Electrostatic Contributions to Protein Stability and Folding Energy

The ability to predict the thermal stability of proteins based on their corresponding sequence is a problem of great fundamental and practical importance. Here we report an approach for calculating the electrostatic contribution to protein stability based on the use of the semimacroscopic protein dipole Langevin dipole (PDLD/S) in its linear response approximation version for self-energy with a dielectric constant, (εpεp) and an effective dielectric for charge–charge interactions (εeffεeff). The method is applied to the test cases of ubiquitin, lipase, dihydrofolate reductase and cold shock proteins with series of εpεp and εeffεeff. It is found that the optimal values of these dielectric constants lead to very promising results, both for the relative stability and the absolute folding energy. Consideration of the specific values of the optimal dielectric constants leads to an exciting conceptual description of the reorganization effect during the folding process. Although this description should be examined by further microscopic studies, the practical use of the current approach seems to offer a powerful tool for protein design and for studies of the energetics of protein folding.This work was supported by NIH Grant GM2449

On the relationship between thermal stability and catalytic power of enzymes

The  possible  relationship  between  the  thermal  stability  and  the  catalytic  power  of  enzymes  is  of   great  current  interest.  In  particular,  it  has  been  suggested  that  thermophilic  or  hyperthermophilic   (Tm)   enzymes   have   lower   catalytic   power   at   a   given   temperature   than   the   corresponding   mesophilic   (Ms)   enzymes,   because   the   thermophilic   enzymes   are   less   flexible   (assuming   that   flexibility   and   catalysis   are   directly   correlated).   These   suggestions   presume   that   the   reduced   dynamics   of   the   thermophilic   enzymes   is   the   reason   for   their   reduced   catalytic   power.   The   present  paper  takes  the  specific  case  of  dihydrofolate  reductase  (DHFR) and explores the validity of the above argument by simulation approaches. It is found that the Tm enzymes have restricted motions in the direction of the folding coordinate, but this is not relevant to the chemical process, since the motions along the reaction coordinate are perpendicular to the folding motions. Moreover, it is shown that the rate of the chemical reaction is determined by the activation barrier and the corresponding reorganization energy, rather than by dynamics or flexibility in the ground state. In fact, as far as flexibility is concerned, we conclude that the displacement along the reaction coordinate is larger in the Tm enzyme than in the Ms enzyme and that the general trend in enzyme catalysis is that the best catalyst involves less motion during the reaction than the less optimal catalyst. The relationship between thermal stability and catalysis appears to reflect the fact that in order to obtain small electrostatic reorganization energy it is necessary to invest some folding energy in the overall preorganization process. Thus, the optimized catalysts are less stable. This trend is clearly observed in the DHFR case

Polarizable molecular interactions in condensed phase and their equivalent nonpolarizable models

Earlier, using phenomenological approach, we showed that in some cases polarizable models of condensed phase systems can be reduced to nonpolarizable equivalent models with scaled charges. Examples of such systems include ionic liquids, TIPnP-type models of water, protein force fields, and others, where interactions and dynamics of inherently polarizable species can be accurately described by nonpolarizable models. To describe electrostatic interactions, the effective charges of simple ionic liquids are obtained by scaling the actual charges of ions by a factor of 1/sqrt(eps_el), which is due to electronic polarization screening effect; the scaling factor of neutral species is more complicated. Here, using several theoretical models, we examine how exactly the scaling factors appear in theory, and how, and under what conditions, polarizable Hamiltonians are reduced to nonpolarizable ones. These models allow one to trace the origin of the scaling factors, determine their values, and obtain important insights on the nature of polarizable interactions in condensed matter systems.Comment: 43 pages, 3 figure

