Characterizing protein energy landscape by self-learning multiscale simulations: application to a designed β-hairpin

Visualization of Self-Assembly and Hydration of a β-Hairpin through Integrated Small and Wide-Angle Neutron Scattering

Fundamental understanding of the structure and assembly of nanoscale building blocks is crucial for the development of novel biomaterials with defined architectures and function. However, accessing self-consistent structural information across multiple length scales is challenging. This limits opportunities to exploit atomic scale interactions to achieve emergent macroscale properties. In this work we present an integrative small- and wide-angle neutron scattering approach coupled with computational modeling to reveal the multiscale structure of hierarchically self-assembled β hairpins in aqueous solution across 4 orders of magnitude in length scale from 0.1 Å to 300 nm. Our results demonstrate the power of this self-consistent cross-length scale approach and allows us to model both the large-scale self-assembly and small-scale hairpin hydration of the model β hairpin CLN025. Using this combination of techniques, we map the hydrophobic/hydrophilic character of this model self-assembled biomolecular surface with atomic resolution. These results have important implications for the multiscale investigation of aqueous peptides and proteins, for the prediction of ligand binding and molecular associations for drug design, and for understanding the self-assembly of peptides and proteins for functional biomaterials.

Contrastive Learning of Coarse-Grained Force Fields

Coarse-grained models have proven helpful for simulating complex systems over long time scales to provide molecular insights into various processes. Methodologies for systematic parametrization of the underlying energy function or force field that describes the interactions among different components of the system are of great interest for ensuring simulation accuracy. We present a new method, potential contrasting, to enable efficient learning of force fields that can accurately reproduce the conformational distribution produced with all-atom simulations. Potential contrasting generalizes the noise contrastive estimation method with umbrella sampling to better learn the complex energy landscape of molecular systems. When applied to the Trp-cage protein, we found that the technique produces force fields that thoroughly capture the thermodynamics of the folding process despite the use of only α-carbons in the coarse-grained model. We further showed that potential contrasting could be applied over large data sets that combine the conformational ensembles of many proteins to improve force field transferability. We anticipate potential contrasting as a powerful tool for building general-purpose coarse-grained force fields.

Solvent-scaling as an alternative to coarse-graining in adaptive-resolution simulations: The adaptive solvent-scaling (AdSoS) scheme

A new approach termed Adaptive Solvent-Scaling (AdSoS) is introduced for performing simulations of a solute embedded in a fine-grained (FG) solvent region itself surrounded by a coarse-grained (CG) solvent region, with a continuous FG ↔ CG switching of the solvent resolution across a buffer layer. Instead of relying on a distinct CG solvent model, the AdSoS scheme is based on CG models defined by a dimensional scaling of the FG solvent by a factor s, accompanied by an s-dependent modulation of the atomic masses and interaction parameters. The latter changes are designed to achieve an isomorphism between the dynamics of the FG and CG models, and to preserve the dispersive and dielectric solvation properties of the solvent with respect to a solute at FG resolution. This scaling approach offers a number of advantages compared to traditional coarse-graining: (i) the CG parameters are immediately related to those of the FG model (no need to parameterize a distinct CG model); (ii) nearly ideal mixing is expected for CG variants with similar s-values (ideal mixing holding in the limit of identical s-values); (iii) the solvent relaxation timescales should be preserved (no dynamical acceleration typical for coarse-graining); (iv) the graining level N_G (number of FG molecules represented by one CG molecule) can be chosen arbitrarily (in particular, N_G = s³ is not necessarily an integer); and (v) in an adaptive-resolution scheme, this level can be varied continuously as a function of the position (without requiring a bundling mechanism), and this variation occurs at a constant number of particles per molecule (no occurrence of fractional degrees of freedom in the buffer layer). By construction, the AdSoS scheme minimizes the thermodynamic mismatch between the different regions of the adaptive-resolution system, leading to a nearly homogeneous scaled solvent density s³ρ. Residual density artifacts in and at the surface of the boundary layer can easily be corrected by means of a grid-based biasing potential constructed in a preliminary pure-solvent simulation. This article introduces the AdSoS scheme and provides an initial application to pure atomic liquids (no solute) with Lennard-Jones plus Coulomb interactions in a slab geometry.

