Fast time scale dynamics of protein backbones: NMR relaxation methods, applications, and functional consequences

Probing conformational dynamics of DNA binding by CO-sensing transcription factor, CooA

The transcription factor CooA is a CRP/FNR (cAMP receptor protein/ fumarate and nitrate reductase) superfamily protein that uses heme to sense carbon monoxide (CO). Allosteric activation of CooA in response to CO binding is currently described as a series of discrete structural changes, without much consideration for the potential role of protein dynamics in the process of DNA binding. This work uses site-directed spin-label electron paramagnetic resonance spectroscopy (SDSL-EPR) to probe slow timescale (μs-ms) conformational dynamics of CooA with a redox-stable nitroxide spin label, and IR spectroscopy to probe the environment at the CO-bound heme. A series of cysteine substitution variants were created to selectively label CooA in key functional regions, the heme-binding domain, the 4/5-loop, the hinge region, and the DNA binding domain. The EPR spectra of labeled CooA variants are compared across three functional states: Fe(III) "locked off", Fe(II)-CO "on", and Fe(II)-CO bound to DNA. We observe changes in the multicomponent EPR spectra at each location; most notably in the hinge region and DNA binding domain, broadening the description of the CooA allosteric mechanism to include the role of protein dynamics in DNA binding. DNA-dependent changes in IR vibrational frequency and band broadening further suggest that there is conformational heterogeneity in the active WT protein and that DNA binding alters the environment of the heme-bound CO.

N-terminal domain of polypyrimidine-tract binding protein is a dynamic folding platform for adaptive RNA recognition

The N-terminal RNA recognition motif domain (RRM1) of polypyrimidine tract binding protein (PTB) forms an additional C-terminal helix α3, which docks to one edge of the β-sheet upon binding to a stem-loop RNA containing a UCUUU pentaloop. Importantly, α3 does not contact the RNA. The α3 helix therefore represents an allosteric means to regulate the conformation of adjacent domains in PTB upon binding structured RNAs. Here we investigate the process of dynamic adaptation by stem-loop RNA and RRM1 using NMR and MD in order to obtain mechanistic insights on how this allostery is achieved. Relaxation data and NMR structure determination of the free protein show that α3 is partially ordered and interacts with the domain transiently. Stem-loop RNA binding quenches fast time scale dynamics and α3 becomes ordered, however microsecond dynamics at the protein-RNA interface is observed. MD shows how RRM1 binding to the stem-loop RNA is coupled to the stabilization of the C-terminal helix and helps to transduce differences in RNA loop sequence into changes in α3 length and order. IRES assays of full length PTB and a mutant with altered dynamics in the α3 region show that this dynamic allostery influences PTB function in cultured HEK293T cells.

Detailed Study of the Interactions between Glycopolymers in the Presence of Metal Ions through Quartz Crystal Microbalance Method

Polymer self-assemblies driven by enthalpic interactions, such as hydrogen bonding and electrostatic interactions, exhibit distinct properties compared to those driven by hydrophobic interactions. Carbohydrate-carbohydrate interactions, which are observed in physiological phenomena, also fall under enthalpic interactions. Our group previously reported on self-assemblies of methacrylate-type glycopolymers carrying mannose units in the presence of calcium ions; however, a detailed study of these interactions was lacking. In this work, we investigated the interactions between glycopolymers using the quartz crystal microbalance (QCM) method. Our quantitative analysis revealed that the interactions between the glycopolymers were influenced by the carbohydrate structures in the side chains, the types of divalent metal ions, and the structures of the polymer main chains. Notably, the strongest interaction was observed in the combination of methacrylate-type glycopolymers carrying mannose units and calcium ions, demonstrating their potential as a driving force for polymer self-assembly.

