Emil Alexov

Rapid grid‐based construction of the molecular surface and the use of induced surface charge to calculate reaction field energies: Applications to the molecular systems and geometric objects

This article describes a number of algorithms that are designed to improve both the efficiency and accuracy of finite difference solutions to the Poisson–Boltzmann equation (the FDPB method) and to extend its range of application. The algorithms are incorporated in the DelPhi program. The first algorithm involves an efficient and accurate semianalytical method to map the molecular surface of a molecule onto a three‐dimensional lattice. This method constitutes a significant improvement over existing methods in terms of its combination of speed and accuracy. The DelPhi program has also been expanded to allow the definition of geometrical objects such as spheres, cylinders, cones, and parallelepipeds, which can be used to describe a system that may also include a standard atomic level depiction of molecules. Each object can have a different dielectric constant and a different surface or volume charge distribution. The improved definition of the surface leads to increased precision in the numerical solutions of the PB equation that are obtained. A further improvement in the precision of solvation energy calculations is obtained from a procedure that calculates induced surface charges from the FDPB solutions and then uses these charges in the calculation of reaction field energies. The program allows for finite difference grids of large dimension; currently a maximum of 5713 can be used on molecules containing several thousand atoms and charges. As described elsewhere, DelPhi can also treat mixed salt systems containing mono‐ and divalent ions and provide electrostatic free energies as defined by the nonlinear PB equation.

Combining Conformational Flexibility and Continuum Electrostatics for Calculating pK a s in Proteins

Protein stability and function relies on residues being in their appropriate ionization states at physiological pH. In situ residue pK(a)s also provides a sensitive measure of the local protein environment. Multiconformation continuum electrostatics (MCCE) combines continuum electrostatics and molecular mechanics force fields in Monte Carlo sampling to simultaneously calculate side chain ionization and conformation. The response of protein to charges is incorporated both in the protein dielectric constant (epsilon(prot)) of four and by explicit conformational changes. The pK(a) of 166 residues in 12 proteins was determined. The root mean square error is 0.83 pH units, and >90% have errors of <1 pH units whereas only 3% have errors >2 pH units. Similar results are found with crystal and solution structures, showing that the methods explicit conformational sampling reduces sensitivity to the initial structure. The outcome also changes little with protein dielectric constant (epsilon(prot) 4-20). Multiconformation continuum electrostatics titrations show coupling of conformational flexibility and changes in ionization state. Examples are provided where ionizable side chain position (protein G), Asn orientation (lysozyme), His tautomer distribution (RNase A), and phosphate ion binding (RNase A and H) change with pH. Disallowing these motions changes the calculated pK(a).

Incorporating protein conformational flexibility into the calculation of pH-dependent protein properties

A method for combining calculations of residue pKas with changes in the position of polar hydrogens has been developed. The Boltzmann distributions of proton positions in hydroxyls and neutral titratable residues are found in the same Monte Carlo sampling procedure that determines the amino acid ionization states at each pH. Electrostatic, Lennard-Jones potentials, and torsion angle energies are considered at each proton position. Many acidic and basic residues are found to have significant electrostatic interactions with either a water- or hydroxyl-containing side chain. Protonation state changes are coupled to reorientation of the neighboring hydroxyl dipoles, resulting in smaller free energy differences between neutral and ionized residues than when the protein is held rigid. Multiconformation pH titration gives better agreement with the experimental pKas for triclinic hen egg lysozyme than conventional rigid protein calculations. The hydroxyl motion significantly increases the protein dielectric response, making it sensitive to the composition of the local protein structure. More than one conformer per residue is often found at a given pH, providing information about the distribution of low-energy lysozyme structures.

Using Multiple Structure Alignments, Fast Model Building, and Energetic Analysis in Fold Recognition and Homology Modeling

We participated in the fold recognition and homology sections of CASP5 using primarily in‐house software. The central feature of our structure prediction strategy involved the ability to generate good sequence‐to‐structure alignments and to quickly transform them into models that could be evaluated both with energy‐based methods and manually. The in‐house tools we used include: a) HMAP (Hybrid Multidimensional Alignment Profile)—a profile‐to‐profile alignment method that is derived from sequence‐enhanced multiple structure alignments in core regions, and sequence motifs in non‐structurally conserved regions. b) NEST–a fast model building program that applies an “artificial evolution” algorithm to construct a model from a given template and alignment. c) GRASP2–a new structure and alignment visualization program incorporating multiple structure superposition and domain database scanning modules. These methods were combined with model evaluation based on all atom and simplified physical‐chemical energy functions. All of these methods were under development during CASP5 and consequently a great deal of manual analysis was carried out at each stage of the prediction process. This interactive model building procedure has several advantages and suggests important ways in which our and other methods can be improved, examples of which are provided. Proteins 2003;53:430–435.

