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At least 181 records · Page 10Linked to original sources
PubMed2005

Tryptophan side chain electrostatic interactions determine edge-to-face vs parallel-displaced tryptophan side chain geometries in the designed beta-hairpin "trpzip2".

The interaction geometries of the four tryptophan (Trp) side chains in the 12-residue designed beta-hairpin trpzip2 are investigated using all-atom explicit-solvent molecular dynamics simulations. The experimentally observed edge-to-face (EtF) pairwise interaction geometries are stable on a time scale of 10 ns. However, removing the electrostatic multipoles of the Trp side chains while retaining the dipoles of the side chains' NH moieties induces a conformational change to a geometry in which three of the four side chains interact in a parallel-displaced (PD) manner. Free energy simulations of the Etf to PD conformational change reveal that, with the side chain multipole moments intact (+MP), the EtF conformation is preferred by 5.79 kcal/mol. Conversely, with only the dipole moments of the side chain NH moieties intact (-MP), the PD conformation's free energy is more favorable by 1.71 kcal/mol. In contrast to energetic similarities for Trp side chain-water electrostatic and Trp side chain-Trp side chain and Trp side chain-water van der Waals, +MP Trp side chain-Trp side chain electrostatic interactions are more favorable by 4.21 kcal/mol in the EtF conformation, while in the -MP case the EtF and PD conformations' Trp side chain-Trp side chain electrostatic energies are nearly identical. The results highlight the importance of electrostatic multipole moments in determining aromatic-aromatic interaction geometries in aqueous biomolecular systems and argue for the inclusion of this physics in simplified models used for protein-ligand docking and protein structure prediction, possibly through a truncated Coulomb term between aromatic moieties.

Computer Simulation↗
PubMed2003

A repertoire of pyridinium-phenyl-methyl cross-talk through a cascade of intramolecular electrostatic interactions.

Direct intramolecular cation-pi interaction between phenyl and pyridinium moieties in 1a(+) has been experimentally evidenced through pH-dependent (1)H NMR titration. The basicity of the pyridinyl group (pK(a) 2.9) in 1a can be measured both from the pH-dependent chemical shifts of the pyridinyl protons as well as from the protons of the neighboring phenyl and methyl groups as a result of electrostatic interaction between the phenyl and the pyridinium ion in 1a(+) at the ground state. The net result of this nearest neighbor electrostatic interaction is that the pyridinium moiety in 1a becomes more basic (pK(a) 2.92) compared to that in the standard 2a (pK(a) 2.56) as a consequence of edge-to-face cation (pyridinium)-pi (phenyl) interaction, giving a free energy of stabilization (DeltaDeltaG(o)pKa) of -2.1 kJ mol(-1). The fact that the pH-dependent downfield shifts of the phenyl and methyl protons give the pK(a) of the pyridine moiety of 1a also suggests that the nearest neighbor cation (pyridinium)-pi (phenyl) interaction also steers the CH (methyl)-pi (phenyl) interaction in tandem. This means that the whole pyridine-phenyl-methyl system in 1a(+) is electronically coupled at the ground state, cross-modulating the physicochemical property of the next neighbor by using the electrostatics as the engine, and the origin of this electrostatics is a far away point in the molecule-the pyridinyl-nitrogen. The relative chemical shift changes and the pK(a) differences show that the cation (pyridinium)-pi (phenyl) interaction is indeed more stable (DeltaDeltaG(o)pKa = -2.1 kJ mol(-1)) than that of the CH (methyl)-pi (phenyl) interaction (DeltaDeltaG(o)pKa = -0.8 kJ mol(-1)). Since the pK(a) of the pyridine moiety in 1a is also obtained through the pH-dependent shifts of both phenyl and methyl protons, it suggests that the net electrostatic mediated charge transfer from the phenyl to the pyridinium and its effect on the CH (methyl)-pi (phenyl) interaction corresponds to DeltaG(o)pKa of the pyridinium ion (approximately 17.5 kJ mol(-1)), which means that the aromatic characters of the phenyl and the pyridinium rings in 1a(+) have been cross-modulated owing to the edge-to-face interaction proportional to this DeltaG(o)pKa change.

Journal Article↗
PubMed2004

Reaction pathways and free energy barriers for alkaline hydrolysis of insecticide 2-trimethylammonioethyl methylphosphonofluoridate and related organophosphorus compounds: electrostatic and steric effects.

