Insights into the local residual entropy of proteins provided by NMR relaxation

Breaking down walls: Continuous potential models for internal motions in NMR spin relaxation

Simple physical models for restricted diffusion in a potential, which provide important insights for NMR spin relaxation, usually are based on free diffusion within rigid boundaries or diffusion in relatively simple continuous potential energy surfaces. The diffusion-in-a-cone model is an example of the former and diffusion in an N-fold cosine potential is an example of the latter. The present work models restricted diffusion for arbitrary potential energy functions on the surface of a cone or a sphere, by expanding the potentials in Fourier or spherical harmonic series, respectively. The results exhibit simple relationships between generalized order parameters and effective correlation times, critical for analysis of experimental spin relaxation data, and illustrate the transition from diffusive-like to jump-like behavior in multi-well potentials.

Interplay of halogen bonding and solvation in protein-ligand binding

Halogen bonding is increasingly utilized in efforts to achieve high affinity and selectivity of molecules designed to bind proteins, making it paramount to understand the relationship between structure, dynamics, and thermodynamic driving forces. We present a detailed analysis addressing this problem using a series of protein-ligand complexes involving single halogen substitutions - F, Cl, Br, and I - and nearly identical structures. Isothermal titration calorimetry reveals an increasingly favorable binding enthalpy from F to I that correlates with the halogen size and σ-hole electropositive character, but is partially counteracted by unfavorable entropy, which is constant from F to Cl and Br, but worse for I. Consequently, the binding free energy is roughly equal for Cl, Br, and I. QM and solvation-free-energy calculations reflect an intricate balance between halogen bonding, hydrogen bonds, and solvation. These advances have the potential to aid future drug design initiatives involving halogenated compounds.

Local Structures in Proteins from Microsecond Molecular Dynamics Simulations: A Symmetry-Based Perspective

We report on a new method for the characterization of local structures in proteins based on extensive molecular dynamics (MD) simulations, here, 1 μs in length. The N-H bond of the Rho GTPase binding domain of plexin-B1 (RBD) serves as a probe and the potential, u(MD), which restricts its internal motion, as a qualifier of the local dynamic structure. u(MD) is derived from the MD trajectory as a function of the polar angles, (θ, φ), which specify the N-H orientation in the protein. u(MD) is statistical in character yielding empirical descriptions. To establish more insightful methodical descriptions, we develop a comprehensive method which approximates u(MD) by combinations of analytical Wigner functions that belong to the D2h point group. These combinations, called u(simulated), make it possible to gain a new perspective of local dynamic structures in proteins based on explicit potentials/free energy surfaces and associated probability densities, entropy, and ordering. A simpler method was developed previously using 100 ns MD simulations. In that case, the traditional "perpendicular N-H ordering" setting centered at Cα-Cα with (θ, φ) = (90, 90) and generally, featuring positive φ, prevailed. u(MD) derived from 1 μs MD simulations is considerably more complex requiring substantial model enhancement. The enhanced method applies to the well-structured sections of the RBD. It only applies partly to its loops where u(MD) extends into the negative-φ region where we detect nonperpendicular N-H ordering. This arrangement requires devising new reference structures and making substantial algorithmic changes, to be performed in future work. Here, we focus on developing the comprehensive method and using it to investigate perpendicular ordering settings. We find that secondary structures (loops) exhibit varying (virtually invariant) potentials with Ag, B2u, and B1u (Ag and B2u) D2h symmetry. Application to RBD dimerization and RBD binding to the GTPase Rac1 is described in the subsequent article. Applications to other probes, proteins, and biological functions, based on explicit local potentials, probability densities, entropy, and ordering, are possible.

Fitting Force Field Parameters to NMR Relaxation Data

We present an approach to optimize force field parameters using time-dependent data from NMR relaxation experiments. To do so, we scan parameters in the dihedral angle potential energy terms describing the rotation of the methyl groups in proteins and compare NMR relaxation rates calculated from molecular dynamics simulations with the modified force fields to deuterium relaxation measurements of T4 lysozyme. We find that a small modification of C^γ methyl groups improves the agreement with experiments both for the protein used to optimize the force field and when validating using simulations of CI2 and ubiquitin. We also show that these improvements enable a more effective a posteriori reweighting of the MD trajectories. The resulting force field thus enables more direct comparison between simulations and side-chain NMR relaxation data and makes it possible to construct ensembles that better represent the dynamics of proteins in solution.

Deep mining of the protein energy landscape

For over half a century, it has been known that protein molecules naturally undergo extensive structural fluctuations, and that these internal motions are intimately related to their functional properties. The energy landscape view has provided a powerful framework for describing the various physical states that proteins visit during their lifetimes. This Perspective focuses on the commonly neglected and often disparaged axis of the protein energy landscape: entropy. Initially seen largely as a barrier to functionally relevant states of protein molecules, it has recently become clear that proteins retain considerable conformational entropy in the "native" state, and that this entropy can and often does contribute significantly to the free energy of fundamental protein properties, processes, and functions. NMR spectroscopy, molecular dynamics simulations, and emerging crystallographic views have matured in parallel to illuminate dynamic disorder of the "ground state" of proteins and their importance in not only transiting between biologically interesting structures but also greatly influencing their stability, cooperativity, and contribution to critical properties such as allostery.

