Generalized born models of macromolecular solvation effects

Theoretical and computational advances in biomolecular NMR spectroscopy

Recent developments in experimental and computational aspects of NMR spectroscopy have had a significant impact on the accuracy and speed of macromolecular structure determination in solution, particularly with regard to systems of high complexity (such as protein complexes). These include experiments designed to provide long-range orientational and translational restraints, improvements in internal coordinate dynamics used for simulated annealing, and the development of database potentials of mean force to improve the description of the non-bonded contacts.

Theory and applications of the generalized Born solvation model in macromolecular simulations

Generalized Born (GB) models provide an attractive way to include some thermodynamic aspects of aqueous solvation into simulations that do not explicitly model the solvent molecules. Here we discuss our recent experience with this model, presenting in detail the way it is implemented and parallelized in the AMBER molecular modeling code. We compare results using the GB model (or GB plus a surface-area based "hydrophobic" term) to explicit solvent simulations for a 10 base-pair DNA oligomer, and for the 108-residue protein thioredoxin. A slight modification of our earlier suggested parameters makes the GB results more like those found in explicit solvent, primarily by slightly increasing the strength of NH [bond] O and NH [bond] N internal hydrogen bonds. Timing and energy stability results are reported, with an eye toward using these model for simulations of larger macromolecular systems and longer time scales.

Modified AutoDock for accurate docking of protein kinase inhibitors

Protein kinases are an important class of enzymes controlling virtually all cellular signaling pathways. Consequently, selective inhibitors of protein kinases have attracted significant interest as potential new drugs for many diseases. Computational methods, including molecular docking, have increasingly been used in the inhibitor design process [1]. We have considered several docking packages in order to strengthen our kinase inhibitor work with computational capabilities. In our experience, AutoDock offered a reasonable combination of accuracy and speed, as opposed to methods that specialize either in fast database searches or detailed and computationally intensive calculations. However, AutoDock did not perform well in cases where extensive hydrophobic contacts were involved, such as docking of SB203580 to its target protein kinase p38. Another shortcoming was a hydrogen bonding energy function, which underestimated the attraction component and, thus, did not allow for sufficiently accurate modeling of the key hydrogen bonds in the kinase-inhibitor complexes. We have modified the parameter set used to model hydrogen bonds, which increased the accuracy of AutoDock and appeared to be generally applicable to many kinase-inhibitor pairs without customization. Binding to largely hydrophobic sites, such as the active site of p38, was significantly improved by introducing a correction factor selectively affecting only carbon and hydrogen energy grids, thus, providing an effective, although approximate, treatment of solvation.

Free-energy component analysis of 40 protein-DNA complexes: a consensus view on the thermodynamics of binding at the molecular level

Noncovalent association of proteins to specific target sites on DNA--a process central to gene expression and regulation--has thus far proven to be idiosyncratic and elusive to generalizations on the nature of the driving forces. The spate of structural information on protein--DNA complexes sets the stage for theoretical investigations on the molecular thermodynamics of binding aimed at identifying forces responsible for specific macromolecular recognition. Computation of absolute binding free energies for systems of this complexity transiting from structural information is a stupendous task. Adopting some recent progresses in treating atomic level interactions in proteins and nucleic acids including solvent and salt effects, we have put together an energy component methodology cast in a phenomenological mode and amenable to systematic improvements and developed a computational first atlas of the free energy contributors to binding in approximately 40 protein-DNA complexes representing a variety of structural motifs and functions. Illustrating vividly the compensatory nature of the free energy components contributing to the energetics of recognition for attaining optimal binding, our results highlight unambiguously the roles played by packing, electrostatics including hydrogen bonds, ion and water release (cavitation) in protein-DNA binding. Cavitation and van der Waals contributions without exception favor complexation. The electrostatics is marginally unfavorable in a consensus view. Basic residues on the protein contribute favorably to binding despite the desolvation expense. The electrostatics arising from the acidic and neutral residues proves unfavorable to binding. An enveloping mode of binding to short stretches of DNA makes for a strong unfavorable net electrostatics but a highly favorable van der Waals and cavitation contribution. Thus, noncovalent protein-DNA association is a system-specific fine balancing act of these diverse competing forces. With the advances in computational methods as applied to macromolecular recognition, the challenge now seems to be to correlate the differential (initial vs. final) energetics to substituent effects in drug design and to move from affinity to specificity.