Pitfalls in measurements of R1 relaxation rates of protein backbone 15N nuclei

The dynamics of the backbone and side-chains of protein are routinely studied by interpreting experimentally determined 15N spin relaxation rates. R1(15N), the longitudinal relaxation rate, reports on fast motions and encodes, together with the transverse relaxation R2, structural information about the shape of the molecule and the orientation of the amide bond vectors in the internal diffusion frame. Determining error-free 15N longitudinal relaxation rates remains a challenge for small, disordered, and medium-sized proteins. Here, we show that mono-exponential fitting is sufficient, with no statistical preference for bi-exponential fitting up to 800 MHz. A detailed comparison of the TROSY and HSQC techniques at medium and high fields showed no statistically significant differences. The least error-prone DD/CSA interference removal technique is the selective inversion of amide signals while avoiding water resonance. The exchange of amide with solvent deuterons appears to affect the rate R1 of solvent-exposed amides in all fields tested and in each DD/CSA interference removal technique in a statistically significant manner. In summary, the most accurate R1(15N) rates in proteins are achieved by selective amide inversion, without the addition of D2O. Importantly, at high magnetic fields stronger than 800 MHz, when non-mono-exponential decay is involved, it is advisable to consider elimination of the shortest delays (typically up to 0.32 s) or bi-exponential fitting.

Conformational Modulation of a Mobile Loop Controls Catalysis in the (βα)8-Barrel Enzyme of Histidine Biosynthesis HisF

The overall significance of loop motions for enzymatic activity is generally accepted. However, it has largely remained unclear whether and how such motions can control different steps of catalysis. We have studied this problem on the example of the mobile active site β1α1-loop (loop1) of the (βα)8-barrel enzyme HisF, which is the cyclase subunit of imidazole glycerol phosphate synthase. Loop1 variants containing single mutations of conserved amino acids showed drastically reduced rates for the turnover of the substrates N'-[(5'-phosphoribulosyl) formimino]-5-aminoimidazole-4-carboxamide ribonucleotide (PrFAR) and ammonia to the products imidazole glycerol phosphate (ImGP) and 5-aminoimidazole-4-carboxamide-ribotide (AICAR). A comprehensive mechanistic analysis including stopped-flow kinetics, X-ray crystallography, NMR spectroscopy, and molecular dynamics simulations detected three conformations of loop1 (open, detached, closed) whose populations differed between wild-type HisF and functionally affected loop1 variants. Transient stopped-flow kinetic experiments demonstrated that wt-HisF binds PrFAR by an induced-fit mechanism whereas catalytically impaired loop1 variants bind PrFAR by a simple two-state mechanism. Our findings suggest that PrFAR-induced formation of the closed conformation of loop1 brings active site residues in a productive orientation for chemical turnover, which we show to be the rate-limiting step of HisF catalysis. After the cyclase reaction, the closed loop conformation is destabilized, which favors the formation of detached and open conformations and hence facilitates the release of the products ImGP and AICAR. Our data demonstrate how different conformations of active site loops contribute to different catalytic steps, a finding that is presumably of broad relevance for the reaction mechanisms of (βα)8-barrel enzymes and beyond.

Parsing Dynamics of Protein Backbone NH and Side-Chain Methyl Groups using Molecular Dynamics Simulations

Experimental NMR spectroscopy and theoretical molecular dynamics (MD) simulations provide complementary insights into protein conformational dynamics and hence into biological function. The present work describes an extensive set of backbone NH and side-chain methyl group generalized order parameters for the Escherichia coli ribonuclease HI (RNH) enzyme derived from 2-μs microsecond MD simulations using the OPLS4 and AMBER-FF19SB force fields. The simulated generalized order parameters are compared with values derived from NMR 15N and 13CH2D spin relaxation measurements. The squares of the generalized order parameters, S2 for the N-H bond vector and Saxis2 for the methyl group symmetry axis, characterize the equilibrium distribution of vector orientations in a molecular frame of reference. Optimal agreement between simulated and experimental results was obtained by averaging S2 or Saxis2 calculated by dividing the simulated trajectories into 50 ns blocks (∼five times the rotational diffusion correlation time for RNH). With this procedure, the median absolute deviations (MAD) between experimental and simulated values of S2 and Saxis2 are 0.030 (NH) and 0.061 (CH3) for OPLS4 and 0.041 (NH) and 0.078 (CH3) for AMBER-FF19SB. The MAD between OPLS4 and AMBER-FF19SB are 0.021 (NH) and 0.072 (CH3). The generalized order parameters for the methyl group symmetry axis can be decomposed into contributions from backbone fluctuations, between-rotamer dihedral angle transitions, and within-rotamer dihedral angle fluctuations. Analysis of the simulation trajectories shows that (i) backbone and side chain conformational fluctuations exhibit little correlation and that (ii) fluctuations within rotamers are limited and highly uniform with values that depend on the number of dihedral angles considered. Low values of Saxis2, indicative of enhanced side-chain flexibility, result from between-rotamer transitions that can be enhanced by increased local backbone flexibility.