DNA base order parameter determination without influence of chemical exchange

Nuclear magnetic resonance (NMR) spectroscopy is a versatile tool used to investigate the dynamic properties of biological macromolecules and their complexes. NMR relaxation data can provide order parameters S2, which represent the mobility of bond vectors reorienting within a molecular frame. Determination of S2 parameters typically involves the use of transverse NMR relaxation rates. However, the accuracy in S2 determination can be diminished by elevation of the transverse relaxation rates through conformational or chemical exchange involving protonation/deprotonation or non-Watson-Crick base-pair states of nucleic acids. Here, we propose an approach for determination of S2 parameters without the influence of exchange processes. This approach utilizes transverse and longitudinal 13C chemical shift anisotropy (CSA) - dipole-dipole (DD) cross-correlation rates instead of 13C transverse relaxation rates. Anisotropy in rotational diffusion is taken into consideration. An application of this approach to nucleotide base CH groups of a uniformly 13C/15N-labeled DNA duplex is demonstrated.

Allostery in the dynamic coactivator domain KIX occurs through minor conformational micro-states

The coactivator KIX of CBP uses two binding surfaces to recognize multiple activators and exhibits allostery in ternary complex formation. Activator•coactivator interactions are central to transcriptional regulation, yet the microscopic origins of allostery in dynamic proteins like KIX are largely unknown. Here, we investigate the molecular recognition and allosteric manifestations involved in two KIX ternary systems c-Myb•KIX•MLL and pKID•KIX•MLL. Exploring the hypothesis that binary complex formation prepays an entropic cost for positive cooperativity, we utilize molecular dynamics simulations, side chain methyl order parameters, and differential scanning fluorimetry (DSF) to explore conformational entropy changes in KIX. The protein's configurational micro-states from structural clustering highlight the utility of protein plasticity in molecular recognition and allostery. We find that apo KIX occupies a wide distribution of lowly-populated configurational states. Each binding partner has its own suite of KIX states that it selects, building a model of molecular recognition fingerprints. Allostery is maximized with MLL pre-binding, which corresponds to the observation of a significant reduction in KIX micro-states observed when MLL binds. With all binding partners, the changes in KIX conformational entropy arise predominantly from changes in the most flexible loop. Likewise, we find that a small molecule and mutations allosterically inhibit/enhance activator binding by tuning loop dynamics, suggesting that loop-targeting chemical probes could be developed to alter KIX•activator interactions. Experimentally capturing KIX stabilization is challenging, particularly because of the disordered nature of particular activators. However, DSF melting curves allow for inference of relative entropic changes that occur across complexes, which we compare to our computed entropy changes using simulation methyl order parameters.

How Much Entropy Is Contained in NMR Relaxation Parameters?

Solution-state NMR relaxation experiments are the cornerstone to study internal protein dynamics at an atomic resolution on time scales that are faster than the overall rotational tumbling time τ_R. Since the motions described by NMR relaxation parameters are connected to thermodynamic quantities like conformational entropies, the question arises how much of the total entropy is contained within this tumbling time. Using all-atom molecular dynamics simulations of the T4 lysozyme, we found that entropy buildup is rather fast for the backbone, such that the majority of the entropy is indeed contained in the short-time dynamics. In contrast, the contribution of the slow dynamics of side chains on time scales beyond τ_R on the side-chain conformational entropy is significant and should be taken into account for the extraction of accurate thermodynamic properties.

Conformational Entropy from Mobile Bond Vectors in Proteins: A Viewpoint that Unifies NMR Relaxation Theory and Molecular Dynamics Simulation Approaches

A new method for determining conformational entropy in proteins is reported. Proteins prevail as conformational ensembles, p ∝ exp(-u). By selecting a bond vector (e.g., N-H) as a conformation representative, molecular dynamics simulations can provide (relative to a reference structure) p as approximate Boltzmann probability density and u as N-H potential of mean force (POMF). The latter is as accurate as implied by the force field but statistical in character; this limits the insights it can provide and its utilization. Conformational entropy is given exclusively by u. Deriving it from POMFs renders it accurate but statistical in character. Previously, we devised explicit (i.e., analytical but not exact) potentials made of Wigner functions, D_0K^L, with L ≤ 4, which closely resemble the corresponding POMFs in form; hence, they also approach the latter in accuracy. Such potentials can be beneficially characterized/compared in terms of composition, symmetry, and associated order parameters. In this study, we develop a method for deriving conformational entropy from them, which also features the benefits specified above. The method developed is applied to the dimerization of the Rho GTPase-binding domain of plexin-B1. Insights into local ordering, entropy compensation, and features of allostery are gained. In previous work, we developed the slowly relaxing local structure (SRLS) approach for the analysis of NMR relaxation from restricted bond vector motion in proteins. SRLS comprises explicit (restricting) potentials of the kind developed here. It also comprises diffusion tensors describing the local motion and related features of local geometry. The complete model fits experimental data. In future work, the explicit potentials developed here will be inserted unchanged in SRLS-based data fitting, thereby improving the picture of structural dynamics. Given that SRLS is unique in featuring potentials that can closely approach the corresponding POMFs in accuracy, the present study is an important step toward generally improving protein dynamics by NMR relaxation.

