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

Amongst the many complex processes taking place in living cells, transport of cargoes across the cytosceleton is fundamental to cell viability and activity. To move cargoes between the different cell parts, cells employ Molecular Motors. The motors operate by transporting cargoes along the so-called cellular micro-tubules, namely rope-like structures that connect, for instance, the cell-nucleus and outer membrane. We introduce a new Markov Chain, the killed Quasi-Random-Walk, for such transport molecules and derive properties like the maximal run length and time. Furthermore we introduce permuted balance, which is a more flexible extension of the ordinary reversibility and introduce the notion of Time Duality, which compares certain passage times pathwise. We give a number of sufficient conditions for Time Duality based on the geometry of the transition graph. Both notions are closely related to properties of the killed Quasi-Random-Walk.

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.

Active particle is a general term used to label a large set of different systems, spanning from a flock of birds flying in a coordinated pattern to a school of fish abruptly changing its direction or to a bacterium self-propelling itself while foraging nourishment. The common property shared by these systems is that their constituent agents, e.g. birds, fishes, or bacteria, are capable of harvesting energy from the surrounding environment and converting it into self-propulsion and directed motion. This peculiar feature characterizes them as out-of-equilibrium systems, in fact, the process of energy consumption and dissipation generates microscopically irreversible dynamics and drives them far from thermal equilibrium. Thanks to their intrinsic out-of-equilibrium nature, active particle systems often display characteristic patterns and behaviors that are not observed in equilibrium physics systems, such as collective motion or motility-induced phase separation. These features prompted the development of theories and algorithms to simulate and study active particles, giving rise to paradigmatic models capable of describing these phenomena, such as the Vicsek model for collective motion, the run-and-tumble model, or the active Brownian particle model. At the same time, synthetic agents have been designed to reproduce the behaviors of these natural active particle systems, and their evolution could play a fundamental role in the nanotechnology of the 21st century and the development of novel medical treatments, in particular controlled drug delivery. A specific type of active particle that uses its directed motion to move at the microscale is called a microswimmer. Examples of these agents are bacteria exploring their surroundings while searching for food or escaping external threats, spermatozoa looking for the egg, or artificial Janus particles designed for specific tasks. Active agents at these scales use different swimming mechanisms, such as rotating flagella or phoretic motion along chemical gradients that they can create. The outcome of their efforts is determined by the interplay of the translational diffusion intrinsic to the dynamics at these scales and the persistent motion that characterizes their self-propulsion. The problem of finding a specific target in a complex environment is essential for microswimmers and active agents in general. Target search is employed by animals and microorganisms for a variety of purposes, from foraging nourishment to escaping potential threats, such as in the case of bacterial chemotaxis. The study of this process is therefore fundamental to characterize the behavior of these systems in nature. Its complete description could then be employed in designing synthetic microswimmers for addressing specific problems, such as the aforementioned targeted drug delivery and the environmental cleansing of soil and polluted water. Here, we provide a detailed study of the target search process for microswimmers exploring complex environments. To this end, we generalize Transition Path Theory, the rigorous statistical mechanics description of transition processes, to the target-search problem. The most general way of modeling a complex environment that the microswimmer has to navigate is through an external potential. This potential can be characterized by high barriers separating metastable states in the system or by the presence of confining boundaries. If a high energy barrier is located between the initial position of the microswimmer and its target, the target search becomes a rare event. Rare events have been thoroughly investigated in equilibrium physics, and several algorithms have been designed to cope with the separation of timescales intrinsic to these problems and enable their investigation via efficient computer simulations. Despite the large set of tools developed for studying passive particles performing rare transitions, the characterization of this process for non-equilibrium systems, such as active particles, is still lacking. One of the main results of this thesis is the generalization to non-equilibrium systems of the Transition Path Sampling (TPS) algorithm, which was originally designed to simulate rare transitions in passive systems. This algorithm relies on the generation of productive trajectories, i.e. trajectories linking the initial state of the particle to the target state, via a Monte Carlo procedure, without the need of simulating long thermal oscillations in metastable states. These trajectories are then accepted according to a Metropolis criterion and are subsequently used to obtain the transition path ensemble, i.e. the ensemble of all reactive paths that completely characterizes the process. The TPS algorithm relies on microscopic reversibility to generate the productive trajectories, therefore its generalization to out-of-equilibrium systems lacking detailed balance and microscopic reversibility has remained a major challenge. Within this work, after deriving a path integral representation for active Brownian particles, we provide a new rule for the generation and acceptance of productive non-equilibrium trajectories, which reduces to the usual expression for passive particles when the activity of the microswimmer is set to zero. This new rule allows us to generalize the TPS algorithm to the case of active Brownian particles and to obtain a first insight into the counterintuitive target-search pathways explored by these particles. In fact, while passive particles perform barrier crossing following the minimum energy path linking the initial state to the