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We provide a stand-alone software, the BioAFMviewer, which transforms biomolecular structures into the graphical representation corresponding to the outcome of atomic force microscopy (AFM) experiments. The AFM graphics is obtained by performing simulated scanning over the molecular structure encoded in the corresponding PDB file. A versatile molecular viewer integrates the visualization of PDB structures and control over their orientation, while synchronized simulated scanning with variable spatial resolution and tip-shape geometry produces the corresponding AFM graphics. We demonstrate the applicability of the BioAFMviewer by comparing simulated AFM graphics to high-speed AFM observations of proteins. The software can furthermore process molecular movies of conformational motions, e.g. those obtained from servers which model functional transitions within a protein, and produce the corresponding simulated AFM movie. The BioAFMviewer software provides the platform to employ the plethora of structural and dynamical data of proteins in order to help in the interpretation of biomolecular AFM experiments.

Interacting-particle reaction dynamics (iPRD) combines the simulation of dynamical trajectories of interacting particles as in molecular dynamics (MD) simulations with reaction kinetics, in which particles appear, disappear, or change their type and interactions based on a set of reaction rules. This combination facilitates the simulation of reaction kinetics in crowded environments, involving complex molecular geometries such as polymers, and employing complex reaction mechanisms such as breaking and fusion of polymers. iPRD simulations are ideal to simulate the detailed spatiotemporal reaction mechanism in complex and dense environments, such as in signalling processes at cellular membranes, or in nano- to microscale chemical reactors. Here we introduce the iPRD software ReaDDy 2, which provides a Python interface in which the simulation environment, particle interactions and reaction rules can be conveniently defined and the simulation can be run, stored and analyzed. A C++ interface is available to enable deeper and more flexible interactions with the framework. The main computational work of ReaDDy 2 is done in hardware-specific simulation kernels. While the version introduced here provides single- and multi-threading CPU kernels, the architecture is ready to implement GPU and multi-node kernels. We demonstrate the efficiency and validity of ReaDDy 2 using several benchmark examples. ReaDDy 2 is available at the https://readdy.github.io/ website.

To address the large gap between time scales that can be easily reached by molecular simulations and those required to understand protein dynamics, we present a rapid self-consistent approximation of the side chain free energy at every integration step. In analogy with the adiabatic Born-Oppenheimer approximation for electronic structure, the protein backbone dynamics are simulated as preceding according to the dictates of the free energy of an instantaneously-equilibrated side chain potential. The side chain free energy is computed on the fly, allowing the protein backbone dynamics to traverse a greatly smoothed energetic landscape. This computation results in extremely rapid equilibration and sampling of the Boltzmann distribution. Our method, termed Upside, employs a reduced model involving the three backbone atoms, along with the carbonyl oxygen and amide proton, and a single (oriented) side chain bead having multiple locations reflecting the conformational diversity of the side chain's rotameric states. We also introduce a novel, maximum-likelihood method to parameterize the side chain interactions using protein structures. We demonstrate state-of-the-art accuracy for predicting χ1 rotamer states while consuming only milliseconds of CPU time. Our method enables rapidly equilibrating coarse-grained simulations that can nonetheless contain significant molecular detail. We also show that the resulting free energies of the side chains are sufficiently accurate for de novo folding of some proteins.

We describe an approach for integrating distance restraints from Double Electron-Electron Resonance (DEER) spectroscopy into Rosetta with the purpose of modeling alternative protein conformations from an initial experimental structure. Fundamental to this approach is a multilateration algorithm that harnesses sets of interconnected spin label pairs to identify optimal rotamer ensembles at each residue that fit the DEER decay in the time domain. Benchmarked relative to data analysis packages, the algorithm yields comparable distance distributions with the advantage that fitting the DEER decay and rotamer ensemble optimization are coupled. We demonstrate this approach by modeling the protonation-dependent transition of the multidrug transporter PfMATE to an inward facing conformation with a deviation to the experimental structure of less than 2Å C α RMSD. By decreasing spin label rotamer entropy, this approach engenders more accurate Rosetta models that are also more closely clustered, thus setting the stage for more robust modeling of protein conformational changes.