Coarse grained model for exploring voltage dependent ion channels

AbstractThe relationship between the membrane voltage and the gating of voltage activated ion channels and other systems have been a problem of great current interest. Unfortunately, reliable molecular simulations of external voltage effects present a major challenge, since meaningful converging microscopic simulations are not yet available and macroscopic treatments involve major uncertainties in terms of the dielectric used and other key features. This work extends our coarse grained (CG) model to simulations of membrane/protein systems under external potential. Special attention is devoted to a consistent modeling of the effect of external potential due to the electrodes, emphasizing semimacroscopic description of the electrolytes in the solution regions between the membranes and the electrodes, as well as the coupling between the combined potential from the electrodes plus the electrolytes and the protein ionized groups. We also provide a clear connection to microscopic treatment of the electrolytes and thus can explore possible conceptual problems that are hard to resolve by other current approaches. For example, we obtain a clear description of the charge distribution in the entire electrolyte system, including near the electrodes in membrane/electrodes systems (where continuum models do not seem to provide the relevant results). Furthermore, the present treatment provides an insight on the distribution of the electrolyte charges before and after equilibration across the membrane, and thus on the nature of the gating charge. The different aspects of the model have been carefully validated by considering problems ranging for the simple Debye–Huckel, and the Gouy–Chapman models to the evaluation of the electrolyte distribution between two electrodes, as well as the effect of extending the simulation system by periodic replicas. Overall the clear connection to microscopic descriptions combined with the power of the CG modeling seems to offer a powerful tool for exploring the balance between the protein conformational energy and the interaction with the external potential in voltage activated channels. To illustrate these features we present a preliminary study of the gating charge in the voltage activated Kv1.2 channel, using the actual change in the electrolyte charge distribution rather than the conventional macroscopic estimate. We also discuss other special features of the model, which include the ability to capture the effect of changes in the protonation states of the protein residues during the close to open voltage induced transition. This article is part of a Special Issue entitled: Membrane protein structure and function

Constant pH molecular dynamics of proteins in explicit solvent with proton tautomerism

pH is a ubiquitous regulator of biological activity, including protein‐folding, protein‐protein interactions, and enzymatic activity. Existing constant pH molecular dynamics (CPHMD) models that were developed to address questions related to the pH‐dependent properties of proteins are largely based on implicit solvent models. However, implicit solvent models are known to underestimate the desolvation energy of buried charged residues, increasing the error associated with predictions that involve internal ionizable residue that are important in processes like hydrogen transport and electron transfer. Furthermore, discrete water and ions cannot be modeled in implicit solvent, which are important in systems like membrane proteins and ion channels. We report on an explicit solvent constant pH molecular dynamics framework based on multi‐site λ‐dynamics (CPHMD MSλD ). In the CPHMD MSλD framework, we performed seamless alchemical transitions between protonation and tautomeric states using multi‐site λ‐dynamics, and designed novel biasing potentials to ensure that the physical end‐states are predominantly sampled. We show that explicit solvent CPHMD MSλD simulations model realistic pH‐dependent properties of proteins such as the Hen‐Egg White Lysozyme (HEWL), binding domain of 2‐oxoglutarate dehydrogenase (BBL) and N‐terminal domain of ribosomal protein L9 (NTL9), and the p K a predictions are in excellent agreement with experimental values, with a RMSE ranging from 0.72 to 0.84 p K a units. With the recent development of the explicit solvent CPHMD MSλD framework for nucleic acids, accurate modeling of pH‐dependent properties of both major class of biomolecules—proteins and nucleic acids is now possible. Proteins 2014; 82:1319–1331. © 2013 Wiley Periodicals, Inc.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/107513/1/prot24499-sup-0002-suppinfo02.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/107513/2/prot24499-sup-0001-suppinfo01.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/107513/3/prot24499.pd

A two-lane mechanism for selective biological ammonium transport

The transport of charged molecules across biological membranes faces the dual problem of accommodating charges in a highly hydrophobic environment while maintaining selective substrate translocation. This has been the subject of a particular controversy for the exchange of ammonium across cellular membranes, an essential process in all domains of life. Ammonium transport is mediated by the ubiquitous Amt/Mep/Rh transporters that includes the human Rhesus factors. Here, using a combination of electrophysiology, yeast functional complementation and extended molecular dynamics simulations, we reveal a unique two-lane pathway for electrogenic NH4+ transport in two archetypal members of the family, the transporters AmtB from Escherichia coli and Rh50 from Nitrosomonas europaea. The pathway underpins a mechanism by which charged H+ and neutral NH3 are carried separately across the membrane after NH4+ deprotonation. This mechanism defines a new principle of achieving transport selectivity against competing ions in a biological transport process

The Use of Multiscale Molecular Simulations in Understanding a Relationship between the Structure and Function of Biological Systems of the Brain: The Application to Monoamine Oxidase Enzymes

