Charles L. Brooks

Large-scale conformational changes in proteins are often associated with the binding of a substrate. Because conformational changes may be related to the function of an enzyme, understanding the kinetics and energetics of these motions is very important. We have delineated the atomically detailed conformational transition pathway of the phosphotransferase enzyme adenylate kinase (AdK) in the absence and presence of an inhibitor. The computed free energy profiles associated with conformational transitions offer detailed mechanistic insights into, as well as kinetic information on, the ligand binding mechanism. Specifically, potential of mean force calculations reveal that in the ligand-free state, there is no significant barrier separating the open and closed conformations of AdK. The enzyme samples near closed conformations, even in the absence of its substrate. The ligand binding event occurs late, toward the closed state, and transforms the free energy landscape. In the ligand-bound state, the closed conformation is energetically most favored with a large barrier to opening. These results emphasize the underlying dynamic nature of the enzyme and indicate that the conformational transitions in AdK are more intricate than a mere two-state jump between the crystal-bound and -unbound states. Based on the existence of the multiple conformations of the enzyme in the open and closed states, a different viewpoint of ligand binding is presented. Our estimated activation energy barrier for the conformational transition is also in reasonable accord with the experimental findings.

Accurate description of the solvent environment is critical in computer simulations of protein structure and dynamics. An implicit treatment of solvent aims to capture the mean influence of water molecules on the solute via direct estimation of the solvation free energy. It has emerged as a powerful alternative to explicit solvent, and provides a favorable compromise between computational cost and level of detail. We review the current theory and techniques for implicit modeling of nonpolar solvation in the context of simulating protein folding and conformational transitions, and discuss the main directions for further development. It is demonstrated that the current surface area based nonpolar models have severe limitations, including insufficient description of the conformational dependence of solvation, over-estimation of the strength of pair-wise nonpolar interactions, and incorrect prediction of anti-cooperativity for three-body hydrophobic associations. We argue that, to improve beyond current level of accuracy of implicit solvent models, two important aspects of nonpolar solvation need to be incorporated, namely, the length-scale dependence of hydrophobic association and solvent screening of solute–solute dispersion interactions. We recognize that substantial challenges exist in constructing a sufficiently balanced, yet reasonably efficient, implicit solvent protein force field. Nonetheless, most of the fundamental problems are understood, and exciting progress has been made over the last few years. We believe that continual work along the frontiers outlined will greatly improve one’s ability to study protein folding and large conformational transitions at atomistic detail.

Growing evidence suggests that the β-amyloid (Aβ) peptides of Alzheimer's disease are generated in early endosomes and that small oligomers are the principal toxic species. We sought to understand whether and how the solution pH, which is more acidic in endosomes than the extracellular environment, affects the conformational processes of Aβ. Using constant pH molecular dynamics simulations of two model peptides, Aβ(1–28) and Aβ(10–42), we found that the folding landscape of Aβ is strongly modulated by pH and is most favorable for hydrophobically driven aggregation at pH 6. Thus, our theoretical findings substantiate the possibility that Aβ oligomers develop intracellularly before secretion into the extracellular milieu, where they may disrupt synaptic activity or act as seeds for plaque formation.

A three‐dimensional model of the human Calcium‐sensing receptor (CaSR) seven transmembrane domain was built via a novel sequence alignment method based on the conserved contacts in proteins using the crystal structure of bovine rhodopsin as the template. This model was tested by docking NPS 2143, the first identified allosteric antagonist of CaSR. In our model, Glu837 plays a critical role in anchoring the protonated nitrogen atom and hydroxy oxygen atom of NPS 2143. The phenyl moiety of the ligand contacts residues Phe668, Pro672, and Ile841. The naphthalene moiety is surrounded by several hydrophobic residues, including Phe684, Phe688, and Phe821. Our model appears to be consistent with all six residues that have been demonstrated to be critical for NPS 2143 binding, in contrast with existing homology models based on traditional sequence alignment of CaSR to rhodopsin. This provides validation of our sequence alignment method and the use of the rhodopsin backbone as the initial structure in homology modeling of other G protein‐coupled receptors that are not members of the rhodopsin family. Proteins 2008.

