predicting the costructure of small-molecule ligands and their respective target proteins has been a long-standing problem in drug discovery. For weak binding compounds typically identified in fragment-based screening (FBS) campaigns, determination of the correct binding site and correct binding mode is usually done experimentally via X-ray crystallography. For many targets of pharmaceutical interest, however, establishing an X-ray system which allows for sufficient throughput to support a drug discovery project is not possible. In this case, exploration of fragment hits becomes a very laborious and consequently slow process with the generation of protein/ligand cocrystal structures as the bottleneck of the entire process. In this work, we introduce a computational method which is able to reliably predict binding sites and binding modes of fragment-like small molecules using solely the structure of the apoprotein and the ligand's chemical structure as input information. The method is based on molecular dynamics simulations and Markov-state models and can be run as a fully automated protocol requiring minimal human intervention. We describe the application of the method to a representative subset of different target classes and fragments from historical FBS efforts at Boehringer Ingelheim and discuss its potential integration into the overall fragment-based drug discovery workflow.

We investigate system-size effects on the rotational diffusion of membrane proteins and other membrane-embedded molecules in molecular dynamics simulations. We find that the rotational diffusion coefficient slows down relative to the infinite-system value by a factor of one minus the ratio of protein and box areas. This correction factor follows from the hydrodynamics of rotational flows under periodic boundary conditions and is rationalized in terms of Taylor-Couette flow. For membrane proteins like transporters, channels, or receptors in typical simulation setups, the protein-covered area tends to be relatively large, requiring a significant finite-size correction. Molecular dynamics simulations of the protein adenine nucleotide translocase (ANT1) and of a carbon nanotube porin in lipid membranes show that the hydrodynamic finite-size correction for rotational diffusion is accurate in standard-use cases. The dependence of the rotational diffusion on box size can be used to determine the membrane viscosity.

Ensemble refinement produces structural ensembles of flexible and dynamic biomolecules by integrating experimental data and molecular simulations. Here we present two efficient numerical methods to solve the computationally challenging maximum-entropy problem arising from a Bayesian formulation of ensemble refinement. Recasting the resulting constrained weight optimization problem into an unconstrained form enables the use of gradient-based algorithms. In two complementary formulations that differ in their dimensionality, we optimize either the log-weights directly or the generalized forces appearing in the explicit analytical form of the solution. We first demonstrate the robustness, accuracy, and efficiency of the two methods using synthetic data. We then use NMR J-couplings to reweight an all-atom molecular dynamics simulation ensemble of the disordered peptide Ala-5 simulated with the AMBER99SB*-ildn-q force field. After reweighting, we find a consistent increase in the population of the polyproline-II conformations and a decrease of α-helical-like conformations. Ensemble refinement makes it possible to infer detailed structural models for biomolecules exhibiting significant dynamics, such as intrinsically disordered proteins, by combining input from experiment and simulation in a balanced manner.

The SLC26 family of transporters maintains anion equilibria in all kingdoms of life. The family shares a 7 + 7 transmembrane segments inverted repeat architecture with the SLC4 and SLC23 families, but holds a regulatory STAS domain in addition. While the only experimental SLC26 structure is monomeric, SLC26 proteins form structural and functional dimers in the lipid membrane. Here we resolve the structure of an SLC26 dimer embedded in a lipid membrane and characterize its functional relevance by combining PELDOR/DEER distance measurements and biochemical studies with MD simulations and spin-label ensemble refinement. Our structural model reveals a unique interface different from the SLC4 and SLC23 families. The functionally relevant STAS domain is no prerequisite for dimerization. Characterization of heterodimers indicates that protomers in the dimer functionally interact. The combined structural and functional data define the framework for a mechanistic understanding of functional cooperativity in SLC26 dimers.

