Thermodynamics of liquids: standard molar entropies and heat capacities of common solvents from 2PT molecular dynamics

We validate here the Two-Phase Thermodynamics (2PT) method for calculating the standard molar entropies and heat capacities of common liquids. In 2PT, the thermodynamics of the system is related to the total density of states (DoS), obtained from the Fourier Transform of the velocity autocorrelation function. For liquids this DoS is partitioned into a diffusional component modeled as diffusion of a hard sphere gas plus a solid component for which the DoS(υ) → 0 as υ → 0 as for a Debye solid. Thermodynamic observables are obtained by integrating the DoS with the appropriate weighting functions. In the 2PT method, two parameters are extracted from the DoS self-consistently to describe diffusional contributions: the fraction of diffusional modes, f, and DoS(0). This allows 2PT to be applied consistently and without re-parameterization to simulations of arbitrary liquids. We find that the absolute entropy of the liquid can be determined accurately from a single short MD trajectory (20 ps) after the system is equilibrated, making it orders of magnitude more efficient than commonly used perturbation and umbrella sampling methods. Here, we present the predicted standard molar entropies for fifteen common solvents evaluated from molecular dynamics simulations using the AMBER, GAFF, OPLS AA/L and Dreiding II forcefields. Overall, we find that all forcefields lead to good agreement with experimental and previous theoretical values for the entropy and very good agreement in the heat capacities. These results validate 2PT as a robust and efficient method for evaluating the thermodynamics of liquid phase systems. Indeed 2PT might provide a practical scheme to improve the intermolecular terms in forcefields by comparing directly to thermodynamic properties

Advanced techniques for the computer simulation and analysis of biomolecular systems

The Helmholtz free energy is one of the central quantities of classical thermodynamics, as it governs important chemical properties such as equilibria or reaction kinetics. It is, therefore, a desirable quantity to measure, predict, and understand. Unsurprisingly, many methods exist to compute free energy differences between two states of a system. In this thesis, the density of states integration method (DSI) is developed; it detects which subsystems mainly contribute to the free energy difference. The method utilizes the velocity density of states function (VDoS) of each atom to calculate its contribution to the vibrational free energy. It is possible without any approximation to assign fractions of the vibrational free energy to meaningful subsystems, where the local free energy difference is the sum over all atoms comprising that subsystem. In this way, large local changes can be identified (free energy hot-spots), which is crucial for the understanding of free energy differences. The validity and usefulness of DSI is shown via several examples and comparison with state of the art free energy methods. In addition to the development of DSI, this thesis also focuses on free energy barriers in the context of investigating the reaction mechanism of Sirtuin~5, a lysine deacylase class~III. The relationship between the configuration of the enzyme's active site and the height of the reaction barrier is studied by computing minimal energy paths for the catalyzed reaction starting from many different (educt) configurations. Using the power of machine learning, atom-atom distances influencing the activation barrier are identified, allowing for a comprehensive understanding of the interplay of the substrate and residues within the active site of Sirtuin~5. Subsequently, we set out to compute the free energy as a function of the reaction coordinate instead of a minimum energy path. Another theme of this thesis is the computation of spectroscopic observables in a cost effective manner while simultaneously including important features of the experimental setup. The inclusion of solvent molecules and finite temperature effects has a decisive effect on the accuracy of the computed observables. In this context, we highlight the importance of sampling atomic configurations (with and without explicit solvent) and the non-negligible influence of electron correlation on the accuracy of computed observables. Simulation protocols are developed that enable sampling, the inclusion of correlation methods, and large quantum mechanical subsystems at a low computational cost

CHARMM: The biomolecular simulation program

CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecular simulation program. It has been developed over the last three decades with a primary focus on molecules of biological interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estimators, molecular minimization, dynamics, and analysis techniques, and model-building capabilities. The CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical-molecular mechanical force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numerous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983. © 2009 Wiley Periodicals, Inc.J Comput Chem, 2009.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/63074/1/21287_ftp.pd