Insights into mechanisms of MALT1 allostery from NMR and AlphaFold dynamic analyses

Mucosa-associated lymphoid tissue lymphoma-translocation protein 1 (MALT1) is an attractive target for the development of modulatory compounds in the treatment of lymphoma and other cancers. While the three-dimensional structure of MALT1 has been previously determined through X-ray analysis, its dynamic behaviour in solution has remained unexplored. We present here dynamic analyses of the apo MALT1 form along with the E549A mutation. This investigation used NMR 15N relaxation and NOE measurements between side-chain methyl groups. Our findings confirm that MALT1 exists as a monomer in solution, and demonstrate that the domains display semi-independent movements in relation to each other. Our dynamic study, covering multiple time scales, along with the assessment of conformational populations by Molecular Dynamic simulations, Alpha Fold modelling and PCA analysis, put the side chain of residue W580 in an inward position, shedding light at potential mechanisms underlying the allosteric regulation of this enzyme.

NMR Dynamic View of the Destabilization of WW4 Domain by Chaotropic GdmCl and NaSCN

GdmCl and NaSCN are two strong chaotropic salts commonly used in protein folding and stability studies, but their microscopic mechanisms remain enigmatic. Here, by CD and NMR, we investigated their effects on conformations, stability, binding and backbone dynamics on ps-ns and µs-ms time scales of a 39-residue but well-folded WW4 domain at salt concentrations ≤200 mM. Up to 200 mM, both denaturants did not alter the tertiary packing of WW4, but GdmCl exerted more severe destabilization than NaSCN. Intriguingly, GdmCl had only weak binding to amide protons, while NaSCN showed extensive binding to both hydrophobic side chains and amide protons. Neither denaturant significantly affected the overall ps-ns backbone dynamics, but they distinctively altered µs-ms backbone dynamics. This study unveils that GdmCl and NaSCN destabilize a protein before the global unfolding occurs with differential binding properties and µs-ms backbone dynamics, implying the absence of a simple correlation between thermodynamic stability and backbone dynamics of WW4 at both ps-ns and µs-ms time scales.

Prediction of order parameters based on protein NMR structure ensemble and machine learning

The fast motions of proteins at the picosecond to nanosecond timescale, known as fast dynamics, are closely related to protein conformational entropy and rearrangement, which in turn affect catalysis, ligand binding and protein allosteric effects. The most used NMR approach to study fast protein dynamics is the model free method, which uses order parameter S2 to describe the amplitude of the internal motion of local group. However, to obtain order parameter through NMR experiments is quite complex and lengthy. In this paper, we present a machine learning approach for predicting backbone 1H-15N order parameters based on protein NMR structure ensemble. A random forest model is used to learn the relationship between order parameters and structural features. Our method achieves high accuracy in predicting backbone 1H-15N order parameters for a test dataset of 10 proteins, with a Pearson correlation coefficient of 0.817 and a root-mean-square error of 0.131.

Calcium mediated static and dynamic allostery in S100A12: Implications for target recognition by S100 proteins

Structure and functions of S100 proteins are regulated by two distinct calcium binding EF hand motifs. In this work, we used solution-state NMR spectroscopy to investigate the cooperativity between the two calcium binding sites and map the allosteric changes at the target binding site. To parse the contribution of the individual calcium binding events, variants of S100A12 were designed to selectively bind calcium to either the EF-I (N63A) or EF-II (E31A) loop, respectively. Detailed analysis of the backbone chemical shifts for wildtype protein and its mutants indicates that calcium binding to the canonical EF-II loop is the principal trigger for the conformational switch between 'closed' apo to the 'open' Ca2+ -bound conformation of the protein. Elimination of binding in S100-specific EF-I loop has limited impact on the calcium binding affinity of the EF-II loop and the concomitant structural rearrangement. In contrast, deletion of binding in the EF-II loop significantly attenuates calcium affinity in the EF-I loop and the structure adopts a 'closed' apo-like conformation. Analysis of experimental amide nitrogen (15 N) relaxation rates (R1 , R2 , and 15 N-{1 H} NOE) and molecular dynamics (MD) simulations demonstrate that the calcium bound state is relatively floppy with pico-nanosecond motions induced in functionally relevant domains responsible for target recognition such as the hinge domain and the C-terminal residues. Experimental relaxation studies combined with MD simulations show that while calcium binding in the EF-I loop alone does not induce significant motions in the polypeptide chain, EF-I regulates fluctuations in the polypeptide in the presence of bound calcium in the EF-II loop. These results offer novel insights into the dynamic regulation of target recognition by calcium binding and unravels the role of cooperativity between the two calcium binding events in S100A12.

