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Molecular dynamics (MD) simulations are routinely used to study the structure and function of biological molecules. However the accuracy and duration of these simulations are constrained by their computational costs, thus limiting the ability to accurately simulate systems of realistic sizes over biologically relevant time periods. The two most computationally demanding steps in these simulations are (1) determining the charge state of ionizable sites in biomolecules, which is a key input to the simulation, and (2) calculating long range electrostatic interactions during the simulation. Presented here are two novel methods, the <i>direct interaction approximation (DIA)</i> and the <i>hierarchical charge partitioning (HCP) approximation</i>, for speeding up each of these two computations. The average charge state of ionizable sites in biomolecules can be calculated as the statistical average over all possible (2^N) microstates for a molecule, where N is the number of ionizable sites. In general this computation scales exponentially as O(N² 2^N). The DIA is an O(²) approximation for calculating the average charge state of ionizable sites. For each site, the DIA treats direct interactions (interactions involving the site of interest) <i>exactly</i>, while using an <i>average</i> value for indirect interactions (interactions not involving the site of interest). The DIA was tested on two problems. The computation of thermal average properties for the 2-D Ising model of ferromagnetism, and the average charge state of ionizable residues in biomolecules. Compared to the commonly used non-deterministic Monte Carlo method, for the same computational cost, the deterministic DIA was found to be at least as accurate, as measured by RMS error relative to the exact computation. Thus, the DIA may be a practical alternative to the Monte Carlo method for some problems. In atomistic MD simulations, the computation of long range electrostatic interactions, scale as O(<i>n</i>²), where <i>n</i> is the number of atoms. For most biologically relevant timescales the simulations involve 10^12–16 simulation steps. Thus, the computational cost of long range interactions become the limiting factor in the size and duration of MD simulations. The HCP is an O(<i>n</i> log <i>n</i>) approximation for computing long range electrostatic interactions. The approximation is based on multiple levels of natural partitioning of biomolecular structures into a hierarchical set of components. For components that are far from the point of interest, the charge distribution for each component is approximated by a much smaller number of charges. For nearby components, the HCP uses the full set of atomic charges. For large structures the HCP can be several orders of magnitude faster than the exact pairwise O(<i>n</i>²) all-atom computation. For a representative set of structures, the accuracy of the HCP is comparable to the industry standard explicit solvent particle mesh Ewald (PME), and is in general more accurate than the spherical cutoff method. And, unlike the PME, the DIA can be easily extended to implicit solvent GB models. 50 ns implicit solvent simulations for a representative set of four biomolecules suggests that the HCP could be a practical alternative for implicit solvent simulations, and preferable to the cutoff based method. The HCP is available for general use in the open source MD software, NAB within AmberTools. / Ph. D.

Thesis (Ph. D.)--San Diego State University and University of California, San Diego, 2001. / Includes bibliographical references (leaves 545-550).

In this thesis we study the interactions of ions and cationic peptides with a negatively charged lipid bilayer in an ionic solution where the electrostatic interactions are screened. <br /><br /> We first examine the problem of charge renormalization and inversion of a highly charged bilayer with low dielectric constant. To be specific, we consider an asymmetrically charged lipid bilayer, in which only one layer is negatively charged. In particular, we study how dielectric discontinuities and charge correlations among lipid charges and condensed counterions influence the effective charge of the surface. When counterions are monovalent, e. g. , Na⁺, our mean-field approach implies that dielectric discontinuities can enhance counterion condensation. A simple scaling picture shows how the effects of dielectric discontinuities and surface-charge distributions are intertwined: Dielectric discontinuities diminish condensation if the backbone charge is uniformly smeared out while counterions are localized in space; they can, however, enhance condensation when the backbone charge is discrete. In the presence of asymmetric salts such as CaCl₂, we find that the correlation effect, treated at the Gaussian level, is more pronounced when the surface has a lower dielectric constant, inverting the sign of the charge at a smaller value of Ca²⁺ concentration. <br /><br /> In the last chapter we study binding of cationic peptides onto a lipid-bilayer membrane. The peptide not only interacts electrostatically with anionic lipids, rearranging their spatial distributions, but it can also insert hydrophobically into the membrane, expanding the area of its binding layer (i. e. , the outer layer). We examine how peptide charges and peptide insertion (thus area expansion) are intertwined. Our results show that, depending on the bilayer's surface charge density and peptide hydrophobicity, there is an optimal peptide charge yielding the maximum peptide penetration. Our results shed light on the physics behind the activity and selective toxicity of antimicrobial peptides, i. e. , they selectively rupture bacterial membranes while leaving host cells intact.