Computational techniques provide accurate descriptions of the structure and dynamics of biological systems, contributing to their understanding at an atomic level.Classical MD simulations are a precious computational tool for the processes where no chemical reactions take place.QM calculations provide valuable information about the enzyme activity, being able to distinguish among several mechanistic pathways, provided a carefully selected cluster model of the enzyme is considered.Multiscale QM/MM simulation is the method of choice for the computational treatment of enzyme reactions offering quantitative agreement with experimentally determined reaction parameters.Molecular simulation provide insight into the mechanism of both the catalytic activity and inhibition of monoamine oxidases, thus aiding in the rational design of their inhibitors that are all employed and antidepressants and antiparkinsonian drugs. Aging society and therewith associated neurodegenerative and neuropsychiatric diseases, including depression, Alzheimer's disease, obsessive disorders, and Parkinson's disease, urgently require novel drug candidates. Targets include monoamine oxidases A and B (MAOs), acetylcholinesterase (AChE), butyrylcholinesterase (BChE), and various receptors and transporters. For rational drug design it is particularly important to combine experimental synthetic, kinetic, toxicological, and pharmacological information with structural and computational work. This paper describes the application of various modern computational biochemistry methods in order to improve the understanding of a relationship between the structure and function of large biological systems including ion channels, transporters, receptors, and metabolic enzymes. The methods covered stem from classical molecular dynamics simulations to understand the physical basis and the time evolution of the structures, to combined QM, and QM/MM approaches to probe the chemical mechanisms of enzymatic activities and their inhibition. As an illustrative example, the later will focus on the monoamine oxidase family of enzymes, which catalyze the degradation of amine neurotransmitters in various parts of the brain, the imbalance of which is associated with the development and progression of a range of neurodegenerative disorders. Inhibitors that act mainly on MAO A are used in the treatment of depression, due to their ability to raise serotonin concentrations, while MAO B inhibitors decrease dopamine degradation and improve motor control in patients with Parkinson disease. Our results give strong support that both MAO isoforms, A and B, operate through the hydride transfer mechanism. Relevance of MAO catalyzed reactions and MAO inhibition in the context of neurodegeneration will be discussed

Improving pKa calculations of membrane inserting amino acids using replica exchange CpHMD simulations