Reaction pathways and free energy barriers for alkaline hydrolysis of the highly neurotoxic insecticide 2-trimethylammonioethyl methylphosphonofluoridate and related organophosphorus compounds were studied by performing first-principles electronic structure calculations on representative methylphosphonofluoridates, (RO)CH3P(O)F, in which R = CH2CH2N+(CH3)3, CH3, CH2CH2C(CH3)3, CH2CH2CH(CH3)2, CH(CH3)CH2N+(CH3)3, and CH(CH3)CH2N(CH3)2. The dominant reaction pathway was found to be associated with a transition state in which the attacking nucleophile OH- and the leaving group F- are positioned on opposite sides of the plane formed by the three remaining atoms attached to the phosphorus in order to minimize the electrostatic repulsion between these two groups. The free energy barriers calculated for the rate-determining step of the dominant pathway are 12.5 kcal/mol when R = CH2CH2N+(CH3)3, 15.5 kcal/mol when R = CH3, 17.9 kcal/mol when R = CH2CH2C(CH3)3, 16.5 kcal/mol when R = CH2CH2CH(CH3)2, 13.4 kcal/mol when R = CH(CH3)CH2N+(CH3)3, and 18.7 kcal/mol when R = CH(CH(3))CH(2)N(CH(3))(2). The calculated free energy barriers are in good agreement with available experimentally derived activation free energies, i.e. 14.7 kcal/mol when R = CH(3), 13.4 kcal/mol when R = CH2CH2N+(CH3)3, and 13.9 kcal/mol when R = CH(CH3)CH2N+(CH3)3. A detailed analysis of the calculated energetic results and available experimental data suggests that the net charge of the molecule (M) being hydrolyzed is a prominent factor affecting the free energy barrier (DeltaG) for the alkaline hydrolysis of phosphodiesters, phosphonofluoridates, and related organophosphorus compounds. The electrostatic interactions between the attacking nucleophile OH- and the molecule M being hydrolyzed favor such an order of the free energy barrier: DeltaG(M(+)+OH-) < DeltaG(M0+OH-) < DeltaG(M(-)+OH-), where M+, M0, and M- represent the cationic, neutral, and anionic molecules, respectively. The change of the substituent R in (RO)CH(3)P(O)F from CH3 to CH2CH2N+(CH3)3 is associated with both the electrostatic and steric effects on the free energy barrier, but the electrostatic effect dominates the substituent shift of the free energy barrier. This helps to better understand why the alkaline hydrolysis of (RO)CH3P(O)F with R = CH2CH2N+(CH3)3 and CH(CH3)CH2N+(CH3)3 is significantly faster than that with R = CH3. The effect of electrostatic interaction also helps to understand why the rate constants for the alkaline hydrolysis of phosphodiesters, such as intramolecular second messenger adenosine 3',5'-phosphate (cAMP), are generally smaller than those for the alkaline hydrolysis of the phosphonofluoridates and related phosphotriesters.

Electrochemistry↗
PubMed2005

The electrostatic origin of Abraham's solute polarity parameter.

A computational method was developed which relates the empirical linear solvation energy relationship (LSER) solute polarity parameter, S (formerly denoted ), to two more fundamental quantities: a polarizability term and a computed solvent-accessible-surface electrostatic term. Electrostatics computations were conducted explicitly or with dielectric field polarizable continuum models (PCM, SCIPCM, IPCM), employing a density functional theory (B3LYP/6-311G(2df,2p)) or efficient Hartree-Fock (HF/MIDI!) method for 90 polar and nonpolar organic solutes. Electrostatic parameters calculated at electron isodensity solute surfaces were found to produce significantly better correlations with empirical S values than the same electrostatic parameters deduced from a fixed Bondi atomic radii based surface. The best-fit expression was found employing SCIPCM/IPCM at the 0.0004 e(-)/bohr(3) solvent-accessible-surface: S(fit)() = 0.46E - 0.091SigmaV(s)()(2), with squared correlation coefficient = 0.96 and standard deviation = 0.10, where E is a measured solute excess polarizability scale and SigmaV(s)()(2) is a quantum-calculated solute electrostatic descriptor in kcal A/mol. The resulting model is more accurate than previously developed estimation approaches and relies on only two fitted coefficients; it has the potential advantage of applicability to any solute composed of C, H, N, O, S, F, Cl, and Br. Finally, this investigation offers quantitative insight into the relative contributions of solute polarity and solute polarizability to the empirical LSER polarity parameter, S.

