Protein-ligand binding free energy estimation using molecular mechanics and continuum electrostatics. Application to HIV-1 protease inhibitors.

A method is proposed for the estimation of absolute binding free energy of interaction between proteins and ligands. Conformational sampling of the protein-ligand complex is performed by molecular dynamics (MD) in vacuo and the solvent effect is calculated a posteriori by solving the Poisson or the Poisson-Boltzmann equation for selected frames of the trajectory. The binding free energy is written as a linear combination of the buried surface upon complexation, SASbur, the electrostatic interaction energy between the ligand and the protein, Eelec, and the difference of the solvation free energies of the complex and the isolated ligand and protein, deltaGsolv. The method uses the buried surface upon complexation to account for the non-polar contribution to the binding free energy because it is less sensitive to the details of the structure than the van der Waals interaction energy. The parameters of the method are developed for a training set of 16 HIV-1 protease-inhibitor complexes of known 3D structure. A correlation coefficient of 0.91 was obtained with an unsigned mean error of 0.8 kcal/mol. When applied to a set of 25 HIV-1 protease-inhibitor complexes of unknown 3D structures, the method provides a satisfactory correlation between the calculated binding free energy and the experimental pIC5o without reparametrization.

Monte Carlo and modified Tanford-Kirkwood results for macromolecular electrostatics calculations

The understanding of electrostatic interactions is an essential aspect of the complex correlation between structure and function of biological macromolecules. It is also important in protein engineering and design. Theoretical studies of such interactions are predominantly done within the framework of Debye-Huckel theory. A classical example is the Tanford-Kirkwood (TK) model. Besides other limitations, this model assumes an infinitesimally small macromolecule concentration. By comparison to Monte Carlo (MC) simulations, it is shown that TK predictions for the shifts in ion binding constants upon addition of salt become less reliable even at moderately macromolecular concentrations. A simple modification based on colloidal literature is suggested to the TK scheme. The modified TK models suggested here satisfactorily predict MC and experimental shifts in the calcium binding constant as a function of protein concentration for the calbindin D-9k mutant and calmodulin.

Lamé differential equations and electrostatics

The problem of existence and uniqueness of polynomial solutions of the Lamé differential equation A(x)y″ + 2B(x)y′ + C(x)y = 0, where A(x),B(x) and C(x) are polynomials of degree p + 1,p and p - 1, is under discussion. We concentrate on the case when A(x) has only real zeros aj and, in contrast to a classical result of Heine and Stieltjes which concerns the case of positive coefficients rj in the partial fraction decomposition B(x)/A(x) = ∑j p=0 rj/(x - aj), we allow the presence of both positive and negative coefficients rj. The corresponding electrostatic interpretation of the zeros of the solution y(x) as points of equilibrium in an electrostatic field generated by charges rj at aj is given. As an application we prove that the zeros of the Gegenbauer-Laurent polynomials are the points of unique equilibrium in a field generated by two positive and two negative charges. © 2000 American Mathematical Society.

Electrostatics for Chemists

This is an introduction to electrostatics written for those interested in dipole moments, induced dipole moments, etc..

Altering dimerization specificity by changes in surface electrostatics

Arc repressor forms a homodimer in which the subunits intertwine to create a single globular domain. To obtain Arc sequences that fold preferentially as heterodimers, variants with surface patches of excess positive or negative charge were designed. Several but not all oppositely charged sequence pairs showed preferential heterodimer formation. In the most successful design pair, α helix B of one subunit contained glutamic acids at positions 43, 46, 47, 48, and 50, whereas the other subunit contained lysines or arginines at these positions. A continuum electrostatic model captures many features of the experimental results and suggests that the most successful designs include elements of both positive and negative design.

