Hidden Regularity and Universal Classification of Fast Side Chain Motions in Proteins

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.

Molecular Insights into Dipole Relaxation Processes in Water-Lysine Mixtures

Dielectric spectroscopy is a robust method to investigate relaxations of molecular dipoles. It is particularly useful for studies of biological solutions because of the potential of this method to cover a broad range of dynamical time scales typical for such systems. However, this technique does not provide any information about the nature of the molecular motions, which leads to a certain underemployment of dielectric spectroscopy for gaining microscopic understanding of material properties. For such detailed understanding, computer simulations are valuable tools because they can provide information about the nature of molecular motions observed by, for example, dielectric spectroscopy and to further complement them with structural information. In this work, we acquire information about the nature of dipole relaxation, in n-lysine solutions by means of molecular dynamics simulations. Our results indicate that the experimentally observed main relaxation process of n-lysine has different origins for the single monomer and the polypeptide chains. The relaxation of 1-lysine is due to the motions of whole molecules, whereas the experimentally observed relaxation of 3-lysine and 4-lysine is due to the motions of the residues, which, in turn, are promoted by water relaxation. Furthermore, we propose a new structural model of the lysine amino acids, which can quantitatively account for the experimental dielectric relaxation data. Hydrogen bonding and the structure of water are also discussed in terms of their influence on relaxation processes.

Molecular Mechanism, Dynamics, and Energetics of Protein-Mediated Dinucleotide Flipping in a Mismatched DNA: A Computational Study of the RAD4-DNA Complex

DNA damage alters genetic information and adversely affects gene expression pathways leading to various complex genetic disorders and cancers. DNA repair proteins recognize and rectify DNA damage and mismatches with high fidelity. A critical molecular event that occurs during most protein-mediated DNA repair processes is the extrusion of orphaned bases at the damaged site facilitated by specific repairing enzymes. The molecular-level understanding of the mechanism, dynamics, and energetics of base extrusion is necessary to elucidate the molecular basis of protein-mediated DNA damage repair. The present article investigates the molecular mechanism of dinucleotide extrusion in a mismatched DNA (containing a stretch of three contiguous thymidine-thymidine base pairs) facilitated by Radiation sensitive 4 (RAD4), a key DNA repair protein, on an atom-by-atom basis using molecular dynamics (MD) and umbrella-sampling (US) simulations. Using atomistic models of RAD4-free and RAD4-bound mismatched DNA, the free energy profiles associated with extrusion of mismatched partner bases are determined for both systems. The mismatched bases adopted the most stable intrahelical conformation, and their extrusion was unfavorable in RAD4-free mismatched DNA due to the presence of prohibitively high barriers (>12.0 kcal/mol) along the extrusion pathways. Upon binding of RAD4 to the DNA, the global free energy minimum is shifted to the extrahelical state indicating the key role of RAD4-DNA interactions in catalyzing the dinucleotide base extrusion in the DNA-RAD4 complex. The critical residues of RAD4 contributing to the conformational stability of the mismatched bases are identified, and the energetics of insertion of a β-hairpin of RAD4 into the DNA duplex is examined. The conformational energy landscape-based mechanistic insight into RAD4-mediated base extrusion provided here may serve as a useful baseline to understand the molecular basis of xeroderma pigmentosum C (XPC)-mediated DNA damage repair in humans.

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.

Narrowing the gap between experimental and computational determination of methyl group dynamics in proteins

A synergistic analysis of methyl NMR relaxation data and MD simulations identifies ways to improve studies of protein dynamics.

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.

LK peptide side chain dynamics at interfaces are independent of secondary structure

Real-time observation of the ultrafast motions of leucine side chains within model peptides at the water–air interface with representative folds – α-helix, 3₁₀-helix, β-strand – show that interfacial dynamics are mostly determined by surface interactions.

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.

General trends of dihedral conformational transitions in a globular protein

Dihedral conformational transitions are analyzed systematically in a model globular protein, cytochrome P450cam, to examine their structural and chemical dependences through combined conventional molecular dynamics (cMD), accelerated molecular dynamics (aMD) and adaptive biasing force (ABF) simulations. The aMD simulations are performed at two acceleration levels, using dihedral and dual boost, respectively. In comparison with cMD, aMD samples protein dihedral transitions approximately two times faster on average using dihedral boost, and ∼ 3.5 times faster using dual boost. In the protein backbone, significantly higher dihedral transition rates are observed in the bend, coil, and turn flexible regions, followed by the β bridge and β sheet, and then the helices. Moreover, protein side chains of greater length exhibit higher transition rates on average in the aMD-enhanced sampling. Side chains of the same length (particularly Nχ = 2) exhibit decreasing transition rates with residues when going from hydrophobic to polar, then charged and aromatic chemical types. The reduction of dihedral transition rates is found to be correlated with increasing energy barriers as identified through ABF free energy calculations. These general trends of dihedral conformational transitions provide important insights into the hierarchical dynamics and complex free energy landscapes of functional proteins.

Protein dynamics: from rattling in a cage to structural relaxation

We present an overview of protein dynamics based mostly on results of neutron scattering, dielectric relaxation spectroscopy and molecular dynamics simulations. We identify several major classes of protein motions on the time scale from faster than picoseconds to several microseconds, and discuss the coupling of these processes to solvent dynamics. Our analysis suggests that the microsecond backbone relaxation process might be the main structural relaxation of the protein that defines its glass transition temperature, while faster processes present some localized secondary relaxations. Based on the overview, we formulate a general picture of protein dynamics and discuss the challenges in this field.