Journal Article↗
PubMed2005

Electrostatic and covalent interactions in CdTe nanocrystalline assemblies.

This paper focuses on the interactions between cysteamine-stabilized CdTe nanocrystals [CdTe(CA) NCs] and thioglycolic-acid-stabilized CdTe nanocrystals [CdTe(TGA) NCs]. These interactions were examined by the absorption, continuous, and time-resolved photoluminescence (PL) spectra of the electrostatically mixed and the covalently linked NCs assemblies comprised of the oppositely surface charged CdTe(CA) and CdTe(TGA) NCs and by a comparison with those of the corresponding pristine NCs. The CdTe(CA)-CdTe(TGA) coupling is dictated by the surfactant spacer, ranging between 0.93 and 1.14 nm and by electrostatic and covalent interactions, enabling a Förster resonance energy transfer (FRET) process among the NCs. The results revealed an excellent spectral overlap between the emission of the CdTe(TGA) NCs and the absorption of the CdTe(CA) NCs as well as a PL spectral red shift on the formation of electrostatic and covalent interactions. Furthermore, the measurements showed a lifetime ranging between 1.2 and 3 ns for the electrostatically mixed and the covalently linked assemblies, shorter than those of the pristine CdTe(CA) NCs and CdTe(TGA) NCs, both of which measured as approximately 5.5 ns. When CdTe(TGA) NCs performed as the most efficient donors, FRET rates of 10(10)-10(11) s(-1) were calculated for the electrostatically mixed NCs or covalently linked NCs.

Cadmium↗
PubMed2005

Electrostatic double layer force between a sphere and a planar substrate in the presence of previously deposited spherical particles.

A finite element model of the electrostatic double layer interaction between an approaching colloidal particle and a small region of a charged planar surface containing four previously deposited particles is presented. The electrostatic interaction force experienced by the approaching particle is obtained by solving the Poisson-Boltzmann equation with appropriate boundary conditions representing this complex geometry. The interaction forces obtained from the detailed three-dimensional finite element simulations suggest that for the many-body scenario addressed here, the electrostatic double layer repulsion experienced by the approaching particle is less than the corresponding sphere-plate interaction due to the presence of the previously deposited particles. The reduction in force is quite significant when the screening length of the electric double layer becomes comparable to the particle radius (kappaa approximately 1). The results also suggest that the commonly used technique of pairwise addition of binary interactions can grossly overestimate the net electrostatic double layer interaction forces in such situations. The simulation methodology presented here can form a basis for investigating the influence of several previously deposited particles on the electrostatic repulsion experienced by a particle during deposition onto a substrate.

Journal Article↗
PubMed2005

Effect of time on the interfacial and foaming properties of beta-lactoglobulin/acacia gum electrostatic complexes and coacervates at pH 4.2.

The electrostatic complexation between beta-lactoglobulin and acacia gum was investigated at pH 4.2 and 25 degrees C. The binding isotherm revealed a spontaneous exothermic reaction, leading to a DeltaHobs = -2108 kJ mol(-1) and a saturation protein to polysaccharide weight mixing ratio of 2:1. Soluble electrostatic complexes formed in these conditions were characterized by a hydrodynamic diameter of 119 +/- 0.6 nm and a polydispersity index of 0.097. The effect of time on the interfacial and foaming properties of these soluble complexes was investigated at a concentration of 0.1 wt % at two different times after mixing (4 min, referred as t approximately 0 h and t = 24 h). At t approximately 0 h, the mixture is mainly made of aggregating soluble electrostatic complexes, whereas after 24 h these complexes have already insolubilize to form liquid coacervates. The surface elasticity, viscosity and phase angle obtained at low frequency (0.01 Hz) using oscillating bubble tensiometry revealed higher fluidity and less rigidity in the film formed at t approximately 0 h. This observation was confirmed by diminishing bubble experiments coupled with microscopy of the thin film. It was thicker, more homogeneous and contained more water at t approximately 0 h as compared to t = 24 h (thinner film, less water). This led to very different gas permeability's of Kt approximately 0 h = 0.021 cm s(-1) and Kt=24 h) = 0.449 cm s(-1), respectively. Aqueous foams produced with the beta-lactoglobulin/acacia gum electrostatic complexes or coacervates exhibited very different stability. The former (t approximately 0 h) had a stable volume, combining low drainage rate and mainly air bubble disproportionation as the destabilization mechanism. By contrast, using coacervates aged for 24 h, the foam was significantly less stable, combining fast liquid drainage and air bubble destabilization though fast gas diffusion followed by film rupture and bubble coalescence. The strong effect of time on the air/water interfacial properties of the beta-lactoglobulin/acacia gum electrostatic complexes can be understood by their reorganization at the interface to form a coacervate phase that is more fluid/viscous at t approximately 0 h vs rigid/elastic at t = 24 h.

