Aplicação da equação de Poisson-Boltzmann modificada em sistemas biológicos: análise da partição iônica em um eritrócito

Neste trabalho, a partição iônica e o potencial de membrana em um eritrócito são analisados via equação de Poisson-Boltzmann modificada, considerando as interações não eletrostáticas presentes entre os íons e macromoléculas, assim como, o potencial β. Este potencial é atribuído à diferença de potencial químico de referência entre os meios intracelular e extracelular e ao transporte ativo de íons. O potencial de Gibbs-Donnan via equação de Poisson-Boltzmann na presença de carga fixa em um sistema contendo uma membrana semipermeável também é estudado. O método de aproximação paraboloide em elementos finitos em um sistema estacionário e unidimensionalé aplicado para resolver a equação de Poisson-Boltzmann em coordenadas cartesianas e esféricas. O parâmetro de dispersão relativo às interações não eletrostáticas écalculado via teoria de Lifshitz. Os resultados em relação ao potencial de Gibbs-Donnan mostram-se adequados, podendo ser calculado pela equação de Poisson-Boltzmann. No sistema contendo um eritrócito, quando o potencial β é considerado igual a zero, não se verifica a diferença iônica observada experimentalmente entre os meios intracelular e extracelular. Dessa forma, os potenciais não eletrostáticos calculados via teoria de Lifshitz têm apenas uma pequena influência no que se refere à alta concentração de íon K+ no meio intracelular em relação ao íon Na+

A equação de Poisson-Boltzmann em regiões com fronteira irregular

Propomos uma idealização da situação em que uma macromolécula é ionizada em um solvente. Neste modelo a área da superfície da molécula é suposta ser grande com respeito a seu diâmetro. A molécula é considerada como um dielétrico com uma distribuição de cargas em sua superfície. Utilizando as condições de transmissão, a distribuição de Boltzmann no solvente e resultados recentes sobre espaços de Sobolev no contexto de espaços métricos, bem como de integração sobre superfícies irregulares, o problema é formulado em forma variacional. Resultados clássicos do cálculo de variações permitem a resolução analítica do problema.

Protein-Ion Binding Process on Finite Macromolecular Concentration. A Poisson-Boltzmann and Monte Carlo Study

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

pK determination. A mean field, Poisson-Boltzmann approach

A model describing dissociation of monoprotonic acid and a method for the determination of its pK value are presented. The model is based on a mean field approximation. The Poisson-Boltzmann equation, adopting spherical symmetry, is numerically solved, and the solution of its linearized form is written. By use of the pH values of a dilution experiment of galacturonic acid as the entry data, the proposed method allowed estimation of the value of pK = 3.25 at a temperature of 25 degrees C. Values for the complex dimensions and dissociation degree are calculated using experimental pH values for solution concentration values ranging from 0.1 to 60 mM. The present analysis leads to the conclusion that the Poisson-Boltzmann equation or its linear form is equally suited for the description of such systems.

Solution of the Poisson-Boltzmann equation for a system with four ionic species

The analytical solution of the Poisson-Boltzmann equation in an electrolyte with four ionic species (2:2:1:1), in the presence of a charged planar membrane or surface is presented. The function describing the mean electrical potential provides a convenient description that helps the understanding of electrical processes of biological interest.

INTEGRATION OF THE NONLINEAR POISSON BOLTZMANN-EQUATION FOR CHARGED VESICLES IN ELECTROLYTIC SOLUTIONS

The Poisson-Boltzmann equation (PBE), with specific ion-surface interactions and a cell model, was used to calculate the electrostatic properties of aqueous solutions containing vesicles of ionic amphiphiles. Vesicles are assumed to be water- and ion-permeable hollow spheres and specific ion adsorption at the surfaces was calculated using a Volmer isotherm. We solved the PBE numerically for a range of amphiphile and salt concentrations (up to 0.1 M) and calculated co-ion and counterion distributions in the inside and outside of vesicles as well as the fields and electrical potentials. The calculations yield results that are consistent with measured values for vesicles of synthetic amphiphiles.

pH at the micellar interface: Synthesis of pH probes derived from salicylic acid, acid-base dissociation in sodium dodecyl sulfate micelles, and Poisson-Boltzmann simulation