Smale's Conjecture on Mean Values of Polynomials and Electrostatics

2000 Mathematics Subject Classification: Primary 30C10, 30C15, 31B35.

Uma perspectiva computacional sobre catálise enzimática

Enzymes are extremely efficient catalysts. Here, part of the mechanisms proposed to explain this catalytic power will be compared to quantitative experimental results and computer simulations. Influence of the enzymatic environment over species along the reaction coordinate will be analysed. Concepts of transition state stabilisation and reactant destabilisation will be confronted. Divided site model and near-attack conformation hypotheses will also be discussed. Molecular interactions such as covalent catalysis, general acid-base catalysis, electrostatics, entropic effects, steric hindrance, quantum and dynamical effects will also be analysed as sources of catalysis. Reaction mechanisms, in particular that catalysed by protein tyrosine phosphatases, illustrate the concepts.

The effect of the generation and handling in the acquired electrostatic charge in airborne particles

The measurement of the charge distribution in laboratory generated aerosols particles was carried out. Four cases of electrostatic charge acquisition by aerosol particles were evaluated. In two of these cases. the charges acquired by the particles were naturally derived from the aerosol generation procedure itself, without using any additional charging method. Ill the other two cases, a corona charger and an impact charger were utilized as Supplementary methods for charge generation. Two types of aerosol generators were used in the dispersion of particles in the gas Stream: the vibrating orifice generator TSI model 3450 and the rotating plate generator TSI model 3433. In the vibrating orifice generator. a Solution of methylene blue Was used and the generated particles were mono-dispersed. Different mono-aerosols were generated with particle diameters varying from 6.0 x 10(-6) m to 1.4 x 10(-5) m. In the rotating plate generator, a poly-dispersed phosphate rock concentrate with Stokes mean diameter of 1.30 x 10(-6) m and size range between 1.5 x 10(-7) m and 8.0 x 10(-6) m Was utilized as powder material in all tests. In the tests performed with the mono-dispersed particles. the median charges of the particles varied between -3.0 x 10-(16) C and -5.0 x 10(-18) degrees C and a weak dependence between particle size and charge was observed. The particles were predominantly negatively charged. In the tests with the poly-dispersed particles the median charges varied fairly linearly with the particle diameter and were negative. The order of magnitude of the results obtained is in accordance with data reported in the literature. The charge distribution, in this case, was wider, so that an appreciable amount of particles were positively charged. The relative spread of the distribution varied with the charging method. It was also noticed that the corona charger acted very effectively in charging the particles. (C) 2008 Elsevier BY. All rights reserved.

On the fast approximation of Green's functions in MPIE formulations for planar layered media

The numerical implementation of the complex image approach for the Green's function of a mixed-potential integralequation formulation is examined and is found to be limited to low values of k(0) rho (in this context k(0) rho = 2 pirho/ lambda(0), where rho is the distance between the source and the field points of the Green's function and lambda(0) is the free space wavelength). This is a clear limitation for problems of large dimension or high frequency where this limit is easily exceeded. This paper examines the various strategies and proposes a hybrid method whereby most of the above problems can be avoided. An efficient integral method that is valid for large k(0) rho is combined with the complex image method in order to take advantage of the relative merits of both schemes. It is found that a wide overlapping region exists between the two techniques allowing a very efficient and consistent approach for accurately calculating the Green's functions. In this paper, the method developed for the computation of the Green's function is used for planar structures containing both lossless and lossy media.

Perspectives on the electrically induced properties of electrospun cellulose/liquid crystal devices

A mat of electrospun cellulose fibers are deposed on transparent conductive oxide covered glass, and two such plates enclose a nematic liquid crystal. Thus two new types of Cellulose based Polymer Dispersed Liquid Crystal devices, based on hydroxypropylcellulose and Cellulose Acetate and the nematic liquid crystal E7 have been obtained. The current-voltage characteristics indicates ionic type conduction. Heating-cooling cycles have been applied on the samples and the activation energies have been determined. Simultaneously with the thermo-stimulated currents, the optical transmission dependence on the d.c. electric field and temperature was registered. ON-OFF switching times have been determined for different control voltages. (C) 2011 Elsevier B.V. All rights reserved.

