Altruistic Metadynamics: Multisystem Biased Simulation

Probing protein stability: towards a computational atomistic, reliable, affordable, and improvable model

We present an improved application of a recently proposed computational method designed to evaluate the change of free energy as a function of the average value of a suitably chosen collective variable in proteins. The method is based on a full atomistic description of the protein and its environment. The goal is to understand how the protein melting temperature changes upon single-point mutations, because the sign of the temperature variation will allow us to discriminate stabilizing vs. destabilizing mutations in protein sequences. In this refined application the method is based on altruistic well-tempered metadynamics, a variant of multiple-walkers metadynamics. The resulting metastatistics is then modulated by the maximal constrained entropy principle. The latter turns out to be especially helpful in free-energy calculations as it is able to alleviate the severe limitations of metadynamics in properly sampling folded and unfolded configurations. In this work we apply the computational strategy outlined above in the case of the bovine pancreatic trypsin inhibitor, a well-studied small protein, which is a reference for computer simulations since decades. We compute the variation of the melting temperature characterizing the folding-unfolding process between the wild-type protein and two of its single-point mutations that are seen to have opposite effect on the free energy changes. The same approach is used for free energy difference calculations between a truncated form of frataxin and a set of five of its variants. Simulation data are compared to in vitro experiments. In all cases the sign of the change of melting temperature is reproduced, under the further approximation of using an empirical effective mean-field to average out protein-solvent interactions.

Modelling Protein Plasticity: The Example of Frataxin and Its Variants

Frataxin (FXN) is a protein involved in storage and delivery of iron in the mitochondria. Single-point mutations in the FXN gene lead to reduced production of functional frataxin, with the consequent dyshomeostasis of iron. FXN variants are at the basis of neurological impairment (the Friedreich's ataxia) and several types of cancer. By using altruistic metadynamics in conjunction with the maximal constrained entropy principle, we estimate the change of free energy in the protein unfolding of frataxin and of some of its pathological mutants. The sampled configurations highlight differences between the wild-type and mutated sequences in the stability of the folded state. In partial agreement with thermodynamic experiments, where most of the analyzed variants are characterized by lower thermal stability compared to wild type, the D104G variant is found with a stability comparable to the wild-type sequence and a lower water-accessible surface area. These observations, obtained with the new approach we propose in our work, point to a functional switch, affected by single-point mutations, of frataxin from iron storage to iron release. The method is suitable to investigate wide structural changes in proteins in general, after a proper tuning of the chosen collective variable used to perform the transition.

Probing the Structure of Toxic Amyloid-β Oligomers with Electron Spin Resonance and Molecular Modeling

Structural models of the toxic species involved in the development of Alzheimer's disease are of utmost importance to understand the molecular mechanism and to describe early biomarkers of the disease. Among toxic species, soluble oligomers of amyloid-β (Aβ) peptides are particularly important, because they are responsible for spreading cell damages over brain regions, thus rapidly impairing brain functions. In this work we obtain structural information on a carefully prepared Aβ(1-42) sample, representing a toxic state for cell cultures, by combining electron spin resonance spectroscopy and computational models. We exploited the binding of Cu²⁺ to Aβ(1-42) and used copper as a probe for estimating Cu-Cu distances in the oligomers by applying double electron-electron resonance (DEER) pulse sequence. The DEER trace of this sample displays a unique feature that fits well with structural models of oligomers formed by Cu-cross-linked peptide dimers. Because Cu is bound to the Aβ(1-42) N-terminus, for the first time structural constraints that are missing in reported studies are provided at physiological conditions for the Aβ N-termini. These constraints suggest the Aβ(1-42) dimer as the building block of soluble oligomers, thus changing the scenario for any kinetic model of Aβ(1-42) aggregation.

Analyzing and Biasing Simulations with PLUMED

This chapter discusses how the PLUMED plugin for molecular dynamics can be used to analyze and bias molecular dynamics trajectories. The chapter begins by introducing the notion of a collective variable and by then explaining how the free energy can be computed as a function of one or more collective variables. A number of practical issues mostly around periodic boundary conditions that arise when these types of calculations are performed using PLUMED are then discussed. Later parts of the chapter discuss how PLUMED can be used to perform enhanced sampling simulations that introduce simulation biases or multiple replicas of the system and Monte Carlo exchanges between these replicas. This section is then followed by a discussion on how free-energy surfaces and associated error bars can be extracted from such simulations by using weighted histogram and block averaging techniques.

Computational models explain how copper binding to amyloid-β peptide oligomers enhances oxidative pathways

Amyloid-β (Aβ) peptides are intrinsically disordered peptides and their aggregation is the major hallmark of Alzheimer's disease (AD) development.

RNA Structural Dynamics As Captured by Molecular Simulations: A Comprehensive Overview

With both catalytic and genetic functions, ribonucleic acid (RNA) is perhaps the most pluripotent chemical species in molecular biology, and its functions are intimately linked to its structure and dynamics. Computer simulations, and in particular atomistic molecular dynamics (MD), allow structural dynamics of biomolecular systems to be investigated with unprecedented temporal and spatial resolution. We here provide a comprehensive overview of the fast-developing field of MD simulations of RNA molecules. We begin with an in-depth, evaluatory coverage of the most fundamental methodological challenges that set the basis for the future development of the field, in particular, the current developments and inherent physical limitations of the atomistic force fields and the recent advances in a broad spectrum of enhanced sampling methods. We also survey the closely related field of coarse-grained modeling of RNA systems. After dealing with the methodological aspects, we provide an exhaustive overview of the available RNA simulation literature, ranging from studies of the smallest RNA oligonucleotides to investigations of the entire ribosome. Our review encompasses tetranucleotides, tetraloops, a number of small RNA motifs, A-helix RNA, kissing-loop complexes, the TAR RNA element, the decoding center and other important regions of the ribosome, as well as assorted others systems. Extended sections are devoted to RNA-ion interactions, ribozymes, riboswitches, and protein/RNA complexes. Our overview is written for as broad of an audience as possible, aiming to provide a much-needed interdisciplinary bridge between computation and experiment, together with a perspective on the future of the field.

Toward Fast and Accurate Binding Affinity Prediction with pmemdGTI: An Efficient Implementation of GPU-Accelerated Thermodynamic Integration

We report the implementation of the thermodynamic integration method on the pmemd module of the AMBER 16 package on GPUs (pmemdGTI). The pmemdGTI code typically delivers over 2 orders of magnitude of speed-up relative to a single CPU core for the calculation of ligand-protein binding affinities with no statistically significant numerical differences and thus provides a powerful new tool for drug discovery applications.

Multisystem altruistic metadynamics-Well-tempered variant

Metadynamics method has been widely used to enhance sampling in molecular simulations. Its original form suffers two major drawbacks, poor convergence in complex (especially biomolecular) systems and its serial nature. The first drawback has been addressed by introduction of a convergent variant known as well-tempered metadynamics. The second was addressed by introduction of a parallel multisystem metadynamics referred to as altruistic metadynamics. Here, we combine both approaches into well-tempered altruistic metadynamics. We provide mathematical arguments and trial simulations to show that it accurately predicts free energy surfaces.