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PubMed2004

Electrostatic interactions of charged dipolar proteins in reverse micelles.

The electrostatic interactions in a reverse micelle containing a small-ionized protein are studied by Monte Carlo simulation. The electrostatic contribution to the potential of mean force of the protein in the reverse micelle is determined for a neutral protein, a uniformly charged protein, and a uniformly charged protein with a dipole moment. The effect of addition of a simple electrolyte is studied. While symmetrically distributed micellar charge exerts no force on enclosed ionic species, the protein is driven to the micellar wall due to interactions with simple ions. Protein binding to the inner wall of the micelle can be regulated by added salt. The presence of a dipole drives the protein further to the wall. These effects are studied for several proteins characterized by different charges and dipole moments. For a weakly charged protein with a strong dipole moment the contribution of dipolar interaction to the free energy can represent a major driving force for protein solubilization in the microemulsion.

Electrolytes↗
PubMed2004

Optimized Baxter model of protein solutions: electrostatics versus adhesion.

A theory is set up of spherical proteins interacting by screened electrostatics and constant adhesion, in which the effective adhesion parameter is optimized by a variational principle for the free energy. An analytical approach to the second virial coefficient is first outlined by balancing the repulsive electrostatics against part of the bare adhesion. A theory similar in spirit is developed at nonzero concentrations by assuming an appropriate Baxter model as the reference state. The first-order term in a functional expansion of the free energy is set equal to zero which determines the effective adhesion as a function of salt and protein concentrations. The resulting theory is shown to have fairly good predictive power for the ionic-strength dependence of both the second virial coefficient and the osmotic pressure or compressibility of lysozyme up to about 0.2 volume fraction.

Adhesiveness↗
PubMed2005

Longitudinal polarizability of long polymeric chains: quasi-one-dimensional electrostatics as the origin of slow convergence.

The longitudinal linear polarizability alpha(N) of a stereoregular oligomer of size N is proportional to N in the large-N limit, provided the system is nonconducting in that limit. It has long been known that the convergence of alpha(N)/N to the asymptotic alpha(infinity) value is slow. We show that the leading term in the difference between alpha(N)/N and alpha(infinity) is of the order of 1/N. The difference [alpha(N)-alpha(N-1)], as well as alpha(center)(N) (when computationally accessible), also converge to alpha(infinity), but faster, the leading term being of the order of 1/N(2). We also present evidence that in these cases the power law convergence behavior is due to quasi-one-dimensional electrostatics, with one exception. Specifically, in molecular systems the difference between alpha(N)/N and alpha(infinity) has not just one but two sources of the O(1/N) term, with one being due to the aforementioned Coulomb interactions, and the second due to the short ranged exponentially decaying perturbations on chain ends. The major role of electrostatics in the convergence of the remainders is demonstrated by means of a Clausius-Mossotti-type classical model. The conclusions derived from the model are also shown to be applicable in molecular systems, by means of test-case ab initio calculations on linear stacks of H(2) molecules, and on polyacetylene chains. The implications of the modern theory of polarization for extended systems are also discussed.

Journal Article↗
PubMed2005

Computation of electrostatic forces between solvated molecules determined by the Poisson-Boltzmann equation using a boundary element method.

A rigorous approach is proposed to calculate the electrostatic forces among an arbitrary number of solvated molecules in ionic solution determined by the linearized Poisson-Boltzmann equation. The variational principle is used and implemented in the frame of a boundary element method (BEM). This approach does not require the calculation of the Maxwell stress tensor on the molecular surface, therefore it totally avoids the hypersingularity problem in the direct BEM whenever one needs to calculate the gradient of the surface potential or the stress tensor. This method provides an accurate and efficient way to calculate the full intermolecular electrostatic interaction energy and force, which could potentially be used in Brownian dynamics simulation of biomolecular association. The method has been tested on some simple cases to demonstrate its reliability and efficiency, and parts of the results are compared with analytical results and with those obtained by some known methods such as adaptive Poisson-Boltzmann solver.