Computational methods in the study of self-entangled proteins: a critical appraisal

The existence of self-entangled proteins, the native structure of which features a complex topology, unveils puzzling, and thus fascinating, aspects of protein biology and evolution. The discovery that a polypeptide chain can encode the capability to self-entangle in an efficient and reproducible way during folding, has raised many questions, regarding the possible function of these knots, their conservation along evolution, and their role in the folding paradigm. Understanding the function and origin of these entanglements would lead to deep implications in protein science, and this has stimulated the scientific community to investigate self-entangled proteins for decades by now. In this endeavour, advanced experimental techniques are more and more supported by computational approaches, that can provide theoretical guidelines for the interpretation of experimental results, and for the effective design of new experiments. In this review we provide an introduction to the computational study of self-entangled proteins, focusing in particular on the methodological developments related to this research field. A comprehensive collection of techniques is gathered, ranging from knot theory algorithms, that allow detection and classification of protein topology, to Monte Carlo or molecular dynamics strategies, that constitute crucial instruments for investigating thermodynamics and kinetics of this class of proteins.

On-the-Fly Specifications of Reaction Coordinates in Parallel Cascade Selection Molecular Dynamics Accelerate Conformational Transitions of Proteins

Parallel Cascade Selection Molecular Dynamics (PaCS-MD) is an efficient conformational sampling method for generating a set of reactive trajectories that connect a given reactant and a product. In PaCS-MD, initial structures relevant to conformational transitions are reasonably selected by referring to a set of reaction coordinates (RCs), and short-time molecular dynamics (MD) simulations are independently launched from them. To efficiently perform PaCS-MD, specifications of RCs are essential, but specifying reasonable RCs is generally nontrivial. In the present study, we propose on-the-fly specifications of RCs as an extended PaCS-MD. In the present method, n types of RCs are provided as candidates a priori as follows: RC = (X₁, X₂, ..., X _n), and one of the RCs is specified in a cycle-dependent manner, i.e. the reasonable RC is searched at every cycle by evaluating gradients of the RCs, i.e. RC with the steepest gradient for cycle is regarded as the reasonable RC, and conformational resampling proceeds along it, promoting conformational transition of a given protein. For a demonstration, the extended PaCS-MD was applied to reproduce the open-closed conformational transition of T4 lysozyme (T4L). As candidates of possible RCs, (1) root-mean square distance, (2) principal coordinates, (3) accessible surface area, (4) radius of gyration, and (5) end-to-end distance were adopted in the cycle-dependent specifications of RCs. Through the demonstration, the extended PaCS-MD successfully reproduced the conformational transition from the open to closed states of T4L. As a more complicated practice, a dimerization process of diubiquitin was efficiently reproduced with the extended PaCS-MD, showing the high conformational sampling efficiency of the present algorithm. In contrast, the conventional PaCS-MD with a fixed RC sometimes failed to generate a set of reactive trajectories when an unreasonable RC was specified, i.e. the conformational sampling efficiency of PaCS-MD might more or less depend on the specified RCs. Judging from the present demonstrations, on-the-fly specifications of RCs might be effective in reproducing/predicting essential transitions of a given protein.

Metal cofactor modulated folding and target recognition of HIV-1 NCp7

The HIV-1 nucleocapsid 7 (NCp7) plays crucial roles in multiple stages of HIV-1 life cycle, and its biological functions rely on the binding of zinc ions. Understanding the molecular mechanism of how the zinc ions modulate the conformational dynamics and functions of the NCp7 is essential for the drug development and HIV-1 treatment. In this work, using a structure-based coarse-grained model, we studied the effects of zinc cofactors on the folding and target RNA(SL3) recognition of the NCp7 by molecular dynamics simulations. After reproducing some key properties of the zinc binding and folding of the NCp7 observed in previous experiments, our simulations revealed several interesting features in the metal ion modulated folding and target recognition. Firstly, we showed that the zinc binding makes the folding transition states of the two zinc fingers less structured, which is in line with the Hammond effect observed typically in mutation, temperature or denaturant induced perturbations to protein structure and stability. Secondly, We showed that there exists mutual interplay between the zinc ion binding and NCp7-target recognition. Binding of zinc ions enhances the affinity between the NCp7 and the target RNA, whereas the formation of the NCp7-RNA complex reshapes the intrinsic energy landscape of the NCp7 and increases the stability and zinc affinity of the two zinc fingers. Thirdly, by characterizing the effects of salt concentrations on the target RNA recognition, we showed that the NCp7 achieves optimal balance between the affinity and binding kinetics near the physiologically relevant salt concentrations. In addition, the effects of zinc binding on the inter-domain conformational flexibility and folding cooperativity of the NCp7 were also discussed.