Conformational Entropy from Restricted Bond-Vector Motion in Proteins: The Symmetry of the Local Restrictions and Relation to NMR Relaxation

Locally mobile bond-vectors contribute to the conformational entropy of the protein, given by S_k ≡ S/k = -∫(P_eq ln P_eq)dΩ - ln∫dΩ. The quantity P_eq = exp(-u)/Z is the orientational probability density, where Z is the partition function and u is the spatially restricting potential exerted by the immediate internal protein surroundings at the site of the motion of the bond-vector. It is appropriate to expand the potential, u, which restricts local rotational reorientation, in the basis set of the real combinations of the Wigner rotation matrix elements, D_0K^L. For small molecules dissolved in anisotropic media, one typically keeps the lowest even L, L = 2, nonpolar potential in axial or rhombic form. For bond-vectors anchored at the protein, the lowest odd L, L = 1, polar potential is to be used in axial or rhombic form. Here, we investigate the effect of the symmetry and polarity of these potentials on S_k. For L = 1 (L = 2), S_k is the same (differs) for parallel and perpendicular ordering. The plots of S_k as a function of the coefficients of the rhombic L = 1 (L = 2) potential exhibit high-symmetry (specific low-symmetry) patterns with parameter-range-dependent sensitivity. Similar statements apply to analogous plots of the potential minima. S_k is also examined as a function of the order parameters defined in terms of u. Graphs displaying these correlations, and applications illustrating their usage, are provided. The features delineated above are generally useful for devising orienting potentials that best suit given physical circumstances. They are particularly useful for bond-vectors acting as NMR relaxation probes in proteins, when their restricted local motion is analyzed with stochastic models featuring Wigner-function-made potentials. The relaxation probes could also be molecules adsorbed at surfaces, inserted into membranes, or interlocked within metal-organic frameworks.

NMR and computational methods for molecular resolution of allosteric pathways in enzyme complexes

Allostery is a ubiquitous biological mechanism in which a distant binding site is coupled to and drastically alters the function of a catalytic site in a protein. Allostery provides a high level of spatial and temporal control of the integrity and activity of biomolecular assembles composed of proteins, nucleic acids, or small molecules. Understanding the physical forces that drive allosteric coupling is critical to harnessing this process for use in bioengineering, de novo protein design, and drug discovery. Current microscopic models of allostery highlight the importance of energetics, structural rearrangements, and conformational fluctuations, and in this review, we discuss the synergistic use of solution NMR spectroscopy and computational methods to probe these phenomena in allosteric systems, particularly protein-nucleic acid complexes. This combination of experimental and theoretical techniques facilitates an unparalleled detection of subtle changes to structural and dynamic equilibria in biomolecules with atomic resolution, and we provide a detailed discussion of specialized NMR experiments as well as the complementary methods that provide valuable insight into allosteric pathways in silico. Lastly, we highlight two case studies to demonstrate the adaptability of this approach to enzymes of varying size and mechanistic complexity.

Characterization of the dynamics and the conformational entropy in the binding between TAZ1 and CTAD-HIF-1α

The interaction between the C-terminal transactivation domain of HIF-1α (CTAD-HIF-1α) and the transcriptional adapter zinc binding 1 (TAZ1) domain of CREB binding protein participate in the initiation of gene transcription during hypoxia. Unbound CTAD-HIF-1α is disordered but undergoes a disorder-to-order transition upon binding to TAZ1. We have here performed NMR side chain and backbone relaxation studies on TAZ1 and side chain relaxation measurements on CTAD-HIF-1α in order to investigate the role of picosecond to nanosecond dynamics. We find that the internal motions are significantly affected upon binding, both on the side chain and the backbone level. The dynamic response corresponds to a conformational entropy change that contributes substantially to the binding thermodynamics for both binding partners. Furthermore, the conformational entropy change for the well-folded TAZ1 varies upon binding to different IDP targets. We further identify a cluster consisting of side chains in bound TAZ1 and CTAD-HIF-1α that experience extensive dynamics and are part of the binding region that involves the N-terminal end of the LPQL motif in CTAD-HIF-1α; a feature that might have an important role in the termination of the hypoxic response.