Air↗
PubMed1999

Calculating the electrostatic properties of RNA provides new insights into molecular interactions and function.

Solutions to the nonlinear Poisson-Boltzmann equation were used to obtain the electrostatic potentials of RNA molecules that have known three-dimensional structures. The results are described in terms of isopotential contours and surface electrostatic potential maps. Both representations have unexpected features: 'cavities' within isopotential contours and areas of enhanced negative potential on molecular surfaces. Intriguingly, the sites of unusual electrostatic features correspond to functionally important regions, suggesting that electrostatic properties play a key role in RNA recognition and stabilization. These calculations reveal that the electrostatic potentials generated by RNA molecules have a variety of functionally important characteristics that cannot be discerned by simple visual inspection of the molecular structure.

Anticodon↗
PubMedDate not supplied

Electrostatic recognition between superoxide and copper, zinc superoxide dismutase.

Electrostatic forces have been implicated in a variety of biologically important molecular interactions including drug orientation by DNA, protein folding and assembly, substrate binding and catalysis and macromolecular complementarity with inhibitors, drugs and hormones. To examine enzyme-substrate interactions in copper, zinc superoxide dismutase (SOD), we developed a method for the visualization and analysis of an enzyme's three-dimensional electrostatic vector field that allows the contributions of specific residues to be identified. We report here that the arrangement of electrostatic charges in SOD promotes productive enzyme-substrate interaction through substrate guidance and charge complementarity: sequence-conserved residues create an extensive electrostatic field that directs the negatively charged superoxide (O-2) substrate to the highly positive catalytic binding site at the bottom of the active-site channel. Dissection of the electrostatic potential gradient indicated the relative contributions of individual charged residues: Lys 134 and Glu 131 seem to have important roles in directing the long-range approach of O-2, while Arg 141 has local orienting effects. The reported methods of analysis may have general application for the elucidation of intermolecular recognition processes.

Binding Sites↗
PubMed1992

Faster superoxide dismutase mutants designed by enhancing electrostatic guidance.

The enzyme Cu, Zn superoxide dismutase (SOD) protects against oxidative damage by dismuting the superoxide radical O2-. to molecular oxygen and hydrogen peroxide at the active-site Cu ion in a reaction that is rate-limited by diffusion and enhanced by electrostatic guidance. SOD has evolved to be one of the fastest enzymes known (V(max) approximately 2 x 10(9) M-1 s-1). The new crystal structures of human SOD show that amino-acid site chains that are implicated in electrostatic guidance (Glu 132, Glu 133 and Lys 136) form a hydrogen-bonding network. Here we show that site-specific mutants that increase local positive charge while maintaining this orienting network (Glu----Gln) have faster reaction rates and increased ionic-strength dependence, matching brownian dynamics simulations incorporating electrostatic terms. Increased positive charge alone is insufficient: one charge reversal (Glu----Lys) mutant is slower than the equivalent charge neutralization (Glu----Gln) mutant, showing that the newly introduced positive charge disrupts the orienting network. Thus, electrostatically facilitated diffusion rates can be increased by design, provided the detailed structural integrity of the active-site electrostatic network is maintained.

Amino Acid Sequence↗
PubMed1999

Effect of electrostatic charge in plastic spacers on the lung delivery of HFA-salbutamol in children.

