Effective approach for calculations of absolute stability of proteins using focused dielectric constants.
ABSTRACT: The ability to predict the absolute stability of proteins based on their corresponding sequence and structure is a problem of great fundamental and practical importance. In this work, we report an extensive, refinement and validation of our recent approach (Roca et al., FEBS Lett 2007;581:2065-2071) for predicting absolute values of protein stability DeltaG(fold). This approach employs the semimacroscopic protein dipole Langevin dipole method in its linear response approximation version (PDLD/S-LRA) while using the best fitted values of the dielectric constants epsilon'(p) and epsilon'(eff) for the self energy and charge-charge interactions, respectively. The method is validated on a diverse set of 45 proteins. It is found that the best fitted values of both dielectric constants are around 40. However, the self energy of internal residues and the charge-charge interactions of Lys have to be treated with care, using a somewhat lower values of epsilon'(p) and epsilon'(eff). The predictions of DeltaG(fold) reported here, have an average error of only 1.8 kcal/mole compared to the observed values, making our method very promising for estimating protein stability. It also provides valuable insight into the complex electrostatic phenomena taking place in folded proteins.
Project description:In the implicit solvent models of electrolytes (such as the primitive model (PM)), the ions are modeled as point charges in the centers of spheres (hard spheres in the case of the PM). The surfaces of the spheres are not polarizable which makes these models appropriate to use in computer simulations of electrolyte systems where these ions do not leave their host dielectrics. The same assumption makes them inappropriate in simulations where these ions cross dielectric boundaries because the interaction energy of the point charge with the polarization charge induced on the dielectric boundary diverges. In this paper, we propose a procedure to treat the passage of such ions through dielectric interfaces with an interpolation method. Inspired by the "bubble ion" model (in which the ion's surface is polarizable), we define a space-dependent effective dielectric coefficient, ε(eff)(r), for the ion that overlaps with the dielectric boundary. Then, we replace the "bubble ion" with a point charge that has an effective charge q/ε(eff)(r) and remove the portion of the dielectric boundary where the ion overlaps with it. We implement the interpolation procedure using the induced charge computation method [D. Boda, D. Gillespie, W. Nonner, D. Henderson, and B. Eisenberg, Phys. Rev. E 69, 046702 (2004)]. We analyze the various energy terms using a spherical ion passing through an infinite flat dielectric boundary as an example.
Project description:Understanding the connection between protein structure and function requires a quantitative understanding of electrostatic effects. Structure-based electrostatic calculations are essential for this purpose, but their use has been limited by a long-standing discussion on which value to use for the dielectric constants (?(eff) and ?(p)) required in Coulombic and Poisson-Boltzmann models. The currently used values for ?(eff) and ?(p) are essentially empirical parameters calibrated against thermodynamic properties that are indirect measurements of protein electric fields. We determine optimal values for ?(eff) and ?(p) by measuring protein electric fields in solution using direct detection of NMR chemical shift perturbations (CSPs). We measured CSPs in 14 proteins to get a broad and general characterization of electric fields. Coulomb's law reproduces the measured CSPs optimally with a protein dielectric constant (?(eff)) from 3 to 13, with an optimal value across all proteins of 6.5. However, when the water-protein interface is treated with finite difference Poisson-Boltzmann calculations, the optimal protein dielectric constant (?(p)) ranged from 2 to 5 with an optimum of 3. It is striking how similar this value is to the dielectric constant of 2-4 measured for protein powders and how different it is from the ?(p) of 6-20 used in models based on the Poisson-Boltzmann equation when calculating thermodynamic parameters. Because the value of ?(p) = 3 is obtained by analysis of NMR chemical shift perturbations instead of thermodynamic parameters such as pK(a) values, it is likely to describe only the electric field and thus represent a more general, intrinsic, and transferable ?(p) common to most folded proteins.