target state, we found that active particles, thanks to their activity and persistence of motion, can reach the target more often by surfing higher energy regions of the landscape that lie far from the minimum energy path. The second result of this thesis is a systematic characterization of the target-search path ensemble for an active particle exploring an energy landscape. We do so by analyzing the system’s response to changes in the two adimensional parameters that define the parameter space of the model: the Péclet number and the persistence of the active particle. Our findings show that active Brownian particles can increase their target-finding rates by tuning their Péclet number and their persistence according to the shape and characteristics of the external landscape. We perform this analysis in two different landscapes, namely a double-well potential and the Brown-Müller potential, finding robust features in the target-search patterns. In contrast, other observables of the system, e.g. the target-finding rates, are more responsive to the features of the external environment. Interestingly, our results suggest that, differently from what happens for passive particles, the presence of additional metastable states in the system does not hinder the target-search dynamics of active particles. The third original contribution of this Ph.D. thesis is the generalization of the concept of the committor function to target-search problems. The committor function was first introduced in the framework of Transition Path Theory to study reaction processes. If a definition for a reactant and a product state embedded in the configuration space of the system is provided, the committor function quantifies the probability that a trajectory starting in a given configuration reaches the product state before it can enter the reactant. For this reason, it has been proven to be pivotal for a complete characterization of these events and it is often regarded as the optimal reaction coordinate for thermally activated transitions. The target search problem shares many similarities with transition processes since it is characterized by an initial state from which the agent begins its journey and a target state that the particle is aiming to reach, and often some barriers or obstacles separate the two. Exploiting these similarities, we take advantage of the concept of the committor function to fully characterize a target-search process performed by an active agent. First, we derive the Fokker-Planck equation for an active Brownian particle subject to an external potential, and we use its associated probability current to define the committor function for an active agent. Then, we prove that the active committor satisfies the Backward-Kolmogorov equation analogously to the committor for passive particles. We take advantage of this property to efficiently compute the committor function using a finite-difference algorithm, validating it with brute-force simulations. Finally, we further validate our theory with experiments of a camphor self-propelled disk. This self-propelled disk is capable of moving on a water surface and is studied during its exploration of a circular confining environment. We start by analyzing long recorded trajectories of such a disk moving in a Petri dish, and, after defining a reactant and a product region in the system, we proceed to compute the committor function in three different regions contained in the dish. We analyze all the trajectory slices passing through those regions and we measure how many of them hit the product region and how many hit instead the reactant first, and we obtain the committor in the three regions as a function of the angle. Finally, we simulate a long trajectory of an active Brownian particle exploring a circular confining environment, and we compare the committor as an angular function obtained from brute-force simulations with the committor estimated from experimental data.

Submitted by David Turchick (davidturchick@fgvmail.br) on 2011-03-28T21:58:20Z No. of bitstreams: 1 tese_dout_david.pdf: 1028717 bytes, checksum: ebae39f4145a0e8d55de18fe3b119f10 (MD5) / Approved for entry into archive by Andrea Virginio Machado(andrea.machado@fgv.br) on 2011-03-29T11:47:06Z (GMT) No. of bitstreams: 1 tese_dout_david.pdf: 1028717 bytes, checksum: ebae39f4145a0e8d55de18fe3b119f10 (MD5) / Made available in DSpace on 2011-03-31T17:21:14Z (GMT). No. of bitstreams: 1 tese_dout_david.pdf: 1028717 bytes, checksum: ebae39f4145a0e8d55de18fe3b119f10 (MD5) Previous issue date: 2010-09-24 / This thesis collects four papers on monetary economics written under the supervision of Professor Rubens Penha Cysne. The first of these papers assesses the bias occuring in welfare-cost-of-inflation measures due to failing to take into consideration the substitution potential of interest-bearing monies such as bank deposits. The second one tackles the theoretical issue of comparing the generality of the money-in-the-utility-function- and the shopping-time models by studying the properties of the demand curves they generate. The third of these works revisits a classic paper by Stanley Fischer on the correlation between the growth rate of money supply and the rate of capital accumulation on the transition path. Finally, the fourth one concerns the relative standing of each one of six measures of the welfare cost of inflation (one of which is new) with respect to the other five, and an estimate of the maximum relative error one can incur by choosing to employ a particular welfare measure in place of the others. / Esta tese é uma coleção de quatro artigos em economia monetária escritos sob a supervisão do Professor Rubens Penha Cysne. O primeiro desses artigos calcula o viés presente em medidas do custo de bem-estar da inflação devido a não se levar em conta o potencial substitutivo de moedas que rendem juros, como depósitos bancários.[1] O segundo se concentra na questão teórica de se comparar os escopos dos tradicionais modelos money-in-the-utility-function e shopping-time através do estudo das propriedades das curvas de demanda que eles geram.[2] O terceiro desses trabalhos revisita um artigo clássico de Stanley Fischer sobre a correlação entre a taxa de crescimento da oferta monetária e a taxa de acumulação de capital no caminho de transição.[3] Finalmente, o quarto diz respeito à posição relativa de cada uma de seis medidas do custo de bem-estar da inflação (uma das quais é nova) em relação às outras cinco, e uma estimativa do erro relativo máximo em que o pesquisador pode incorrer devido a sua escolha de empregar uma dessas medidas qualquer vis-à-vis as outras.