AIMS: The effect of the electrostatic charge in plastic spacers in vivo on drug delivery to the lung of hydrofluoroalkane (HFA) salbutamol spray was studied in children. METHODS: Five children, aged 7-12 years, were included in a 3-way crossover randomised single-blind trial. Salbutamol HFA spray was delivered on 3 different study days from plastic spacers with mouthpiece. Pre-treatment of the spacers differed between study days: (a) Non-electrostatic 350 ml Babyhaler (coated with benzalkonium chloride) (b) New 350 ml Babyhaler (rinsed in water), and (c) New 145 ml AeroChamber (rinsed in water). Plasma salbutamol was measured before and 5, 10, 15 and 20 min after inhalation of four single puffs of 100 microg salbutamol. Cmax and Cav (5-20min) were calculated as a reflection of lung dose. RESULTS: For Cmax: (A) Non-electrostatic Babyhaler 4.3 ng ml(-1) (B) New Babyhaler 1.9 ng ml(-1) (C) New AeroChamber 1.6 ng ml(-1): AvsB (95% CI for difference 0.5-4.5 ng ml(-1)), A vs C (95% CI for difference 0.7-4.8 ng ml(-1)). The geometric mean ratio for A:B was 2.4 fold, and for A:C was 2.9 fold. The values for Cav were similar with ratios for A:B of 2.4 fold, and A: C of 4.1 fold. The nonelectrostatic Babyhaler delivered a significantly (P<0.05) higher lung dose (for both Cmax and Cav) than either of the other two spacers. CONCLUSIONS: The electrostatic charge in plastic spacers reduces lung dose in children by more than two-fold. This is clinically significant and the use of potentially electrostatically charged spacers should be avoided.

Absorption↗
PubMed2000

Simulation of electrostatic effects in Fab-antigen complex formation.

A model based on the Poisson-Boltzmann equation has been used to model electrostatics in Anti-p24 (HIV-1) Fab-antigen association. The ionization state at different pH values has been simulated and the results have been used to estimate the stability at different pH values and to generate electrostatic potential maps at physiological ionic strength. The analysis of the electrostatic potential at the solvent-accessible surface shows that residues involved in binding are mostly found in the highest, but also in lowest potential regions. Brownian dynamics simulations have been used to estimate the enhancement of the association rate due to electrostatics which appears limited (approximately 2 at 150 mM ionic strength and approximately 3 at 15 mM ionic strength). A much more pronounced effect is observed upon increase of the charge of the diffusing particle. These results compare well with results obtained previously in similar studies on different systems and may serve to estimate the expected order of magnitude of electrostatic effects on association rates in antibody-antigen systems.

Antigens↗
PubMed2005

Elusive contribution of the experimental surface molecular electrostatic potential and promolecule approximation in the empirical estimate of the crystal density.

The aim of this study is to probe the crystal density (D(c)) description in terms of pertinent molecular characteristics and properties. In this purpose, the electrostatic potential was derived from available experimental electron density multipole parameters of molecular compounds with different D(c) magnitudes. The surface electrostatic potential has been analyzed through the positive and negative statistical variances. The surface of the molecule is here corresponding to particular isodensity values according to Bader's topological theory. Following the successful Politzer's method based on quantum mechanics calculations to empirically describe macroscopic properties, the crystal density was regressed on the molecular density and the surface electrostatic potential variance. This latter appears to be a poor statistical descriptor of the crystal density when the experimentally derived electrostatic potential is used and it does not significantly improve the fit of D(c) to molecular density alone. Compared to Politzer's approach based on gas phase isolated molecules, the experimental electrostatic potential is biased by the interactions in the crystal lattice. As an alternative to other sophisticated methods, the promolecule isodensity surface offers a quite useful and straightforward way to define the molecular volumes. The reported description of the crystal density for a set of 50 molecules using the promolecule approach yields satisfactory results.

Journal Article↗
PubMed2005

An analysis of the electrostatic interaction between nucleic acid bases.

Results from several commonly used approximate methods of evaluating electrostatic interactions have been compared to the rigorous, nonexpanded electrostatic energies at both uncorrelated and correlated levels of theory. We examined a number of energy profiles for both hydrogen bonded and stacked configurations of the nucleic acid base pairs. We found that the penetration effects play an extremely important role and the expanded electrostatic energies are significantly underestimated with respect to the ab initio values. Apart from the inability to reproduce the magnitudes of the ab initio electrostatic energy, there are other problems with the available approximate electrostatic models. For example, the distributed multipole analysis, one of the most advanced methods, is extremely sensitive to the basis set and level of theory used to evaluate the multipole moments. Detailed ab initio results are provided that other researchers could use to test their approximate models.

Base Pairing↗
PubMed2006

Computation of methodology-independent ionic solvation free energies from molecular simulations. I. The electrostatic potential in molecular liquids.

