General Protein Data Bank-Based Collective Variables for Protein Folding

Understanding the Energy Landscape of Intrinsically Disordered Protein Ensembles

A substantial portion of various organisms' proteomes comprises intrinsically disordered proteins (IDPs) that lack a defined three-dimensional structure. These IDPs exhibit a diverse array of conformations, displaying remarkable spatiotemporal heterogeneity and exceptional conformational flexibility. Characterizing the structure or structural ensemble of IDPs presents significant conceptual and methodological challenges owing to the absence of a well-defined native structure. While databases such as the Protein Ensemble Database (PED) provide IDP ensembles obtained through a combination of experimental data and molecular modeling, the absence of reaction coordinates poses challenges in comprehensively understanding pertinent aspects of the system. In this study, we leverage the energy landscape visualization method (JCTC, 6482, 2019) to scrutinize four IDP ensembles sourced from PED. ELViM, a methodology that circumvents the need for a priori reaction coordinates, aids in analyzing the ensembles. The specific IDP ensembles investigated are as follows: two fragments of nucleoporin (NUL: 884-993 and NUS: 1313-1390), yeast sic 1 N-terminal (1-90), and the N-terminal SH3 domain of Drk (1-59). Utilizing ELViM enables the comprehensive validation of ensembles, facilitating the detection of potential inconsistencies in the sampling process. Additionally, it allows for identifying and characterizing the most prevalent conformations within an ensemble. Moreover, ELViM facilitates the comparative analysis of ensembles obtained under diverse conditions, thereby providing a powerful tool for investigating the functional mechanisms of IDPs.

Multitask Machine Learning of Collective Variables for Enhanced Sampling of Rare Events

Computing accurate reaction rates is a central challenge in computational chemistry and biology because of the high cost of free energy estimation with unbiased molecular dynamics. In this work, a data-driven machine learning algorithm is devised to learn collective variables with a multitask neural network, where a common upstream part reduces the high dimensionality of atomic configurations to a low dimensional latent space and separate downstream parts map the latent space to predictions of basin class labels and potential energies. The resulting latent space is shown to be an effective low-dimensional representation, capturing the reaction progress and guiding effective umbrella sampling to obtain accurate free energy landscapes. This approach is successfully applied to model systems including a 5D Müller Brown model, a 5D three-well model, the alanine dipeptide in vacuum, and an Au(110) surface reconstruction unit reaction. It enables automated dimensionality reduction for energy controlled reactions in complex systems, offers a unified and data-efficient framework that can be trained with limited data, and outperforms single-task learning approaches, including autoencoders.

Using Data-Reduction Techniques to Analyze Biomolecular Trajectories

This chapter discusses the way in which dimensionality reduction algorithms such as diffusion maps and sketch-map can be used to analyze molecular dynamics trajectories. The first part discusses how these various algorithms function as well as practical issues such as landmark selection and how these algorithms can be used when the data to be analyzed comes from enhanced sampling trajectories. In the later part a comparison between the results obtained by applying various algorithms to two sets of sample data is performed and discussed. This section is then followed by a summary of how one algorithm in particular, sketch-map, has been applied to a range of problems. The chapter concludes with a discussion on the directions that we believe this field is currently moving.

Adaptive enhanced sampling with a path-variable for the simulation of protein folding and aggregation

In this article, we present a novel adaptive enhanced sampling molecular dynamics (MD) method for the accelerated simulation of protein folding and aggregation. We introduce a path-variable L based on the un-biased momenta p and displacements dq for the definition of the bias s applied to the system and derive 3 algorithms: general adaptive bias MD, adaptive path-sampling, and a hybrid method which combines the first 2 methodologies. Through the analysis of the correlations between the bias and the un-biased gradient in the system, we find that the hybrid methodology leads to an improved force correlation and acceleration in the sampling of the phase space. We apply our method on SPC/E water, where we find a conservation of the average water structure. We then use our method to sample dialanine and the folding of TrpCage, where we find a good agreement with simulation data reported in the literature. Finally, we apply our methodologies on the initial stages of aggregation of a hexamer of Alzheimer's amyloid β fragment 25-35 (Aβ 25-35) and find that transitions within the hexameric aggregate are dominated by entropic barriers, while we speculate that especially the conformation entropy plays a major role in the formation of the fibril as a rate limiting factor.

Extending the range and physical accuracy of coarse-grained models: Order parameter dependent interactions

Order parameters (i.e., collective variables) are often used to describe the behavior of systems as they capture different features of the free energy surface. Yet, most coarse-grained (CG) models only employ two- or three-body non-bonded interactions between the CG particles. In situations where these interactions are insufficient for the CG model to reproduce the structural distributions of the underlying fine-grained (FG) model, additional interactions must be included. In this paper, we introduce an approach to expand the basis sets available in the multiscale coarse-graining (MS-CG) methodology by including order parameters. Then, we investigate the ability of an additive local order parameter (e.g., density) and an additive global order parameter (i.e., distance from a hard wall) to improve the description of CG models in interfacial systems. Specifically, we study methanol liquid-vapor coexistence, acetonitrile liquid-vapor coexistence, and acetonitrile liquid confined by hard-wall plates, all using single site CG models. We find that the use of order parameters dramatically improves the reproduction of structural properties of interfacial CG systems relative to the FG reference as compared with pairwise CG interactions alone.