Predicting biomolecular function from 3D dynamics : sequence-sensitive coarse-grained elastic network model coupled to machine learning

La dynamique structurelle des biomolécules est intimement liée à leur fonction, mais très coûteuse à étudier expériementalement. Pour cette raison, de nombreuses méthodologies computationnelles ont été développées afin de simuler la dynamique structurelle biomoléculaire. Toutefois, lorsque l'on s'intéresse à la modélisation des effects de milliers de mutations, les méthodes de simulations classiques comme la dynamique moléculaire, que ce soit à l'échelle atomique ou gros-grain, sont trop coûteuses pour la majorité des applications. D'autre part, les méthodes d'analyse de modes normaux de modèles de réseaux élastiques gros-grain (ENM pour "elastic network model") sont très rapides et procurent des solutions analytiques comprenant toutes les échelles de temps. Par contre, la majorité des ENMs considèrent seulement la géométrie du squelette biomoléculaire, ce qui en fait de mauvais choix pour étudier les effets de mutations qui ne changeraient pas cette géométrie. Le "Elastic Network Contact Model" (ENCoM) est le premier ENM sensible à la séquence de la biomolécule à l'étude, ce qui rend possible son utilisation pour l'exploration efficace d'espaces conformationnels complets de variants de séquence. La présente thèse introduit le pipeline computationel ENCoM-DynaSig-ML, qui réduit les espaces conformationnels prédits par ENCoM à des Signatures Dynamiques qui sont ensuite utilisées pour entraîner des modèles d'apprentissage machine simples. ENCoM-DynaSig-ML est capable de prédire la fonction de variants de séquence avec une précision significative, est complémentaire à toutes les méthodes existantes, et peut générer de nouvelles hypothèses à propos des éléments importants de dynamique structurelle pour une fonction moléculaire donnée. Nous présentons trois exemples d'étude de relations séquence-dynamique-fonction: la maturation des microARN, le potentiel d'activation de ligands du récepteur mu-opioïde et l'efficacité enzymatique de l'enzyme VIM-2 lactamase. Cette application novatrice de l'analyse des modes normaux est rapide, demandant seulement quelques secondes de temps de calcul par variant de séquence, et est généralisable à toute biomolécule pour laquelle des données expérimentale de mutagénèse sont disponibles.The dynamics of biomolecules are intimately tied to their functions but experimentally elusive, making their computational study attractive. When modelling the effects of thousands of mutations, time-stepping methods such as classical or enhanced sampling molecular dynamics are too costly for most applications. On the other hand, normal mode analysis of coarse-grained elastic network models (ENMs) provides fast analytical dynamics spanning all timescales. However, the vast majority of ENMs consider backbone geometry alone, making them a poor choice to study point mutations which do not affect the equilibrium structure. The Elastic Network Contact Model (ENCoM) is the first sequence-sensitive ENM, enabling its use for the efficient exploration of full conformational spaces from sequence variants. The present work introduces the ENCoM-DynaSig-ML computational pipeline, in which the ENCoM conformational spaces are reduced to Dynamical Signatures and coupled to simple machine learning algorithms. ENCoM-DynaSig-ML predicts the function of sequence variants with significant accuracy, is complementary to all existing methods, and can generate new hypotheses about which dynamical features are important for the studied biomolecule's function. Examples given are the maturation efficiency of microRNA variants, the activation potential of mu-opioid receptor ligands and the effect of point mutations on VIM-2 lactamase's enzymatic efficiency. This novel application of normal mode analysis is very fast, taking a few seconds CPU time per variant, and is generalizable to any biomolecule on which experimental mutagenesis data exist

