Exploiting molecular dynamics in Nested Sampling simulations of small peptides

Nested Sampling (NS) is a parameter space sampling algorithm which can be used for sampling the equilibrium thermodynamics of atomistic systems. NS has previously been used to explore the potential energy surface of a coarse-grained protein model and has significantly outperformed parallel tempering when calculating heat capacity curves of Lennard-Jones clusters. The original NS algorithm uses Monte Carlo (MC) moves; however, a variant, Galilean NS, has recently been introduced which allows NS to be incorporated into a molecular dynamics framework, so NS can be used for systems which lack efficient prescribed MC moves. In this work we demonstrate the applicability of Galilean NS to atomistic systems. We present an implementation of Galilean NS using the Amber molecular dynamics package and demonstrate its viability by sampling alanine dipeptide, both in vacuo and implicit solvent. Unlike previous studies of this system, we present the heat capacity curves of alanine dipeptide, whose calculation provides a stringent test for sampling algorithms. We also compare our results with those calculated using replica exchange molecular dynamics (REMD) and find good agreement. We show the computational effort required for accurate heat capacity estimation for small peptides. We also calculate the alanine dipeptide Ramachandran free energy surface for a range of temperatures and use it to compare the results using the latest Amber force field with previous theoretical and experimental results.We acknowledge support from the Leverhulme Trust (Grant F/00 215/BL(NSB, CV and DLW)) and the EPSRC (Grants EP/J020281/1(DLW), EP/J010847/1 (GC) and a Doctoral Training Award (RJB)).This is the final version of the article. It first appeared from Elsevier via http://dx.doi.org/10.1016/j.cpc.2015.12.00

Exploiting the potential energy landscape to sample free energy

We review a number of recently developed strategies for enhanced sampling of complex systems based on knowledge of the potential energy landscape. We describe four approaches, replica exchange, Kirkwood sampling, superposition-enhanced nested sampling, and basin sampling, and show how each of them can exploit information for low-lying potential energy minima obtained using basin-hopping global optimization. Characterizing these minima is generally much faster than equilibrium thermodynamic sampling, because large steps in configuration space between local minima can be used without concern for maintaining detailed balance.The authors gratefully acknowledge financial support from the EPSRC and the ERC. S.M acknowledges financial support from the Gates Cambridge Scholarship.This is the accepted manuscript. The final published version is available at http://onlinelibrary.wiley.com/doi/10.1002/wcms.1217/abstract

Energy Landscapes for Proteins: From Single Funnels to Multifunctional Systems

This report advances the hypothesis that multifunctional systems may be associated with multifunnel potential and free energy landscapes, with particular focus on biomolecules. It compares systems that exhibit single, double, and multiple competing structures, and contrasts multifunnel landscapes associated with misfolded amyloidogenic oligomers, which presumably do not arise as an evolutionary target. In this context, intrinsically disordered proteins could be considered intrinsically multifunctional molecules, associated with multifunnel landscapes. Potential energy landscape theory enables biomolecules to be treated in a common framework together with self‐organizing and multifunctional systems based on inorganic materials, atomic and molecular clusters, crystal polymorphs, and soft matter.epsr

Energy Landscapes for Proteins: From Single Funnels to Multifunctional Systems

This report advances the hypothesis that multifunctional systems may be associated with multifunnel potential and free energy landscapes, with particular focus on biomolecules. It compares systems that exhibit single, double, and multiple competing structures, and contrasts multifunnel landscapes associated with misfolded amyloidogenic oligomers, which presumably do not arise as an evolutionary target. In this context, intrinsically disordered proteins could be considered intrinsically multifunctional molecules, associated with multifunnel landscapes. Potential energy landscape theory enables biomolecules to be treated in a common framework together with self‐organizing and multifunctional systems based on inorganic materials, atomic and molecular clusters, crystal polymorphs, and soft matter.epsr

Nested basin-sampling

We report an embarrassingly parallel method for the evaluation of thermodynaproperties over an energy landscape exhibiting broken ergodicity, nested basin-samp(NBS). We also introduce the No Galilean U-Turn Sampler (NoGUTS), a new sapling scheme based on the No U-Turn Sampler (NUTS) introduced by Hoffman Gelman (2014) that works with the Galilean Monte Carlo scheme introduced by Betcourt (2012) to aid the efficient generation of new live points. NoGUTS can be thouof as a form of reflective slice sampling with an automatic stopping criterion. We ply this approach to a benchmark atomic cluster of 31 Lennard-Jones atoms, whexhibits a low temperature solid-solid heat capacity peak. The calculated heatpacity is compared with results generated by parallel tempering (PT), basin-samplparallel tempering (BSPT), and standard nested sampling (NS) simulations. NBSproduces the full heat capacity curve predicted by PT and BSPT, whilst the NS calation with similar computational cost fails to resolve the low temperature solid-sophase transition.This work was supported by the EPSRC Cambridge NanoDTC, EP/G037221/1

Theory of coherent two-dimensional vibrational spectroscopy

Two-dimensional (2D) vibrational spectroscopy has emerged as one of the most important experimental techniques useful to study the molecular structure and dynamics in condensed phases. Theory and computation have also played essential and integral roles in its development through the nonlinear optical response theory and computational methods such as molecular dynamics (MD) simulations and electronic structure calculations. In this article, we present the fundamental theory of coherent 2D vibrational spectroscopy and describe computational approaches to simulate the 2D vibrational spectra. The classical approximation to the quantum mechanical nonlinear response function is invoked from the outset. It is shown that the third-order response function can be evaluated in that classical limit by using equilibrium or non-equilibrium MD simulation trajectories. Another simulation method is based on the assumptions that the molecular vibrations can still be described quantum mechanically and that the relevant molecular response functions are evaluated by the numerical integration of the Schrodinger equation. A few application examples are presented to help the researchers in this and related areas to understand the fundamental principles and to use these methods for their studies with 2D vibrational spectroscopic techniques. In summary, this exposition provides an overview of current theoretical efforts to understand the 2D vibrational spectra and an outlook for future developments. c.Published under license by AIP Publishing