Structure and dynamics of the cyanobacterial regulator SipA

The small, 78-residue long, regulator SipA interacts with the non-bleaching sensor histidine kinase (NblS). We have solved the solution structure of SipA on the basis of 990 nuclear Overhauser effect- (NOE-) derived distance constraints. The average pairwise root-mean-square deviation (RMSD) for the twenty best structures for the backbone residues, obtained by CYANA, was 1.35 ± 0.21 Å, and 1.90 ± 0.16 Å when all heavy atoms were considered (the target function of CYANA was 0.540 ± 0.08). The structure is that of a β-II class protein, basically formed by a five-stranded β-sheet composed of antiparallel strands following the arrangement: Gly6-Leu11 (β-strand 1), which packs against Leu66-Val69 (β-strand 5) on one side, and against Gly36-Thr42 (β-strand 2) on the other side; Trp50-Phe54 (β-strand 3); and Gly57-Leu60 (β-strand 4). The protein is highly mobile, as shown by measurements of R1, R2, NOE and ηxy relaxation parameters, with an average order parameter () of 0.70; this mobility encompasses movements in different time scales. We hypothesize that this high flexibility allows the interaction with other proteins (among them NblS), and it explains the large conformational stability of SipA.

Analytical Framework to Understand the Origins of Methyl Side-Chain Dynamics in Protein Assemblies

Side-chain motions play an important role in understanding protein structure, dynamics, protein-protein, and protein-ligand interactions. However, our understanding of protein side-chain dynamics is currently limited by the lack of analytical tools. Here, we present a novel analytical framework employing experimental nuclear magnetic resonance (NMR) relaxation measurements at atomic resolution combined with molecular dynamics (MD) simulation to characterize with a high level of detail the methyl side-chain dynamics in insoluble protein assemblies, using amyloid fibrils formed by the prion HET-s. We use MD simulation to interpret experimental results, where rotameric hops, including methyl group rotation and χ1/χ2 rotations, cannot be completely described with a single correlation time but rather sample a broad distribution of correlation times, resulting from continuously changing local structure in the fibril. Backbone motion similarly samples a broad range of correlation times, from ∼100 ps to μs, although resulting from mostly different dynamic processes; nonetheless, we find that the backbone is not fully decoupled from the side-chain motion, where changes in side-chain dynamics influence backbone motion and vice versa. While the complexity of side-chain motion in protein assemblies makes it very challenging to obtain perfect agreement between experiment and simulation, our analytical framework improves the interpretation of experimental dynamics measurements for complex protein assemblies.

Three-dimensional solution structure, dynamics and binding of thioredoxin m from Pisum sativum

Thioredoxins (TRXs) are ubiquitous small, globular proteins involved in cell redox processes. In this work, we report the solution structure of TRX m from Pisum sativum (pea), which has been determined on the basis of 1444 nuclear Overhauser effect- (NOE-) derived distance constraints. The average pairwise root-mean-square deviation (RMSD) for the 20 best structures for the backbone residues (Val7-Glu102) was 1.42 ± 0.15 Å, and 1.97 ± 0.15 Å when all heavy atoms were considered. The structure corresponds to the typical fold of TRXs, with a central five-stranded β-sheet flanked by four α-helices. Some residues had an important exchange dynamic contribution: those around the active site; at the C terminus of β-strand 3; and in the loop preceding α-helix 4. Smaller NOE values were observed at the N and C-terminal residues forming the elements of the secondary structure or, alternatively, in the residues belonging to the loops between those elements. A peptide derived from pea fructose-1,6-biphosphatase (FBPase), comprising the preceding region to the regulatory sequence of FBPase (residues Glu152 to Gln179), was bound to TRX m with an affinity in the low micromolar range, as measured by fluorescence and NMR titration experiments. Upon peptide addition, the intensities of the cross-peaks of all the residues of TRX m were affected, as shown by NMR. The value of the dissociation constant of the peptide from TRX m was larger than that of the intact FBPase, indicating that there are additional factors in other regions of the polypeptide chain of the latter protein affecting the binding to thioredoxin.