Le projet européen ANGELS a pour but de construire un robot anguille capable de naviguer par le sens électrique et de se scinder en plusieurs mono-agents pour des besoins d’exploration. Dans le cadre de ce projet, mon travail a consisté à élaborer un modèle de perception inspiré du poisson électrique, le challenge étant de faire de ce modèle un modèle de perception rapide et embarquable pour une détection en ligne par un engin sous-marin robotisé équipé du modèle. Deux modèles de perception ont été construits, s’appuyant tous deux sur une géométrie simple mais réaliste de capteur. Les deux modèles baptisés «modèle poly-sphérique » et « modèle des réflexions » provenant respectivement d’une intuition physique et d’une méthode mathématique appropriée se calibrent une fois pour toute avec un simulateur électrique, pourrevêtir in fine une forme analytique. Couplés aux modèles existant de réponses électriques d’objets, les modèles de perception ont permis de faire effectuer à un robot capteur des tâches basiques d’évitement et de détection, ce qui est à ce jour une première dans l’histoire. En parallèle, nous avons développé un formalisme générique de réponse d’objet permettant d’étendre le champ d’applicabilité des modèles de perception. Enfin, nous avons commencé à estimerl’impact d’une géométrie complexe de capteur présentant de larges surfaces isolantes sur la mesure pour envisager la modélisation du sens électrique par un capteur de forme arbitraire. / The goal of the European project ANGELS is to build an eel-like robot capable to navigate by the electric sense and to divide itself in several mono-agents for exploration purposes. In the context of this project my work consisted in creating a perception model inspired from the electric fish with the virtue of being fast and so, to be usable in-line. Two models of perception were built and were based on a simple but realistic geometry of sensor. The two models named after the « poly-spherical model » and the « reflexions model » which come respectively from a physical intuition and an appropriate mathematical model are calibrated once for all with an electrical simulator in order to have analytical forms. Coupled with models of the electrical response of objects, the two models of perception permit the robot to achieve some basic tasks like detection and obstacles’ avoidance, which is a novelty in the history. In addition we have built a generic formalism of theelectrical response that extents the application of the models of perception. Finally we have begun to estimate the influence of a complex geometry of sensor, that exhibs large insulating surfaces, on the measurement in order to open the way for the rapid modelling of a sensor of arbitrary shape.

Usando geometrias do tipo ponta e plano estudou-se as características elétricas da descarga corona positiva e negativa. Mediram-se as distribuições da densidade de corrente elétrica e do campo elétrico sobre o plano coletor dos íons. São discutidos os resultados obtidos para o sistema ponta planos e para o sistema em que o campo elétrico externo é aplicado através de uma placa adicional colocada perto da ponta. Neste último caso os resultados são interpretados com um modelo teórico que supõe que os íons se movem direção perpendicular entre as placas, sob a ação de um campo constante e lateralmente sob o campo de repulsão da carga espacial. / Electric characteristics of a positive and negative corona discharge were studied for geometries of the type point and plane. The electric current density and the electric field distributions on the collector plane were measured. We discuss the results obtained with the point and plane geometry and with the geometry were a external electric field is applied by means of an additional metallic plate fixed near the point. For the latter geometry the results were interpreted by using a theoretical model in which it is assumed that the ions drift in the direction perpendicular to the plates under a constant electric field and laterally under the field of the ionic space charge.

