Time Scales of Conformational Gating in a Lipid-Binding Protein

How proteins modify water dynamics

Much of biology happens at the protein-water interface, so all dynamical processes in this region are of fundamental importance. Local structural fluctuations in the hydration layer can be probed by ¹⁷O magnetic relaxation dispersion (MRD), which, at high frequencies, measures the integral of a biaxial rotational time correlation function (TCF)-the integral rotational correlation time. Numerous ¹⁷O MRD studies have demonstrated that this correlation time, when averaged over the first hydration shell, is longer than in bulk water by a factor 3-5. This rotational perturbation factor (RPF) has been corroborated by molecular dynamics simulations, which can also reveal the underlying molecular mechanisms. Here, we address several outstanding problems in this area by analyzing an extensive set of molecular dynamics data, including four globular proteins and three water models. The vexed issue of polarity versus topography as the primary determinant of hydration water dynamics is resolved by establishing a protein-invariant exponential dependence of the RPF on a simple confinement index. We conclude that the previously observed correlation of the RPF with surface polarity is a secondary effect of the correlation between polarity and confinement. Water rotation interpolates between a perturbed but bulk-like collective mechanism at low confinement and an exchange-mediated orientational randomization (EMOR) mechanism at high confinement. The EMOR process, which accounts for about half of the RPF, was not recognized in previous simulation studies, where only the early part of the TCF was examined. Based on the analysis of the experimentally relevant TCF over its full time course, we compare simulated and measured RPFs, finding a 30% discrepancy attributable to force field imperfections. We also compute the full ¹⁷O MRD profile, including the low-frequency dispersion produced by buried water molecules. Computing a local RPF for each hydration shell, we find that the perturbation decays exponentially with a decay "length" of 0.3 shells and that the second and higher shells account for a mere 3% of the total perturbation measured by ¹⁷O MRD. The only long-range effect is a weak water alignment in the electric field produced by an electroneutral protein (not screened by counterions), but this effect is negligibly small for ¹⁷O MRD. By contrast, we find that the ¹⁷O TCF is significantly more sensitive to the important short-range perturbations than the other two TCFs examined here.

The geometry of protein hydration

Based on molecular dynamics simulations of four globular proteins in dilute aqueous solution, with three different water models, we examine several, essentially geometrical, aspects of the protein-water interface that remain controversial or incompletely understood. First, we compare different hydration shell definitions, based on spatial or topological proximity criteria. We find that the best method for constructing monolayer shells with nearly complete coverage is to use a 5 Šwater-carbon cutoff and a 4 Šwater-water cutoff. Using this method, we determine a mean interfacial water area of 11.1 Ų which appears to be a universal property of the protein-water interface. We then analyze the local coordination and packing density of water molecules in the hydration shells and in subsets of the first shell. The mean polar water coordination number in the first shell remains within 1% of the bulk-water value, and it is 5% lower in the nonpolar part of the first shell. The local packing density is obtained from additively weighted Voronoi tessellation, arguably the most physically realistic method for allocating space between protein and water. We find that water in all parts of the first hydration shell, including the nonpolar part, is more densely packed than in the bulk, with a shell-averaged density excess of 6% for all four proteins. We suggest reasons why this value differs from previous experimental and computational results, emphasizing the importance of a realistic placement of the protein-water dividing surface and the distinction between spatial correlation and packing density. The protein-induced perturbation of water coordination and packing density is found to be short-ranged, with an exponential decay "length" of 0.6 shells. We also compute the protein partial volume, analyze its decomposition, and argue against the relevance of electrostriction.

Molecular dynamics simulations of apo and holo forms of fatty acid binding protein 5 and cellular retinoic acid binding protein II reveal highly mobile protein, retinoic acid ligand, and water molecules

Structural and dynamic properties from a series of 300 ns molecular dynamics, MD, simulations of two intracellular lipid binding proteins, iLBPs, (Fatty Acid Binding Protein 5, FABP5, and Cellular Retinoic Acid Binding Protein II, CRABP-II) in both the apo form and when bound with retinoic acid reveal a high degree of protein and ligand flexibility. The ratio of FABP5 to CRABP-II in a cell may determine whether it undergoes natural apoptosis or unrestricted cell growth in the presence of retinoic acid. As a result, FABP5 is a promising target for cancer therapy. The MD simulations presented here reveal distinct differences in the two proteins and provide insight into the binding mechanism. CRABP-II is a much larger, more flexible protein that closes upon ligand binding, where FABP5 transitions to an open state in the holo form. The traditional understanding obtained from crystal structures of the gap between two β-sheets of the β-barrel common to iLBPs and the α-helix cap that forms the portal to the binding pocket is insufficient for describing protein conformation (open vs. closed) or ligand entry and exit. When the high degree of mobility between multiple conformations of both the ligand and protein are examined via MD simulation, a new mode of ligand motion that improves understanding of binding dynamics is revealed.

Nuclear magnetic relaxation by the dipolar EMOR mechanism: General theory with applications to two-spin systems

In aqueous systems with immobilized macromolecules, including biological tissue, the longitudinal spin relaxation of water protons is primarily induced by exchange-mediated orientational randomization (EMOR) of intra- and intermolecular magnetic dipole-dipole couplings. We have embarked on a systematic program to develop, from the stochastic Liouville equation, a general and rigorous theory that can describe relaxation by the dipolar EMOR mechanism over the full range of exchange rates, dipole coupling strengths, and Larmor frequencies. Here, we present a general theoretical framework applicable to spin systems of arbitrary size with symmetric or asymmetric exchange. So far, the dipolar EMOR theory is only available for a two-spin system with symmetric exchange. Asymmetric exchange, when the spin system is fragmented by the exchange, introduces new and unexpected phenomena. Notably, the anisotropic dipole couplings of non-exchanging spins break the axial symmetry in spin Liouville space, thereby opening up new relaxation channels in the locally anisotropic sites, including longitudinal-transverse cross relaxation. Such cross-mode relaxation operates only at low fields; at higher fields it becomes nonsecular, leading to an unusual inverted relaxation dispersion that splits the extreme-narrowing regime into two sub-regimes. The general dipolar EMOR theory is illustrated here by a detailed analysis of the asymmetric two-spin case, for which we present relaxation dispersion profiles over a wide range of conditions as well as analytical results for integral relaxation rates and time-dependent spin modes in the zero-field and motional-narrowing regimes. The general theoretical framework presented here will enable a quantitative analysis of frequency-dependent water-proton longitudinal relaxation in model systems with immobilized macromolecules and, ultimately, will provide a rigorous link between relaxation-based magnetic resonance image contrast and molecular parameters.