A THEORETICAL INVESTIGATION EXAMINING DNA CONFORMATIONAL CHANGES AND THEIR EFFECTS ON GLYCOSYLASE FUNCTION

Glycosylase enzymes initiate the process of base excision repair (BER) in order to prevent the irreversible modification of the genome. In the BER process a damaged DNA base is recognized, removed from the DNA sequence, and then the remaining abasic site is repaired. Glycosylase enzymes are responsible for the base recognition mechanism and catalysis of the base excision. One of the most studied glycosylase superfamilies is uracil DNA glycosylase (UDG). The UDG superfamily has demonstrated specificity for excising uracil, which is the deamination product of cytosine, from DNA sequences of prokaryotes and eukaryotes. Mismatch-specific uracil DNA glycosylase (MUG) is a member of the UDG superfamily, and interestingly has shown specificity for both uracil and xanthine bases. The following dissertation provides an anlaysis on the recognition mechanism of E. coli MUG for deaminated DNA bases. Glycosylase enzymes require the damaged base to be flipped out of the base stack, and into an active site for catalysis of the N-glycosidic cleavage. Typically, recognition of substrates by enzymes is characterized by binding affinities, but in the following work the binding of E.Coli MUG is broken down into contributions from the base flipping and enzyme binding equilibria. Since DNA conformational changes play a large role in UDG systems, the robustness of molecular mechanics Poisson-Boltzmann surface area (MM/PBSA) free energy method was evaluated for a DNA conformational change. The A-form to B-form DNA conformational free energy differences were calculated using MM/PBSA, and compared with free energy differences determined with a more rigorous umbrella sampling method. MM/PBSA calculations of the free energy difference between A-form and B-form DNA are shown to be in very close agreement with the PMF result determined using an umbrella sampling approach. The sensitivity to solvent model and force field used during conformational sampling was also established for the MM/PBSA free energies. In order to determine the influence of base flipping conformational changes on the MUG recognition process, PMF profiles were generated for each of the damaged bases (uracil, xanthine, oxanine, inosine). Agreement was displayed between the base pair stability trends from the umbrella sampling, and the enzyme activities from experiment. Interaction energies and structural analyses were used to examine the MUG enzyme, which revealed regions of the active site critical for binding xanthine and uracil substrates. Site-directed mutagenesis experiments were performed on MUG to determine the role of specific amino acids in the recognition mechanism. Mutations were studied further through modeling and molecular dynamics (MD) simulations of the unbound and bound proteins

Free energy and kinetics in protein-ligand binding: experimental measurements and computational estimates

Virtually all biochemical activities are mediated by the organization and recognition of biological macromolecules. An accurate characterization of the thermodynamics and kinetics governing the formation of supramolecular complexes is required to deeply understand the molecular principles driving all biological interactions. Thermodynamics provides the driving force of protein-ligand binding and is quantified by the binding free energies or the equilibrium dissociation constants. Since the interacting partners are out of equilibrium in vivo, the thermodynamic description of binding needs to be complemented by the knowledge of the kinetic rates. Nowadays, various biophysical experimental techniques can determine thermodynamic and kinetic properties, which are still difficult to be efficiently predicted by computational methods mainly because of the limited force field accuracy and the high computational cost. During my Ph.D., I applied molecular dynamics (MD)-based methods to characterize the thermodynamics and kinetics of inter-molecular interactions. First, I worked on a new enhanced MD-based protocol to simulate protein-ligand dissociation events. This approach provides a realistic description of the evolution of the system to an external perturbation accounting for the natural forces driving the dissociation mechanisms. By applying this computational approach to two pharmaceutically relevant kinases, I was able to rank two series of compounds on unbinding kinetics and to get qualitative mechanistic and path information on the underlying unbinding events, providing additional valuable information to be used in the optimization of lead compounds. Then, I developed an innovative computational method to estimate free energies applicable to systems of arbitrary complexity. Despite the number of challenges to be overcome, the method is very promising being able to provide accurate free energy estimates. Therefore, computer simulations emerged as a valuable tool to obtain information on both the thermodynamic and kinetic aspects governing the formation of supramolecular complexes, which might be used in the rational optimization of lead compounds