Reconstruction of protein side-chain conformational free energy surfaces from NMR-derived methyl axis order parameters

Correlated Response of Protein Side-Chain Fluctuations and Conformational Entropy to Ligand Binding

The heterogeneous fast side-chain dynamics of proteins plays crucial roles in molecular recognition and binding. Site-specific NMR experiments quantify these motions by measuring the model-free order parameter (O_axis²) on a scale of 0 (most flexible) to 1 (least flexible) for each methyl-containing residue of proteins. Here, we have examined ligand-induced variations in the fast side-chain dynamics and conformational entropy of calmodulin (CaM) using five different CaM-peptide complexes. O_axis² of CaM in the ligand-free (O_axis,U²) and ligand-bound (O_axis,B²) states are calculated from molecular dynamics trajectories and conformational energy surfaces obtained using the adaptive biasing force (ABF) method. ΔO_axis² = O_axis,B² - O_axis,U² follows a Gaussian-like unimodal distribution whose second moment is a potential indicator of the binding affinity of these complexes. The probability for the binding-induced O_axis,U² → O_axis,B² transition decreases with increasing magnitude of ΔO_axis², indicating that large flexibility changes are improbable for side chains of CaM after ligand binding. A linear correlation established between ΔO_axis² and the conformational entropy change of the protein makes possible the determination of the conformational entropy of binding of protein-ligand complexes. The results not only underscore the functional importance of fast side-chain fluctuations but also highlight key motional and thermodynamic correlates of protein-ligand binding.

Validating the CHARMM36m protein force field with LJ-PME reveals altered hydrogen bonding dynamics under elevated pressures

The pressure-temperature phase diagram is important to our understanding of the physics of biomolecules. Compared to studies on temperature effects, studies of the pressure dependence of protein dynamic are rather limited. Molecular dynamics (MD) simulations with fine-tuned force fields (FFs) offer a powerful tool to explore the influence of thermodynamic conditions on proteins. Here we evaluate the transferability of the CHARMM36m (C36m) protein force field at varied pressures compared with NMR data using ubiquitin as a model protein. The pressure dependences of J couplings for hydrogen bonds and order parameters for internal motion are in good agreement with experiment. We demonstrate that the C36m FF combined with the Lennard-Jones particle-mesh Ewald (LJ-PME) method is suitable for simulations in a wide range of temperature and pressure. As the ubiquitin remains stable up to 2500 bar, we identify the mobility and stability of different hydrogen bonds in response to pressure. Based on those results, C36m is expected to be applied to more proteins in the future to further investigate protein dynamics under elevated pressures.

Measuring Entropy in Molecular Recognition by Proteins

Molecular recognition by proteins is fundamental to the molecular basis of biology. Dissection of the thermodynamic landscape governing protein-ligand interactions has proven difficult because determination of various entropic contributions is quite challenging. Nuclear magnetic resonance relaxation measurements, theory, and simulations suggest that conformational entropy can be accessed through a dynamical proxy. Here, we review the relationship between measures of fast side-chain motion and the underlying conformational entropy. The dynamical proxy reveals that the contribution of conformational entropy can range from highly favorable to highly unfavorable and demonstrates the potential of this key thermodynamic variable to modulate protein-ligand interactions. The dynamical so-called entropy meter also refines the role of solvent entropy and directly determines the loss in rotational-translational entropy that occurs upon formation of high-affinity complexes. The ability to quantify the roles of entropy through an entropy meter based on measurable dynamical properties promises to highlight its role in protein function.

Direct Determination of Site-Specific Noncovalent Interaction Strengths of Proteins from NMR-Derived Fast Side Chain Motional Parameters

A novel approach to accurately determine residue-specific noncovalent interaction strengths (ξ) of proteins from NMR-measured fast side chain motional parameters (O_axis²) is presented. By probing the environmental sensitivity of side chain conformational energy surfaces of individual residues of a diverse set of proteins, the microscopic connections between ξ, O_axis², conformational entropy (S_conf), conformational barriers, and rotamer stabilities established here are found to be universal among proteins. The results reveal that side chain flexibility and conformational entropy of each residue decrease with increasing ξ and that for each residue type there exists a critical range of ξ, determined primarily by the mean side chain conformational barriers, within which flexibility of any residue can be reversibly tuned from highly flexible (with O_axis² ∼ 0) to highly restricted (with O_axis² ∼ 1) by increasing ξ by ∼3 kcal/mol. Beyond this critical range of ξ, both side chain flexibility and conformational entropy are insensitive to ξ. The interrelationships between conformational dynamics, conformational entropy, and noncovalent interactions of protein side chains established here open up new avenues to probe perturbation-induced (for example, ligand-binding, temperature, pressure) changes in fast side chain dynamics and thermodynamics of proteins by comparing their conformational energy surfaces in the native and perturbed states.