We combine single-molecule Förster resonance energy transfer (single-molecule FRET) experiments with extensive all-atom molecular dynamics (MD) simulations (>100 μs) to characterize the conformational ensembles of single-stranded (ss) DNA and RNA in solution. From MD simulations with explicit dyes attached to single-stranded nucleic acids via flexible linkers, we calculate FRET efficiencies and fluorescence anisotropy decays. We find that dispersion-corrected water models alleviate the problem of overly abundant interactions between fluorescent dyes and the aromatic ring systems of nucleobases. To model dye motions in a computationally efficient and conformationally exhaustive manner, we introduce a dye-conformer library, built from simulations of dinucleotides with covalently attached dye molecules. We use this library to calculate FRET efficiencies for dT 19 , dA 19 , and rA 19 simulated without explicit labels over a wide range of salt concentrations. For end-labeled homopolymeric pyrimidine ssDNA, MD simulations with the parmBSC1 force field capture the overall trend in salt-dependence of single-molecule FRET based distance measurements. For homopolymeric purine ssRNA and ssDNA, the DESRES and parmBSC1 force fields, respectively, provide useful starting points, even though our comparison also identifies clear deviations from experiment.

Artificial channels made of carbon nanotube (CNT) porins are promising candidates for applications in filtration and molecular delivery devices. Their symmetric shape and high mechanical, chemical, and thermal stability ensure well-defined transport properties, and at the same time make them ideal model systems for more complicated membrane protein pores. As the technology to produce and tune CNTs advances, simulations can aid in the design of customized membrane porins. Here we concentrate on CNTs embedded in lipid membranes. To derive design guidelines, we systematically studied the interaction of CNT porins with their surrounding lipids. For our simulations, we developed an AMBER- and Lipid14-compatible parameterization scheme for CNTs with different chirality and with functional groups attached to their rim, and a flexible coarse-grained description for open-ended CNTs fitting to the MARTINI lipid model. We found that the interaction with lipid acyl chains is independent of the CNT chirality and the chemical details of functional groups at the CNT rims. The latter, however, are important for the interactions with lipid head groups, and for water permeability. The orientation and permeability of the pore are mainly determined by how well its hydrophobicity pattern matches the membrane. By identifying the factors that determine the structure both of isolated CNTs in lipid membranes and of CNT clusters, we set the foundation for a targeted design of CNT-membrane systems.

The balance of normal and radial (lateral) diffusion of oxygen in phospholipid membranes is critical for biological function. Based on the Smoluchowski equation for the inhomogeneous solubility-diffusion model, Bayesian analysis (BA) can be applied to molecular dynamics trajectories of oxygen to extract the free energy and the normal and radial diffusion profiles. This paper derives a theoretical formalism to convert these profiles into characteristic times and lengths associated with entering, escaping, or completely crossing the membrane. The formalism computes mean first passage times and holds for any process described by rate equations between discrete states. BA of simulations of eight model membranes with varying lipid composition and temperature indicate that oxygen travels 3 to 5 times further in the radial than in the normal direction when crossing the membrane in a time of 15 to 32 ns, thereby confirming the anisotropy of passive oxygen transport in membranes. Moreover, the preceding times and distances estimated from the BA are compared to the aggregate of 280 membrane exits explicitly observed in the trajectories. BA predictions for the distances of oxygen radial diffusion within the membrane are statistically indistinguishable from the corresponding simulation values, yet BA oxygen exit times from the membrane interior are approximately 20% shorter than the simulation values, averaged over seven systems. The comparison supports the BA approach and, therefore, the applicability of the Smoluchowski equation to membrane diffusion. Given the shorter trajectories required for the BA, these results validate the BA as a computationally attractive alternative to direct observation of exits when estimating characteristic times and radial distances. The effect of collective membrane undulations on the BA is also discussed.

We present a method to calculate the fully anisotropic rotational diffusion tensor from molecular dynamics simulations. Our approach is based on fitting the time-dependent covariance matrix of the quaternions that describe the rigid-body rotational dynamics. Explicit analytical expressions have been derived for the covariances by Favro, which are valid irrespective of the degree of anisotropy. We use these expressions to determine an optimal rotational diffusion tensor from trajectory data. The molecular structures are aligned against a reference by optimal rigid-body superposition. The quaternion covariances can then be obtained directly from the rotation matrices used in the alignment. The rotational diffusion tensor is determined by a fit to the time-dependent quaternion covariances, or directly by Laplace transformation and matrix diagonalization. To quantify uncertainties in the fit, we derive analytical expressions and compare them with the results of Brownian dynamics simulations of anisotropic rotational diffusion. We apply the method to microsecond long trajectories of the Dickerson-Drew B-DNA dodecamer and of horse heart myoglobin. The anisotropic rotational diffusion tensors calculated from simulations agree well with predictions from hydrodynamics.