DelPhi: a comprehensive suite for DelPhi software and associated resources

BackgroundAccurate modeling of electrostatic potential and corresponding energies becomes increasingly important for understanding properties of biological macromolecules and their complexes. However, this is not an easy task due to the irregular shape of biological entities and the presence of water and mobile ions.ResultsHere we report a comprehensive suite for the well-known Poisson-Boltzmann solver, DelPhi, enriched with additional features to facilitate DelPhi usage. The suite allows for easy download of both DelPhi executable files and source code along with a makefile for local installations. The users can obtain the DelPhi manual and parameter files required for the corresponding investigation. Non-experienced researchers can download examples containing all necessary data to carry out DelPhi runs on a set of selected examples illustrating various DelPhi features and demonstrating DelPhi’s accuracy against analytical solutions.ConclusionsDelPhi suite offers not only the DelPhi executable and sources files, examples and parameter files, but also provides links to third party developed resources either utilizing DelPhi or providing plugins for DelPhi. In addition, the users and developers are offered a forum to share ideas, resolve issues, report bugs and seek help with respect to the DelPhi package. The resource is available free of charge for academic users from URL: http://compbio.clemson.edu/DelPhi.php

On the Dielectric “Constant” of Proteins: Smooth Dielectric Function for Macromolecular Modeling and Its Implementation in DelPhi

Implicit methods for modeling protein electrostatics require dielectric properties of the system to be known, in particular, the value of the dielectric constant of protein. While numerous values of the internal protein dielectric constant were reported in the literature, still there is no consensus of what the optimal value is. Perhaps this is due to the fact that the protein dielectric constant is not a “constant” but is a complex function reflecting the properties of the protein’s structure and sequence. Here, we report an implementation of a Gaussian-based approach to deliver the dielectric constant distribution throughout the protein and surrounding water phase by utilizing the 3D structure of the corresponding macromolecule. In contrast to previous reports, we construct a smooth dielectric function throughout the space of the system to be modeled rather than just constructing a “Gaussian surface” or smoothing molecule–water boundary. Analysis on a large set of proteins shows that (a) the average dielectric constant inside the protein is relatively low, about 6–7, and reaches a value of about 20–30 at the protein’s surface, and (b) high average local dielectric constant values are associated with charged residues while low dielectric constant values are automatically assigned to the regions occupied by hydrophobic residues. In terms of energetics, a benchmarking test was carried out against the experimental pKa’s of 89 residues in staphylococcal nuclease (SNase) and showed that it results in a much better RMSD (= 1.77 pK) than the corresponding calculations done with a homogeneous high dielectric constant with an optimal value of 10 (RMSD = 2.43 pK).

Progress in the prediction of pKa values in proteins

The pKa‐cooperative aims to provide a forum for experimental and theoretical researchers interested in protein pKa values and protein electrostatics in general. The first round of the pKa‐cooperative, which challenged computational labs to carry out blind predictions against pKas experimentally determined in the laboratory of Bertrand Garcia‐Moreno, was completed and results discussed at the Telluride meeting (July 6–10, 2009). This article serves as an introduction to the reports submitted by the blind prediction participants that will be published in a special issue of PROTEINS: Structure, Function and Bioinformatics. Here, we briefly outline existing approaches for pKa calculations, emphasizing methods that were used by the participants in calculating the blind pKa values in the first round of the cooperative. We then point out some of the difficulties encountered by the participating groups in making their blind predictions, and finally try to provide some insights for future developments aimed at improving the accuracy of pKa calculations. Proteins 2011;

Molecular mechanisms of disease-causing missense mutations.

Genetic variations resulting in a change of amino acid sequence can have a dramatic effect on stability, hydrogen bond network, conformational dynamics, activity and many other physiologically important properties of proteins. The substitutions of only one residue in a protein sequence, so-called missense mutations, can be related to many pathological conditions and may influence susceptibility to disease and drug treatment. The plausible effects of missense mutations range from affecting the macromolecular stability to perturbing macromolecular interactions and cellular localization. Here we review the individual cases and genome-wide studies that illustrate the association between missense mutations and diseases. In addition, we emphasize that the molecular mechanisms of effects of mutations should be revealed in order to understand the disease origin. Finally, we report the current state-of-the-art methodologies that predict the effects of mutations on protein stability, the hydrogen bond network, pH dependence, conformational dynamics and protein function.

A pragmatic approach to structure based calculation of coupled proton and electron transfer in proteins

The coupled motion of electrons and protons occurs in many proteins. Using appropriate tools for calculation, the three-dimensional protein structure can show how each protein modulates the observed electron and proton transfer reactions. Some of the assumptions and limitations involved in calculations that rely on continuum electrostatics to calculate the energy of charges in proteins are outlined. Approaches that mix molecular mechanics and continuum electrostatics are described. Three examples of the analysis of reactions in photosynthetic reaction centers are given: comparison of the electrochemistry of hemes in different sites; analysis of the role of the protein in stabilizing the early charge separated state in photosynthesis; and calculation of the proton uptake and protein motion coupled to the electron transfer from the primary (Q(A)) to secondary (Q(B)) quinone. Different mechanisms for stabilizing intra-protein charged cofactors are highlighted in each reaction.

On the pH-optimum of activity and stability of proteins

Biological macromolecules evolved to perform their function in specific cellular environment (subcellular compartments or tissues); therefore, they should be adapted to the biophysical characteristics of the corresponding environment, one of them being the characteristic pH. Many macromolecular properties are pH dependent, such as activity and stability. However, only activity is biologically important, while stability may not be crucial for the corresponding reaction. Here, we show that the pH‐optimum of activity (the pH of maximal activity) is correlated with the pH‐optimum of stability (the pH of maximal stability) on a set of 310 proteins with available experimental data. We speculate that such a correlation is needed to allow the corresponding macromolecules to tolerate small pH fluctuations that are inevitable with cellular function. Our findings rationalize the efforts of correlating the pH of maximal stability and the characteristic pH of subcellular compartments, as only pH of activity is subject of evolutionary pressure. In addition, our analysis confirmed the previous observation that pH‐optimum of activity and stability are not correlated with the isoelectric point, pI, or with the optimal temperature. Proteins 2010.