Enzymes are immensely powerful and efficient heterogenous catalysts which are essential for life. As essential to life as enzymes are, it is still not well understood exactly how they enhance the rate of their catalyzed reactions up to 19 orders of magnitude over their solution phase counterpart reactions. Recent research has focused on sub--picosecond motions coupled to the reaction coordinate, called rate--promoting vibrations, which are important components of several well--known enzymatic mechanisms and build upon previous models of enzyme activity. Herein I present two studies which are expressly focused on providing tools and knowledge to understand how dynamics affects enzymatic reactions. First, I present a method for the calculation of kinetic isotope effects from first principles, using transition path sampling and centroid molecular dynamics. This method allows for the calculation of kinetic isotope effects without the assumptions necessitated by transition state theory or free energy perturbation methods. It was found that this method could calculate the primary H/D kinetic isotope effect of the conversion of benzyl alcohol to benzaldehyde in yeast alcohol dehydrogenase to within the margin of error of experimentally measured kinetic isotope effects of the same reaction. Second, I examined the role that evolution plays in the preservation of these rate--promoting vibrations, by performing a transition path sampling study of two lactate dehydrogenases, those of Plasmodium falciparum and Cryptosporidium parvum, which evolved through separate gene duplication events from a common malate dehydrogenase ancestor. It was found that though both lactate dehydrogenases share the same rate--promoting vibration, and indeed share the rate--promoting vibration found in other lactate dehydrogenases, the sequence variations in lactate dehydrogenase from P. falciparum causes a diminished contribution of the motions to the reaction coordinate. The studies presented in this dissertation contribute to the our understanding of enzymes on an atomistic level, as well as providing tools necessary for designing novel de novo enzymes and targeted drugs for enzymes of disease--causing organisms.

Orientador: Maurice de Koning / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-08-08T20:27:57Z (GMT). No. of bitstreams: 1 PomaBernaola_AdolfoMaximo_M.pdf: 3697892 bytes, checksum: a07c1ad647a61d9862283f697732410e (MD5) Previous issue date: 2007 / Resumo: Nesta dissertação abordamos o estudo de uma das limitações da simulação atomística denominada o evento raro, quem é responsável pela limitação temporal, exemplos de problemas que envolvem os eventos raros são, o enovelamento de proteínas, mudanças conformacionais de moléculas, reações químicas (em solução), difusão de sólidos e os processos de nucleação numa transição de fase de 1a ordem, entre outros. Métodos convencionais como Dinâmica Molecular (MD) ou Monte Carlo (MC) são úteis para explorar a paisagem de energia potencial de sistemas muito complexos, mas em presença de eventos raros se tornam muito ineficientes, devido à falta de estatística na amostragem do evento. Estes métodos gastam muito tempo computacional amostrando as configurações irrelevantes e não as transições de interesse. Neste sentido o método Transition Path Sampling (TPS), desenvolvido por D. Chandler e seus colaboradores, consegue explorar a paisagem de energia potencial e obter um conjunto de verdadeiras trajetórias dinâmicas que conectam os estados metaestáveis em presença de evento raros. A partir do ensemble de caminhos a constante de reação e o mecanismo de reação podem ser extraídos com muito sucesso. Neste trabalho de mestrado implementamos com muito sucesso o método TPS e realizamos uma comparação quantitativa em relação ao método MC configuracional num problema padrão da isomerização de uma molécula diatômica imersa num líquido repulsivo tipo Weeks-Chandler-Andersen (WCA). A aplicação destes métodos mostrou como o ambiente, na forma de solvente, pode afetar a cinética de um evento raro / Abstract: In this dissertation we aproach the study of one of the limitations of the atomistic simulation called the rare event, which is responsible for the temporal limitation. Examples of problems that involve the rare event are the folding protein, conformational changes in molecules, chemical reactions (in solution), solid diffusion, and the processes of nucleation in a first-order phase transition, among other. Conventional methods as Molecular Dynamics (MD) or Monte Carlo (MC) are useful to explore the potencial energy landscape of very complex systems, but in presence of rare events they become very inefficient, due to lack of statistics in the sampling of the event. These methods spend much computational time sampling the irrelevant configurations and not the transition of interest. In this sense, the Transition Path Sampling (TPS) method, developed by D. Chandler and his collaborators, can explore the potential energy landscape and get a set of true dynamical trajectories that connect the metastable states in presence of the rare events. From this ensemble of trajectories the rate constant and the mechanism of reaction can be extracted with great success. In this work we implemented the TPS method and carried out a quantitative comparison in relation to the configurational MC method in a standard problem of the isomerization of a diatomic molecule immersed in a Weeks-Chandler-Andersen (WCA) repulsive fluid. The application of these methods showed as the environment, in the form of solvent, can affect the kinetic of a rare event / Mestrado / Física Estatistica e Termodinamica / Mestre em Física