We present an algorithm to calculate free energies and rates from molecular simulations on biased potential energy surfaces. As input, it uses the accumulated times spent in each state or bin of a histogram and counts of transitions between them. Optimal unbiased equilibrium free energies for each of the states/bins are then obtained by maximizing the likelihood of a master equation (i.e., first-order kinetic rate model). The resulting free energies also determine the optimal rate coefficients for transitions between the states or bins on the biased potentials. Unbiased rates can be estimated, e.g., by imposing a linear free energy condition in the likelihood maximization. The resulting "dynamic histogram analysis method extended to detailed balance" (DHAMed) builds on the DHAM method. It is also closely related to the transition-based reweighting analysis method (TRAM) and the discrete TRAM (dTRAM). However, in the continuous-time formulation of DHAMed, the detailed balance constraints are more easily accounted for, resulting in compact expressions amenable to efficient numerical treatment. DHAMed produces accurate free energies in cases where the common weighted-histogram analysis method (WHAM) for umbrella sampling fails because of slow dynamics within the windows. Even in the limit of completely uncorrelated data, where WHAM is optimal in the maximum-likelihood sense, DHAMed results are nearly indistinguishable. We illustrate DHAMed with applications to ion channel conduction, RNA duplex formation, α-helix folding, and rate calculations from accelerated molecular dynamics. DHAMed can also be used to construct Markov state models from biased or replica-exchange molecular dynamics simulations. By using binless WHAM formulated as a numerical minimization problem, the bias factors for the individual states can be determined efficiently in a preprocessing step and, if needed, optimized globally afterward.

An important limitation of standard classical molecular dynamics simulations is the inability to make or break chemical bonds. This restricts severely our ability to study processes that involve even the simplest of chemical reactions, the transfer of a proton. Existing approaches for allowing proton transfer in the context of classical mechanics are rather cumbersome and have not achieved widespread use and routine status. Here we reconsider the combination of molecular dynamics with periodic stochastic proton hops. To ensure computational efficiency, we propose a non-Boltzmann acceptance criterion that is heuristically adjusted to maintain the correct or desirable thermodynamic equilibria between different protonation states and proton transfer rates. Parameters are proposed for hydronium, Asp, Glu, and His. The algorithm is implemented in the program CHARMM and tested on proton diffusion in bulk water and carbon nanotubes and on proton conductance in the gramicidin A channel. Using hopping parameters determined from proton diffusion in bulk water, the model reproduces the enhanced proton diffusivity in carbon nanotubes and gives a reasonable estimate of the proton conductance in gramicidin A.

Transitions between metastable states govern many fundamental processes in physics, chemistry and biology, from nucleation events in phase transitions to the folding of proteins. The free energy surfaces underlying these processes can be obtained from simulations using enhanced sampling methods. However, their altered dynamics makes kinetic and mechanistic information difficult or impossible to extract. Here, we show that, with replica exchange molecular dynamics (REMD), one can not only sample equilibrium properties but also extract kinetic information. For systems that strictly obey first-order kinetics, the procedure to extract rates is rigorous. For actual molecular systems whose long-time dynamics are captured by kinetic rate models, accurate rate coefficients can be determined from the statistics of the transitions between the metastable states at each replica temperature. We demonstrate the practical applicability of the procedure by constructing master equation (Markov state) models of peptide and RNA folding from REMD simulations.