Proximal distributions from angular correlations: a measure of the onset of coarse-graining

In this work we examine and extend the theory of proximal radial distribution functions for molecules in solution. We point out two formal extensions, the first of which generalizes the proximal distribution function hierarchy approach to the complete, angularly dependent molecular pair distribution function. Second, we generalize from the traditional right-handed solute-solvent proximal distribution functions to the left-handed distributions. The resulting neighbor hierarchy convergence is shown to provide a measure of the coarse-graining of the internal solute sites with respect to the solvent. Simulation of the test case of a deca-alanine peptide shows that this coarse-graining measure converges at a length scale of approximately 5 amino acids for the system considered.

Perspective: Coarse-grained models for biomolecular systems

By focusing on essential features, while averaging over less important details, coarse-grained (CG) models provide significant computational and conceptual advantages with respect to more detailed models. Consequently, despite dramatic advances in computational methodologies and resources, CG models enjoy surging popularity and are becoming increasingly equal partners to atomically detailed models. This perspective surveys the rapidly developing landscape of CG models for biomolecular systems. In particular, this review seeks to provide a balanced, coherent, and unified presentation of several distinct approaches for developing CG models, including top-down, network-based, native-centric, knowledge-based, and bottom-up modeling strategies. The review summarizes their basic philosophies, theoretical foundations, typical applications, and recent developments. Additionally, the review identifies fundamental inter-relationships among the diverse approaches and discusses outstanding challenges in the field. When carefully applied and assessed, current CG models provide highly efficient means for investigating the biological consequences of basic physicochemical principles. Moreover, rigorous bottom-up approaches hold great promise for further improving the accuracy and scope of CG models for biomolecular systems.

Coarse-grained molecular simulations of large biomolecules

Recently, we saw a dramatic increase in the number of researches that rely on coarse-grained (CG) simulations for large biomolecules. Here, first, we briefly describe recently developed and used CG models for proteins and nucleic acids. Balance between structure-based and physico-chemical terms is a key issue. We also discuss the multiscale algorithms used to derive CG parameters. Next, we comment on the dynamics used in CG simulations with an emphasis on the importance of hydrodynamic interactions. We then discuss the pros and cons of CG simulations. Finally, we overview recent exciting applications of CG simulations. Publicly available tools and software for CG simulations are also summarized.

Frustration, specific sequence dependence, and nonlinearity in large-amplitude fluctuations of allosteric proteins

Proteins have often evolved sequences so as to acquire the ability for regulation via allosteric conformational change. Here we investigate how allosteric dynamics is designed through sequences with nonlinear interaction features. First, for 71 allosteric proteins of which two, open and closed, structures are available, a statistical survey of interactions using an all-atom model with effective solvation shows that those residue contact interactions specific to one of the two states are significantly weaker than are the contact interactions shared by the two states. This interaction feature indicates there is underlying sequence design to facilitate conformational change. Second, based on the energy landscape theory, we implement these interaction features into a new atomic-interaction-based coarse-grained model via a multiscale simulation protocol (AICG). The AICG model outperforms standard coarse-grained models for predictions of the native-state mean fluctuations and of the conformational change direction. Third, using the new model for adenylate kinase, we show that intrinsic fluctuations in one state contain rare and large-amplitude motions nearly reaching the other state. Such large-amplitude motions are realized partly by sequence specificity and partly by the nonlinear nature of contact interactions, leading to cracking. Both features enhance conformational transition rates.