Role of Conformational Entropy in Molecular Recognition by TAZ1 of CBP

The globular transcriptional adapter zinc binding 1 (TAZ1) domain of CREB binding protein participates in protein-protein interactions that are involved in transcriptional regulation. TAZ1 binds numerous targets, of which many are intrinsically disordered proteins that undergo a disorder-to-order transition to various degrees. One such target is the disordered transactivation domain of transcription factor RelA (TAD-RelA), which with its interaction with TAZ1 is involved in transcriptional regulation of genes in NF-κB signaling. We have here performed nuclear magnetic resonance backbone and side-chain relaxation studies to investigate the influence of RelA-TA2 (residues 425-490 in TAD-RelA) binding on the subnanosecond internal motions of TAZ1. We find a considerable dynamic response on both the backbone and side-chain levels, which corresponds to a conformational entropy change that contributes significantly to the binding energetics. We further show that the microscopic origins of the dynamic response of TAZ1 vary depending on the target. This study demonstrates that folded protein domains that are able to interact with various targets are not dynamically passive but can have a significant role in the motional response upon target association.

Characterization of Internal Protein Dynamics and Conformational Entropy by NMR Relaxation

Recent studies suggest that the fast timescale motion of methyl-bearing side chains may play an important role in mediating protein activity. These motions have been shown to encapsulate the residual conformational entropy of the folded state that can potentially contribute to the energetics of protein function. Here, we provide an overview of how to characterize these motions using nuclear magnetic resonance (NMR) spin relaxation methods. The strengths and limitations of several techniques are highlighted in order to assist with experimental design. Particular emphasis is placed on the practical aspects of sample preparation, data collection, data fitting, and statistical analysis. Additionally, discussion of the recently refined "entropy meter" is presented and its use in converting NMR observables to conformational entropy is illustrated. Taken together, these methods should yield new insights into the complex interplay between structure and dynamics in protein function.

An NMR Confirmation for Increased Folded State Entropy Following Loop Truncation

Previous studies conducted on flexible loop regions in proteins revealed that the energetic consequences of changing loop length predominantly arise from the entropic cost of ordering a loop during folding. However, in an earlier study of human acylphosphatase (hmAcP) using experimental and computational approaches, we showed that thermodynamic stabilization upon loop truncation can be attributed mainly to the increased entropy of the folded state. Here, using 15N NMR spectroscopy, we studied the effect of loop truncation on hmAcP backbone dynamics on the picosecond-nanosecond timescale with the aim of confirming the effect of folded state entropy on protein stability. NMR-relaxation-derived N-H squared generalized order parameters reveal that loop truncation results in a significant increase in protein conformational flexibility. Comparison of these results with previously acquired all-atom molecular dynamics simulation, analyzed here in terms of squared generalized NMR order parameters, demonstrates general agreement between the two methods. The NMR study not only provides direct evidence for the enhanced conformational entropy of the folded state of hmAcP upon loop truncation but also gives a quantitative measure of the observed effects.

Wetting of the Protein Active Site Leads to Non-Marcusian Reaction Kinetics

Enzymes exist in continuously fluctuating water bath dramatically affecting their function. Water not only forms the solvation shell but also penetrates into the protein interior. Changing the wetting pattern of the protein's active site in response to altering redox state initiates a highly nonlinear structural change and non-Gaussian electrostatic fluctuations at the active site. The free-energy surfaces of electron transfer are highly nonparabolic (non-Marcusian), as shown by atomistic molecular dynamics simulations of hydrated ferredoxin protein and by an analytical model in agreement with simulations. The reorganization energy of electron transfer passes through a spike marking equal probabilities of the wet and dry states of the active site. The activation thermodynamics affected by wetting leads to a non-Arrhenius, passing through a maximum, plot for the reaction rate vs the inverse temperature.

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.

Self-Consistent Framework Connecting Experimental Proxies of Protein Dynamics with Configurational Entropy

The recently developed NMR techniques enable estimation of protein configurational entropy change from the change in the average methyl order parameters. This experimental observable, however, does not directly measure the contribution of intramolecular couplings, protein main-chain motions, or angular dynamics. Here, we carry out a self-consistent computational analysis of the impact of these missing contributions on an extensive set of molecular dynamics simulations of different proteins undergoing binding. Specifically, we compare the configurational entropy change in protein complex formation as obtained by the maximum information spanning tree approximation (MIST), which treats the above entropy contributions directly, and the change in the average NMR methyl and NH order parameters. Our parallel implementation of MIST allows us to treat hard angular degrees of freedom as well as couplings up to full pairwise order explicitly, while still involving a high degree of sampling and tackling molecules of biologically relevant sizes. First, we demonstrate a remarkably strong linear relationship between the total configurational entropy change and the average change in both methyl and backbone-NH order parameters. Second, in contrast to canonical assumptions, we show that the main-chain and angular terms contribute significantly to the overall configurational entropy change and also scale linearly with it. Consequently, linear models starting from the average methyl order parameters are able to capture the contribution of main-chain and angular terms well. After applying the quantum-mechanical harmonic oscillator entropy formalism, we establish a similarly strong linear relationship for X-ray crystallographic B-factors. Finally, we demonstrate that the observed linear relationships remain robust against drastic undersampling and argue that they reflect an intrinsic property of compact proteins. Despite their remarkable strength, however, the above linear relationships yield estimates of configurational entropy change whose accuracy appears to be sufficient for qualitative applications only.