Thesis. 1976. M.S.--Massachusetts Institute of Technology. Dept. of Ocean Engineering. / Microfiche copy available in Archives and Engineering. / Includes bibliographical references. / by George Economou. / M.S.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemistry, 1970. / Includes bibliographical references (leaves 327-332). / by John David Ramshaw. / Ph.D.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 1979. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Bibliography: leaves 122-126. / by Peter Michael Hirsch. / M.S.

Calmodulin (CaM) is an essential protein found in all eukaryotes ranging from vertebrates to unicellular organisms such as Paramecia. CaM is a calcium sensor protein composed of two domains (N and C) responsible for the regulation of numerous calcium-mediated signaling pathways. Four calcium ions bind to CaM, changing its conformation and determining how it recognizes and regulates its cellular targets. Since the discovery of CaM, most studies have focused on the role of its calcium-saturated form. However, an increasing number of target proteins have been discovered that preferentially bind apo (calcium-depleted) CaM. My study focused on understanding how apo CaM recognizes drugs and protein sequences, and how those interactions differ from those of calcium-saturated CaM. I have used spectroscopic methods to explore CaM binding the drug Trifluoperazine (TFP) and the IQ-motif of the type 2 Voltage-Dependent Sodium Channel (Nav1.2IQp). These studies have shown that both TFP and Nav1.2IQp preferentially bind to the "semi-open" conformation of apo CaM. TFP was shown to be an unusual allosteric effector of calcium binding to CaM. Using 15N-HSQC NMR spectroscopy, I determined the stoichiometry of TFP binding to apo Cam to be 2:1 and to (Ca2+)4-CaM to be 4:1 TFP:CaM. That difference in stoichiometry determined whether TFP decreased or increased the affinity of CaM for calcium. Analysis of residue-specific chemical shift differences indicated that TFP binding to apo and (Ca2+)4-CaM perturbed the C-domain more than the N-domain, prompting high-resolution structural studies of the isolated C-domain of CaM. Crystallographic studies of TFP bound to a calcium-saturated C-domain fragment of CaM (CaM76-148) revealed that CaM adopted an "open" tertiary conformation. The unit cell contained two protein and 4 drug molecules. The orientation of TFP revealed that its trifluoromethyl group was found in two alternative positions (one in each protein in the unit cell), and that Met 144 acted as a gatekeeper to select the orientation of TFP. In contrast to TFP binding to the "open" conformation of calcium-saturated CaM76-148, my NMR studies showed that TFP bound the "semi-open" conformation of apo CaM76-148. TFP interacted with CaM residues near the perimeter of the hydrophobic pocket, but did not contact residues that are solvent-accessible only in the "open" form. Allosteric effects due to TFP binding were observed in the calcium-binding loops of apo CaM76-148. These properties suggest that TFP may antagonize interactions between apo CaM and target proteins such as ion channels that preferentially bind apo CaM. Nav1.2, is responsible for the passage of Na+ ion across cellular membranes. Apo binding of CaM to Nav1.2 poises it for action upon calcium release in the cell. My NMR studies of CaM binding to the Nav1.2 IQ-motif sequence (Nav1.2IQp) showed that the C-domain of apo CaM was necessary and sufficient for binding. My high-resolution structure of the isolated C-domain of CaM bound to Nav1.2IQp revealed that the domain adopted a "semi-open" conformation. At the interface between the IQ-motif and CaM, the highly conserved I and two Y residues of Nav1.2IQp interacted with hydrophobic residues of CaM, while the invariant Q residue interacted with residues in the loop between helices F and G of CaM. This is the first CaM-IQ complex to be determined by NMR; the only other available structure of apo CaM bound to an IQ-motif was determined crystallographically. To accomplish its regulatory roles in response to cellular Ca2+ fluxes, CaM has evolved multiple binding interfaces that are allosterically linked to its Ca2+-ligation state. My studies of CaM binding to TFP and NaV1.2 demonstrate the versatility of CaM functioning as a regulatory protein comprised of domains having separable functions.