A Bayesian-based methodology is developed to estimate diffusion tensors from molecular dynamics simulations of permeants in anisotropic media, and is applied to oxygen in lipid bilayers. By a separation of variables in the Smoluchowski diffusion equation, the multidimensional diffusion is reduced to coupled one-dimensional diffusion problems that are treated by discretization. The resulting diffusivity profiles characterize the membrane transport dynamics as a function of the position across the membrane, discriminating between diffusion normal and parallel to the membrane. The methodology is first validated with neat water, neat hexadecane, and a hexadecane slab surrounded by water, the latter being a simple model for a lipid membrane. Next, a bilayer consisting of pure 1-palmitoyl 2-oleoylphosphatidylcholine (POPC), and a bilayer mimicking the lipid composition of the inner mitochondrial membrane, including cardiolipin, are investigated. We analyze the detailed time evolution of oxygen molecules, in terms of both normal diffusion through and radial diffusion inside the membrane. Diffusion is fast in the more loosely packed interleaflet region, and anisotropic, with oxygen spreading more rapidly in the membrane plane than normal to it. Visualization of the propagator shows that oxygen enters the membrane rapidly, reaching its thermodynamically favored center in about 1 ns, despite the free energy barrier at the headgroup region. Oxygen transport is quantified by computing the oxygen permeability of the membranes and the average radial diffusivity, which confirm the anisotropy of the diffusion. The position-dependent diffusion constants and free energies are used to construct compartmental models and test assumptions used in estimating permeability, including Overton's rule. In particular, a hexadecane slab surrounded by water is found to be a poor model of oxygen transport in membranes because the relevant energy barriers differ substantially.

A one-dimensional diffusion equation is derived for the time evolution of the orientational factor, κ 2 , in the Förster energy transfer rate. The κ 2 -dependent diffusion coefficient is obtained in three different ways: (1) by requiring the κ 2 autocorrelation function, calculated using the κ 2 diffusion equation, to be single-exponential with the exact characteristic time; (2) by projecting the multidimensional diffusion equation for the transition dipoles onto κ 2 using the local equilibrium approximation; and (3) by requiring exact and approximate κ 2 trajectories to be as close as possible using a Bayesian approach. Within the framework of this simple theory, the distance dependence of the fluorescence resonance energy transfer (FRET) efficiency can be calculated for all values of the ratio of the rotational correlation time of the transition dipoles to the lifetime of the donor excited state. The theoretical predictions are compared to the exact values obtained from Brownian dynamics simulations of the reorientation of the donor and acceptor transition dipoles.

We investigate the dependence of single-particle diffusion coefficients on the size and shape of the simulation box in molecular dynamics simulations of fluids and lipid membranes. We find that the diffusion coefficients of lipids and a carbon nanotube embedded in a lipid membrane diverge with the logarithm of the box width. For a neat Lennard-Jones fluid in flat rectangular boxes, diffusion becomes anisotropic, diverging logarithmically in all three directions with increasing box width. In elongated boxes, the diffusion coefficients normal to the long axis diverge linearly with the height-to-width ratio. For both lipid membranes and neat fluids, this behavior is predicted quantitatively by hydrodynamic theory. Mean-square displacements in the neat fluid exhibit intermediate regimes of anomalous diffusion, with t ln t and t(3/2) components in flat and elongated boxes, respectively. For membranes, the large finite-size effects, and the apparent inability to determine a well-defined lipid diffusion coefficient from simulation, rationalize difficulties in comparing simulation results to each other and to those from experiments.

Molecular modeling and molecular dynamics simulations play an important role in the functional characterization of complex I. With its large size and complicated function, linking quinone reduction to proton pumping across a membrane, complex I poses unique modeling challenges. Nonetheless, simulations have already helped in the identification of possible proton transfer pathways. Simulations have also shed light on the coupling between electron and proton transfer, thus pointing the way in the search for the mechanistic principles underlying the proton pump. In addition to reviewing what has already been achieved in complex I modeling, we aim here to identify pressing issues and to provide guidance for future research to harness the power of modeling in the functional characterization of complex I. This article is part of a Special Issue entitled Respiratory complex I, edited by Volker Zickermann and Ulrich Brandt., (Copyright © 2016 Elsevier B.V. All rights reserved.)

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.