The study of the H+ concentration at the micellar interface is a convenient system for modeling the distribution of H+ at interfaces. We have synthesized salicylic acid derivatives to analyze the proton dissociation of both the carboxylic and phenol groups of' the probes, determining spectrophotometrically the apparent pK(a)'s (pK(ap)) in sodium dodecyl Sulfate, SDS, micelles with and without added salt. The synthesized probes were 2-hydroxy-5-(2-trimethylammoniumacetyl)benzoate; 2-hydroxy-5-(2-dimethylhexadecylammoniumacetyl)benzoate- 2-hydroxy-5-(2-dimethylhexadecylammoniumhexanoyl)benzoate-, 2-hydroxy-5-(2-diniethylhexadecylammoniumundecanoyl)betizoate; 2-hydroxy-5-acetylbenzoic acids and 2-hydroxy-5-dodecanoylbenzoic acid. Upon incorporation into SDS micelles the pK(ap)'s of both carboxylic and phenol groups increased by ca. 3 pH units and NaCl addition caused a decrease in the probe-incorporated pKap. The experimental results were fitted with a cell model Poisson-Boltzmann (P-B) equation taking in consideration the effect of salt on the aggregation number of SDS and using the distance of' the dissociating group as a parameter. The conformations of the probes were analyzed theoretically using two dielectric constants, e.g., 2 and 78. Both the P-B analysis and conformation calculations can be interpreted by assuming that the acid groups dissociate very close to, or at, the interface. Our results are consistent with the assumption that the intrinsic pK(a)'s of both carboxylic and phenol groups of the salicylic acid probes used here can be taken as those in water. Using this assumption the micellar and salt effects on the pKap's of the (trialkylammonium)benzoate probes were described accurately using a cell model P-B analysis. (c) 2005 Elsevier B.V. All rights reserved.

Aplicação da equação de Paisson-Boltzmann com condição de contorno para regulação carga-potencial a sistemas polieletrolíticos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Calculations of the free energy of interaction of the c-Fos−c-Jun coiled coil: Effects of the solvation model and the inclusion of polarization effects

The leucine zipper region of activator protein-1 (AP-1) comprises the c-Jun and c-Fos proteins and constitutes a well-known coiled coil protein−protein interaction motif. We have used molecular dynamics (MD) simulations in conjunction with the molecular mechanics/Poisson−Boltzmann generalized-Born surface area [MM/PB(GB)SA] methods to predict the free energy of interaction of these proteins. In particular, the influence of the choice of solvation model, protein force field, and water potential on the stability and dynamic properties of the c-Fos−c-Jun complex were investigated. Use of the AMBER polarizable force field ff02 in combination with the polarizable POL3 water potential was found to result in increased stability of the c-Fos−c-Jun complex. MM/PB(GB)SA calculations revealed that MD simulations using the POL3 water potential give the lowest predicted free energies of interaction compared to other nonpolarizable water potentials. In addition, the calculated absolute free energy of binding was predicted to be closest to the experimental value using the MM/GBSA method with independent MD simulation trajectories using the POL3 water potential and the polarizable ff02 force field, while all other binding affinities were overestimated.

Docking and free energy simulations to predict conformational domains involved in hCG-LH receptor interactions using recombinant antibodies

Single chain fragment variables (ScFvs) have been extensively employed in studying the protein-protein interactions. ScFvs derived from phage display libraries have an additional advantage of being generated against a native antigen, circumventing loss of information on conformational epitopes. In the present study, an attempt has been made to elucidate human chorionic gonadotropin (hCG)-luteinizing hormone (LH) receptor interactions by using a neutral and two inhibitory ScFvs against hCG. The objective was to dock a computationally derived model of these ScFvs onto the crystal structure of hCG and understand the differential roles of the mapped epitopes in hCG-LH receptor interactions. An anti-hCG ScFv, whose epitope was mapped previously using biochemical tools, served as the positive control for assessing the quality of docking analysis. To evaluate the role of specific side chains at the hCG-ScFv interface, binding free energy as well as residue interaction energies of complexes in solution were calculated using molecular mechanics Poisson-Boltzmann/surface area method after performing the molecular dynamic simulations on the selected hCG-ScFv models and validated using biochemical and SPR analysis. The robustness of these calculations was demonstrated by comparing the theoretically determined binding energies with the experimentally obtained kinetic parameters for hCG-ScFv complexes. Superimposition of hCG-ScFv model onto a model of hCG complexed with the 51-266 residues of LH receptor revealed importance of the residues previously thought to be unimportant for hormone binding and response. This analysis provides an alternate tool for understanding the structure-function analysis of ligand-receptor interactions. Proteins 2011;79:3108-3122. (C) 2011 Wiley-Liss, Inc.

Binding of BIS like and other ligands with the GSK-3 beta kinase: a combined docking and MM-PBSA study

Binding of several bisindolylmaleimide (BIS) like (BIS-3, BIS-8 and UCN1) and other ligands (H89, SB203580 and Y27632) with the glycogen synthase kinase-3 (GSK-3 beta) has been studied using combined docking, molecular dynamics and Poisson-Boltzmann surface area analysis approaches. The study generated novel binding modes of these ligands that can rationalize why some ligands inhibit GSK-3 beta while others do not. The relative binding free energies associated with these binding modes are in agreement with the corresponding measured specificities. This study further provides useful insight regarding possible existence of multiple conformations of some ligands like H89 and BIS-8. It is also found that binding modes of BIS-3, BIS-8 and UCN1 with GSK-3 beta and PDK1 kinases are similar. These new insights are expected to be useful for future rational design of novel, more potent GSK-3 beta-specific inhibitors as promising therapeutics.