Protein molecular dynamics with the generalized Born/ACE solvent model

Implicit solvent models are increasingly important for the study of proteins in aqueous solution. Here, the generalized Born (GB) solvent polarization model as implemented in the analytical ACE potential [Schaefer and Karplus (1996) J Phys Chem 100:1578] is used to perform molecular dynamics simulations of two small, homologous proteins: the immunoglobulin-binding domain of streptococcal protein G and the Ras binding domain of Raf. Several model parameterizations are compared through more than 60 ns of simulation. Results are compared with two simpler solvent models-an accessible surface area model and a distant-dependent dielectric model, with finite-difference Poisson calculations, with existing explicit solvent simulations, and with experimental data. The simpler models yield stable but distorted structures. The best GB/ACE implementation uses a set of atomic Voronoi volumes reported recently, obtained by averaging over a large database of crystallographic protein structures. A 20% reduction is applied to the volumes, compensating in an average sense for an excessive de-screening of individual charges inherent in the ACE self-energy and for an undersolvation of dipolar groups inherent in the GB screening function. This GB/ACE parameterization yields stable trajectories on the 0.5-1-ns time scale that deviate moderately (approximately 1.5-2.5 A) from the X-ray structure, reproduce approximately the surface distribution of charged, polar, and hydrophobic groups, and reproduce accurately backbone flexibility as measured by amide NMR-order parameters. Over longer time scales (1.5-3 ns), some of the protein G runs escape from the native energy basin and deviate strongly (3 A) from the native structure. The conformations sampled during the transition out of the native energy basin are overstabilized by the GB/ACE solvation model, as compared with a numerical treatment of the full dielectric continuum model.

Rapid boundary element solvation electrostatics calculations in folding simulations: successful folding of a 23-residue peptide

Solvation effects play a profound role in the energetics of protein folding. While a continuum dielectric model of solvation may provide a sufficiently accurate estimate of the solvation effects, until now this model was too computationally expensive and unstable for folding simulations. Here we proposed a fast yet accurate and robust implementation of the boundary element solution of the Poisson equation, the REBEL algorithm. Using our earlier double-energy scheme, we included for the first time the mathematically rigorous continuous REBEL solvation term in our Biased Probability Monte Carlo (BPMC) simulations of the peptide folding. The free energy of a 23-residue beta beta alpha-peptide was then globally optimized with and without the solvation electrostatics contribution. An ensemble of beta beta alpha conformations was found at and near the global minimum of the energy function with the REBEL electrostatic solvation term. Much poorer correspondence to the native solution structure was found in the "control" simulations with a traditional method to account for solvation via a distance-dependent dielectric constant. Each simulation took less than 40 h (21 h without electrostatic solvation calculation) on a single Alpha 677 MHz CPU and involved more than 40,000 solvation energy evaluations. This work demonstrates for the first time that such a simulation can be performed in a realistic time frame. The proposed procedure may eliminate the energy evaluation accuracy bottleneck in folding simulations.

Molecular modeling of nucleic acid structure: electrostatics and solvation

This unit presents an overview of computer simulation techniques as applied to nucleic acid systems, ranging from simple in vacuo molecular modeling techniques to more complete all-atom molecular dynamics treatments that include an explicit representation of the environment. The third in a series of four units, this unit focuses on critical issues in solvation and the treatment of electrostatics.

From folding theories to folding proteins: a review and assessment of simulation studies of protein folding and unfolding

Beginning with simplified lattice and continuum "minimalist" models and progressing to detailed atomic models, simulation studies have augmented and directed development of the modern landscape perspective of protein folding. In this review we discuss aspects of detailed atomic simulation methods applied to studies of protein folding free energy surfaces, using biased-sampling free energy methods and temperature-induced protein unfolding. We review studies from each on systems of particular experimental interest and assess the strengths and weaknesses of each approach in the context of "exact" results for both free energies and kinetics of a minimalist model for a beta-barrel protein. We illustrate in detail how each approach is implemented and discuss analysis methods that have been developed as components of these studies. We describe key insights into the relationship between protein topology and the folding mechanism emerging from folding free energy surface calculations. We further describe the determination of detailed "pathways" and models of folding transition states that have resulted from unfolding studies. Our assessment of the two methods suggests that both can provide, often complementary, details of folding mechanism and thermodynamics, but this success relies on (a) adequate sampling of diverse conformational regions for the biased-sampling free energy approach and (b) many trajectories at multiple temperatures for unfolding studies. Furthermore, we find that temperature-induced unfolding provides representatives of folding trajectories only when the topology and sequence (energy) provide a relatively funneled landscape and "off-pathway" intermediates do not exist.

Review: protein design--where we were, where we are, where we're going

Protein design has become a powerful approach for understanding the relationship between amino acid sequence and 3-dimensional structure. In the past 5 years, there have been many breakthroughs in the development of computational methods that allow the selection of novel sequences given the structure of a protein backbone. Successful design of protein scaffolds has now paved the way for new endeavors to design function. The ability to design sequences compatible with a fold may also be useful in structural and functional genomics by expanding the range of proteins used for fold recognition and for the identification of functionally important domains from multiple sequence alignments.