Cette thèse explore les effets macroéconomiques et distributionnels de la taxation dans l’économie américaine. Les trois premiers chapitres prennent en considération l’interaction entre l’entrepreneuriat et la distribution de richesse tandis que le dernier discute l’arbitrage du mode de financement d’une diminution d’impôt sur les sociétés sous la contrainte de neutralité fiscale pour le gouvernement. Spécifiquement, le chapitre 1 en utilisant les données du Panel Study of Income Dynamics (PSID) , fournit des évidences selon lesquelles le capital humain ou l’expérience entrepreneuriale est quantitativement important pour expliquer les disparités de revenu et de richesse entre les individus au cours de leur cycle de vie. Pour saisir ces tendances, je considère le modèle d’entrepreneuriat de Cagetti et De Nardi (2006), modifié pour prendre en compte la dynamique du cycle de vie. J’introduis également l’accumulation de l’experience entrepreneuriale, laquelle rend les entrepreneurs plus productifs. Je calibre ensuite deux versions du modèle (avec et sans accumulation d’expérience d’entreprise) en fonction des mêmes données américaines. Les résultats montrent que le modèle avec accumulation d’expérience réplique le mieux les données. La question de recherche du chapitre 2 est opportune à la réforme fiscale récente adoptée aux États-Unis, laquelle est un changement majeur du code fiscal depuis la loi de réforme fiscale de 1986. Le Tax Cuts and Jobs Act (TCJA) voté en décembre 2017 a significativement changé la manière dont le revenu d’affaires est imposé aux États-Unis. Je considère alors le modèle d’équilibre général dynamique avec choix d’occupations développé au Chapitre 1 pour une évaluation quantitative des effets macroéconomiques du TCJA, tant dans le court terme que dans le long terme. Le TCJA est modélisé selon ses trois provisions clés : un nouveau taux de déduction de 20% pour les firmes non- incorporées, une baisse du taux fiscal statutaire pour sociétés incorporées de 35% à 21% et la réduction de 39.6% à 37% du taux marginal supérieur pour les individus. Je trouve que l’économie connait un taux de croissance du PIB de 0.90% sur une fenêtre fiscale de dix ans et le stock de capital en moyenne augmente de 2.12%. Ces résultats sont consis- tants aux évaluations faites par le Congressional Budget Office et le Joint Committee on vi Taxation. Avec des provisions provisoires, le TCJA génère une réduction dans l’inégalité de la richesse et celle du revenu mais l’opposé se réalise une fois que les provisions sont faites permanentes. Dans les deux scénarios, la population subit une perte de bien-être et exprime un faible soutien. Le chapitre 3 répond à la question normative: Les entrepreneurs devraient-ils être imposés différemment? Par conséquent, j’analyse quantitativement la désirabilité d’une taxation basée sur l’occupation dans un modèle à générations imbriquées avec entrepreneuriat et une prise en compte explicite des cohortes transitionnelles. La reforme principale étudiée est le passage d’une taxation progressive fédérale identique tant pour les revenus du travail que pour le bénéfice d’entreprise au niveau individuel à un régime fiscal différentiel où le profit d’affaires fait face à un taux d’imposition proportionnel pendant que le revenu du travail est toujours soumis au code de taxation progressive. Je trouve qu’une taxe proportionnelle de 40% imposée aux entrepreneurs est optimale. Plus générale- ment, je montre que le taux d’imposition optimal varie entre 15% et 50%, augmentant avec l’aversion du planificateur pour les inégalités et diminuant avec son évaluation rel- ative du bien-être des générations futures. Dans le contexte de la réforme fiscalité des entreprises, le chapitre 4 évalue les compromis de neutralité fiscale de revenu dans le financement d’une réduction de l’impôt des sociétés. Pour respecter la neutralité fiscale, le gouvernement utilise trois instruments pour équilibrer son budget, à savoir l’impôt sur le revenu du travail, les dividendes et les gains en capital. Je construis ensuite un modèle d’équilibre général parcimonieux pour obtenir des multiplicateurs budgétaires équilibrés associés à une réforme de l’impôt sur les sociétés. En utilisant un calibration standard de l’économie américaine, je montre que les multiplicateurs liés à