Residual Entropy and Critical Behavior of Two Interacting Boson Species in a Double Well

Motivated by the importance of entanglement and correlation indicators in the analysis of quantum systems, we study the equilibrium and the bipartite residual entropy in a two-species Bose–Hubbard dimer when the spatial phase separation of the two species takes place. We consider both the zero and non-zero-temperature regime. We present different kinds of residual entropies (each one associated with a different way of partitioning the system), and we show that they strictly depend on the specific quantum phase characterizing the two species (supermixed, mixed or demixed) even at finite temperature. To provide a deeper physical insight into the zero-temperature scenario, we apply the fully-analytical variational approach based on su(2) coherent states and provide a considerably good approximation of the entanglement entropy. Finally, we show that the effectiveness of bipartite residual entropy as a critical indicator at non-zero temperature is unchanged when considering a restricted combination of energy eigenstates.

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.

Imaginative Order from Reasonable Chaos: Conformation-Driven Activity and Reactivity in Exploring Protein–Ligand Interactions

Sir Derek Barton’s seminal work on steroid conformational analysis opened up a new era of enquiry into how the preferred conformation of any molecule could have profound effects on its physical–chemical properties and activities. Conformation-based effects on molecular activity and reactivity continue to manifest, with one key area of investigation currently focussed on conformational entropy in driving protein–ligand interactions. Carrying on from Barton’s initial insight on natural product conformational properties, new questions now address how conformational flexibility within a bioactive natural product structural framework (reasonable chaos), can be directed to confer dynamically new protein–ligand interactions beyond the basic lock–key model (imaginative order). Here we summarise our work on exploring conformational diversity from fluorinated natural product fragments, and how this approach of conformation-coupled diversity-oriented synthesis can be used to iteratively derive ligands with enhanced specificity against highly homologous protein domains. Our results demonstrate that the conformation entropic states of highly conserved protein domains differ significantly, and this conformational diversity, beyond primary sequence analysis, can be duly captured and exploited by natural-product derived ligands with complementary conformational dynamics for enhancing recognition specificity in drug lead discovery.

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.

Conformational Entropy as Collective Variable for Proteins

Many enhanced sampling methods rely on the identification of appropriate collective variables. For proteins, even small ones, finding appropriate descriptors has proven challenging. Here we suggest that the NMR S² order parameter can be used to this effect. We trace the validity of this statement to the suggested relation between S² and conformational entropy. Using the S² order parameter and a surrogate for the protein enthalpy in conjunction with metadynamics or variationally enhanced sampling, we are able to reversibly fold and unfold a small protein and draw its free energy at a fraction of the time that is needed in unbiased simulations. We also use S² in combination with the free energy flooding method to compute the unfolding rate of this peptide. We repeat this calculation at different temperatures to obtain the unfolding activation energy.

Nanosecond Dynamics of Gαi1 Bound to Nucleotides or Ric-8A, a Gα Chaperone with GEF Activity

Resistance to Inhibitors of Cholinesterase A (Ric-8A) is a 60-kDa cytosolic protein that has chaperone and guanine nucleotide exchange (GEF) activity toward heterotrimeric G protein α subunits of the i, q, and 12/13 classes, catalyzing the release of GDP from Gα and subsequent binding of GTP. In the absence of GTP or GTP analogs, and subsequent to GDP release, Gα forms a stable nucleotide-free complex with Ric-8A. In this study, time-resolved fluorescence anisotropy measurements were employed to detect local motions of Gαi1 labeled at selected sites with Alexa 488 (C5) fluorescent dye (Ax) in the GDP, GTPγS (collectively, GXP), and Ric-8A-bound states. Sites selected for Alexa 488 (C5) derivatization were in the α-helical domain (residue 106), the α-helical domain-Ras-like domain hinge (residue 63), Switch I (residue 180), Switch II (residue 209), Switch III (residue 238), the α4 helix (residue 305), and at the junction between the purine-binding subsite in the β6-α5 loop and the C-terminal α helix (residue 330). In the GXP-bound states, the Alexa fluorophore reports local motions with correlation times ranging from 1.0 to 1.8 ns. The dynamics at Ax180 is slower in Gαi1•GDP than in Gαi1•GTPγS. The reverse is true at Ax209. The order parameters, S(2), for Alexa probes at switch residues are high (0.78-0.88) in Gαi1•GDP and lower (0.67-0.75) in Gαi1•GTPγS, although in crystal structures, switch segments are more ordered in the latter. Local motions at Ax63, Ax180, Ax209, and Ax330 are all markedly slower (2.3-2.8 ns) in Gαi1:Ric-8A than in Gαi1•GXP, and only modest (± 0.1) differences in S(2) are observed at most sites in Gαi1:Ric-8A relative to Gαi1•GXP. The slow dynamics suggests long-range correlated transitions within an ensemble of states and, particularly in the hinge and switch segments that make direct contact with Ric-8A. Induction of Gαi1 structural heterogeneity by Ric-8A provides a mechanism for nucleotide release.

