Prediction of protein relative enthalpic stability from molecular dynamics simulations of the folded and unfolded states.

For proteins of known structure, the relative enthalpic stability with respect to wild-type, ΔΔH(U), can be estimated by direct computation of the folded and unfolded state energies. We propose a model by which the change in stability upon mutation can be predicted from all-atom molecular dynamics simulations for the folded state and a peptide-based model for the unfolded state. The unfolding enthalpies are expressed in terms of environmental and hydration-solvent reorganization contributions that readily allow a residue-specific analysis of ΔΔH(U). The method is applied to estimate the relative enthalpic stability of variants with buried charged groups in T4 lysozyme. The predicted relative stabilities are in good agreement with experimental data. Environmental factors are observed to contribute more than hydration to the overall ΔΔH(U). The residue-specific analysis finds that the effects of burying charge are both localized and long-range. The enthalpy for hydration-solvent reorganization varies considerably among different amino-acid types, but because the variant folded state structures are similar to those of the wild-type, the hydration-solvent reorganization contribution to ΔΔH(U) is localized at the mutation site, in contrast to environmental contributions. Overall, mutation of apolar and polar amino acids to charged amino acids are destabilizing, but the reasons are complex and differ from site to site.

Dual role of protein phosphorylation in DNA activator/coactivator binding.

Binding free energies are calculated for the phosphorylated and unphosphorylated complexes between the kinase inducible domain (KID) of the DNA transcriptional activator cAMP response element binding (CREB) protein and the KIX domain of its coactivator, CREB-binding protein (CBP). To our knowledge, this is the first application of a method based on a potential of mean force (PMF) with restraining potentials to compute the binding free energy of protein-protein complexes. The KID:KIX complexes are chosen here because of their biological relevance to the DNA transcription process and their relatively small size (81 residues for the KIX domain of CBP, and 28 residues for KID). The results for pKID:KIX and KID:KIX are -9.55 and -4.96 kcal/mol, respectively, in good agreement with experimental estimates (-8.8 and -5.8 kcal/mol, respectively). A comparison between specific contributions to protein-protein binding for the phosphorylated and unphosphorylated complexes reveals a dual role for the phosphorylation of KID at Ser-133 in effecting a more favorable free energy of the bound system: 1), stabilization of the unbound conformation of phosphorylated KID due to favorable intramolecular interactions of the phosphate group of Ser-133 with the charged groups of an arginine-rich region spanning both α-helices, which lowers the configurational entropy; and 2), more favorable intermolecular electrostatic interactions between pSer-133 and Arg-131 of KID, and Lys-662, Tyr-658, and Glu-666 of KIX. Charge reduction through ligand phosphorylation emerges as a possible mechanism for controlling the unbound state conformation of KID and, ultimately, gene expression. This work also demonstrates that the PMF-based method with restraining potentials provides an added benefit in that important elements of the binding pathway are evidenced. Furthermore, the practicality of the PMF-based method for larger systems is validated by agreement with experiment. In addition, we provide a somewhat differently structured exposition of the PMF-based method with restraining potentials and outline its generalization to systems in which both protein and ligand may adopt unbound conformations that are different from those of the bound state.

Contribution of charged groups to the enthalpic stabilization of the folded states of globular proteins.

In this paper we use the results from all-atom molecular dynamics (MD) simulations of proteins and peptides to assess the individual contribution of charged atomic groups to the enthalpic stability of the native state of globular proteins and investigate how the distribution of charged atomic groups in terms of solvent accessibility relates to protein enthalpic stability. The contributions of charged groups is calculated using a comparison of nonbonded interaction energy terms from equilibrium simulations of charged amino acid dipeptides in water (the "unfolded state") and charged amino acids in globular proteins (the "folded state"). Contrary to expectation, the analysis shows that many buried, charged atomic groups contribute favorably to protein enthalpic stability. The strongest enthalpic contributions favoring the folded state come from the carboxylate (COO(-)) groups of either Glu or Asp. The contributions from Arg guanidinium groups are generally somewhat stabilizing, while N(+)(3) groups from Lys contribute little toward stabilizing the folded state. The average enthalpic gain due to the transfer of a methyl group in an apolar amino acid from solution to the protein interior is described for comparison. Notably, charged groups that are less exposed to solvent contribute more favorably to protein native-state enthalpic stability than charged groups that are solvent exposed. While solvent reorganization/release has favorable contributions to folding for all charged atomic groups, the variation in folded state stability among proteins comes mainly from the change in the nonbonded interaction energy of charged groups between the unfolded and folded states. A key outcome is that the calculated enthalpic stabilization is found to be inversely proportional to the excess charge density on the surface, in support of an hypothesis proposed previously.