Algorithms↗
PubMed2005

Mixtures of charged colloid and neutral polymer: influence of electrostatic interactions on demixing and interfacial tension.

The equilibrium phase behavior of a binary mixture of charged colloids and neutral, nonadsorbing polymers is studied within free-volume theory. A model mixture of charged hard-sphere macroions and ideal, coarse-grained, effective-sphere polymers is mapped first onto a binary hard-sphere mixture with nonadditive diameters and then onto an effective Asakura-Oosawa model [S. Asakura and F. Oosawa, J. Chem. Phys. 22, 1255 (1954)]. The effective model is defined by a single dimensionless parameter-the ratio of the polymer diameter to the effective colloid diameter. For high salt-to-counterion concentration ratios, a free-volume approximation for the free energy is used to compute the fluid phase diagram, which describes demixing into colloid-rich (liquid) and colloid-poor (vapor) phases. Increasing the range of electrostatic interactions shifts the demixing binodal toward higher polymer concentration, stabilizing the mixture. The enhanced stability is attributed to a weakening of polymer depletion-induced attraction between electrostatically repelling macroions. Comparison with predictions of density-functional theory reveals a corresponding increase in the liquid-vapor interfacial tension. The predicted trends in phase stability are consistent with observed behavior of protein-polysaccharide mixtures in food colloids.

Journal Article↗
PubMed2005

A self-consistent transport model for molecular conduction based on extended Hückel theory with full three-dimensional electrostatics.

We present a transport model for molecular conduction involving an extended Hückel theoretical treatment of the molecular chemistry combined with a nonequilibrium Green's function treatment of quantum transport. The self-consistent potential is approximated by CNDO (complete neglect of differential overlap) method and the electrostatic effects of metallic leads (bias and image charges) are included through a three-dimensional finite element method. This allows us to capture spatial details of the electrostatic potential profile, including effects of charging, screening, and complicated electrode configurations employing only a single adjustable parameter to locate the Fermi energy. As this model is based on semiempirical methods it is computationally inexpensive and flexible compared to ab initio models, yet at the same time it is able to capture salient qualitative features as well as several relevant quantitative details of transport. We apply our model to investigate recent experimental data on alkane dithiol molecules obtained in a nanopore setup. We also present a comparison study of single molecule transistors and identify electronic properties that control their performance.

Journal Article↗
PubMed2005

A regularized and renormalized electrostatic coupling Hamiltonian for hybrid quantum-mechanical-molecular-mechanical calculations.

We describe a regularized and renormalized electrostatic coupling Hamiltonian for hybrid quantum-mechanical (QM)-molecular-mechanical (MM) calculations. To remedy the nonphysical QM/MM Coulomb interaction at short distances arising from a point electrostatic potential (ESP) charge of the MM atom and also to accommodate the effect of polarized MM atom in the coupling Hamiltonian, we propose a partial-wave expansion of the ESP charge and describe the effect of a s-wave expansion, extended over the covalent radius r(c), of the MM atom. The resulting potential describes that, at short distances, large scale cancellation of Coulomb interaction arises intrinsically from the localized expansion of the MM point charge and the potential self-consistently reduces to 1r(c) at zero distance providing a renormalization to the Coulomb energy near interatomic separations. Employing this renormalized Hamiltonian, we developed an interface between the Car-Parrinello molecular-dynamics program and the classical molecular-dynamics simulation program Groningen machine for chemical simulations. With this hybrid code we performed QM/MM calculations on water dimer, imidazole carbon monoxide (CO) complex, and imidazole-heme-CO complex with CO interacting with another imidazole. The QM/MM results are in excellent agreement with experimental data for the geometry of these complexes and other computational data found in literature.

Carbon Monoxide↗
PubMed2005

The electrostatic potential generated by topological atoms. II. Inverse multipole moments.

