How Much Entropy Is Contained in NMR Relaxation Parameters?

Side-chain dynamics of the α1B -adrenergic receptor determined by NMR via methyl relaxation

G protein-coupled receptors (GPCRs) are medically important membrane proteins that sample inactive, intermediate, and active conformational states characterized by relatively slow interconversions (~μs-ms). On a faster timescale (~ps-ns), the conformational landscape of GPCRs is governed by the rapid dynamics of amino acid side chains. Such dynamics are essential for protein functions such as ligand recognition and allostery. Unfortunately, technical challenges have almost entirely precluded the study of side-chain dynamics for GPCRs. Here, we investigate the rapid side-chain dynamics of a thermostabilized α1B -adrenergic receptor (α1B -AR) as probed by methyl relaxation. We determined order parameters for Ile, Leu, and Val methyl groups in the presence of inverse agonists that bind orthosterically (prazosin, tamsulosin) or allosterically (conopeptide ρ-TIA). Despite the differences in the ligands, the receptor's overall side-chain dynamics are very similar, including those of the apo form. However, ρ-TIA increases the flexibility of Ile1764×56 and possibly of Ile2145×49 , adjacent to Pro2155×50 of the highly conserved P5×50 I3×40 F6×44 motif crucial for receptor activation, suggesting differences in the mechanisms for orthosteric and allosteric receptor inactivation. Overall, increased Ile side-chain rigidity was found for residues closer to the center of the membrane bilayer, correlating with denser packing and lower protein surface exposure. In contrast to two microbial membrane proteins, in α1B -AR Leu exhibited higher flexibility than Ile side chains on average, correlating with the presence of Leu in less densely packed areas and with higher protein-surface exposure than Ile. Our findings demonstrate the feasibility of studying receptor-wide side-chain dynamics in GPCRs to gain functional insights.

Thermodynamic forces from protein and water govern condensate formation of an intrinsically disordered protein domain

Liquid-liquid phase separation (LLPS) can drive a multitude of cellular processes by compartmentalizing biological cells via the formation of dense liquid biomolecular condensates, which can function as membraneless organelles. Despite its importance, the molecular-level understanding of the underlying thermodynamics of this process remains incomplete. In this study, we use atomistic molecular dynamics simulations of the low complexity domain (LCD) of human fused in sarcoma (FUS) protein to investigate the contributions of water and protein molecules to the free energy changes that govern LLPS. Both protein and water components are found to have comparably sizeable thermodynamic contributions to the formation of FUS condensates. Moreover, we quantify the counteracting effects of water molecules that are released into the bulk upon condensate formation and the waters retained within the protein droplets. Among the various factors considered, solvation entropy and protein interaction enthalpy are identified as the most important contributions, while solvation enthalpy and protein entropy changes are smaller. These results provide detailed molecular insights on the intricate thermodynamic interplay between protein- and solvation-related forces underlying the formation of biomolecular condensates.

Epigenetic CpG duplex marks probed by an evolved DNA reader via a well-tempered conformational plasticity

5-methylcytosine (mC) and its TET-oxidized derivatives exist in CpG dyads of mammalian DNA and regulate cell fate, but how their individual combinations in the two strands of a CpG act as distinct regulatory signals is poorly understood. Readers that selectively recognize such novel 'CpG duplex marks' could be versatile tools for studying their biological functions, but their design represents an unprecedented selectivity challenge. By mutational studies, NMR relaxation, and MD simulations, we here show that the selectivity of the first designer reader for an oxidized CpG duplex mark hinges on precisely tempered conformational plasticity of the scaffold adopted during directed evolution. Our observations reveal the critical aspect of defined motional features in this novel reader for affinity and specificity in the DNA/protein interaction, providing unexpected prospects for further design progress in this novel area of DNA recognition.

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.

