Three entropic classes of side chain in a globular protein

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.

Companion Simulations and Modeling to NMR-Based Dynamical Studies of Proteins

NMR-based studies of protein dynamics and molecular simulations have a synergistic relationship. Molecular simulations, in combination with interpretative theoretical models, leverage the dynamical information obtained from NMR. They provide the concrete physical schema underlying the quantities measured by NMR, and help extend the range of applications beyond the strictly dynamic properties. NMR data in turn provide concrete data to test and improve the potential functions used for simulation of dynamics of proteins. The concept of time correlation functions is central to the understanding of many dynamical processes. Their evaluation through atomistic simulations is discussed, with application to different dynamical quantities measured by NMR. While advances in computers have made such atomistic simulations almost routine, the companion use of simple interpretive models is stressed, to provide not just numbers but physical insight.

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.

Dynamical Transition of Collective Motions in Dry Proteins

Water is widely assumed to be essential for protein dynamics and function. In particular, the well-documented "dynamical" transition at ∼200  K, at which the protein changes from a rigid, nonfunctional form to a flexible, functional state, as detected in hydrogenated protein by incoherent neutron scattering, requires hydration. Here, we report on coherent neutron scattering experiments on perdeuterated proteins and reveal that a transition occurs in dry proteins at the same temperature resulting primarily from the collective heavy-atom motions. The dynamical transition discovered is intrinsic to the energy landscape of dry proteins.

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.

Banding of NMR-derived methyl order parameters: implications for protein dynamics

Our understanding of protein folding, stability, and function has begun to more explicitly incorporate dynamical aspects. Nuclear magnetic resonance has emerged as a powerful experimental method for obtaining comprehensive site-resolved insight into protein motion. It has been observed that methyl-group motion tends to cluster into three "classes" when expressed in terms of the popular Lipari-Szabo model-free squared generalized order parameter. Here the origins of the three classes or bands in the distribution of order parameters are examined. As a first step, a Bayesian based approach, which makes no a priori assumption about the existence or number of bands, is developed to detect the banding of Oaxis2 values derived either from NMR experiments or molecular dynamics simulations. The analysis is applied to seven proteins with extensive molecular dynamics simulations of these proteins in explicit water to examine the relationship between O2 and fine details of the motion of methyl bearing side chains. All of the proteins studied display banding, with some subtle differences. We propose a very simple yet plausible physical mechanism for banding. Finally, our Bayesian method is used to analyze the measured distributions of methyl group motions in the catabolite activating protein and several of its mutants in various liganded states and discuss the functional implications of the observed banding to protein dynamics and function.

Microscopic insights into the NMR relaxation-based protein conformational entropy meter

Conformational entropy is a potentially important thermodynamic parameter contributing to protein function. Quantitative measures of conformational entropy are necessary for an understanding of its role but have been difficult to obtain. An empirical method that utilizes changes in conformational dynamics as a proxy for changes in conformational entropy has recently been introduced. Here we probe the microscopic origins of the link between conformational dynamics and conformational entropy using molecular dynamics simulations. Simulation of seven proteins gave an excellent correlation with measures of side-chain motion derived from NMR relaxation. The simulations show that the motion of methyl-bearing side chains are sufficiently coupled to that of other side chains to serve as excellent reporters of the overall side-chain conformational entropy. These results tend to validate the use of experimentally accessible measures of methyl motion--the NMR-derived generalized order parameters--as a proxy from which to derive changes in protein conformational entropy.