Quantum chemical topology defines finite atoms, whose bounded electron density generates a well-defined electrostatic potential. A multipole expansion based on spherical tensors provides a potential that is formally convergent outside the divergence sphere. Part I of this series [P. L. A. Popelier and M. Rafat, Chem. Phys. Lett.376, 148 (2003)] showed that a continuous multipole expansion expands the convergence region, thereby allowing the electrostatic potential to be evaluated at short range. Here, we propose a different method, based on "inverse" multipole moments, enabling an expansion that converges everywhere. These moments are defined by inverse (i.e., negative) powers of the magnitude of the position vector describing the electron density inside the atom. We illustrate this technique on nitrogen in N(2), oxygen in H(2)O, and oxygen in the phenolic group of the amino acid tyrosine. The proposed method constitutes a considerable advance over the method presented in Part I.

Journal Article↗
PubMed2005

Effective electrostatic interactions in solutions of polyelectrolyte stars with rigid rodlike arms.

In solutions of star-branched polyelectrolytes, electrostatic interactions between charged arms on neighboring stars can compete with intrastar interactions and rotational entropy to induce anisotropy in the orientational distribution of arms. We explore the influence of arm orientational anisotropy on effective star-star interactions for model stars comprising rigid rodlike arms with evenly spaced charged monomers interacting via an effective screened-Coulomb (Yukawa) potential. Monte Carlo simulation and density-functional theory are used to compute the arm orientational distributions and effective pair potentials between weakly charged stars. For comparison, a torque balance analysis is performed to obtain the configuration and energy of the ground state, in which the torque vanishes on each arm of the two-star system. The degree of anisotropy is found to increase with the strength of electrostatic interactions and proximity of the stars. As two stars begin to overlap, the forward arms are pushed back by interstar arm-arm repulsion, but partially interdigitate due to rotational entropy. At center-center separations approaching complete overlap, the arms relax to an isotropic distribution. For nonoverlapping stars, anisotropy-induced changes in the intra- and interstar arm-arm interactions largely cancel and the effective pair interactions are then well approximated by a simple Yukawa potential, as predicted by linear-response theory for a continuum model of isotropic stars [A. R. Denton, Phys. Rev. E 67, 11804 (2003)]. For overlapping stars, the effective pair interactions in the simple rigid-arm-Yukawa model agree closely with simulations of a molecular model that includes flexible arms and explicit counterions [A. Jusufi et al., Phys. Rev. Lett. 88, 018301 (2002); J. Chem. Phys. 116, 11011 (2002)].

Journal Article↗
PubMed2006

Electrostatic surface interactions in mixtures of symmetric and asymmetric electrolytes: a Monte Carlo study.

Canonical Monte Carlo simulations of the interaction between a uniformly charged spherical particle and a discretely charged planar surface in solutions of symmetric and asymmetric electrolytes were performed. To assess the nature of the interactions, the force exerted on the colloidal particle perpendicular to the planar surface was calculated. Attractive minima in the interaction force between the similarly charged surfaces reveal the occurrence of two phenomena: long-range attraction of electrostatic origin and short-range attraction due to depletion effects. The degree of electrostatic coupling determines the magnitude and range of like-charge attraction between the two surfaces.

Journal Article↗
PubMed2006

A new quantum method for electrostatic solvation energy of protein.

A new method that incorporates the conductorlike polarizable continuum model (CPCM) with the recently developed molecular fractionation with conjugate caps (MFCC) approach is developed for ab initio calculation of electrostatic solvation energy of protein. The application of the MFCC method makes it practical to apply CPCM to calculate electrostatic solvation energy of protein or other macromolecules in solution. In this MFCC-CPCM method, calculation of protein solvation is divided into calculations of individual solvation energies of fragments (residues) embedded in a common cavity defined with respect to the entire protein. Besides computational efficiency, the current approach also provides additional information about contribution to protein solvation from specific fragments. Numerical studies are carried out to calculate solvation energies for a variety of peptides including alpha helices and beta sheets. Excellent agreement between the MFCC-CPCM result and those from the standard full system CPCM calculation is obtained. Finally, the MFCC-CPCM calculation is applied to several real proteins and the results are compared to classical molecular mechanics Poisson-Boltzmann (MM/PB) and quantum Divid-and-Conque Poisson-Boltzmann (D&C-PB) calculations. Large wave function distortion energy (solute polarization energy) is obtained from the quantum calculation which is missing in the classical calculation. The present study demonstrates that the MFCC-CPCM method is readily applicable to studying solvation of proteins.