Tese de mestrado em Bioquímica, apresentada à Universidade de Lisboa, através da Faculdade de Ciências, 2017O pH é um dos parâmetros fisiológicos mais importantes, influenciando as propriedades dos solutos, alterando a distribuição da ocupação de protões lábeis. Caso estes se encontrem em grupos químicos relevantes para a estabilidade conformacional, uma mudança no estado de protonação poderá conduzir a uma transição conformacional significativa. Os principais tipos de biomoléculas contêm grupos tituláveis em zonas estruturalmente importantes, logo uma mudança no seu estado de protonação, e consequentemente na carga, afeta a função das biomoléculas. O facto do pH estar intimamente implicado na maioria dos processos bioquímicos ilustra bem o caráter relevante do pH para a vida, estando também envolvido em doenças como o cancro ou o Alzheimer. Métodos de dinâmica molecular a pH constante (CpHMD) costumam ser utilizados para modelar sistemas onde a captura correcta do acoplamento das conformações com mudanças no estado de protonação é necessária. Vários métodos de CpHMD foram desenvolvidos e implementados nos mais diversos campos de forças. O CpHMD usado neste trabalho denomina-se titulação estocástica devido aos estados de protonação discretos serem amostrados e aceites pelo critério de Metropolis. Este método de CpHMD foi usado para estudar os valores de pKa de aminoácidos tituláveis na interface de uma membrana lipídica de fosfatidilcolina. A mudança no ambiente electrostático em redor do resíduo dita a variação do seu pKa. Ao inserir na membrana apolar, os amino´acidos tendem a estabilizar a sua forma neutra, de tal modo que, a nossa metodologia sentiu dificuldades a amostrar suficientes estados ionizados para ser possível calcular o pKa em zonas mais inseridas com a confiança desejada. Geralmente quando se estuda um sistema onde figuram barreiras cinéticas difíceis de transpor usando apenas dinâmica molecular, os métodos de amostragem aumentada são uma solução viável. De entre as técnicas mais comuns, o replica exchange (RE) parece ser a mais adequada ao nosso sistema. Métodos como metadynamics ou umbrella sampling, poderiam auxiliar no aumento da amostragem de estados inseridos contudo provavelmente representam desafios superiores em termos de implementação no contexto do CpHMD. Assim sendo, desenvolvemos o nosso método de RE baseadas em pH (pHRE), complementando o nosso método de CpHMD, tal como já tinha sido desenvolvido por outros grupos na literatura. Nesta metodologia, cada réplica é simulada a um pH único e trocas entre pares de pHs são testadas periodicamente. O critério de aceitação da troca baseia-se na diferença entre os valores de pH dos pares de simulações, bem como na diferença entre estados de protonação dos grupos tituláveis. Neste trabalho, aplicámos a nova metodologia de pHRE aos pentapéptidos anteriormente estudados, numa tentativa de obter valores de pKa dos resíduos tituláveis em zonas inseridas que não tenham sido possíveis de determinar face à falta de amostragem. O objectivo foi concluído com sucesso uma vez que o método de pHRE permite que todos os valores de pH amostrem conformações com inserções semelhantes. Os valores de pH com preferência para o estado carregado, mais moroso de amostrar em configurações inseridas, e que mais dificilmente atingiriam estas inserções em simulações de CpHMD, conseguem desta forma aumentar a qualidade da amostragem nestas zonas. A melhoria da amostragem está portanto diretamente relacionada com a mistura das réplicas que, por sua vez, poderá ser maximizada diminuindo o espaçamento entre os valores de pH escolhidos ou aumentando a periodicidade das tentativas de troca entre replicados. Contudo, aumentar a frequência de trocas poderá ter um efeito secundário nefasto, tendo em conta que caso uma troca entre replicados afete a probabilidade da troca seguinte, pode favorecer ou desfavorecer um estado de protonação particular. Os melhores resultados deste trabalho foram obtidos simulando 4 valores de pH e com um tRE de 20 ps. Porém, dado que o sistema apenas tinha um resíduo a titular, todas as simulações de pHRE apresentaram uma boa eficiência a nível de mistura de réplicas, apesar do tRE de 100 ps divergir em algumas zonas de inserção das restantes, o que sugere que ainda não terá convergido. De notar, que em dois dos resíduos não foi possível acelerar a amostragem, ficando estas excepções a dever-se ao leque de valores de pH simulados ter sido demasiado limitado. Um novo método para definir o nível de inserção foi também introduzido neste trabalho. Este foi comparado com os métodos alternativos mais usuais que utilizam todos os lípidos da membrana ou apenas o mais próximo. Usando todos os lípidos, a inserção medida será tão sobrestimada quanto a deformação local causada na membrana durante esse processo. Calculando a inserção apenas com o lípido mais próximo, é possível contornar a deformação, mas um novo problema surge quando o desvio que é provocado nesta referência única não representa corretamente a irregularidade introduzida na membrana. O novo método aqui proposto, faz uso de um cutoff até ao qual todos os lípidos são contabilizados. Desta forma, é possível obter valores de inserção correlacionados com o estado de solvatação e minimizar as imprecisões associadas com a troca do lípido mais próximo. Apesar da melhor descrição das interações na zona da interface, este modo de calcular a inserção tem pouca influência nos perfis de pKa. O pHRE consegue claramente melhorar a amostragem do CpHMD, bem como os perfis de pKa associados. No futuro, esta metodologia de amostragem aumentada será adoptada, mesmo para estudar processos bioquímicos dependentes do pH cujas limitações de amostragem não sejam tão evidentes quanto as existentes na interface de uma membrana.PH is one of the most important solution parameters since it influences the properties of solute molecules with labile hydrogen atoms. It plays a major role in most biochemical processes by, among other, inducing protein conformational changes and affecting protein–lipid interactions. Constant-pH molecular dynamics (CpHMD) methods have been used to model such systems since they are able to correctly capture the conformational/protonation coupling. To investigate the pKa values of titrable amino acids at the water/membrane interface, a previous CpHMD study [1] have shown that, upon insertion, the titrable sites are prone to adopt a neutral state. In that work, we encountered some difficulties to sample ionized conformations in inserted regions with CpHMD, since most residues retained their neutral state upon insertion/desolvation in the timescale of our simulations. When facing kinetic traps in molecular dynamics simulations, enhanced sampling techniques are a widely used solution. Since our sampling problems are related with a favored protonation state, we implemented a pH-based replica exchange (pHRE)[2]. In this method, a unique pH value is assigned to each simulation replica and attempts to exchange the simulated pH value are periodically performed between replica pairs. The acceptance criterion is dictated by the difference between the exchanging pairs of pH values and protonation states of titrable sites. Here, we have used the pHRE methodology, a newly developed method to calculate insertion, and more rigorous criteria to define the acceptable protonation sampling, to provide a more accurate description of the membrane influence on the pKa profiles of titrable amino acids. A more thorough characterization of protein–membrane interactions, membrane deformation and solvation effects is obtained by using a cutoff based insertion method. Since in pHRE, due to replica mixing, all pH values sample similar insertion regions, a larger amount of inserted conformations in the ionized state are obtained. To further improve pHRE sample capability, a high frequency of exchange attempts should be selected. Our efficient pHRE results outperformed previous CpHMD ones, granting more sampling in less simulation time. In the future, pHRE will eventually replace CpHMD as our go-to method to study pH dependent phenomena