Assessing the applicability of 19F labeled tryptophan residues to quantify protein dynamics

Nuclear magnetic resonance (NMR) spectroscopy is uniquely suited to study the dynamics of biomolecules in solution. Most NMR studies exploit the spins of proton, carbon and nitrogen isotopes, as these atoms are highly abundant in proteins and nucleic acids. As an alternative and complementary approach, fluorine atoms can be introduced into biomolecules at specific sites of interest. These labels can then be used as sensitive probes for biomolecular structure, dynamics or interactions. Here, we address if the replacement of tryptophan with 5-fluorotryptophan residues has an effect on the overall dynamics of proteins and if the introduced fluorine probe is able to accurately report on global exchange processes. For the four different model proteins (KIX, Dcp1, Dcp2 and DcpS) that we examined, we established that ¹⁵N CPMG relaxation dispersion or EXSY profiles are not affected by the 5-fluorotryptophan, indicating that this replacement of a proton with a fluorine has no effect on the protein motions. However, we found that the motions that the 5-fluorotryptophan reports on can be significantly faster than the backbone motions. This implies that care needs to be taken when interpreting fluorine relaxation data in terms of global protein motions. In summary, our results underscore the great potential of fluorine NMR methods, but also highlight potential pitfalls that need to be considered.

Ligands selectively tune the local and global motions of neurotensin receptor 1 (NTS1)

Nuclear magnetic resonance (NMR) studies have revealed that fast methyl sidechain dynamics can report on entropically-driven allostery. Yet, NMR applications have been largely limited to the super-microsecond motional regimes of G protein-coupled receptors (GPCRs). We use ¹³C^ε-methionine chemical shift-based global order parameters to test if ligands affect the fast dynamics of a thermostabilized GPCR, neurotensin receptor 1 (NTS₁). We establish that the NTS₁ solution ensemble includes substates with lifetimes on several, discrete timescales. The longest-lived states reflect those captured in agonist- and inverse agonist-bound crystal structures, separated by large energy barriers. We observe that the rapid fluctuations of individual methionine residues, superimposed on these long-lived states, respond collectively with the degree of fast, global dynamics correlating with ligand pharmacology. This approach lends confidence to interpreting spectra in terms of local structure and methyl dihedral angle geometry. The results suggest a role for sub-microsecond dynamics and conformational entropy in GPCR ligand discrimination.

Pressure, motion, and conformational entropy in molecular recognition by proteins

The thermodynamics of molecular recognition by proteins is a central determinant of complex biochemistry. For over a half-century, detailed cryogenic structures have provided deep insight into the energetic contributions to ligand binding by proteins. More recently, a dynamical proxy based on NMR-relaxation methods has revealed an unexpected richness in the contributions of conformational entropy to the thermodynamics of ligand binding. Here, we report the pressure dependence of fast internal motion within the ribonuclease barnase and its complex with the protein barstar. In what we believe is a first example, we find that protein dynamics are conserved along the pressure-binding thermodynamic cycle. The femtomolar affinity of the barnase-barstar complex exists despite a penalty by -TΔS_conf of +11.7 kJ/mol at ambient pressure. At high pressure, however, the overall change in side-chain dynamics is zero, and binding occurs with no conformational entropy penalty, suggesting an important role of conformational dynamics in the adaptation of protein function to extreme environments. Distinctive clustering of the pressure sensitivity is observed in response to both pressure and binding, indicating the presence of conformational heterogeneity involving less efficiently packed alternative conformation(s). The structural segregation of dynamics observed in barnase is striking and shows how changes in both the magnitude and the sign of regional contributions of conformational entropy to the thermodynamics of protein function are possible.

Probing Methyl Group Dynamics in Proteins by NMR Cross-Correlated Dipolar Relaxation and Molecular Dynamics Simulations

Nuclear magnetic resonance (NMR) spin relaxation is the most informative approach to experimentally probe the internal dynamics of proteins on the picosecond to nanosecond time scale. At the same time, molecular dynamics (MD) simulations of biological macromolecules are steadily improving through better physical models, enhanced sampling methods, and increased computational power, and they provide exquisite information about flexibility and its role in protein stability and molecular interactions. Many examples have shown that MD is now adept in probing protein backbone motion, but improvements are still required toward a quantitative description of the dynamics of side chains, for example, probed by the dynamics of methyl groups. Thus far, the comparison of computation with experiment for side chain dynamics has primarily focused on the relaxation of ¹³C and ²H nuclei induced by autocorrelated variation of spin interactions. However, the cross-correlation of ¹³C-¹H dipolar interactions in methyl groups offers an attractive alternative. Here, we establish a computational framework to extract cross-correlation relaxation parameters of methyl groups in proteins from all-atom MD simulations. To demonstrate the utility of the approach, cross-correlation relaxation rates of ubiquitin are computed from MD simulations performed with the AMBER99SB*-ILDN and CHARMM36 force fields. Simulation results were found to agree well with those obtained by experiment. Moreover, the data obtained with the two force fields are highly consistent.