Computer Simulation↗
PubMed2006

The dependence of electrostatic solvation energy on dielectric constants in Poisson-Boltzmann calculations.

The Poisson-Boltzmann equation gives the electrostatic free energy of a solute molecule (with dielectric constant epsilon(l)) solvated in a continuum solvent (with dielectric constant epsilon(s)). Here a simple formula is presented that accurately predicts the electrostatic free energy for all combinations of epsilon(l) and epsilon(s) from the calculation on a single set of epsilon(l) and epsilon(s) values.

Algorithms↗
PubMed2006

Electrostatic interactions in dissipative particle dynamics using the Ewald sums.

The electrostatic interactions in dissipative particle dynamics (DPD) simulations are calculated using the standard Ewald [Ann. Phys. 64, 253 (1921)] sum method. Charge distributions on DPD particles are included to prevent artificial ionic pair formation. This proposal is an alternative method to that introduced recently by Groot [J. Chem. Phys. 118, 11265 (2003)] where the electrostatic field was solved locally on a lattice. The Ewald method is applied to study a bulk electrolyte and polyelectrolyte-surfactant solutions. The structure of the fluid is analyzed through the radial distribution function between charged particles. The results are in good agreement with those reported by Groot for the same systems. We also calculated the radius of gyration of a polyelectrolyte in salt solution as a function of solution pH and degree of ionization of the chain. The radius of gyration increases with the net charge of the polymer in agreement with the trend found in static light scattering experiments of polystyrene sulfonate solutions.

Journal Article↗
PubMed2004

Electrostatically optimized Ras-binding Ral guanine dissociation stimulator mutants increase the rate of association by stabilizing the encounter complex.

Association of two proteins can be described as a two-step process, with the formation of an encounter complex followed by desolvation and establishment of a tight complex. Here, by using the computer algorithm PARE, we designed a set of mutants of the Ras effector protein Ral guanine nucleotide dissociation stimulator (RalGDS) with optimized electrostatic steering. The fastest binding RalGDS mutant, M26K,D47K,E54K, binds Ras 14-fold faster and 25-fold tighter compared with WT. A linear correlation was found between the calculated and experimental data, with a correlation coefficient of 0.97 and a slope of 0.65 for the 24 mutants produced. The data suggest that increased electrostatic steering specifically stabilizes the encounter complex and transition state. This conclusion is backed up by Phi analysis of the encounter complex and transition state of the RalGDS(M26K,D47K,E54K)/Ras complex, with both values being close to 1. Upon further formation of the final complex, the increased Coulombic interactions are probably counterbalanced by the cost of desolvation of charges, keeping the dissociation rate constant almost unchanged. This mechanism is also reflected by the mutual compensation of enthalpy and entropy changes quantified by isothermal titration calorimetry. The binding constants of the faster binding RalGDS mutants toward Ras are similar to those of Raf, the most prominent Ras effector, suggesting that the design methodology may be used to switch between signal transduction pathways.

Binding Sites↗
PubMed2004

Time-resolved energy transfer in DNA sequence detection using water-soluble conjugated polymers: the role of electrostatic and hydrophobic interactions.

We have investigated the energy transfer processes in DNA sequence detection by using cationic conjugated polymers and peptide nucleic acid (PNA) probes with ultrafast pump-dump-emission spectroscopy. Pump-dump-emission spectroscopy provides femtosecond temporal resolution and high sensitivity and avoids interference from the solvent response. The energy transfer from donor (the conjugated polymer) to acceptor (a fluorescent molecule attached to a PNA terminus) has been time resolved. The results indicate that both electrostatic and hydrophobic interactions contribute to the formation of cationic conjugated polymers/PNA-C/DNA complexes. The two interactions result in two different binding conformations. This picture is supported by the average donor-acceptor separations as estimated from time-resolved and steady-state measurements. Electrostatic interactions dominate at low concentrations and in mixed solvents.

