Properties of low-dimensional collective variables in the molecular dynamics of biopolymers

The description of the dynamics of a complex, high-dimensional system in terms of a low-dimensional set of collective variables Y can be fruitful if the low dimensional representation satisfies a Langevin equation with drift and diffusion coefficients which depend only on Y. We present a computational scheme to evaluate whether a given collective variable provides a faithful low-dimensional representation of the dynamics of a high-dimensional system. The scheme is based on the framework of finite-difference Langevin-equation, similar to that used for molecular-dynamics simulations. This allows one to calculate the drift and diffusion coefficients in any point of the full-dimensional system. The width of the distribution of drift and diffusion coefficients in an ensemble of microscopic points at the same value of Y indicates to which extent the dynamics of Y is described by a simple Langevin equation. Using a simple protein model we show that collective variables often used to describe biopolymers display a non-negligible width both in the drift and in the diffusion coefficients. We also show that the associated effective force is compatible with the equilibrium free--energy calculated from a microscopic sampling, but results in markedly different dynamical properties

Integrative structural and dynamical biology with PLUMED-ISDB

Accurate structural models of biological systems can be obtained by properly combining experimental data with a priori physico-chemical knowledge. Here we present PLUMED-ISDB, an open-source, freely-available module of the popular PLUMED library, which enables the simultaneous determination of structure and dynamics of conformationally heterogeneous systems by integrating experimental data with a priori information. This integration is achieved using metainference, a general Bayesian framework that accounts for both noise in the data and their ensemble-averaged nature. PLUMED-ISDB implements different types of experimental data, such as several NMR observables, FRET, SAXS and cryo-electron microscopy data, and enables modelling structure and dynamics of individual proteins, protein complexes, membrane proteins, RNA and DNA, using a variety of enhanced sampling methods and resolutions of the system

Metadynamic sampling of the free energy landscapes of proteins coupled with a Monte Carlo algorithm

Metadynamics is a powerful computational tool to obtain the free energy landscape of complex systems. The Monte Carlo algorithm has proven useful to calculate thermodynamic quantities associated with simplified models of proteins, and thus to gain an ever-increasing understanding on the general principles underlying the mechanism of protein folding. We show that it is possible to couple metadynamics and Monte Carlo algorithms to obtain the free energy of model proteins in a way which is computationally very economical.Comment: Submitted to Gen

Determination of Protein Structural Ensembles by Hybrid-Resolution SAXS Restrained Molecular Dynamics

Small-angle X-ray scattering (SAXS) experiments provide low-resolution but valuable information about the dynamics of biomolecular systems, which could be ideally integrated into molecular dynamics (MD) simulations to accurately determine conformational ensembles of flexible proteins. The applicability of this strategy is hampered by the high computational cost required to calculate scattering intensities from three-dimensional structures. We previously presented a hybrid resolution method that makes atomistic SAXS-restrained MD simulation feasible by adopting a coarse-grained approach to efficiently back-calculate scattering intensities; here, we extend this technique, applying it in the framework of metainference with the aim to investigate the dynamical behavior of flexible biomolecules. The efficacy of the method is assessed on the K63-diubiquitin, showing that the inclusion of SAXS restraints is effective in generating a reliable conformational ensemble, improving the agreement with independent experimental data

Maximum voluntary ventilation is more strongly associated with energy expenditure during simple activities of daily living than measures of airflow obstruction or respiratory muscle strength in patients with COPD

This is a retrospective analysis of data in which we explored the association between energy expenditure (EE) and lung function in patients with chronic obstructive pulmonary disease (COPD). A total of 36 participants (20 males; forced expiratory volume in 1 second (FEV1) of 48 ± 15% predicted) underwent measures of indirect calorimetry whilst performing five simple activities of daily living. Maximal voluntary ventilation was the only lung function parameter associated with EE. These data highlight the limited extent to which the FEV1 is related to the functional performance of patients with COPD

Molecular dynamics ensemble refinement of the heterogeneous native state of NCBD using chemical shifts and NOEs

