Rigorous treatment of pairwise and many-body electrostatic interactions among dielectric spheres at the Debye-Hückel level.

Electrostatic interactions among colloidal particles are often described using the venerable (two-particle) Derjaguin-Landau-Verwey-Overbeek (DLVO) approximation and its various modifications. However, until the recent development of a many-body theory exact at the Debye-Hückel level (Yu in Phys Rev E 102:052404, 2020), it was difficult to assess the errors of such approximations and impossible to assess the role of many-body effects. By applying the exact Debye-Hückel level theory, we quantify the errors inherent to DLVO and the additional errors associated with replacing many-particle interactions by the sum of pairwise interactions (even when the latter are calculated exactly). In particular, we show that: (1) the DLVO approximation does not provide sufficient accuracy at shorter distances, especially when there is an asymmetry in charges and/or sizes of interacting dielectric spheres; (2) the pairwise approximation leads to significant errors at shorter distances and at large and moderate Debye lengths and also gets worse with increasing asymmetry in the size of the spheres or magnitude or placement of the charges. We also demonstrate that asymmetric dielectric screening, i.e., the enhanced repulsion between charged dielectric bodies immersed in media with high dielectric constant, is preserved in the presence of free ions in the medium.

Extending electrostatics of dielectric spheres to arbitrary charge distributions with applications to biosystems.

A previously developed classical model of electrostatic interactions, based on a formalism of dielectric spheres, which has been found to have surprising accuracy for S state atoms, is extended by allowing higher-order moments of the intrinsic charge distribution. Two methods to introduce the charge distribution (point moments at the center vs surface charge) are shown to be equivalent and are compared with another common model for polarizable atoms that utilizes polarizable point dipoles. Unlike the polarizable point dipole model, the polarizable spheres models do not suffer from a divergence at small separation of atoms and are easily generalized to higher multipoles.

Can dielectric spheres accurately model atomic-scale interactions?

We calculate the polarization portion of electrostatic interactions at the atomic scale using quantum mechanical methods such as density functional theories (DFT) and the coupled cluster approach, and using classical methods such as a surface charge method and a polarizable force field. The agreement among various methods is investigated. Using the coupled clusters method CCSD(T) with large basis sets as the reference, we find that for systems comprising two to six atoms and ions in S-states the classical surface charge method performs much better than commonly used DFT methods with moderate basis sets such as B3LYP/6-31G(d,p). The remarkable performance of the classical approach comes as a surprise. The present results indicate that the use of a rigorous formalism of classical electrostatics can be better justified for determining molecular interactions at intermediate distances than some of the widely used methods of quantum chemistry. PACS numbers: 41.20.Cv,32.10.Dk, 87.10.Tf.

Using dissociation energies to predict observability of b- and y-peaks in mass spectra of short peptides. II. Results for hexapeptides with non-polar side chains.

RATIONALE: The hypothesis that dissociation energies can serve as a predictor of observability of b- and y-peaks is tested for seven hexapeptides. If the hypothesis holds true for large classes of peptides, one would be able to improve the scoring accuracy of peptide identification tools by excluding theoretical peaks that cannot be observed in practical product ion spectra due to various physical, chemical or thermodynamic considerations. METHODS: Product ion m/z spectra of hexapeptides AAAAAA, AAAFAA, AAAVAA, AAFAAA, AAVAAA, AAFFAA and AAVVAA have been acquired on a Finnigan LTQ XL mass spectrometer in the collision-induced dissociation (CID) activation mode on a grid of activation times 0.05 to 100 ms and normalized collision energy 10 to 35%. Dissociation energies were calculated for all fragmentation channels leading to b- and y-fragments at the TPSS/6-31G(d,p) level of the density functional theory. RESULTS: It was demonstrated that the m/z peaks observed in the product ion spectra correspond to the fragmentation channels with dissociation energies below a certain threshold value. However, there is no direct correlation between the most intense m/z peaks and the lowest dissociation energies. Using the dissociation energies, it was predicted that out of 63 theoretically possible peaks in the b- and y-series of the seven hexapeptides, 19 should not be observable in practical spectra. In the experiments, 24 peaks were not observed, including all 19 predicted. CONCLUSIONS: Dissociation energies alone are not sufficient for predicting ion intensity relationships in product ion m/z spectra. Nevertheless, the present data suggest that dissociation energies appear to be good predictors of observability of b- and y-peaks and potentially very useful for filtering theoretical peaks of each candidate peptide in peptide identification tools. Published 2012. This article is a US Government work and is in the public domain in the USA.

