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.