Solvation energy density occlusion approximation for evaluation of desolvation penalties in biomolecular interactions

In calculations involving many displacements of an interacting pair of biomolecules, such as brownian dynamics, the docking of a substrate/ligand to an enzyme/receptor, or the screening of a large number of ligands as prospective inhibitors for a particular receptor site, there is a need for rapid evaluation of the desolvation penalties of the interacting pair. Although continuum electrostatic treatments with distinct dielectric constants for solute and solvent provide an account of the electrostatics of solvation and desolvation, it is necessary to re-solve the Poisson equation, at considerable computational cost, for each displacement of the interacting pair. We present a new method that uses a formulation of continuum electrostatic solvation in terms of the solvation energy density and approximates desolvation in terms of the occlusion of this density. We call it the SEDO approximation. It avoids the need to re-solve the Poisson equation, as desolvation is now estimated by an integral over the occluded volume. Test calculations are presented for some simple model systems and for some real systems that have previously been studied using the Poisson equation approach: MHC class I protein-peptide complexes and a congeneric series of human immunodeficiency virus type 1 (HIV-1) protease--ligand complexes. For most of the systems considered, the trends and magnitudes of the desolvation component of interaction energies obtained using the SEDO approximation are in reasonable correlation with those obtained by re-solving the Poisson equation. In most cases, the error introduced by the SEDO approximation is much less than that of the often-used test-charge approximation for the charge-charge components of intermolecular interactions. Proteins 2001;43:12-27.

Macromolecular electrostatics: continuum models and their growing pains

Theoretical understanding of macromolecular electrostatics has advanced substantially over the past year. Continuum models have given promising results for calculating protein-ligand binding free energy differences, as well as pK(a)s and redox properties, particularly with explicit treatment of multiple conformers. Generalized Born and other techniques have led to the first molecular dynamics simulations of proteins and RNA with continuum solvent. Continuum and microscopic descriptions of dielectric relaxation have been critically compared.

Molecular dynamics simulation of nucleic acids

We review molecular dynamics simulations of nucleic acids, including those completed from 1995 to 2000, with a focus on the applications and results rather than the methods. After the introduction, which discusses recent advances in the simulation of nucleic acids in solution, we describe force fields for nucleic acids and then provide a detailed summary of the published literature. We emphasize simulations of small nucleic acids ( approximately 6 to 24 mer) in explicit solvent with counterions, using reliable force fields and modern simulation protocols that properly represent the long-range electrostatic interactions. We also provide some limited discussion of simulation in the absence of explicit solvent. Absent from this discussion are results from simulations of protein-nucleic acid complexes and modified DNA analogs. Highlights from the molecular dynamics simulation are the spontaneous observation of A B transitions in duplex DNA in response to the environment, specific ion binding and hydration, and reliable representation of protein-nucleic acid interactions. We close by examining major issues and the future promise for these methods.

Modeling salt-mediated electrostatics of macromolecules: the discrete surface charge optimization algorithm and its application to the nucleosome

Much progress has been achieved on quantitative assessment of electrostatic interactions on the all-atom level by molecular mechanics and dynamics, as well as on the macroscopic level by models of continuum solvation. Bridging of the two representations-an area of active research-is necessary for studying integrated functions of large systems of biological importance. Following perspectives of both discrete (N-body) interaction and continuum solvation, we present a new algorithm, DiSCO (Discrete Surface Charge Optimization), for economically describing the electrostatic field predicted by Poisson-Boltzmann theory using a discrete set of Debye-Hückel charges distributed on a virtual surface enclosing the macromolecule. The procedure in DiSCO relies on the linear behavior of the Poisson-Boltzmann equation in the far zone; thus contributions from a number of molecules may be superimposed, and the electrostatic potential, or equivalently the electrostatic field, may be quickly and efficiently approximated by the summation of contributions from the set of charges. The desired accuracy of this approximation is achieved by minimizing the difference between the Poisson-Boltzmann electrostatic field and that produced by the linearized Debye-Hückel approximation using our truncated Newton optimization package. DiSCO is applied here to describe the salt-dependent electrostatic environment of the nucleosome core particle in terms of several hundred surface charges. This representation forms the basis for modeling-by dynamic simulations (or Monte Carlo)-the folding of chromatin. DiSCO can be applied more generally to many macromolecular systems whose size and complexity warrant a model resolution between the all-atom and macroscopic levels.