Using dissociation energies to predict observability of b- and y-peaks in mass spectra of short peptides.

RATIONALE: Peptide identification reliability can be improved by excluding from analysis those m/z peaks of candidate peptides which cannot be observed in practice due to various physical, chemical or thermodynamic considerations. We propose using dissociation energies (as opposed to proton affinities) as a predictor of observability of different m/z peaks in spectra of short peptides. METHODS: Mass spectra of the tetrapeptides AAAA, AAFA, AAVA, AFAA, AVAA, AFFA, and AVVA were measured in the collision-induced dissociation (CID) activation mode on a grid of activation times 0.05 to 100 ms and normalized collision energy 10 to 35%. The lowest energy geometries and vibrational spectra were calculated for the precursor ions and their charged and neutral fragments using density functional theory (DFT) at the TPSS/6-31G(d,p) level. Dissociation energies were calculated for all fragmentation channels leading to b- or y-fragments. RESULTS: It is demonstrated that m/z peaks observed in the mass spectra correspond to the fragmentation channels with the lowest dissociation energies. Using 50 kcal/mol as the cut-off value of dissociation energy, it was predicted that 28 out of 42 possible peaks in the b- and y-series of the seven tetrapeptides can be observed in mass spectra. In the experiments, 26 b- or y-peaks were observed, all of which are among the 28 predicted ones. CONCLUSIONS: The use of dissociation energies generalizes the use of proton affinities for semi-quantitative predictions of relative intensities of different m/z peaks of short peptides. Further advances in this direction will pave the way for reliable quantitative predictions and, hence, for a significant improvement in robustness and accuracy of peptide and protein identification tools.

Rigorous treatment of electrostatics for spatially varying dielectrics based on energy minimization.

An energy minimization formulation of electrostatics that allows computation of the electrostatic energy and forces to any desired accuracy in a system with arbitrary dielectric properties is presented. An integral equation for the scalar charge density is derived from an energy functional of the polarization vector field. This energy functional represents the true energy of the system even in nonequilibrium states. Arbitrary accuracy is achieved by solving the integral equation for the charge density via a series expansion in terms of the equation's kernel, which depends only on the geometry of the dielectrics. The streamlined formalism operates with volume charge distributions only, not resorting to introducing surface charges by hand. Therefore, it can be applied to any spatial variation of the dielectric susceptibility, which is of particular importance in applications to biomolecular systems. The simplicity of application of the formalism to real problems is shown with analytical and numerical examples.

Theoretical framework for NMR residual dipolar couplings in unfolded proteins.

A theoretical framework for the prediction of nuclear magnetic resonance (NMR) residual dipolar couplings (RDCs) in unfolded proteins under weakly aligning conditions is presented. The unfolded polypeptide chain is modeled as a random flight chain while the alignment medium is represented by a set of regularly arranged obstacles. For the case of bicelles oriented perpendicular to the magnetic field, a closed-form analytical result is derived. With the obtained analytical expression the RDCs are readily accessible for any locus along the chain, for chains of differing length, and for varying bicelle concentrations. The two general features predicted by the model are (i) RDCs in the center segments of a polypeptide chain are larger than RDCs in the end segments, resulting in a bell-shaped sequential distribution of RDCs, and (ii) couplings are larger for shorter chains than for longer chains at a given bicelle concentration. Experimental data available from the literature confirm the first prediction of the model, providing a tool for recognizing fully unfolded polypeptide chains. With less certainty experimental data appear to support the second prediction as well. However, more systematic experimental studies are needed in order to validate or disprove the predictions of the model. The presented framework is an important step towards a solid theoretical foundation for the analysis of experimentally measured RDCs in unfolded proteins in the case of alignment media such as polyacrylamide gels and neutral bicelle systems which align biomacromolecules by a steric mechanism. Various improvements and generalizations are possible within the suggested approach.