Vignesh Kasinath

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.

A 13C labeling strategy reveals a range of aromatic side chain motion in calmodulin.

NMR relaxation experiments often require site-specific isotopic enrichment schemes in order to allow for quantitative interpretation. Here we describe a new labeling scheme for site-specific (13)C-(1)H enrichment of a single ortho position of aromatic amino acid side chains in an otherwise perdeuterated background by employing a combination of [4-(13)C]erythrose and deuterated pyruvate during growth on deuterium oxide. This labeling scheme largely eliminates undesired contributions to (13)C relaxation and greatly simplifies the fitting of relaxation data using the Lipari-Szabo model-free formalism. This approach is illustrated with calcium-saturated vertebrate calmodulin and oxidized flavodoxin from Cyanobacterium anabaena . Analysis of (13)C relaxation in the aromatic groups of calcium-saturated calmodulin indicates a wide range of motion in the subnanosecond time regime.

On the relationship between NMR-derived amide order parameters and protein backbone entropy changes.

Molecular dynamics simulations are used to analyze the relationship between NMR‐derived squared generalized order parameters of amide NH groups and backbone entropy. Amide order parameters (O2NH) are largely determined by the secondary structure and average values appear unrelated to the overall flexibility of the protein. However, analysis of the more flexible subset (O2NH < 0.8) shows that these report both on the local flexibility of the protein and on a different component of the conformational entropy than that reported by the side chain methyl axis order parameters, O2axis. A calibration curve for backbone entropy vs. O2NH is developed, which accounts for both correlations between amide group motions of different residues, and correlations between backbone and side chain motions. This calibration curve can be used with experimental values of O2NH changes obtained by NMR relaxation measurements to extract backbone entropy changes, for example, upon ligand binding. In conjunction with our previous calibration for side chain entropy derived from measured O2axis values this provides a prescription for determination of the total protein conformational entropy changes from NMR relaxation measurements. Proteins 2015; 83:922–930.

Entropy in molecular recognition by proteins

Significance Molecular recognition by proteins is a key element of biology. Appreciation of the underlying thermodynamics has been incomplete because of uncertainty in several contributions to the entropy. Here, we demonstrate a way to measure changes in protein conformational entropy using a dynamical proxy provided by NMR relaxation methods. We find that conformational entropy can contribute significantly and variably to the thermodynamics of binding. In addition, we determine the contribution of rotational-translational entropy loss upon forming a high-affinity complex involving a protein. The contribution of solvent entropy is also recalibrated. Thus, a more complete view of entropy in binding has been established and shows that inclusion of conformational entropy is necessary to understanding the origins of high-affinity interactions involving proteins. Molecular recognition by proteins is fundamental to molecular biology. Dissection of the thermodynamic energy terms governing protein–ligand interactions has proven difficult, with determination of entropic contributions being particularly elusive. NMR relaxation measurements have suggested that changes in protein conformational entropy can be quantitatively obtained through a dynamical proxy, but the generality of this relationship has not been shown. Twenty-eight protein–ligand complexes are used to show a quantitative relationship between measures of fast side-chain motion and the underlying conformational entropy. We find that the contribution of conformational entropy can range from favorable to unfavorable, which demonstrates the potential of this thermodynamic variable to modulate protein–ligand interactions. For about one-quarter of these complexes, the absence of conformational entropy would render the resulting affinity biologically meaningless. The dynamical proxy for conformational entropy or “entropy meter” also allows for refinement of the contributions of solvent entropy and the loss in rotational-translational entropy accompanying formation of high-affinity complexes. Furthermore, structure-based application of the approach can also provide insight into long-lived specific water–protein interactions that escape the generic treatments of solvent entropy based simply on changes in accessible surface area. These results provide a comprehensive and unified view of the general role of entropy in high-affinity molecular recognition by proteins.

A Sharp Thermal Transition of Fast Aromatic‐Ring Dynamics in Ubiquitin

Aromatic amino acid side chains have a rich role within proteins and are often central to their structure and function. Suitable isotopic-labelling strategies enable studies of sub-nanosecond aromatic-ring dynamics using solution NMR relaxation methods. Surprisingly, it was found that the three aromatic side chains in human ubiquitin show a sharp thermal dynamical transition at approximately 312 K. Hydrostatic pressure has little effect on the low-temperature behavior, but somewhat decreases the amplitude of motion in the high-temperature regime. Therefore, below the transition temperature, ring motion is largely librational. Above this temperature, a complete ring-rotation process that is fully consistent with a continuous diffusion not requiring the transient creation of a large activated free volume occurs. Molecular dynamics simulations qualitatively corroborate this view and reinforce the notion that the dynamical character of the protein interior has much more liquid-alkane-like properties than previously appreciated.

Dynamic and Thermodynamic Response of the Ras Protein Cdc42Hs upon Association with the Effector Domain of PAK3

Human cell division cycle protein 42 (Cdc42Hs) is a small, Rho-type guanosine triphosphatase involved in multiple cellular processes through its interactions with downstream effectors. The binding domain of one such effector, the actin cytoskeleton-regulating p21-activated kinase 3, is known as PBD46. Nitrogen-15 backbone and carbon-13 methyl NMR relaxation was measured to investigate the dynamical changes in activated GMPPCP·Cdc42Hs upon PBD46 binding. Changes in internal motion of the Cdc42Hs, as revealed by methyl axis order parameters, were observed not only near the Cdc42Hs-PBD46 interface but also in remote sites on the Cdc42Hs molecule. The binding-induced changes in side-chain dynamics propagate along the long axis of Cdc42Hs away from the site of PBD46 binding with sharp distance dependence. Overall, the binding of the PBD46 effector domain on the dynamics of methyl-bearing side chains of Cdc42Hs results in a modest rigidification, which is estimated to correspond to an unfavorable change in conformational entropy of approximately -10kcalmol(-1) at 298K. A cluster of methyl probes closest to the nucleotide-binding pocket of Cdc42Hs becomes more rigid upon binding of PBD46 and is proposed to slow the catalytic hydrolysis of the γ phosphate moiety. An additional cluster of methyl probes surrounding the guanine ring becomes more flexible on binding of PBD46, presumably facilitating nucleotide exchange mediated by a guanosine exchange factor. In addition, the Rho insert helix, which is located at a site remote from the PBD46 binding interface, shows a significant dynamic response to PBD46 binding.

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. Proteins 2014; 82:2106–2117.