Molecular dynamics simulations of PPI dendrimer-drug complexes

Dendrimeric nanoparticles are potential drug delivery devices which can enhance the solubility of hydrophobic drugs, thus increasing their bioavailability and sustained release action. A quantitative understanding of the dendrimer-drug interactions can give valuable insight into the solubility and release profile of hydrophobic drug molecules in various solvent conditions. Fully atomistic molecular dynamics (MD) simulations have been performed to study the interactions of G5 PPIEDA (G5 ethylenediamine cored poly(propylene imine)) dendrimer and two well known drugs (Famotidine and Indomethacin) at different pH conditions. The study suggested that at low pH the dendrimer-drug complexes are thermodynamically unstable as compared to neutral and high pH conditions. Calculated Potential of Mean Force (PMF) by umbrella sampling showed that the release of drugs from the dendrimer at low pH is spontaneous, median release at neutral pH and slow release at high pH. In addition, Molecular Mechanics Poisson-Boltzmann Surface Area (MM-PBSA) binding free energy calculations were also performed at each umbrella sampling window to identify the various energy contributions. To understand the effect of dendrimer chemistry and topology on the solubility and release profile of drugs, this study is extended to explore the solubility and release profile of phenylbutazone drug complexed with G3 poly(amidoamine) and G4 diaminobutane cored PPI dendrimers. The results indicate that the pH-induced conformational changes in dendrimer, ionization states, dendrimer type and pK(a) of the guest molecules influence the free energy barrier and stability of complexation, and thus regulate drug loading, solubility and release.

Electrostatic Interactions Between Glycosaminoglycan Molecules

The electrostatic interactions between nearest-neighbouring chondroitin sulfate glycosaminoglycan (CS-GAG) molecular chains are obtained on the bottle brush conformation of proteoglycan aggrecan based on an asymptotic solution of the Poisson-Boltzmann equation the CS-GAGs satisfy under the physiological conditions of articular cartilage. The present results show that the interactions are associated intimately with the minimum separation distance and mutual angle between the molecular chains themselves. Further analysis indicates that the electrostatic interactions are not only expressed to be purely exponential in separation distance and decrease with the increasing mutual angle but also dependent sensitively on the saline concentration in the electrolyte solution within the tissue, which is in agreement with the existed relevant conclusions.

Solute transport in nanochannels with roughness-like structures

Newfound attention has been given to solute transport in nanochannels. Because the electric double layer (EDL) thickness is comparable to characteristic channel dimensions, nanochannels have been used to separate ionic species with a constant charge-to-size ratio (i.e., electrophoretic mobility) that otherwise cannot be separated in electroosmotic or pressure- driven flow along microchannels. In nanochannels, the electrical fields within the EDL cause transverse ion distributions and thus yield charge-dependent mean ion speeds in the flow. Surface roughness is usually inevitable during microfabrication of microchannels or nanochannels. Surface roughness is usually inevitable during the fabrication of nanochannels. In the present study, we develop a numerical model to investigate the transport of charged solutes in nanochannels with hundreds of roughness-like structures. The model is based on continuum theory that couples Navier-Stokes equations for flows, Poisson-Boltzmann equation for electrical fields, and Nernst-Planck equation for solute transports. Different operating conditions are considered and the solute transport patterns in rough channels are compared with those in smooth channels. Results indicate that solutes move slower in rough nanochannels than in smooth ones for both pressure- driven and electroosmotic flows. Moreover, solute separation can be significantly improved by surface roughness under certain circumstances.

Ground-state energy shifts of H-like Ti under dense and hot plasma conditions

In this study, by adopting the ion sphere model, the self-consistent. field method is used with the Poisson-Boltzmann equation and the Dirac equation to calculate the ground-state energies of H-like Ti at a plasma electron density from 10(22) cm(-3) to 10(24) cm(-3) and the electron temperature from 100 eV to 3600 eV. The ground-state energy shifts of H-like Ti show different trends with the electron density and the electron temperature. It is shown that the energy shifts increase with the increase in the electron density and decrease with the increase in the electron temperature. The energy shifts are sensitive to the electron density, but only sensitive to the low electron temperature. In addition, an accurately fitting formula is obtained to fast estimate the ground-state energies of H-like Ti. Such fitted formula can also be used to estimate the critical electron density of pressure ionization for the ground state of H-like Ti.