Critical analysis and extension of the Hirshfeld atoms in molecules

The computational approach to the Hirshfeld [Theor. Chim. Acta 44, 129 (1977)] atom in a molecule is critically investigated, and several difficulties are highlighted. It is shown that these difficulties are mitigated by an alternative, iterative version, of the Hirshfeld partitioning procedure. The iterative scheme ensures that the Hirshfeld definition represents a mathematically proper information entropy, allows the Hirshfeld approach to be used for charged molecules, eliminates arbitrariness in the choice of the promolecule, and increases the magnitudes of the charges. The resulting "Hirshfeld-I charges" correlate well with electrostatic potential derived atomic charges

Two complementary molecular energy decomposition schemes: the Mayer and Ziegler-Rauk methods in comparison

In the present paper we discuss and compare two different energy decomposition schemes: Mayer's Hartree-Fock energy decomposition into diatomic and monoatomic contributions [Chem. Phys. Lett. 382, 265 (2003)], and the Ziegler-Rauk dissociation energy decomposition [Inorg. Chem. 18, 1558 (1979)]. The Ziegler-Rauk scheme is based on a separation of a molecule into fragments, while Mayer's scheme can be used in the cases where a fragmentation of the system in clearly separable parts is not possible. In the Mayer scheme, the density of a free atom is deformed to give the one-atom Mulliken density that subsequently interacts to give rise to the diatomic interaction energy. We give a detailed analysis of the diatomic energy contributions in the Mayer scheme and a close look onto the one-atom Mulliken densities. The Mulliken density ρA has a single large maximum around the nuclear position of the atom A, but exhibits slightly negative values in the vicinity of neighboring atoms. The main connecting point between both analysis schemes is the electrostatic energy. Both decomposition schemes utilize the same electrostatic energy expression, but differ in how fragment densities are defined. In the Mayer scheme, the electrostatic component originates from the interaction of the Mulliken densities, while in the Ziegler-Rauk scheme, the undisturbed fragment densities interact. The values of the electrostatic energy resulting from the two schemes differ significantly but typically have the same order of magnitude. Both methods are useful and complementary since Mayer's decomposition focuses on the energy of the finally formed molecule, whereas the Ziegler-Rauk scheme describes the bond formation starting from undeformed fragment densities

A semi-grand canonical Monte Carlo simulation model for ion binding to ionizable surfaces: proton binding of carboxylated latex particles as a case study

In this paper, we present a computer simulation study of the ion binding process at an ionizable surface using a semi-grand canonical Monte Carlo method that models the surface as a discrete distribution of charged and neutral functional groups in equilibrium with explicit ions modelled in the context of the primitive model. The parameters of the simulation model were tuned and checked by comparison with experimental titrations of carboxylated latex particles in the presence of different ionic strengths of monovalent ions. The titration of these particles was analysed by calculating the degree of dissociation of the latex functional groups vs. pH curves at different background salt concentrations. As the charge of the titrated surface changes during the simulation, a procedure to keep the electroneutrality of the system is required. Here, two approaches are used with the choice depending on the ion selected to maintain electroneutrality: counterion or coion procedures. We compare and discuss the difference between the procedures. The simulations also provided a microscopic description of the electrostatic double layer (EDL) structure as a function of p H and ionic strength. The results allow us to quantify the effect of the size of the background salt ions and of the surface functional groups on the degree of dissociation. The non-homogeneous structure of the EDL was revealed by plotting the counterion density profiles around charged and neutral surface functional groups.

Effect of the surface charge discretization on electric double layers. A Monte Carlo simulation study

The structure of the electric double layer in contact with discrete and continuously charged planar surfaces is studied within the framework of the primitive model through Monte Carlo simulations. Three different discretization models are considered together with the case of uniform distribution. The effect of discreteness is analyzed in terms of charge density profiles. For point surface groups,a complete equivalence with the situation of uniformly distributed charge is found if profiles are exclusively analyzed as a function of the distance to the charged surface. However, some differences are observed moving parallel to the surface. Significant discrepancies with approaches that do not account for discreteness are reported if charge sites of finite size placed on the surface are considered.