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.

Probing the dynamic landscape of peptides in molecular assemblies by synergized NMR experiments and MD simulations

Peptides or proteins containing small biomolecular aggregates, such as micelles, bicelles, droplets and nanodiscs, are pivotal in many fields ranging from structural biology to pharmaceutics. Monitoring dynamics of such systems has been limited by the lack of experimental methods that could directly detect their fast (picosecond to nanosecond) timescale dynamics. Spin relaxation times from NMR experiments are sensitive to such motions, but their interpretation for biomolecular aggregates is not straightforward. Here we show that the dynamic landscape of peptide-containing molecular assemblies can be determined by a synergistic combination of solution state NMR experiments and molecular dynamics (MD) simulations. Solution state NMR experiments are straightforward to implement without an excessive amount of sample, while direct combination of spin relaxation data to MD simulations enables interpretation of dynamic landscapes of peptides and other aggregated molecules. To demonstrate this, we interpret NMR data from transmembrane, peripheral, and tail anchored peptides embedded in micelles. Our results indicate that peptides and detergent molecules do not rotate together as a rigid body, but peptides rotate in a viscous medium composed of detergent micelle. Spin relaxation times also provide indirect information on peptide conformational ensembles. This work gives new perspectives on peptide dynamics in complex biomolecular assemblies.

Insights into Modeling Approaches in Chemistry: Assessing Ligand-Protein Binding Thermodynamics Based on Rigid-Flexible Model Molecules

In the field of chemistry, model compounds find extensive use for investigating complex objects. One prime example of such object is the protein-ligand supramolecular interaction. Prediction the enthalpic and entropic contribution to the free energy associated with this process, as well as the structural and dynamic characteristics of protein-ligand complexes poses considerable challenges. This review exemplifies modeling approaches used to study protein-ligand binding (PLB) thermodynamics by employing pairs of conformationally constrained/flexible model molecules. Strategically designing the model molecules can reduce the number of variables that influence thermodynamic parameters. This enables scientists to gain deeper insights into the enthalpy and entropy of PLB, which is relevant for medicinal chemistry and drug design. The model studies reviewed here demonstrate that rigidifying ligands may induce compensating changes in the enthalpy and entropy of binding. Some "rules of thumb" have started to emerge on how to minimize entropy-enthalpy compensation and design efficient rigidified or flexible ligands.

NMR Relaxation Experiments Probe Monomer-Fibril Interaction and Identify Critical Interacting Residues Responsible for Distinct Tau Fibril Morphologies

Tau aggregation is governed by secondary processes, a major pathological pathway for tau protein fibril propagation, yet its molecular mechanism remains unknown. This work uses saturation transfer and lifetime line-broadening experiments to identify the critical residues involved in these secondary processes. Distinct residue-specific NMR relaxation parameters were obtained for the truncated three repeat tau construct (K19) in equilibrium with structurally different, self-aggregated (saK19) or heparin-induced (hK19) fibrils. The interacting residues are restricted to R3 repeat for hK19 and to R3, R4, and R' repeats for saK19 fibrils. Furthermore, the relaxation profiles of tau monomers in equilibrium with the structurally comparable, in vitro pathological fibrils (tauAD and tauCTE) were similar but distinct from hK19 or saK19 fibrils. Thus, residue-specific relaxation identifies the important residues involved in the binding of monomers to the fibrils. The relaxation profile of the monomers in equilibrium with the NMR invisible fibril seeds potentially distinguishes the distinct structures of tau fibrils.

