Comparison of different schemes to treat long-range electrostatic interactions in molecular dynamics simulations of a protein crystal.

Eight molecular dynamics simulations of a ubiquitin crystal unit cell were performed to investigate the effect of different schemes to treat the long-range electrostatic interactions as well as the need to include counter ions. A crystal system was chosen as the test system, because the higher charge density compared with a protein in solution makes it more sensitive to the way of treating the electrostatic interactions. Three different schemes of treating the long-range interactions were compared: straight cutoff, reaction-field approximation, and a lattice-sum method (P3M). For each of these schemes, two simulations were performed, one with and one without the counter ions. Two additional simulations with a reaction-field force and different initial placements of the counter ions were performed to examine the effect of the initial positions of the ions. The inclusion of long-range electrostatic interactions using either a reaction-field or a lattice-sum method proved to be necessary for the simulation of crystals. These two schemes did not differ much in their ability to reproduce the crystallographic structure. The inclusion of counter ions, on the other hand, seems not necessary for obtaining a stable simulation. The initial positions of the ions have a visible but small effect on the simulation.

Computational analysis of PKA-balanol interactions.

Protein kinases are important targets for designing therapeutic drugs. This paper illustrates a computational approach to extend the usefulness of a single protein-inhibitor structure in aiding the design of protein kinase inhibitors. Using the complex structure of the catalytic subunit of PKA (cPKA) and balanol as a guide, we have analyzed and compared the distribution of amino acid types near the protein-ligand interface for nearly 400 kinases. This analysis has identified a number of sites that are more variable in amino acid types among the kinases analyzed, and these are useful sites to consider in designing specific protein kinase inhibitors. On the other hand, we have found kinases whose protein-ligand interfaces are similar to that of the cPKA-balanol complex and balanol can be a useful lead compound for developing effective inhibitors for these kinases. Generally, this approach can help us discover new drug targets for an existing class of compounds that have already been well characterized pharmacologically. The relative significance of the charge/polarity of residues at the protein-ligand interface has been quantified by carrying out computational sensitivity analysis in which the charge/polarity of an atom or functional group was turned off/on, and the resulting effects on binding affinity have been examined. The binding affinity was estimated by using an implicit-solvent model in which the electrostatic contributions were obtained by solving the Poisson equation and the hydrophobic effects were accounted for by using surface-area dependent terms. The same sensitivity analysis approach was applied to the ligand balanol to develop a pharmacophoric model for searching new drug leads from small-molecule libraries. To help evaluate the binding affinity of designed inhibitors before they are made, we have developed a semiempirical approach to improve the predictive reliability of the implicit-solvent binding model.

Effect of artificial periodicity in simulations of biomolecules under Ewald boundary conditions: a continuum electrostatics study.

Ewald and related methods are nowadays routinely used in explicit-solvent simulations of biomolecules, although they impose an artificial periodicity in systems which are inherently non-periodic. The consequences of this approximation should be assessed, since they may crucially affect the reliability of computer simulations under Ewald boundary conditions. In the present study we use a method based on continuum electrostatics to investigate the nature and magnitude of possible periodicity-induced artifacts on the potentials of mean force for conformational equilibria in biomolecules. Three model systems and pathways are considered: polyalanine oligopeptides (unfolding), a DNA tetranucleotide (separation of the strands), and the protein Sac7d (conformations from a molecular dynamics simulation). Artificial periodicity may significantly affect these conformational equilibria, in each case stabilizing the most compact conformation of the biomolecule. Three factors enhance periodicity-induced artifacts: (i) a solvent of low dielectric permittivity; (ii) a solute size which is non-negligible compared to the size of the unit cell; and (iii) a non-neutral solute. Neither the neutrality of the solute nor the absence of charge pairs at distances exceeding half the edge of the unit cell do guarantee the absence of artifacts.

Determinants of ligand binding to cAMP-dependent protein kinase.

Protein kinases are essential for the regulation of cellular growth and metabolism. Since their dysfunction leads to debilitating diseases, they represent key targets for pharmaceutical research. The rational design of kinase inhibitors requires an understanding of the determinants of ligand binding to these proteins. In the present study, a theoretical model based on continuum electrostatics and a surface-area-dependent nonpolar term is used to calculate binding affinities of balanol derivatives, H-series inhibitors, and ATP analogues toward the catalytic subunit of cAMP-dependent protein kinase (cAPK or protein kinase A). The calculations reproduce most of the experimental trends and provide insight into the driving forces responsible for binding. Nonpolar interactions are found to govern protein-ligand affinity. Hydrogen bonds represent a negligible contribution, because hydrogen bond formation in the complex requires the desolvation of the interacting partners. However, the binding affinity is decreased if hydrogen-bonding groups of the ligand remain unsatisfied in the complex. The disposition of hydrogen-bonding groups in the ligand is therefore crucial for binding specificity. These observations should be valuable guides in the design of potent and specific kinase inhibitors.