Carboxylic acid dimers are useful model systems for understanding the interplay of hydrogen bonding, hydrophobic effects, and entropy in self-association and assembly. Through extensive sampling with a classical force field and careful free energy analysis, it is demonstrated that both hydrogen bonding and hydrophobic interactions are indeed important for dimerization of carboxylic acids (except formic acid). The dimers are only weakly ordered, and the degree of ordering increases with stronger hydrophobic interactions between longer alkyl chains. Comparison of calculated and experimental dimerization constants reveals a systematic tendency for excessive self-aggregation in current classical force fields. Qualitative and quantitative information on the thermodynamics of hydrogen bonding and hydrophobic interactions derived from these simulations is in excellent agreement with existing results from experiment and theory. These results provide a verification from first principles of previous estimations based on two statistical mechanical hydrophobic theories. We also revisit and clarify the fundamental statistical thermodynamics formalism for calculating absolute binding constants, external entropy, and solvation entropy changes upon association from detailed free energy simulations. This analysis is believed to be useful for a wide range of applications including computational studies of protein−ligand and protein−protein binding.

We evaluate the pK_a of dihydrofolate (H₂F) at the N⁵ position in three ternary complexes with Escherichia coli dihydrofolate reductase (ecDHFR), namely ecDHFR(NADP⁺:H₂F) in the closed form (1), and the Michaelis complexes ecDHFR(NADPH:H₂F) in the closed (2) and occluded (3) forms, by performing free energy perturbation with molecular dynamics simulations (FEP/MD). Our simulations suggest that in the Michaelis complex the pK_a is modulated by the Met20 loop fluctuations, providing the largest pK_a shift in substates with a “tightly closed” loop conformation; in the “partially closed/open” substates, the pK_a is similar to that in the occluded complex. Conducive to the protonation, tightly closing the Met20 loop enhances the interactions of the cofactor and the substrate with the Met20 side chain and aligns the nicotinamide ring of the cofactor coplanar with the pterin ring of the substrate. Overall, the present study favors the hypothesis that N⁵ is protonated directly from solution and provides further insights into the mechanism of the substrate protonation.

The selectivity filter of K ⁺ channels provides specific coordinative interactions between dipolar carbonyl ligands, water, and the permeant cation, which allow for selective flow of K ⁺ over (most importantly) Na ⁺ across the cell membrane. Although a structural viewpoint attributes K ⁺ selectivity to coordination geometry provided by the filter, recent molecular dynamics simulation studies attribute it to dynamic and unique chemical/electrostatic properties of the filter's carbonyl ligands. Here we provide a simple theoretical analysis of K ⁺ and Na ⁺ complexation with water in the context of simplified binding site models and bulk solution. Our analysis reveals that water molecules and carbonyl groups can both provide K ⁺ selective environments if equivalent constraints are imposed on the coordination number of the complex. Absence of such constraints annihilates selectivity, demonstrating that whether a coordinating ligand is a water molecule or a carbonyl group, “external” or “topological” constraints/forces must be imposed on an ion-coordinated complex to elicit selective binding. These forces must inevitably originate from the channel protein, because in bulk water, which, by definition, presents a nonselective medium, the coordination number is allowed to relax to suit the ion. We show that the coordination geometry of K ⁺ channel binding sites is replicated by 8-fold complexation of K ⁺ in both water and simplified binding site models due to dominance of local interactions within a complex and is thus a requirement for topologically constraining the coordination number to a specific value.

The immune system responds to the introduction of foreign antigens by rapidly evolving antibodies with increasing affinity for the antigen (i.e., maturation). To investigate the factors that control this process at the molecular level, we have assessed the changes in flexibility that accompany ligand binding at four stages of maturation in the 4-4-20 antibody. Our studies, based on molecular dynamics, indicate that increased affinity for the target ligand is associated with a decreased entropic cost to binding. The entropy of binding is unfavorable, opposing favorable enthalpic contributions that arise during complex formation. Computed binding free energies for the various antibody–ligand complexes qualitatively reproduce the trends observed in the experimentally derived values, although the absolute magnitude of free-energy differences is overestimated. Our results support the existence of a correlation between high-affinity interactions and decreased protein flexibility in this series of antibody molecules. This observation is likely to be a general feature of molecular association processes and key to the molecular evolution of antibody responses.