Entropy in molecular recognition by 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.

The Dynameomics Entropy Dictionary: A Large-Scale Assessment of Conformational Entropy across Protein Fold Space

Molecular dynamics (MD) simulations contain considerable information with regard to the motions and fluctuations of a protein, the magnitude of which can be used to estimate conformational entropy. Here we survey conformational entropy across protein fold space using the Dynameomics database, which represents the largest existing data set of protein MD simulations for representatives of essentially all known protein folds. We provide an overview of MD-derived entropies accounting for all possible degrees of dihedral freedom on an unprecedented scale. Although different side chains might be expected to impose varying restrictions on the conformational space that the backbone can sample, we found that the backbone entropy and side chain size are not strictly coupled. An outcome of these analyses is the Dynameomics Entropy Dictionary, the contents of which have been compared with entropies derived by other theoretical approaches and experiment. As might be expected, the conformational entropies scale linearly with the number of residues, demonstrating that conformational entropy is an extensive property of proteins. The calculated conformational entropies of folding agree well with previous estimates. Detailed analysis of specific cases identifies deviations in conformational entropy from the average values that highlight how conformational entropy varies with sequence, secondary structure, and tertiary fold. Notably, α-helices have lower entropy on average than do β-sheets, and both are lower than coil regions.

Entropy redistribution controls allostery in a metalloregulatory protein

Allosteric communication between two ligand-binding sites in a protein is a central aspect of biological regulation that remains mechanistically unclear. Here we show that perturbations in equilibrium picosecond-nanosecond motions impact zinc (Zn)-induced allosteric inhibition of DNA binding by the Zn efflux repressor CzrA (chromosomal zinc-regulated repressor). DNA binding leads to an unanticipated increase in methyl side-chain flexibility and thus stabilizes the complex entropically; Zn binding redistributes these motions, inhibiting formation of the DNA complex by restricting coupled fast motions and concerted slower motions. Allosterically impaired CzrA mutants are characterized by distinct nonnative fast internal dynamics "fingerprints" upon Zn binding, and DNA binding is weakly regulated. We demonstrate the predictive power of the wild-type dynamics fingerprint to identify key residues in dynamics-driven allostery. We propose that driving forces arising from dynamics can be harnessed by nature to evolve new allosteric ligand specificities in a compact molecular scaffold.

Side-chain dynamics analysis of KE07 series

The significant improvement of KE07 series in catalytic activities shows the great success of computational design approaches combined with directed evolution in protein design. Understanding the protein dynamics in the evolutionary optimization process of computationally designed enzyme will provide profound implication to study enzyme function and guide protein design. Here, side chain squared generalized order parameters and entropy of each protein are calculated using 50ns molecular dynamics simulation data in both apo and bound states. Our results show a correlation between the increase of side chain motion amplitude and catalytic efficiency. By analyzing the relationship between these two values, we find side chain squared generalized order parameter is linearly related to side chain entropy, which indicates the computationally designed KE07 series have similar dynamics property with natural enzymes.

Distinct Roles for Conformational Dynamics in Protein-Ligand Interactions

Conformational dynamics has an established role in enzyme catalysis, but its contribution to ligand binding and specificity is largely unexplored. Here we used the Tiam1 PDZ domain and an engineered variant (QM PDZ) with broadened specificity to investigate the role of structure and conformational dynamics in molecular recognition. Crystal structures of the QM PDZ domain both free and bound to ligands showed structural features central to binding (enthalpy), while nuclear-magnetic-resonance-based methyl relaxation experiments and isothermal titration calorimetry revealed that conformational entropy contributes to affinity. In addition to motions relevant to thermodynamics, slower microsecond to millisecond switching was prevalent in the QM PDZ ligand-binding site consistent with a role in ligand specificity. Our data indicate that conformational dynamics plays distinct and fundamental roles in tuning the affinity (conformational entropy) and specificity (excited-state conformations) of molecular interactions. More broadly, our results have important implications for the evolution, regulation, and design of protein-ligand interactions.

Accurate determination of rates from non-uniformly sampled relaxation data

The application of non-uniform sampling (NUS) to relaxation experiments traditionally used to characterize the fast internal motion of proteins is quantitatively examined. Experimentally acquired Poisson-gap sampled data reconstructed with iterative soft thresholding are compared to regular sequentially sampled (RSS) data. Using ubiquitin as a model system, it is shown that 25 % sampling is sufficient for the determination of quantitatively accurate relaxation rates. When the sampling density is fixed at 25 %, the accuracy of rates is shown to increase sharply with the total number of sampled points until eventually converging near the inherent reproducibility of the experiment. Perhaps contrary to some expectations, it is found that accurate peak height reconstruction is not required for the determination of accurate rates. Instead, inaccuracies in rates arise from inconsistencies in reconstruction across the relaxation series that primarily manifest as a non-linearity in the recovered peak height. This indicates that the performance of an NUS relaxation experiment cannot be predicted from comparison of peak heights using a single RSS reference spectrum. The generality of these findings was assessed using three alternative reconstruction algorithms, eight different relaxation measurements, and three additional proteins that exhibit varying degrees of spectral complexity. From these data, it is revealed that non-linearity in peak height reconstruction across the relaxation series is strongly correlated with errors in NUS-derived relaxation rates. Importantly, it is shown that this correlation can be exploited to reliably predict the performance of an NUS-relaxation experiment by using three or more RSS reference planes from the relaxation series. The RSS reference time points can also serve to provide estimates of the uncertainty of the sampled intensity, which for a typical relaxation times series incurs no penalty in total acquisition time.