Atomistic simulations can provide valuable, experimentally-verifiable insights into protein folding mechanisms, but existing ab initio simulation methods are restricted to only the smallest proteins due to severe computational speed limits. The folding of larger proteins has been studied using native-centric potential functions, but such models omit the potentially crucial role of non-native interactions. Here, we present an algorithm, entitled DBFOLD, which can predict folding pathways for a wide range of proteins while accounting for the effects of non-native contacts. In addition, DBFOLD can predict the relative rates of different transitions within a protein’s folding pathway. To accomplish this, rather than directly simulating folding, our method combines equilibrium Monte-Carlo simulations, which deploy enhanced sampling, with unfolding simulations at high temperatures. We show that under certain conditions, trajectories from these two types of simulations can be jointly analyzed to compute unknown folding rates from detailed balance. This requires inferring free energies from the equilibrium simulations, and extrapolating transition rates from the unfolding simulations to lower, physiologically-reasonable temperatures at which the native state is marginally stable. As a proof of principle, we show that our method can accurately predict folding pathways and Monte-Carlo rates for the well-characterized Streptococcal protein G. We then show that our method significantly reduces the amount of computation time required to compute the folding pathways of large, misfolding-prone proteins that lie beyond the reach of existing direct simulation. Our algorithm, which is available online , can generate detailed atomistic models of protein folding mechanisms while shedding light on the role of non-native intermediates which may crucially affect organismal fitness and are frequently implicated in disease.

An ongoing challenge in protein chemistry is to identify the underlying interaction energies that capture protein dynamics. The traditional trade-off in biomolecular simulation between accuracy and computational efficiency is predicated on the assumption that detailed force fields are typically well-parameterized, obtaining a significant fraction of possible accuracy. We re-examine this trade-off in the more realistic regime in which parameterization is a greater source of error than the level of detail in the force field. To address parameterization of coarse-grained force fields, we use the contrastive divergence technique from machine learning to train from simulations of 450 proteins. In our procedure, the computational efficiency of the model enables high accuracy through the precise tuning of the Boltzmann ensemble. This method is applied to our recently developed Upside model, where the free energy for side chains is rapidly calculated at every time-step, allowing for a smooth energy landscape without steric rattling of the side chains. After this contrastive divergence training, the model is able to de novo fold proteins up to 100 residues on a single core in days. This improved Upside model provides a starting point both for investigation of folding dynamics and as an inexpensive Bayesian prior for protein physics that can be integrated with additional experimental or bioinformatic data.

The most frequently used approach for protein structure prediction is currently homology modeling. The 3D model building phase of this methodology is critical for obtaining an accurate and biologically useful prediction. The most widely employed tool to perform this task is MODELLER. This program implements the \"modeling by satisfaction of spatial restraints\" strategy and its core algorithm has not been altered significantly since the early 1990s. In this work, we have explored the idea of modifying MODELLER with two effective, yet computationally light strategies to improve its 3D modeling performance. Firstly, we have investigated how the level of accuracy in the estimation of structural variability between a target protein and its templates in the form of σ values profoundly influences 3D modeling. We show that the σ values produced by MODELLER are on average weakly correlated to the true level of structural divergence between target-template pairs and that increasing this correlation greatly improves the program's predictions, especially in multiple-template modeling. Secondly, we have inquired into how the incorporation of statistical potential terms (such as the DOPE potential) in the MODELLER's objective function impacts positively 3D modeling quality by providing a small but consistent improvement in metrics such as GDT-HA and lDDT and a large increase in stereochemical quality. Python modules to harness this second strategy are freely available at https://github.com/pymodproject/altmod. In summary, we show that there is a large room for improving MODELLER in terms of 3D modeling quality and we propose strategies that could be pursued in order to further increase its performance.