Base Sequence↗
PubMed2005

Rapid electrostatic evolution at the binding site for cytochrome c on cytochrome c oxidase in anthropoid primates.

Cytochrome c (CYC) oxidase (COX), a multisubunit enzyme that functions in mitochondrial aerobic energy production, catalyzes the transfer of electrons from CYC to oxygen and participates in creating the electrochemical gradient used for ATP synthesis. Modeling three-dimensional structural data on COX and CYC reveals that 57 of the >1,500 COX residues can be implicated in binding CYC. Because of the functional importance of the transfer of electrons to oxygen, it might be expected that natural selection would drastically constrain amino acid replacement rates of CYC and COX. Instead, in anthropoid primates, although not in other mammals, CYC and COX show markedly accelerated amino acid replacement rates, with the COX acceleration being much greater at the positions that bind CYC than at those that do not. Specifically, in the anthropoid lineage descending from the last common ancestor of haplorhines (tarsiers and anthropoids) to that of anthropoids (New World monkeys and catarrhines) and that of catarrhines (Old World monkeys and apes, including humans), a minimum of 27 of the 57 COX amino acid residues that bind CYC were replaced, most frequently from electrostatically charged to noncharged residues. Of the COX charge-bearing residues involved in binding CYC, half (11 of 22) have been replaced with uncharged residues. CYC residues that interact with COX residues also frequently changed, but only two of the CYC changes altered charge. We suggest that reducing the electrostatic interaction between COX and CYC was part of the adaptive evolution underlying the emergence of anthropoid primates.

Adaptation, Physiological↗
PubMed2006

Multiconformation continuum electrostatics analysis of the NhaA Na+/H+ antiporter of Escherichia coli with functional implications.

Sodium proton antiporters are essential enzymes that catalyze the exchange of sodium ions for protons across biological membranes. Protonations and deprotonations of individual amino acid residues and of clusters formed by these residues play an important role in activating these enzymes and in the mechanism of transport. We have used multiconformation continuum electrostatics method to investigate the protonation states of residues in the sodium proton exchanger NhaA from Escherichia coli, the structure of which has been determined recently by x-ray crystallography. Our calculations identify four clusters of electrostatically tightly interacting residues as well as long-range interactions between residues required for activation. The importance of many of these residues has been demonstrated by the characterization of site-directed mutants. A number of residues with extreme pKa values, including several of the "pH sensor," can only undergo protonation/deprotonation reactions subsequent to conformational changes. The results of the calculations provide valuable information on the activation of the antiporter and the role of individual amino acid residues, and provide a solid framework for further experiments.

Amino Acid Sequence↗
PubMed2006

Order N algorithm for computation of electrostatic interactions in biomolecular systems.

Poisson-Boltzmann electrostatics is a well established model in biophysics; however, its application to large-scale biomolecular processes such as protein-protein encounter is still limited by the efficiency and memory constraints of existing numerical techniques. In this article, we present an efficient and accurate scheme that incorporates recently developed numerical techniques to enhance our computational ability. In particular, a boundary integral equation approach is applied to discretize the linearized Poisson-Boltzmann equation; the resulting integral formulas are well conditioned and are extended to systems with arbitrary numbers of biomolecules. The solution process is accelerated by Krylov subspace methods and a new version of the fast multipole method. In addition to the electrostatic energy, fast calculations of the forces and torques are made possible by using an interpolation procedure. Numerical experiments show that the implemented algorithm is asymptotically optimal O(N) in both CPU time and required memory, and application to the acetylcholinesterase-fasciculin complex is illustrated.

Acetylcholinesterase↗