The recent availability of long equilibrium simulations of protein folding in atomistic detail for more than 10 proteins allows us to identify the key interactions driving folding. We find that the collective fraction of native amino acid contacts, Q, captures remarkably well the transition states for all the proteins with a folding free energy barrier. Going beyond this global picture, we devise two different measures to quantify the importance of individual interresidue contacts in the folding mechanism: (i) the log-ratio of lifetimes of contacts during folding transition paths and in the unfolded state and (ii) a Bayesian measure of how predictive the formation of each contact is for being on a transition path. Both of these measures indicate that native, or near-native, contacts are important for determining mechanism, as might be expected. More remarkably, however, we found that for almost all the proteins, with the designed protein α3D being a notable exception, nonnative contacts play no significant part in determining folding mechanisms.

We explore the theoretical foundation of different string methods used to find dominant reaction pathways in high-dimensional configuration spaces. Pathways are assessed by the amount of reactive flux they carry and by their orientation relative to the committor function. By examining the effects of transforming between different collective coordinates that span the same underlying space, we unmask artificial coordinate dependences in strings optimized to follow the free energy gradient. In contrast, strings optimized to follow the drift vector produce reaction pathways that are significantly less sensitive to reparameterizations of the collective coordinates. The differences in these paths arise because the drift vector depends on both the free energy gradient and the diffusion tensor of the coarse collective variables. Anisotropy and position dependence of diffusion tensors arise commonly in spaces of coarse variables, whose generally slow dynamics are obtained by nonlinear projections of the strongly coupled atomic motions. We show here that transition paths constructed to account for dynamics by following the drift vector will (to a close approximation) carry the maximum reactive flux both in systems with isotropic position dependent diffusion and in systems with constant but anisotropic diffusion. We derive a simple method for calculating the committor function along paths that follow the reactive flux. Lastly, we provide guidance for the practical implementation of the dynamic string method.

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.

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.

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.

Polyamines are small, organic polycations that are ubiquitous and essential to all forms of life. Currently, how polyamines are transported across membranes is not understood. Recent studies have suggested that ATP13A2 and its close homologs, collectively known as P5B-ATPases, are polyamine transporters at endo-/lysosomes. Loss-of-function mutations of ATP13A2 in humans cause hereditary early-onset Parkinson's disease. To understand the polyamine transport mechanism of ATP13A2, we determined high-resolution cryoelectron microscopy (cryo-EM) structures of human ATP13A2 in five distinct conformational intermediates, which together, represent a near-complete transport cycle of ATP13A2. The structural basis of the polyamine specificity was revealed by an endogenous polyamine molecule bound to a narrow, elongated cavity within the transmembrane domain. The structures show an atypical transport path for a water-soluble substrate, in which polyamines may exit within the cytosolic leaflet of the membrane. Our study provides important mechanistic insights into polyamine transport and a framework to understand the functions and mechanisms of P5B-ATPases.

Drug delivery mitigates toxic side effects and poor pharmacokinetics of life-saving therapeutics and enhances treatment efficacy. However, direct cytoplasmic delivery of drugs and vaccines into cells has remained out of reach. We find that liposomes studded with 0.8-nm-wide carbon nanotube porins (CNTPs) function as efficient vehicles for direct cytoplasmic drug delivery by facilitating fusion of lipid membranes and complete mixing of the membrane material and vesicle interior content. Fusion kinetics data and coarse-grained molecular dynamics simulations reveal an unusual mechanism where CNTP dimers tether the vesicles, pull the membranes into proximity, and then fuse their outer and inner leaflets. Liposomes containing CNTPs in their membranes and loaded with an anticancer drug, doxorubicin, were effective in delivering the drug to cancer cells, killing up to 90% of them. Our results open an avenue for designing efficient drug delivery carriers compatible with a wide range of therapeutics.