Molecular dynamics simulations of the hyperthermophilic protein sac7d from Sulfolobus acidocaldarius: contribution of salt bridges to thermostability.

Hyperthermophilic proteins often possess an increased number of surface salt bridges compared with their mesophilic homologues. However, salt bridges are generally thought to be of minor importance in protein stability at room temperature. In an effort to understand why this may no longer be true at elevated temperatures, we performed molecular dynamics simulations of the hyperthermophilic protein Sac7d at 300 K, 360 K, and 550 K. The three trajectories are stable on the nanosecond timescale, as evidenced by the analysis of several time-resolved properties. The simulations at 300 K and (to a lesser extent) 360 K are also compatible with nuclear Overhauser effect-derived distances. Raising the temperature from 300 K to 360 K results in a less favourable protein-solvent interaction energy, and a more favourable intraprotein interaction energy. Both effects are almost exclusively electrostatic in nature and dominated by contributions due to charged side-chains. The reduced solvation is due to a loss of spatial and orientational structure of water around charged side-chains, which is a consequence of the increased thermal motion in the solvent. The favourable change in the intraprotein Coulombic interaction energy is essentially due to the tightening of salt bridges. Assuming that charged side-chains are on average more distant from one another in the unfolded state than in the folded state, it follows that salt bridges may contribute to protein stability at elevated temperatures because (i) the solvation free energy of charged side-chains is more adversely affected in the unfolded state than in the folded state by an increase in temperature, and (ii) due to the tightening of salt bridges, unfolding implies a larger unfavourable increase in the intraprotein Coulombic energy at higher temperature. Possible causes for the unexpected stability of the protein at 550 K are also discussed.

Fluctuation and cross-correlation analysis of protein motions observed in nanosecond molecular dynamics simulations.

Nanosecond molecular dynamics simulations of bovine pancreatic trypsin inhibitor and lysozyme in water are analyzed in terms of backbone atomic positional fluctuations and dynamical cross-correlations. It is found that although the molecular systems are stable, B-factors calculated over a time period as long as 500 ps are not representative for the motions within the proteins. This is especially true for the most mobile residues. On a nanosecond time-scale, the B-factors calculated from the simulations of the proteins in solution are considerably larger than those obtained by structure refinement of the proteins in crystals, based on X-ray data. The time evolution of the atomic fluctuations shows that for large portions of the proteins under study, atomic positional fluctuations are not yet converged after a nanosecond. Cross-correlations do not converge faster than the fluctuations themselves. Most display very erratic behavior if the sampling covers less than about 200 ps. It is also shown that inclusion of mobile atoms into the procedure used to remove rigid-body motion from the simulation can lead to spurious correlations between the motions of the atoms at the surface of the protein.

Investigation of protein unfolding and stability by computer simulation.

Structural, dynamic and energetic properties of proteins in solution can be studied in atomic detail by molecular dynamics computer simulation. Protein unfolding can be caused by a variety of driving forces induced in different ways: increased temperature or pressure, change of solvent composition, or protein amino acid mutation. The stability and unfolding of four different proteins (bovine pancreatic trypsin inhibitor, hen egg white lysozyme, the surfactant protein C and the DNA-binding domain of the 434 repressor) have been studied by applying the afore-mentioned driving forces and also to some artificial forces. The results give a picture of protein (in)stability and possible unfolding pathways, and are compared to experimental data where possible.

Computational approaches to study protein unfolding: hen egg white lysozyme as a case study.

Four methods are compared to drive the unfolding of a protein: (1) high temperature (T-run), (2) high pressure (P-run), (3) by imposing a gradual increase in the mean radius of the protein using a penalty function added to the physical interaction function (F-run, radial force driven unfolding), and (4) by weak coupling of the difference between the temperature of the radially outward moving atoms and the radially inward moving atoms to an external temperature bath (K-run, kinetic energy driven unfolding). The characteristic features of the four unfolding pathways are analyzed in order to detect distortions due to the size or the type of the applied perturbation, as well as the features that are common to all of them. Hen egg white lysozyme is used as a test system. The simulations are analyzed and compared to experimental data like 1H-NMR amide proton exchange-folding competition, heat capacity, and compressibility measurements.