Intracellular environment can change protein conformational dynamics in cells through weak interactions

Conformational dynamics is important for protein functions, many of which are performed in cells. How the intracellular environment may affect protein conformational dynamics is largely unknown. Here, loop conformational dynamics is studied for a model protein in Escherichia coli cells by using nuclear magnetic resonance (NMR) spectroscopy. The weak interactions between the protein and surrounding macromolecules in cells hinder the protein rotational diffusion, which extends the dynamic detection timescale up to microseconds by the NMR spin relaxation method. The loop picosecond to microsecond dynamics is confirmed by nanoparticle-assisted spin relaxation and residual dipolar coupling methods. The loop interactions with the intracellular environment are perturbed through point mutation of the loop sequence. For the sequence of the protein that interacts stronger with surrounding macromolecules, the loop becomes more rigid in cells. In contrast, the mutational effect on the loop dynamics in vitro is small. This study provides direct evidence that the intracellular environment can modify protein loop conformational dynamics through weak interactions.

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.

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.

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.

Slowly Relaxing Local Structure Analysis of 15N Relaxation from the Proteins p50 and Human Neutrophil Gelatinase-Associated Lipocalin: New Insights into the Dynamic Structure of β-Barrel Proteins

Nuclear magnetic resonance relaxation analysis is a powerful method for studying the internal mobility of proteins. We have developed for analysis the slowly relaxing local structure (SRLS) approach. SRLS is general in its nature in several respects, including the tensorial representation of the physical quantities comprising the dynamic model. By controlling tensor symmetry, a broad range of systems can be treated with physical relevance, typically with data-fitting techniques. In simple limits, SRLS yields the traditional model-free (MF) method. In the present context, MF simplicity means featuring the highest possible tensor symmetry. This renders MF-based data-fitting susceptible to the usage of fit parameters, yielding physically ill-defined results. A typical candidate is the R_ex term, devised to represent ms-μs motions but often invoked by the fitting scheme just to improve the statistics. Here, we consider two such cases using the N-H bond as probe and the proteins p50 and human neutrophil gelatinase-associated lipocalin as paradigm systems. We illustrate the harm caused by the physically unjustified involvement of R_ex in MF-based ¹⁵N relaxation analysis. Then, we show that forgoing the usage of R_ex, SRLS analysis of the very same experimental data provides interesting new information.

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.

Identification of allosteric fingerprints of alpha-synuclein aggregates in matrix metalloprotease-1 and substrate-specific virtual screening with single molecule insights

Alpha-synuclein (aSyn) has implications in pathological protein aggregations in neurodegeneration. Matrix metalloproteases (MMPs) are broad-spectrum proteases and cleave aSyn, leading to aggregation. Previous reports showed that allosteric communications between the two domains of MMP1 on collagen fibril and fibrin depend on substrates, activity, and ligands. This paper reports quantification of allostery using single molecule measurements of MMP1 dynamics on aSyn-induced aggregates by calculating Forster Resonance Energy Transfer (FRET) between two dyes attached to the catalytic and hemopexin domains of MMP1. The two domains of MMP1 prefer open conformations that are inhibited by a single point mutation E219Q of MMP1 and tetracycline, an MMP inhibitor. A two-state Poisson process describes the interdomain dynamics, where the two states and kinetic rates of interconversion between them are obtained from histograms and autocorrelations of FRET values. Since a crystal structure of aSyn-bound MMP1 is unavailable, binding poses were predicted by molecular docking of MMP1 with aSyn using ClusPro. MMP1 dynamics were simulated using predicted binding poses and compared with the experimental interdomain dynamics to identify an appropriate pose. The selected aSyn-MMP1 binding pose near aSyn residue K45 was simulated and analyzed to define conformational changes at the catalytic site. Allosteric residues in aSyn-bound MMP1 exhibiting strong correlations with the catalytic motif residues were compared with allosteric residues in free MMP1, and aSyn-specific residues were identified. The allosteric residues in aSyn-bound MMP1 are K281, T283, G292, G327, L328, E329, R337, F343, G345, N346, Y348, G353, Q354, D363, Y365, S366, S367, F368, P371, R372, V374, K375, A379, F391, A394, R399, M414, F419, V426, and C466. Shannon entropy was defined to quantify MMP1 dynamics. Virtual screening was performed against a site on selected aSyn-MMP1 binding poses, which showed that lead molecules differ between free MMP1 and substrate-bound MMP1. Also, identifying aSyn-specific allosteric residues in MMP1 enabled further selection of lead molecules. In other words, virtual screening needs to take substrates into account for potential substrate-specific control of MMP1 activity in the future. Molecular understanding of interactions between MMP1 and aSyn-induced aggregates may open up the possibility of degrading aggregates by targeting MMPs.