Many proteins display complex dynamical properties that are often intimately linked to their biological functions. As the native state of a protein is best described as an ensemble of conformations, it is important to be able to generate models of native state ensembles with high accuracy. Due to limitations in sampling efficiency and force field accuracy it is, however, challenging to obtain accurate ensembles of protein conformations by the use of molecular simulations alone. Here we show that dynamic ensemble refinement, which combines an accurate atomistic force field with commonly available nuclear magnetic resonance (NMR) chemical shifts and NOEs, can provide a detailed and accurate description of the conformational ensemble of the native state of a highly dynamic protein. As both NOEs and chemical shifts are averaged on timescales up to milliseconds, the resulting ensembles reflect the structural heterogeneity that goes beyond that probed, e.g., by NMR relaxation order parameters. We selected the small protein domain NCBD as object of our study since this protein, which has been characterized experimentally in substantial detail, displays a rich and complex dynamical behaviour. In particular, the protein has been described as having a molten-globule like structure, but with a relatively rigid core. Our approach allowed us to describe the conformational dynamics of NCBD in solution, and to probe the structural heterogeneity resulting from both short- and long-timescale dynamics by the calculation of order parameters on different time scales. These results illustrate the usefulness of our approach since they show that NCBD is rather rigid on the nanosecond timescale, but interconverts within a broader ensemble on longer timescales, thus enabling the derivation of a coherent set of conclusions from various NMR experiments on this protein, which could otherwise appear in contradiction with each other

Sequence Specificity in the Entropy-Driven Binding of a Small Molecule and a Disordered Peptide

Approximately one-third of the human proteome is made up of proteins that are entirely disordered or that contain extended disordered regions. Although these disordered proteins are closely linked with many major diseases, their binding mechanisms with small molecules remain poorly understood, and a major concern is whether their specificity can be sufficient for drug development. Here, by studying the interaction of a small molecule and a disordered peptide from the oncogene protein c-Myc, we describe a "specific-diffuse" binding mechanism that exhibits sequence specificity despite being of entropic nature. By combining NMR spectroscopy, biophysical measurements, statistical inference, and molecular simulations, we provide a quantitative measure of such sequence specificity and compare it to the case of the interaction of urea, which is diffuse but not specific. To investigate whether this type of binding can generally modify intermolecular interactions, we show that it leads to an inhibition of the aggregation of the peptide. These results suggest that the binding mechanism that we report may create novel opportunities to discover drugs that target disordered proteins in their monomeric states in a specific manner.G.T.H. is supported by the Churchill Scholarship and the Gates Cambridge Trust Scholarship

Metadynamic metainference : enhanced sampling of the metainference ensemble using metadynamics

Accurate and precise structural ensembles of proteins and macromolecular complexes can be obtained with metainference, a recently proposed Bayesian inference method that integrates experimental information with prior knowledge and deals with all sources of errors in the data as well as with sample heterogeneity. The study of complex macromolecular systems, however, requires an extensive conformational sampling, which represents a separate challenge. To address such challenge and to exhaustively and efficiently generate structural ensembles we combine metainference with metadynamics and illustrate its application to the calculation of the free energy landscape of the alanine dipeptide

Hierarchy of folding and unfolding events of protein G, CI2, and ACBP from explicit-solvent simulations

The study of the mechanism which is at the basis of the phenomenon of protein folding requires the knowledge of multiple folding trajectories under biological conditions. Using a biasing molecular-dynamics algorithm based on the physics of the ratchet-and-pawl system, we carry out all-atom, explicit solvent simulations of the sequence of folding events which proteins G, CI2, and ACBP undergo in evolving from the denatured to the folded state. Starting from highly disordered conformations, the algorithm allows the proteins to reach, at the price of a modest computational effort, nativelike conformations, within a root mean square deviation (RMSD) of approximately 1 . A scheme is developed to extract, from the myriad of events, information concerning the sequence of native contact formation and of their eventual correlation. Such an analysis indicates that all the studied proteins fold hierarchically, through pathways which, although not deterministic, are well-defined with respect to the order of contact formation. The algorithm also allows one to study unfolding, a process which looks, to a large extent, like the reverse of the major folding pathway. This is also true in situations in which many pathways contribute to the folding process, like in the case of protein G