Project description:The contributions of electrostatic interactions to the binding stability of barnase and barstar were studied by the Poisson-Boltzmann model with three different protocols: a), the dielectric boundary specified as the van der Waals (vdW) surface of the protein along with a protein dielectric constant (epsilon (p)) of 4; b), the dielectric boundary specified as the molecular (i.e., solvent-exclusion (SE)) surface along with epsilon (p) = 4; and c), "SE + epsilon (p) = 20." The "vdW + epsilon (p) = 4" and "SE + epsilon (p) = 20" protocols predicted an overall electrostatic stabilization whereas the "SE + epsilon (p) = 4" protocol predicted an overall electrostatic destabilization. The "vdW + epsilon (p) = 4" protocol was most consistent with experiment. It quantitatively reproduced the observed effects of 17 mutations neutralizing charged residues lining the binding interface and the measured coupling energies of six charge pairs across the interface and reasonably rationalized the experimental ionic strength and pH dependences of the binding constant. In contrast, the "SE + epsilon (p) = 4" protocol predicted significantly larger coupling energies of charge pairs whereas the "SE + epsilon (p) = 20" protocol did not predict any pH dependence. This study calls for further scrutiny of the different Poisson-Boltzmann protocols and demonstrates potential danger in drawing conclusions on electrostatic contributions based on a particular calculation protocol.
Project description:The widely used Born model describes the electrostatic response of continuous media using static dielectric constants. However, when applied to a liquid environment, a comparison of Born model predictions with experimental values (e.g., transfer free energies and pK(a) shifts) found that agreement is only achieved by using physically unrealistic dielectric constants for proteins, lipids, etc., and/or equally unrealistic atomic radii. This leads to questions concerning the physical origins for this failure of the Born model. We partially resolve this question by applying the Langevin-Debye (LD) model of a continuous distribution of point, polarizable dipoles, a model that contains an added dependence of the electrostatic response on the solvent's optical dielectric constant and both gas- and liquid-phase dipole moments, features absent in the Born model to which the LD model reduces for weak fields. The LD model is applied to simple representations of three biologically relevant systems: (i) globular proteins, (ii) lipid bilayers, and (iii) membrane proteins. The linear Born treatment greatly overestimates both the self-energy and the transfer free energy from water to hydrophobic environments (e.g., a protein interior). By using the experimental dielectric constant, the energy cost of charge burial in either globular or membrane proteins of the Born model is reduced by almost 50% with the nonlinear theory as is the pK(a) shift, and the shifts agree well with experimental trends.
Project description:Experimental pK values of ionizable sidechains provide the most direct test for models representing dielectric shielding within the interior of a protein. However, only the strongly shifted pK values are particularly useful for discriminating among models. NMR titration studies have usually found only one or two such shifted pK values in each protein, so that the fitting of the experimental data to a uniform internal dielectric (epsilon(int)) model is not well constrained. The observed variation among proteins for such epsilon(int) estimates may reflect nonuniformity of dielectric shielding within each protein interior or qualitative differences between individual proteins. The differential amide kinetic acidities for a series of metal-substituted rubredoxins are shown to be consistent with Poisson-Boltzmann predictions of dielectric shielding that is relatively uniform for all of the amides that are sensitive to the metal charge, a region which corresponds to roughly 1/3 of the internal volume. The effective epsilon(int) values near 6 that are found in this study are significantly lower than many such estimates derived from sidechain pK measurements. The differing timeframes in which dielectric relaxation can respond to the highly transient peptide anion as compared to the longer lived states of the charged sidechains offers an explanation for the lower apparent dielectric constant deduced from these measurements.
Project description:The fusion domain of the influenza coat protein hemagglutinin HA2, bound to dodecyl phosphocholine micelles, was recently shown to adopt a structure consisting of two antiparallel ?-helices, packed in an exceptionally tight hairpin configuration. Four interhelical H(?) to C?O aliphatic H-bonds were identified as factors stabilizing this fold. Here, we report evidence for an additional stabilizing force: a strong charge-dipole interaction between the N-terminal Gly(1) amino group and the dipole moment of helix 2. pH titration of the amino-terminal (15)N resonance, using a methylene-TROSY-based 3D NMR experiment, and observation of Gly(1 13)C' show a strongly elevated pK = 8.8, considerably higher than expected for an N-terminal amino group in a lipophilic environment. Chemical shifts of three C-terminal carbonyl carbons of helix 2 titrate with the protonation state of Gly(1)-N, indicative of a close proximity between the N-terminal amino group and the axis of helix 2, providing an optimal charge-dipole stabilization of the antiparallel hairpin fold. pK values of the side-chain carboxylate groups of Glu(11) and Asp(19) are higher by about 1 and 0.5 unit, respectively, than commonly seen for solvent-exposed side chains in water-soluble proteins, indicative of dielectric constants of ? = ?30 (Glu(11)) and ?60 (Asp(19)), placing these groups in the headgroup region of the phospholipid micelle.