Changes in conformational dynamics of basic side chains upon protein-DNA association

Basic side chains play major roles in recognition of nucleic acids by proteins. However, dynamic properties of these positively charged side chains are not well understood. In this work, we studied changes in conformational dynamics of basic side chains upon protein–DNA association for the zinc-finger protein Egr-1. By nuclear magnetic resonance (NMR) spectroscopy, we characterized the dynamics of all side-chain cationic groups in the free protein and in the complex with target DNA. Our NMR order parameters indicate that the arginine guanidino groups interacting with DNA bases are strongly immobilized, forming rigid interfaces. Despite the strong short-range electrostatic interactions, the majority of the basic side chains interacting with the DNA phosphates exhibited high mobility, forming dynamic interfaces. In particular, the lysine side-chain amino groups exhibited only small changes in the order parameters upon DNA-binding. We found a similar trend in the molecular dynamics (MD) simulations for the free Egr-1 and the Egr-1–DNA complex. Using the MD trajectories, we also analyzed side-chain conformational entropy. The interfacial arginine side chains exhibited substantial entropic loss upon binding to DNA, whereas the interfacial lysine side chains showed relatively small changes in conformational entropy. These data illustrate different dynamic characteristics of the interfacial arginine and lysine side chains.

Solution NMR Spectroscopy for the Study of Enzyme Allostery

Allostery is a ubiquitous biological regulatory process in which distant binding sites within a protein or enzyme are functionally and thermodynamically coupled. Allosteric interactions play essential roles in many enzymological mechanisms, often facilitating formation of enzyme-substrate complexes and/or product release. Thus, elucidating the forces that drive allostery is critical to understanding the complex transformations of biomolecules. Currently, a number of models exist to describe allosteric behavior, taking into account energetics as well as conformational rearrangements and fluctuations. In the following Review, we discuss the use of solution NMR techniques designed to probe allosteric mechanisms in enzymes. NMR spectroscopy is unequaled in its ability to detect structural and dynamical changes in biomolecules, and the case studies presented herein demonstrate the range of insights to be gained from this valuable method. We also provide a detailed technical discussion of several specialized NMR experiments that are ideally suited for the study of enzymatic allostery.

A dynamic look backward and forward

The 2015 Gunther Laukien Prize recognized solution NMR studies of protein dynamics and thermodynamics. This Perspective surveys aspects of the development and application of NMR spin relaxation for investigations of protein flexibility and function over multiple time scales in solution. Methods highlighted include analysis of overall rotational diffusion, theoretical descriptions of R1ρ relaxation, and molecular dynamics simulations to interpret NMR spin relaxation. Applications are illustrated for the zinc-finger domain Xfin-31, the calcium-binding proteins calbindin D9k and calmodulin, and the bZip transcription factor of GCN4.

Protein Allostery and Conformational Dynamics

The functions of many proteins are regulated through allostery, whereby effector binding at a distal site changes the functional activity (e.g., substrate binding affinity or catalytic efficiency) at the active site. Most allosteric studies have focused on thermodynamic properties, in particular, substrate binding affinity. Changes in substrate binding affinity by allosteric effectors have generally been thought to be mediated by conformational transitions of the proteins or, alternatively, by changes in the broadness of the free energy basin of the protein conformational state without shifting the basin minimum position. When effector binding changes the free energy landscape of a protein in conformational space, the change affects not only thermodynamic properties but also dynamic properties, including the amplitudes of motions on different time scales and rates of conformational transitions. Here we assess the roles of conformational dynamics in allosteric regulation. Two cases are highlighted where NMR spectroscopy and molecular dynamics simulation have been used as complementary approaches to identify residues possibly involved in allosteric communication. Perspectives on contentious issues, for example, the relationship between picosecond-nanosecond local and microsecond-millisecond conformational exchange dynamics, are presented.

Using NMR spectroscopy to elucidate the role of molecular motions in enzyme function

Conformational motions play an essential role in enzyme function, often facilitating the formation of enzyme-substrate complexes and/or product release. Although considerable debate remains regarding the role of molecular motions in the conversion of enzymatic substrates to products, numerous examples have found motions to be crucial for optimization of enzyme scaffolds, effective substrate binding, and product dissociation. Conformational fluctuations are often rate-limiting to enzyme catalysis, primarily through product release, with the chemical reaction occurring much more quickly. As a result, the direct involvement of motions at various stages along the enzyme reaction coordinate remains largely unknown and untested. In the following review, we describe the use of solution NMR techniques designed to probe various timescales of molecular motions and detail examples in which motions play a role in propagating catalytic effects from the active site and directly participate in essential aspects of enzyme function.