Intrinsically disordered proteins/regions (IDPs/IDRs) are prevalent in allosteric regulation. It was previously thought that intrinsic disorder is favorable for maximizing the allosteric coupling. Here, we propose a comprehensive ensemble model to compare the roles of both order-order transition and disorder-order transition in allosteric effect. It is revealed that the MWC pathway (order-order transition) has a higher probability than the EAM pathway (disorder-order transition) in allostery, suggesting a complicated role of IDPs/IDRs in regulatory proteins. In addition, an analytic formula for the maximal allosteric coupling response is obtained, which shows that too stable or too unstable state is unfavorable to endow allostery, and is thus helpful for rational design of allosteric drugs.

Significance With data proliferating across many disciplines, data analysts often wish to identify abrupt changes in complex systems with many measured quantities—a problem complicated by the fact that a given change might affect only a few of these quantities. We developed a method that accurately identifies changes in such systems by searching concurrently for change times and the subset of measured quantities that change at each of these times. This work was motivated by the challenge of detecting biologically interesting structural changes in proteins, but our method may prove useful in diverse application domains. Research on change-point detection, the classical problem of detecting abrupt changes in sequential data, has focused predominantly on datasets with a single observable. A growing number of time series datasets, however, involve many observables, often with the property that a given change typically affects only a few of the observables. We introduce a general statistical method that, given many noisy observables, detects points in time at which various subsets of the observables exhibit simultaneous changes in data distribution and explicitly identifies those subsets. Our work is motivated by the problem of identifying the nature and timing of biologically interesting conformational changes that occur during atomic-level simulations of biomolecules such as proteins. This problem has proved challenging both because each such conformational change might involve only a small region of the molecule and because these changes are often subtle relative to the ever-present background of faster structural fluctuations. We show that our method is effective in detecting biologically interesting conformational changes in molecular dynamics simulations of both folded and unfolded proteins, even in cases where these changes are difficult to detect using alternative techniques. This method may also facilitate the detection of change points in other types of sequential data involving large numbers of observables—a problem likely to become increasingly important as such data continue to proliferate in a variety of application domains.

The role of electrostatic interactions and mutations that change charge states in intrinsically disordered proteins (IDPs) is well-established, but many disease-associated mutations in IDPs are charge-neutral. The Val66Met single nucleotide polymorphism (SNP) in precursor brain-derived neurotrophic factor (BDNF) is one of the earliest SNPs to be associated with neuropsychiatric disorders, and the underlying molecular mechanism is unknown. Here we report on over 250 μs of fully-atomistic, explicit solvent, temperature replica-exchange molecular dynamics (MD) simulations of the 91 residue BDNF prodomain, for both the V66 and M66 sequence. The simulations were able to correctly reproduce the location of both local and non-local secondary structure changes due to the Val66Met mutation, when compared with NMR spectroscopy. We find that the change in local structure is mediated via entropic and sequence specific effects. We developed a hierarchical sequence-based framework for analysis and conceptualization, which first identifies \"blobs\" of 4-15 residues representing local globular regions or linkers. We use this framework within a novel test for enrichment of higher-order (tertiary) structure in disordered proteins; the size and shape of each blob is extracted from MD simulation of the real protein (RP), and used to parameterize a self-avoiding heterogenous polymer (SAHP). The SAHP version of the BDNF prodomain suggested a protein segmented into three regions, with a central long, highly disordered polyampholyte linker separating two globular regions. This effective segmentation was also observed in full simulations of the RP, but the Val66Met substitution significantly increased interactions across the linker, as well as the number of participating residues. The Val66Met substitution replaces β-bridging between V66 and V94 (on either side of the linker) with specific side-chain interactions between M66 and M95. The protein backbone in the vicinity of M95 is then free to form β-bridges with residues 31-41 near the N-terminus, which condenses the protein. A significant role for Met/Met interactions is consistent with previously-observed non-local effects of the Val66Met SNP, as well as established interactions between the Met66 sequence and a Met-rich receptor that initiates neuronal growth cone retraction.