l’impôt sur le revenu du travail et l’impôt sur les dividendes sont négatifs, suggérant ainsi un compromis entre une réduction de l’impôt des sociétés et ces deux taux d’imposition. D’autre part, le multiplicateur lié à l’impôt sur les gains en capital est positif, ce qui prédit une coordination d’une double réduction des taux d’imposition des sociétés et des gains en capital. De plus, les gains de bien-être des différents scénarios sont mitigés. / This thesis explores the macroeconomic and distributional effects of taxation in the U.S. economy. The first three chapters take advantage of the interplay between entrepreneurship and wealth distribution while the last one discusses the trade-offs when financing a corporate tax cut under revenue neutrality. Specifically, Chapter 1 provides evidence using the Panel Study of Income Dynamics (PSID) that occupation-specific human capital or business experience is quantitatively important in explaining income and wealth disparities among individuals over their life cycle. To capture the data patterns, I build on Cagetti and De Nardi (2006) occupational choice model, modified to feature life-cycle dynamics. I also introduce managerial skill accumulation which leads entrepreneurs to become more productive with experience. I then calibrate two versions of the model (with and without accumulation of business experience) to the same U.S. data. Results show that the model with business experience margin is the closest one. Chapter 2's research question is timely to the recent tax reform enacted in the US, which is a major change of the tax code since the 1986 Tax Reform Act. The Tax Cuts and Jobs Act (TCJA) as of December 2017 significantly altered how business income is taxed in the US. I consider a dynamic general equilibrium model of entrepreneurship developed in Chapter 1 to provide a quantitative assessment of the macroeconomic effects of the TCJA, both in the short run and in the long run. The TCJA is modeled by its three key provisions: a new 20-percent-deduction rate for pass-throughs, a drop in the statutory tax rate for corporations from 35% to 21% and the reduction to 37% of the top marginal tax rate for individuals from 39.6%. I find that the economy experiences, a GDP growth rate of 0.90% over a ten-year window and average capital stock increases by 2.12%. These results are consistent with estimates made by the congressional budget office and the joint committee on taxation. With temporary provisions, the TCJA delivers a reduction in wealth and income inequality but the opposite occurs once provisions are made permanent. In both scenarios, the population suffers a welfare loss and finds them difficult to support. Chapter 3 answers the normative question: Should entrepreneurs be taxed differently? Accordingly, I quantitatively investigate the desirability of occupation-based taxation in the entrepreneurship model of Chapter 1, when transitional cohorts are explicitly taken into account. The main experiment is to move from the federal single progressive taxation for both labor income and business profit at the individual level to a differential tax regime where business income faces a proportional tax rate and labor income is still subject to the progressive scheme. I find that a tax rate of 40% is optimal. More generally, the optimal tax rate varies between 15% and 50%, increasing with the planner's aversion to inequality and decreasing with its relative valuation of future generations' welfare. In the context of business tax reform, chapter 4 assesses revenue-neutral trade-offs when financing a corporate tax cut. To meet revenue neutrality, the policymaker uses three instruments to balance the government budget, namely labor income tax, dividend tax, and capital gains tax. I then construct a parsimonious general equilibrium model to derive balanced fiscal multipliers associated with corporate tax reform. Using a standard calibration, I show that both labor income tax and dividend tax multipliers are negative, suggesting a trade-off between a corporate tax cut and these two tax rates. On the other hand, the multiplier related to the capital gains tax is positive, which predicts the coordination of a double cut in both corporate and capital gains tax rates. Moreover, the welfare gains of the different scenarios are mixed.