In-Cell Structural Biology by NMR: The Benefits of the Atomic Scale

In-cell structural biology aims at extracting structural information about proteins or nucleic acids in their native, cellular environment. This emerging field holds great promise and is already providing new facts and outlooks of interest at both fundamental and applied levels. NMR spectroscopy has important contributions on this stage: It brings information on a broad variety of nuclei at the atomic scale, which ensures its great versatility and uniqueness. Here, we detail the methods, the fundamental knowledge, and the applications in biomedical engineering related to in-cell structural biology by NMR. We finally propose a brief overview of the main other techniques in the field (EPR, smFRET, cryo-ET, etc.) to draw some advisable developments for in-cell NMR. In the era of large-scale screenings and deep learning, both accurate and qualitative experimental evidence are as essential as ever to understand the interior life of cells. In-cell structural biology by NMR spectroscopy can generate such a knowledge, and it does so at the atomic scale. This review is meant to deliver comprehensive but accessible information, with advanced technical details and reflections on the methods, the nature of the results, and the future of the field.

Thermodynamics of globular protein native structure

The temperature dependence of the partial heat capacity of the native protein structure in an aqueous solution has been analyzed. It is shown that the strictly linear temperature dependence is due to the contributions of the vibrational and conformational components, which indicates volume consistensy and the absence of conformational transitions up to the main two-state transition. The two-level structural and functional organization of the protein three-dimensional structure are considered in relation to the energy and conformational entropy properties in accordance with the principles of the organization of the protein macromolecule.Communicated by Ramaswamy H. Sarma.

Structures of highly flexible intracellular domain of human α7 nicotinic acetylcholine receptor

The intracellular domain (ICD) of Cys-loop receptors mediates diverse functions. To date, no structure of a full-length ICD is available due to challenges stemming from its dynamic nature. Here, combining nuclear magnetic resonance (NMR) and electron spin resonance experiments with Rosetta computations, we determine full-length ICD structures of the human α7 nicotinic acetylcholine receptor in a resting state. We show that ~57% of the ICD residues are in highly flexible regions, primarily in a large loop (loop L) with the most mobile segment spanning ~50 Å from the central channel axis. Loop L is anchored onto the MA helix and virtually forms two smaller loops, thereby increasing its stability. Previously known motifs for cytoplasmic binding, regulation, and signaling are found in both the helices and disordered flexible regions, supporting the essential role of the ICD conformational plasticity in orchestrating a broad range of biological processes.

The intracellular domain (ICD) of Cys-loop receptors mediates many of their functions, but no complete structure of a Cys-loop receptor ICD is available to date. Here, the authors combine NMR and ESR spectroscopy to determine the full-length ICD structures of the human α7 nicotinic acetylcholine receptor (α7nAChR).

Double Mutant of Chymotrypsin Inhibitor 2 Stabilized through Increased Conformational Entropy

The conformational heterogeneity of a folded protein can affect not only its function but also stability and folding. We recently discovered and characterized a stabilized double mutant (L49I/I57V) of the protein CI2 and showed that state-of-the-art prediction methods could not predict the increased stability relative to the wild-type protein. Here, we have examined whether changed native-state dynamics, and resulting entropy changes, can explain the stability changes in the double mutant protein, as well as the two single mutant forms. We have combined NMR relaxation measurements of the ps-ns dynamics of amide groups in the backbone and the methyl groups in the side chains with molecular dynamics simulations to quantify the native-state dynamics. The NMR experiments reveal that the mutations have different effects on the conformational flexibility of CI2: a reduction in conformational dynamics (and entropy estimated from this) of the native state of the L49I variant correlates with its decreased stability, while increased dynamics of the I57V and L49I/I57V variants correlates with their increased stability. These findings suggest that explicitly accounting for changes in native-state entropy might be needed to improve the predictions of the effect of mutations on protein stability.