Modeling chemical bonding effects for protein electron crystallography: the transferable fragmental electrostatic potential (TFESP) method.

This paper addresses the problem of determining the electrostatic potential of large proteins by the superposition of potentials calculated for small fragments. The use of different atomic and molecular fragments is considered for reproducing the molecular electrostatic potential of different conformations of N-acetylalanine methylamide (NAAMA) with an acceptable degree of error as measured by conventional R factors used in crystallographic structure refinement. Three different divisions of NAAMA are tested, producing fragments that incorporate increasingly more complete descriptions of molecular bonding with diminishing accuracy in geometric fit to the parent molecule: single atoms in molecules, bonded atoms in molecules and selected functional groups, such as the backbone peptide moiety, or the alpha-carbon, beta-carbon and their associated H atoms. In the resolution range 2.5-25A, the fairly straightforward use of single atoms in molecules reduces the calculated R factors by 5-15% over a free-atom superposition. No significant further improvement was found at the lowest resolutions with a superposition of single bonds in molecules and R factors were found to degrade with larger fragments at higher resolutions because of poor geometry fits to the atoms of the parent molecule. Because the potential distribution even for single atoms depends on the environment, the best accuracy will be obtained by using a library of fragment potentials calculated for each type of atom as a function of important protein conformations.

Decomposition of protein experimental compressibility into intrinsic and hydration shell contributions.

The experimental determination of protein compressibility reflects both the protein intrinsic compressibility and the difference between the compressibility of water in the protein hydration shell and bulk water. We use molecular dynamics simulations to explore the dependence of the isothermal compressibility of the hydration shell surrounding globular proteins on differential contributions from charged, polar, and apolar protein-water interfaces. The compressibility of water in the protein hydration shell is accounted for by a linear combination of contributions from charged, polar, and apolar solvent-accessible surfaces. The results provide a formula for the deconvolution of experimental data into intrinsic and hydration contributions when a protein of known structure is investigated. The physical basis for the model is the variation in water density shown by the surface-specific radial distribution functions of water molecules around globular proteins. The compressibility of water hydrating charged atoms is lower than bulk water compressibility, the compressibility of water hydrating apolar atoms is somewhat larger than bulk water compressibility, and the compressibility of water around polar atoms is about the same as the compressibility of bulk water. We also assess whether hydration water compressibility determined from small compound data can be used to estimate the compressibility of hydration water surrounding proteins. The results, based on an analysis from four dipeptide solutions, indicate that small compound data cannot be used directly to estimate the compressibility of hydration water surrounding proteins.

Potentials of mean force for the interaction of blocked alanine dipeptide molecules in water and gas phase from MD simulations.

We calculate potentials of mean force (PMFs) for the intermolecular interaction of two blocked alanine dipeptide (AcAlaNHMe) molecules in water and gas phase at two temperatures, 278 and 300 K, from all-atom molecular dynamics simulations. Simple models based on buried solvent accessible surface and one-dimensional potentials derived from distance-based radial distribution functions are not capable of expressing the short- and long-range complexity of the solute-solute interactions in water. Instead, radial and angular variations in the PMFs are observed with the two-dimensional potentials. The strength of the interactions for specific relative orientations of the molecules in the two-dimensional PMFs is more than double that observed in the one-dimensional PMFs. The populations of specific blocked alanine dipeptide conformations in water, such as alpha(R) and PPII, vary with temperature, and most significantly, with the distance between the centers of mass. A preference for helical conformations is observed at close encounter between molecules.

Adhesive-cohesive model for protein compressibility: an alternative perspective on stability.

As a dynamic property of folded proteins, protein compressibility provides important information about the forces that govern structural stability. We relate intrinsic compressibility to stability by using molecular dynamics to identify a molecular basis for the variation in compressibility among globular proteins. We find that excess surface charge accounts for this variation not only for the proteins simulated by molecular dynamics but also for a larger set of globular proteins. This dependence on charge distribution forms the basis for an adhesive-cohesive model of protein compressibility in which attractive forces from solvent compete with tertiary interactions that favor folding. Further, a newly recognized correlation between compressibility and the heat capacity of unfolding infers a link between compressibility and the enthalpy of unfolding. This linkage, together with the adhesive-cohesive model for compressibility, leads to the conclusion that folded proteins can gain enthalpic stability from a uniform distribution of charged atoms, as opposed to partitioning charge to the protein surface. Whether buried charged groups can be energetically stabilizing is a fundamental, yet controversial, question regarding protein structure. The analysis reported here implies that one mechanism to gain enthalpic stability involves positioning charge inside the protein in an optimal structural arrangement.