The computation of ionic solvation free energies from atomistic simulations is a surprisingly difficult problem that has found no satisfactory solution for more than 15 years. The reason is that the charging free energies evaluated from such simulations are affected by very large errors. One of these is related to the choice of a specific convention for summing up the contributions of solvent charges to the electrostatic potential in the ionic cavity, namely, on the basis of point charges within entire solvent molecules (M scheme) or on the basis of individual point charges (P scheme). The use of an inappropriate convention may lead to a charge-independent offset in the calculated potential, which depends on the details of the summation scheme, on the quadrupole-moment trace of the solvent molecule, and on the approximate form used to represent electrostatic interactions in the system. However, whether the M or P scheme (if any) represents the appropriate convention is still a matter of on-going debate. The goal of the present article is to settle this long-standing controversy by carefully analyzing (both analytically and numerically) the properties of the electrostatic potential in molecular liquids (and inside cavities within them). Restricting the discussion to real liquids of "spherical" solvent molecules (represented by a classical solvent model with a single van der Waals interaction site), it is concluded that (i) for Coulombic (or straight-cutoff truncated) electrostatic interactions, the M scheme is the appropriate way of calculating the electrostatic potential; (ii) for non-Coulombic interactions deriving from a continuously differentiable function, both M and P schemes generally deliver an incorrect result (for which an analytical correction must be applied); and (iii) finite-temperature effects, including intermolecular orientation correlations and a preferential orientational structure in the neighborhood of a liquid-vacuum interface, must be taken into account. Applications of these results to the computation methodology-independent ionic solvation free energies from molecular simulations will be the scope of a forthcoming article.

Journal Article↗
PubMed2001

Electrostatics of nanosystems: application to microtubules and the ribosome.

Evaluation of the electrostatic properties of biomolecules has become a standard practice in molecular biophysics. Foremost among the models used to elucidate the electrostatic potential is the Poisson-Boltzmann equation; however, existing methods for solving this equation have limited the scope of accurate electrostatic calculations to relatively small biomolecular systems. Here we present the application of numerical methods to enable the trivially parallel solution of the Poisson-Boltzmann equation for supramolecular structures that are orders of magnitude larger in size. As a demonstration of this methodology, electrostatic potentials have been calculated for large microtubule and ribosome structures. The results point to the likely role of electrostatics in a variety of activities of these structures.

Algorithms↗
PubMed1998

Direct molecular level measurements of the electrostatic properties of a protein surface.

In this work, we used direct measurements with the surface force apparatus to determine the pH-dependent electrostatic charge density of a single binding face of streptavidin. Mean field calculations have been used with considerable success to model electrostatic potential fields near protein surfaces, but these models and their inherent assumptions have not been tested directly at the molecular level. Using the force apparatus and immobilized, oriented monolayers of streptavidin, we measured a pI of 5-5.5 for the biotin-binding face of the protein. This differs from the pI of 6.3 for the soluble protein and confirms that we probed the local electrostatic features of the macromolecule. With finite difference solutions of the linearized Poisson-Boltzmann equation, we then calculated the pH-dependent charge densities adjacent to the same face of the protein. These calculated values agreed quantitatively with those obtained by direct force measurements. Although our study focuses on the pH-dependence of surface electrostatics, this direct approach to probing the electrostatic features of proteins is applicable to investigations of any perturbations that alter the charge distribution of the surfaces of immobilized molecules.

Binding Sites↗
PubMed1999

Tanford-Kirkwood electrostatics for protein modeling.

Solvent plays a significant role in determining the electrostatic potential energy of proteins, most notably through its favorable interactions with charged residues and its screening of electrostatic interactions. These energetic contributions are frequently ignored in computational protein design and protein modeling methodologies because they are difficult to evaluate rapidly and accurately. To address this deficiency, we report a revised form of the original Tanford-Kirkwood continuum electrostatic model [Tanford, C. & Kirkwood, J. G. (1957) J. Am. Chem. Soc. 79, 5333-5339], which accounts for the effects of solvent polarization on charged atoms in proteins. The Tanford-Kirkwood model was modified to increase its speed and to improve its sensitivity to the details of protein structure. For the 37 electrostatic self-energies of the polar side-chains in bovine pancreatic trypsin inhibitor, and their 666 interaction energies, the modified Tanford-Kirkwood potential of mean force differs from a computationally intensive numerical potential (DelPhi) by root-mean-square errors of 0.6 kcal/mol and 0.08 kcal/mol, respectively. The Tanford-Kirkwood approach makes possible a realistic treatment of electrostatics in computationally demanding protein modeling calculations. For example, pH titration calculations for ovomucoid third domain that model polar side-chain relaxation (including >2 x 10(23) rotamer conformations of the protein) provide pKa values of unprecedented accuracy.

Models, Theoretical↗