How does it really move? Recent progress in the investigation of protein nanosecond dynamics by NMR and simulation

Nuclear magnetic resonance (NMR) spin relaxation experiments currently probe molecular motions on timescales from picoseconds to nanoseconds. The detailed interpretation of these motions in atomic detail benefits from complementarity with the results from molecular dynamics (MD) simulations. In this mini-review, we describe the recent developments in experimental techniques to study the backbone dynamics from ¹⁵N relaxation and side-chain dynamics from ¹³C relaxation, discuss the different analysis approaches from model-free to dynamics detectors, and highlight the many ways that NMR relaxation experiments and MD simulations can be used together to improve the interpretation and gain insights into protein dynamics.

Explicit Models of Motion to Understand Protein Side-Chain Dynamics

Nuclear magnetic relaxation is widely used to probe protein dynamics. For decades, most analyses of relaxation in proteins have relied successfully on the model-free approach, forgoing mechanistic descriptions of motion. Model-free types of correlation functions cannot describe a large carbon-13 relaxation dataset in protein side chains. Here, we use molecular dynamics simulations to design explicit models of motion and solve Fokker-Planck diffusion equations. These models of motion provide better agreement with relaxation data, mechanistic insight, and a direct link to configuration entropy.

Microsecond MD Simulations of the Plexin-B1 RBD: N-H Probability Density as Descriptor of Structural Dynamics, Dimerization-Related Conformational Entropy, and Transient Dimer Asymmetry

Amide-bond equilibrium probability density, P_eq = exp(-u) (u, local potential), and associated conformational entropy, S_k = -∫P_eq (ln P_eq) dΩ ─ln ∫dΩ, are derived for the Rho GTPase binding domain of Plexin-B1 (RBD) as monomer and dimer from 1 μs MD simulations. The objective is to elucidate the effect of dimerization on the dynamic structure of the RBD. Dispersed (peaked) P_eq functions indicate "flexibility" ("rigidity"; the respective concepts are used below in this context). The L1 and L3 loops are throughout highly flexible, the L2 loop and the secondary structure elements are generally rigid, and the L4 loop is flexible in the monomer and rigid in the dimer. Overall, many residues are more flexible in the dimer. These features, and their implications, are discussed. Unexpectedly, we find that monomer unit 1 of the dimer (in short, d1) is unusually flexible, whereas monomer unit 2 (in short, d2) is as rigid as the RBD monomer. This is revealed due to their engagement in slow-to-intermediate conformational exchange detected previously by ¹⁵N relaxation experiments. Such motions occur with rates on the order of 10³-10⁴ s^-1; hence, they cannot be completely sampled over the course of 1 μs simulation. However, the extent to which rigid d2 is affected is small enough to enable physically relevant analysis. The entropy difference between d2 and the monomer yields an entropic contribution of -7 ± 0.7 kJ/mol to the free energy of RBD dimerization. In previous work aimed at similar objectives we used 50-100 ns MD simulations. Those results and the present result differ considerably. In summary, bond-vector P_eq functions derived directly from long MD simulations are useful descriptors of protein structural dynamics and provide accurate conformational entropy. Within the scope of slow conformational exchange, they can be useful, even in the presence of incomplete sampling.

Explicit models of motions to analyze NMR relaxation data in proteins

Nuclear Magnetic Resonance (NMR) is a tool of choice to characterize molecular motions. In biological macromolecules, pico- to nano-second motions, in particular, can be probed by nuclear spin relaxation rates which depend on the time fluctuations of the orientations of spin interaction frames. For the past 40 years, relaxation rates have been successfully analyzed using the Model Free (MF) approach which makes no assumption on the nature of motions and reports on the effective amplitude and time-scale of the motions. However, obtaining a mechanistic picture of motions from this type of analysis is difficult at best, unless complemented with molecular dynamics (MD) simulations. In spite of their limited accuracy, such simulations can be used to obtain the information necessary to build explicit models of motions designed to analyze NMR relaxation data. Here, we present how to build such models, suited in particular to describe motions of methyl-bearing protein side-chains and compare them with the MF approach. We show on synthetic data that explicit models of motions are more robust in the presence of rotamer jumps which dominate the relaxation in methyl groups of protein side-chains. We expect this work to motivate the use of explicit models of motion to analyze MD and NMR data.