Enzymes direct chemical reactions with precision and speed, making life as we know it possible. How they do this is still not completely understood, but the relatively recent discovery of subpicosecond protein motion coupled to the reaction coordinate has provided a crucial piece of the puzzle. This type of motion is called a rate-promoting vibration (RPV) and has been seen in a number of different enzymatic systems. It typically involves a compression of the active site of the enzyme which lowers the barrier for the reaction to occur. In this work we present a number of studies that probe these motions in two dehydrogenase enzymes, yeast alcohol dehydrogenase (YADH) and homologs of lactate dehydrogenase (LDH). The goal of the study on the reaction of YADH was to probe the role of the protein in proton tunneling in the enzyme, which was suggested to occur from experimental kinetic isotope effect studies. We did this using transition path sampling (TPS), which perturbatively generates ensembles of reactive trajectories to observe transitions between stable states, such as chemical reactions. By applying a quantum method that can account for proton tunneling, centroid molecular dynamics, and generating reactive trajectory ensembles with and without the method, we were able to observe the change in barrier to proton transfer upon application of the tunneling method. We found that there was little change in the barrier, showing that classical over-the-barrier transfer is dominant over tunneling in the proton transfer in YADH. We also applied the knowledge of RPVs to identify a new class of allosteric molecules, which modulate enzymatic reaction not by changing a binding affinity, but by disrupting the reactive motion of enzymes. We showed, through design of a novel allosteric effector for human heart LDH, applying TPS to a system with and without the small molecule bound, and analysis of the reaction coordinate of the reactive trajectory ensemble, that the molecule was able to disrupt the motion of the protein such that it was no longer coupled to the reaction. We also examined the subpicosecond motions of two other LDHs, from Plasmodium falciparum and Cryptosporidium parvum, which evolved separately from previously studied LDHs. We found, using TPS and reaction coordinate identification, that while the LDH from C. parvum had similar dynamics to the earlier LDHs, the LDH from P. falciparum had a earlier transition-state associated with proton transfer, not hydride transfer. This is likely due to this LDH having a larger active site pocket, increasing the amount of motion necessary for proton transfer, and, thus, the barrier to proton transfer. More work is necessary in this system to determine whether the protein is coupled with the search for the reactive conformation for proton transfer. Protein motion coupled to the particle transfer in dehydrogenases plays an important role in their reactions and there is still much work to be done to understand the extent and role of RPVs.

Proteins are involved in numerous functions in the human body, including chemical transport, molecular recognition, and catalysis. To perform their function most proteins must adopt a specific structure (often referred to as the folded structure). A microscopic description of folding is an important prerequisite for elucidating the underlying basis of protein misfolding and rational drug design. However, protein folding occurs on heterogeneous length and time scales, presenting a grand challenge to both experiments and simulations. In computer simulations, challenges are generally mitigated by adopting coarse-grained descriptions of the physical environment, employing enhanced sampling strategies, and improving computing code and hardware. While significant advances have been made in these areas, for numerous systems a large spatiotemporal gap between experiment and simulations still exists, due to the limited time and length scales achieved by simulation, and the inability of many experimental techniques to probe fast motions and short distances. In this thesis, kinetic transition networks (KTNs) are constructed for various protein folding systems, via approaches based on the potential energy landscape (PEL) framework. By applying geometry optimisation techniques, the PEL is discretised into stationary points (i.e.~low-energy minima and the transition states that connect them). Essentially, minima characterise the low-lying regions of the PEL (thermodynamics) and transition states encode the motion between these regions (dynamics). Principles from statistical mechanics and unimolecular rate theory may then be employed to derive free energy surfaces and folding rates, respectively, from the KTN. Furthermore, the PEL framework can take advantage of parallel and distributed computing, since stationary points from separate simulations can be easily integrated into one KTN. Moreover, the use of geometry optimisation facilitates greater conformational sampling than conventional techniques based on molecular dynamics. Accordingly, this framework presents an appealing means of probing complex processes, such as protein folding. In this dissertation, we demonstrate the application of state-of-the-art theory, combining PEL analysis and KTNs to three diverse protein systems. First, to improve the efficiency of protein folding simulations, the intrinsic rigidity of proteins is exploited by implementing a local rigid body (LRB) approach. The LRB approach effectively integrates out irrelevant degrees of freedom from the geometry optimisation procedure and further accelerates conformational sampling. The effects of this approach on the underlying PEL are analysed in a systematic fashion for a model protein (tryptophan zipper\,1). We demonstrate that conservative local rigidification can reproduce the thermodynamic and dynamic properties for the model protein. Next, the PEL framework is employed to model large-scale conformational changes in proteins, which have conventionally been difficult to probe in silico. Methods based on geometry optimisation have proved useful in overcoming the broken ergodicity issue, which is associated with proteins that switch morphology. The latest PEL-based approaches are utilised to investigate the most extreme case of fold-switching found in the literature:~the α-helical hairpin to β-barrel transition of the C-terminal domain of RfaH, a bacterial transcription factor. PEL techniques are employed to construct the free energy landscape (FEL) for the refolding process and to discover mechanistic details of the transition at an atomistic level. The final part of the thesis focuses on modelling intrinsically disordered proteins (IDPs). Due to their inherent structural plasticity, IDPs are generally difficult to characterise, both experimentally and via simulations. An approach for studying IDPs within the PEL framework is implemented and tested with various contemporary potential energy functions. The cytoplasmic tail of the human cluster of differentiation 4 (CD4), implicated in HIV-1 infection, is characterised. Metastable states identified on the FEL help to unify, and are consistent with, several earlier predictions.