Rapid Determination of Fast Protein Dynamics from NMR Chemical Exchange Saturation Transfer Data

Functional motions of (15)N-labeled proteins can be monitored by solution NMR spin relaxation experiments over a broad range of timescales. These experiments however typically take of the order of several days to a week per protein. Recently, NMR chemical exchange saturation transfer (CEST) experiments have emerged to probe slow millisecond motions complementing R1ρ and CPMG-type experiments. CEST also simultaneously reports on site-specific R1 and R2 parameters. It is shown here how CEST-derived R1 and R2 relaxation parameters can be measured within a few hours at an accuracy comparable to traditional relaxation experiments. Using a "lean" version of the model-free approach S(2) order parameters can be determined that match those from the standard model-free approach applied to (15)N R1, R2 , and {(1)H}-(15)N NOE data. The new methodology, which is demonstrated for ubiquitin and arginine kinase (42 kDa), should serve as an effective screening tool of protein dynamics from picosecond-to-millisecond timescales.

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.

Distance-Based Configurational Entropy of Proteins from Molecular Dynamics Simulations

Estimation of configurational entropy from molecular dynamics trajectories is a difficult task which is often performed using quasi-harmonic or histogram analysis. An entirely different approach, proposed recently, estimates local density distribution around each conformational sample by measuring the distance from its nearest neighbors. In this work we show this theoretically well grounded the method can be easily applied to estimate the entropy from conformational sampling. We consider a set of systems that are representative of important biomolecular processes. In particular: reference entropies for amino acids in unfolded proteins are obtained from a database of residues not participating in secondary structure elements;the conformational entropy of folding of β2-microglobulin is computed from molecular dynamics simulations using reference entropies for the unfolded state;backbone conformational entropy is computed from molecular dynamics simulations of four different states of the EPAC protein and compared with order parameters (often used as a measure of entropy);the conformational and rototranslational entropy of binding is computed from simulations of 20 tripeptides bound to the peptide binding protein OppA and of β2-microglobulin bound to a citrate coated gold surface. This work shows the potential of the method in the most representative biological processes involving proteins, and provides a valuable alternative, principally in the shown cases, where other approaches are problematic.

Structure and Dynamics of Phospholipid Nanodiscs from All-Atom and Coarse-Grained Simulations

We investigated structural and dynamical properties of nanodiscs comprising dimyristoylphosphatidylcholine (DMPC) lipids and major scaffold protein MSP1Δ(1-22) from human apolipoprotein A-1 using combined all-atom and coarse-grained (CG) molecular dynamics (MD) simulations. The computational efficiency of the Martini-CG force field enables the spontaneous self-assembly of lipids and scaffold proteins into stable nanodisc structures on time scales up to tens of microseconds. Subsequent all-atom and CG-MD simulations reveal that the lipids in the nanodisc have lower configurational entropy and higher acyl tail order than in a lamellar bilayer phase. These altered average properties arise from rather differential behavior of lipids, depending on their location in the nanodisc. Since the scaffold proteins exert constrictive forces from the outer rim of the disc toward its center, lipids at the center of the nanodisc are highly ordered, whereas annular lipids that are in contact with the MSP proteins are remarkably disordered due to perturbed packing. Although specific differences between all-atom and CG simulations are also evident, the results obtained at both levels of resolution are in overall good agreement with each other and provide atomic level interpretations of recent experiments. Thus, the present study highlights the applicability of multiscale simulation approaches for nanodisc systems and opens the way for future applications, including the study of nanodisc-embedded membrane proteins.

Changing the topology of protein backbone: the effect of backbone cyclization on the structure and dynamics of a SH3 domain

Understanding of the effects of the backbone cyclization on the structure and dynamics of a protein is essential for using protein topology engineering to alter protein stability and function. Here we have determined, for the first time, the structure and dynamics of the linear and various circular constructs of the N-SH3 domain from protein c-Crk. These constructs differ in the length and amino acid composition of the cyclization region. The backbone cyclization was carried out using intein-mediated intramolecular chemical ligation between the juxtaposed N- and the C-termini. The structure and backbone dynamics studies were performed using solution NMR. Our data suggest that the backbone cyclization has little effect on the overall three-dimensional structure of the SH3 domain: besides the termini, only minor structural changes were found in the proximity of the cyclization region. In contrast to the structure, backbone dynamics are significantly affected by the cyclization. On the subnanosecond time scale, the backbone of all circular constructs on average appears more rigid than that of the linear SH3 domain; this effect is observed over the entire backbone and is not limited to the cyclization site. The backbone mobility of the circular constructs becomes less restricted with increasing length of the circularization loop. In addition, significant conformational exchange motions (on the sub-millisecond time scale) were found in the N-Src loop and in the adjacent β-strands in all circular constructs studied in this work. These effects of backbone cyclization on protein dynamics have potential implications for the stability of the protein fold and for ligand binding.