Project description:Using SEC HPLC and fluorescence anisotropy, absorption spectra were assigned to the specific oligomeric structures found with phycocyanin. The absorption spectra were used to quantify the population of each oligomeric form of the protein as a function of both urea concentration and temperature. Phycocyanin hexamers dissociate to trimers with equilibrium constants of 10(-6) to 10(-5). Phycocyanin trimers dissociate to monomers with equilibrium constants of 10(-15) to 10(-12). Both dissociation constants increase linearly with increasing urea concentration, and deltaG(o) values calculated from the equilibrium constants fit best with an exponential function. Our findings appear in contrast with the commonly used linear extrapolation model, deltaG(urea)(o) = deltaG(water)(o) + A[denaturant], in which a linear relationship exists between the free energy of protein unfolding or loss of quaternary structure and the denaturant concentration. Our data examines a smaller range of denaturant concentration than generally used, which might partially explain the inconsistency.
Project description:Molecular simulations often use explicit-solvent models. Sometimes explicit-solvent models can give inaccurate values for basic liquid properties, such as the density, heat capacity, and permittivity, as well as inaccurate values for molecular transfer free energies. Such errors have motivated the development of more complex solvents, such as polarizable models. We describe an alternative here. We give new fixed-charge models of solvents for molecular simulations--water, carbon tetrachloride, chloroform, and dichloromethane. Normally, such solvent models are parametrized to agree with experimental values of the neat liquid density and enthalpy of vaporization. Here, in addition to those properties, our parameters are chosen to give the correct dielectric constant. We find that these new parametrizations also happen to give better values for other properties, such as the self-diffusion coefficient. We believe that parametrizing fixed-charge solvent models to fit experimental dielectric constants may provide better and more efficient ways to treat solvents in computer simulations.
Project description:The influence of the cell shape on the dielectric and conductometric properties of biological cell suspensions has been investigated from a theoretical point of view presenting an analytical solution of the electrostatic problem in the case of prolate and oblate spheroidal geometries. The model, which extends to spheroidal geometries the approach developed by other researchers in the case of a spherical geometry, takes explicitly into account the charge distributions at the cell membrane interfaces. The presence of these charge distributions, which govern the trans-membrane potential DeltaV, produces composite dielectric spectra with two contiguous relaxation processes, known as the alpha-dispersion and the beta-dispersion. By using this approach, we present a series of dielectric spectra for different values of the different electrical parameters (the permittivity epsilon and the electrical conductivity sigma, together with the surface conductivity gamma due to the surface charge distribution) that define the whole behavior of the system. In particular, we analyze the interplay between the parameters governing the alpha-dispersion and those influencing the beta-dispersion. Even if these relaxation processes generally occur in well-separated frequency ranges, it is worth noting that, for certain values of the membrane conductivity, the high-frequency dispersion attributed to the Maxwell-Wagner effect is influenced not only by the bulk electrical parameters of the different adjacent media, but also by the surface conductivity at the two membrane interfaces.
Project description:The ability to deposit high-quality inorganic semiconductors and dielectrics from solution at low process temperatures (?200 °C) has become a very important research focus. During the course of our investigation, we identify the presence of an induced dipole present in solid state solution processed inorganic oxide insulator layers processed at reduced temperature (200-350 °C) from either molecular precursors, or well-dispersed metal oxide nanoparticles. Chemical composition analysis coupled with electrical measurements shows that the dielectric instability occurs due to proton migration via the Grotthuss mechanism inducing a long lived dipole disorder. Thus we established conditions for suppressing this effect to afford "ideal" high-k dielectric layer. Using this methodology, solution processed all inorganic thin film transistors (TFTs) with charge carrier mobilities exceeding 6 cm2 V-1 s-1 operating at low voltage (5 V) have been achieved. In addition, we show the broad utility of the perovskite high-k dielectric when processed with state of the art polymer and single crystal organic semiconductors yielding mobilities of approx. 7 cm2 V-1 s-1 at only 4 V. These transparent devices demonstrate excellent electrical device stability and a threshold voltage shift of only 0.41 V over 14 h, which is comparable, or better than sputtered oxide films.