We develop statistical methods for tackling two important problems in genetic association studies. First, we propose a Bayesian approach to overcome the winner's curse in genetic studies. Second, we consider a Bayesian latent variable model for analyzing longitudinal family data with pleiotropic phenotypes. Winner's curse in genetic association studies refers to the estimation bias of the reported odds ratios (OR) for an associated genetic variant from the initial discovery samples. It is a consequence of the sequential procedure in which the estimated effect of an associated genetic marker must first pass a stringent significance threshold. We propose a hierarchical Bayes method in which a spike-and-slab prior is used to account for the possibility that the significant test result may be due to chance. We examine the robustness of the method using different priors corresponding to different degrees of confidence in the testing results and propose a Bayesian model averaging procedure to combine estimates produced by different models. The Bayesian estimators yield smaller variance compared to the conditional likelihood estimator and outperform the latter in the low power studies. We investigate the performance of the method with simulations and applications to four real data examples. Pleiotropy occurs when a single genetic factor influences multiple quantitative or qualitative phenotypes, and it is present in many genetic studies of complex human traits. The longitudinal family studies combine the features of longitudinal studies in individuals and cross-sectional studies in families. Therefore, they provide more information about the genetic and environmental factors associated with the trait of interest. We propose a Bayesian latent variable modeling approach to model multiple phenotypes simultaneously in order to detect the pleiotropic effect and allow for longitudinal and/or family data. An efficient MCMC algorithm is developed to obtain the posterior samples by using hierarchical centering and parameter expansion techniques. We apply spike and slab prior methods to test whether the phenotypes are significantly associated with the latent disease status. We compute Bayes factors using path sampling and discuss their application in testing the significance of factor loadings and the indirect fixed effects. We examine the performance of our methods via extensive simulations and apply them to the blood pressure data from a genetic study of type 1 diabetes (T1D) complications.

We develop statistical methods for tackling two important problems in genetic association studies. First, we propose a Bayesian approach to overcome the winner's curse in genetic studies. Second, we consider a Bayesian latent variable model for analyzing longitudinal family data with pleiotropic phenotypes. Winner's curse in genetic association studies refers to the estimation bias of the reported odds ratios (OR) for an associated genetic variant from the initial discovery samples. It is a consequence of the sequential procedure in which the estimated effect of an associated genetic marker must first pass a stringent significance threshold. We propose a hierarchical Bayes method in which a spike-and-slab prior is used to account for the possibility that the significant test result may be due to chance. We examine the robustness of the method using different priors corresponding to different degrees of confidence in the testing results and propose a Bayesian model averaging procedure to combine estimates produced by different models. The Bayesian estimators yield smaller variance compared to the conditional likelihood estimator and outperform the latter in the low power studies. We investigate the performance of the method with simulations and applications to four real data examples. Pleiotropy occurs when a single genetic factor influences multiple quantitative or qualitative phenotypes, and it is present in many genetic studies of complex human traits. The longitudinal family studies combine the features of longitudinal studies in individuals and cross-sectional studies in families. Therefore, they provide more information about the genetic and environmental factors associated with the trait of interest. We propose a Bayesian latent variable modeling approach to model multiple phenotypes simultaneously in order to detect the pleiotropic effect and allow for longitudinal and/or family data. An efficient MCMC algorithm is developed to obtain the posterior samples by using hierarchical centering and parameter expansion techniques. We apply spike and slab prior methods to test whether the phenotypes are significantly associated with the latent disease status. We compute Bayes factors using path sampling and discuss their application in testing the significance of factor loadings and the indirect fixed effects. We examine the performance of our methods via extensive simulations and apply them to the blood pressure data from a genetic study of type 1 diabetes (T1D) complications.

In this thesis we examine methodologies for determining free energy differences (FEDs) of phases via Monte Carlo simulation. We identify and address three generic issues that arise in FED calculations; the choice of representation, the choice of estimator, and the choice of sampling strategy. In addition we discuss how the classical framework may be extended to take into account quantum effects. Key words: Phase Mapping, Phase Switch, Lattice Switch, Simulated Tempering, Multi-stage, Weighted Histogram Analysis Method, Fast Growth, Jarzynski method, Umbrella, Multicanonical, Path Integral Monte Carlo, Path Sampling, Multihamiltonian, fluctuation theorem.