Membrane targeting of the BECN1-containing class III PI 3-kinase (PI3KC3) complexes is pivotal to the regulation of autophagy. The interaction of PI3KC3 complex II and its ubiquitously expressed inhibitor, Rubicon, was mapped to the first β sheet of the BECN1 BARA domain and the UVRAG BARA2 domain by hydrogen-deuterium exchange and cryo-EM. These data suggest that the BARA β sheet 1 unfolds to directly engage the membrane. This mechanism was confirmed using protein engineering, giant unilamellar vesicle assays, and molecular simulations. Using this mechanism, a BECN1 β sheet-1 derived peptide activates both PI3KC3 complexes I and II, while HIV-1 Nef inhibits complex II. These data reveal how BECN1 switches on and off PI3KC3 binding to membranes. The observations explain how PI3KC3 inhibition by Rubicon, activation by autophagy-inducing BECN1 peptides, and inhibition by HIV-1 Nef are mediated by the switchable ability of the BECN1 BARA domain to partially unfold and insert into membranes.

Abstract: The oxysterol-binding protein-related protein (ORP) family is essential to sterol transfer and sterol-dependent signal transduction in eukaryotes. The crystal structure of one ORP family member, yeast Osh4, is known in apo and sterol-bound states. In the bound state, a 29 residue N-terminal lid region covers the opening of the cholesterol-binding tunnel, preventing cholesterol exchange. Equilibrium and steered molecular dynamics (MD) simulations of Osh4 were carried out to characterize the mechanism of cholesterol exchange. While most of the structural core was stable during the simulations, the lid was partly opened in the apo equilibrium MD simulation. Helix α7, which undergoes the largest conformational change in the crystallized bound and apo states, is conformationally coupled to the opening of the lid. The movement of α7 helps create a docking site for donor or acceptor membranes in the open state. In the steered MD simulations of cholesterol dissociation, we observed complete opening of the lid covering the cholesterol-binding tunnel. Cholesterol was found to exit the binding pocket in a step-wise process involving (i) the breaking of water-mediated hydrogen bonds and van der Waals contacts within the binding pocket, (ii) opening of the lid covering the binding pocket, and (iii) breakage of transient cholesterol contacts with the rim of the pocket and hydrophobic residues on the interior face of the lid. [Copyright &y& Elsevier]

Sensation of light is essential for all organisms. The eye-less nematode Caenorhabditis elegans detects UV and blue light to evoke escape behavior. The photosensor LITE-1 absorbs UV photons with an unusually high extinction coefficient, involving essential tryptophans. Here, we modeled the structure and dynamics of LITE-1 using AlphaFold2-multimer and molecular dynamics (MD) simulations and performed mutational and behavioral assays in C. elegans to characterize its function. LITE-1 resembles olfactory and gustatory receptors from insects, recently shown to be tetrameric ion channels. We identified residues required for channel gating, light absorption, and mechanisms of photo-oxidation, involving a likely binding site for the peroxiredoxin PRDX-2. Furthermore, we identified the binding pocket for a putative chromophore. Several residues lining this pocket have previously been established as essential for LITE-1 function. A newly identified critical cysteine pointing into the pocket represents a likely chromophore attachment site. We derived a model for how photon absorption, via a network of tryptophans and other aromatic amino acids, induces an excited state that is transferred to the chromophore. This evokes conformational changes in the protein, possibly leading to a state receptive to oxidation of cysteines and, jointly, to channel gating. Electrophysiological data support the idea that LITE-1 is a photon and H 2 O 2 -coincidence detector. Other proteins with similarity to LITE-1, specifically C. elegans GUR-3, likely use a similar mechanism for photon detection. Thus, a common protein fold and assembly, used for chemoreception in insects, possibly by binding of a particular compound, may have evolved into a light-activated ion channel. [Display omitted] • LITE-1 is a C. elegans UV/blue light receptor of unknown structure and mechanism • AlphaFold2 multimer and MD simulation suggest LITE-1 to be a tetrameric ion channel • A putative aromatic amino acid network and a chromophore may jointly detect photons • Light detection and photo-oxidation may cooperate to gate the nociceptive channel C. elegans senses noxious UV/blue light via LITE-1 photoreceptors. Based on AlphaFold2 multimer models and MD simulations, Hanson et al. suggest that LITE-1 is a light- and oxidation-gated ion channel. Mutagenesis identifies residues needed for channel gating, detecting photons and photo-oxidation products, and binding to a putative chromophore. [ABSTRACT FROM AUTHOR]