On the ability of molecular dynamics force fields to recapitulate NMR derived protein side chain order parameters

Molecular dynamics (MD) simulations have become a central tool for investigating various biophysical questions with atomistic detail. While many different proxies are used to qualify MD force fields, most are based on largely structural parameters such as the root mean square deviation from experimental coordinates or nuclear magnetic resonance (NMR) chemical shifts and residual dipolar couplings. NMR derived Lipari-Szabo squared generalized order parameter (O(2) ) values of amide NH bond vectors of the polypeptide chain were also often employed for refinement and validation. However, with a few exceptions, side chain methyl symmetry axis order parameters have not been incorporated into experimental reference sets. Using a test set of five diverse proteins, the performance of several force fields implemented in the NAMDD simulation package was examined. It was found that simulations employing explicit water implemented using the TIP3 model generally performed significantly better than those using implicit water in reproducing experimental methyl symmetry axis O(2) values. Overall the CHARMM27 force field performs nominally better than two implementations of the Amber force field. It appeared that recent quantum mechanics modifications to side chain torsional angles of leucine and isoleucine in the Amber force field have significantly hindered proper motional modeling for these residues. There remained significant room for improvement as even the best correlations of experimental and simulated methyl group Lipari-Szabo generalized order parameters fall below an R(2) of 0.8.

The unusual internal motion of the villin headpiece subdomain

The thermostable 36-residue subdomain of the villin headpiece (HP36) is the smallest known cooperatively folding protein. Although the folding and internal dynamics of HP36 and close variants have been extensively studied, there has not been a comprehensive investigation of side-chain motion in this protein. Here, the fast motion of methyl-bearing amino acid side chains is explored over a range of temperatures using site-resolved solution nuclear magnetic resonance deuterium relaxation. The squared generalized order parameters of methyl groups extensively spatially segregate according to motional classes. This has not been observed before in any protein studied using this methodology. The class segregation is preserved from 275 to 305 K. Motions detected in Helix 3 suggest a fast timescale of conformational heterogeneity that has not been previously observed but is consistent with a range of folding and dynamics studies. Finally, a comparison between the order parameters in solution with previous results based on solid-state nuclear magnetic resonance deuterium line shape analysis of HP36 in partially hydrated powders shows a clear disagreement for half of the sites. This result has significant implications for the interpretation of data derived from a variety of approaches that rely on partially hydrated protein samples.

Conformational dynamics and distribution of nitroxide spin labels

Long-range distance measurements based on paramagnetic relaxation enhancement (PRE) in NMR, quantification of surface water dynamics near biomacromolecules by Overhauser dynamic nuclear polarization (DNP) and sensitivity enhancement by solid-state DNP all depend on introducing paramagnetic species into an otherwise diamagnetic NMR sample. The species can be introduced by site-directed spin labeling, which offers precise control for positioning the label in the sequence of a biopolymer. However, internal flexibility of the spin label gives rise to dynamic processes that potentially influence PRE and DNP behavior and leads to a spatial distribution of the electron spin even in solid samples. Internal dynamics of spin labels and their static conformational distributions have been studied mainly by electron paramagnetic resonance spectroscopy and molecular dynamics simulations, with a large body of results for the most widely applied methanethiosulfonate spin label MTSL. These results are critically discussed in a unifying picture based on rotameric states of the group that carries the spin label. Deficiencies in our current understanding of dynamics and conformations of spin labeled groups and of their influence on NMR observables are highlighted and directions for further research suggested.

Conformational contribution to thermodynamics of binding in protein-peptide complexes through microscopic simulation

We extract the thermodynamics of conformational changes in biomacromolecular complexes from the distributions of the dihedral angles of the macromolecules. These distributions are obtained from the equilibrium configurations generated via all-atom molecular dynamics simulations. The conformational thermodynamics data we obtained for calmodulin-peptide complexes using our methodology corroborate well with the experimentally observed conformational and binding entropies. The conformational free-energy changes and their contributions for different peptide-binding regions of calmodulin are evaluated microscopically.

Three entropic classes of side chain in a globular protein

The relationship between the NMR methyl group axial order parameter and the side chain conformational entropy is investigated in inhibitor-bound and apo human HIV protease using molecular dynamics simulation. Three distinct entropic classes of methyl-bearing side chains, determined by the topological distance of the methyl group from the protein backbone (i.e., the number of χ-bonds between the Cα and the carbon of the CH3 group), are revealed by atomistic trajectory analyses performed in the local frame of reference of individual methyl probes. The results demonstrate that topologically equivalent methyl groups experience similar nonbonded microenvironments regardless of the type of residues to which they are attached. Similarly, methyl groups that belong to the same side chain but that are not topologically equivalent exhibit different thermodynamic and dynamic properties. The two-parameter classification (based upon entropy and methyl axial order parameter) of side chains described here permits improved estimates of the conformational entropies of proteins from NMR motional parameters.