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Daniel M. Zuckerman
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Equilibrium sampling of biomolecules remains an unmet challenge after more than 30 years of atomistic simulation. Efforts to enhance sampling capability, which are reviewed here, range from the development of new algorithms to parallelization to novel uses of hardware. Special focus is placed on classifying algorithms -- most of which are underpinned by a few key ideas -- in order to understand their fundamental strengths and limitations. Although algorithms have proliferated, progress resulting from novel hardware use appears to be more clear-cut than from algorithms alone, partly due to the lack of widely used sampling measures.
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This chapter reviews the differential geometry-based solvation and electrolyte transport for biomolecular solvation that have been developed over the past decade. A key component of these methods is the differential geometry of surfaces theory, as applied to the solvent-solute boundary. In these approaches, the solvent-solute boundary is determined by a variational principle that determines the major physical observables of interest, for example, biomolecular surface area, enclosed volume, electrostatic potential, ion density, electron density, etc. Recently, differential geometry theory has been used to define the surfaces that separate the microscopic (solute) domains for biomolecules from the macroscopic (solvent) domains. In these approaches, the microscopic domains are modeled with atomistic or quantum mechanical descriptions, while continuum mechanics models (including fluid mechanics, elastic mechanics, and continuum electrostatics) are applied to the macroscopic domains. This multiphysics description is integrated through an energy functional formalism and the resulting Euler-Lagrange equation is employed to derive a variety of governing partial differential equations for different solvation and transport processes; e.g., the Laplace-Beltrami equation for the solvent-solute interface, Poisson or Poisson-Boltzmann equations for electrostatic potentials, the Nernst-Planck equation for ion densities, and the Kohn-Sham equation for solute electron density. Extensive validation of these models has been carried out over hundreds of molecules, including proteins and ion channels, and the experimental data have been compared in terms of solvation energies, voltage-current curves, and density distributions. We also propose a new quantum model for electrolyte transport.
Riboswitches are cis-acting regulatory RNA elements prevalently located in the leader sequences of bacterial mRNA. An adenine sensing riboswitch cis-regulates adeninosine deaminase gene (add) in Vibrio vulnificus. The structural mechanism regulating its conformational changes upon ligand binding mostly remains to be elucidated. In this open framework it has been suggested that the ligand stabilizes the interaction of the distal kissing loop complex. Using accurate full-atom molecular dynamics with explicit solvent in combination with enhanced sampling techniques and advanced analysis methods it could be possible to provide a more detailed perspective on the formation of these tertiary contacts. In this work, we used umbrella sampling simulations to study the thermodynamics of the kissing loop complex in the presence and in the absence of the cognate ligand. We enforced the breaking/formation of the loop-loop interaction restraining the distance between the two loops. We also assessed the convergence of the results by using two alternative initialization protocols. A structural analysis was performed using a novel approach to analyze base contacts. Our simulations qualitatively indicated that the ligand could stabilize the kissing loop complex. We also compared with previously published simulation studies. Kissing complex stabilization given by the ligand was compatible with available experimental data. However, the dependence of its value on the initialization protocol of the umbrella sampling simulations posed some questions on the quantitative interpretation of the results and called for better converged enhanced sampling simulations.
RNA function is intimately related to its structural dynamics. Molecular dynamics simulations are useful for exploring biomolecular flexibility but are severely limited by the accessible timescale. Enhanced sampling methods allow this timescale to be effectively extended in order to probe biologically-relevant conformational changes and chemical reactions. Here, we review the role of enhanced sampling techniques in the study of RNA systems. We discuss the challenges and promises associated with the application of these methods to force-field validation, exploration of conformational landscapes and ion/ligand-RNA interactions, as well as catalytic pathways. Important technical aspects of these methods, such as the choice of the biased collective variables and the analysis of multi-replica simulations, are examined in detail. Finally, a perspective on the role of these methods in the characterization of RNA dynamics is provided.
Markov state models (MSMs) have been widely used to analyze computer simulations of various biomolecular systems. They can capture conformational transitions much slower than an average or maximal length of a single molecular dynamics (MD) trajectory from the set of trajectories used to build the MSM. A rule of thumb claiming that the slowest implicit timescale captured by an MSM should be comparable by the order of magnitude to the aggregate duration of all MD trajectories used to build this MSM has been known in the field. However, this rule have never been formally proved. In this work, we present analytical results for the slowest timescale in several types of MSMs, supporting the above rule. We conclude that the slowest implicit timescale equals the product of the aggregate sampling and four factors that quantify: (1) how much statistics on the conformational transitions corresponding to the longest implicit timescale is available, (2) how good the sampling of the destination Markov state is, (3) the gain in statistics from using a sliding window for counting transitions between Markov states, and (4) a bias in the estimate of the implicit timescale arising from finite sampling of the conformational transitions. We demonstrate that in many practically important cases all these four factors are on the order of unity, and we analyze possible scenarios that could lead to their significant deviation from unity. Overall, we provide for the first time analytical results on the slowest timescales captured by MSMs. These results can guide further practical applications of MSMs to biomolecular dynamics and allow for higher computational efficiency of simulations.
DNA microarrays are devices that are able, in principle, to detect and quantify the presence of specific nucleic acid sequences in complex biological mixtures. The measurement consists in detecting fluorescence signals from several spots on the microarray surface onto which different probe sequences are grafted. One of the problems of the data analysis is that the signal contains a noisy background component due to non-specific binding. This paper presents a physical model for background estimation in Affymetrix Genechips. It combines two different approaches. The first is based on the sequence composition, specifically its sequence dependent hybridization affinity. The second is based on the strong correlation of intensities from locations which are the physical neighbors of a specific spot on the chip. Both effects are incorporated in a background functional which contains 24 free parameters, fixed by minimization on a training data set. In all data analyzed the sequence specific parameters, obtained by minimization, are found to strongly correlate with empirically determined stacking free energies for RNA/DNA hybridization in solution. Moreover, there is an overall agreement with experimental background data and we show that the physics-based model proposed in this paper performs on average better than purely statistical approaches for background calculations. The model thus provides an interesting alternative method for background subtraction schemes in Affymetrix Genechips.
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