Ion-dependent structure, dynamics, and allosteric coupling in a non-selective cation channel

The selectivity filter (SF) determines which ions are efficiently conducted through ion channel pores. NaK is a non-selective cation channel that conducts Na⁺ and K⁺ with equal efficiency. Crystal structures of NaK suggested a rigid SF structure, but later solid-state NMR and MD simulations questioned this interpretation. Here, we use solution NMR to characterize how bound Na⁺ vs. K⁺ affects NaK SF structure and dynamics. We find that the extracellular end of the SF is flexible on the ps-ns timescale regardless of bound ion. On a slower timescale, we observe a structural change between the Na⁺ and K⁺-bound states, accompanied by increased structural heterogeneity in Na⁺. We also show direct evidence that the SF structure is communicated to the pore via I88 on the M2 helix. These results support a dynamic SF with multiple conformations involved in non-selective conduction. Our data also demonstrate allosteric coupling between the SF and pore-lining helices in a non-selective cation channel that is analogous to the allosteric coupling previously demonstrated for K⁺-selective channels, supporting the generality of this model.

NaK is a bacterial non-selective cation channel. Here, the authors use solution NMR to show that selectivity filter (SF) in NaK is dynamic, with structural differences between the Na+ and K + -bound states. The conformation of the SF is communicated to the pore-lining helices similarly as in the K + -selective channels.

TRACT revisited: an algebraic solution for determining overall rotational correlation times from cross-correlated relaxation rates

Accurate rotational correlation times ([Formula: see text]) are critical for quantitative analysis of fast timescale NMR dynamics. As molecular weights increase, the classic derivation of [Formula: see text] using transverse and longitudinal relaxation rates becomes increasingly unsuitable due to the non-trivial contribution of remote dipole-dipole interactions to longitudinal relaxation. Derivations using cross-correlated relaxation experiments, such as TRACT, overcome these limitations but are erroneously calculated in 65% of the citing literature. Herein, we developed an algebraic solutions to the Goldman relationship that facilitate rapid, point-by-point calculations for straightforward identification of appropriate spectral regions where global tumbling is likely to be dominant. The rigid-body approximation of the Goldman relationship has been previously shown to underestimate TRACT-based rotational correlation time estimates. This motivated us to develop a second algebraic solution that employs a simplified model-free spectral density function including an order parameter term that could, in principle, be set to an average backbone S² ≈ 0.9 to further improve the accuracy of [Formula: see text] estimation. These solutions enabled us to explore the boundaries of the Goldman relationship as a function of the H-N internuclear distance ([Formula: see text]), difference of the two principal components of the axially-symmetric ¹⁵N CSA tensor ([Formula: see text]), and angle of the CSA tensor relative to the N-H bond vector ([Formula: see text]). We hope our algebraic solutions and analytical strategies will increase the accuracy and application of the TRACT experiment.

Influence of Monomer Structures for Polymeric Multivalent Ligands: Consideration of the Molecular Mobility of Glycopolymers

Molecular mobility is important for interactions of biofunctional polymers with target molecules. Monomer structures for synthetic biofunctional polymers are usually selected based on their compatibility with polymerization systems, whereas the influence of monomer structures on the interaction with target molecules is hardly considered. In this report, we evaluate the correlation between the monomer structures of glycopolymers and their interactions with concanavalin A (ConA) with respect to the molecular mobility. Two types of glycopolymers bearing mannose are synthesized with acrylamide or acrylate monomers. Despite the similar structures, except for amide or ester bonds in the side chains, the acrylate-type glycopolymers exhibit stronger interaction with ConA both in the isothermal titration calorimetry measurement and in a hemagglutination inhibition assay. Characterization of the acrylate-type glycopolymers suggests that the higher binding constant arises from the higher molecular mobility of mannose units, which results from the rotational freedom of ester bonds in their side chains.

Structural Dynamics from NMR Relaxation by SRLS Analysis: Local Geometry, Potential Energy Landscapes, and Spectral Densities

We have developed the two-body coupled-rotator slowly relaxing local structure (SRLS) approach for elucidating protein dynamics by nuclear magnetic resonance (NMR) relaxation. The rotators are represented by diffusion tensors D₁ for overall protein tumbling and D₂ for locally ordered probe motion. D₁ and D₂ are coupled dynamically by a potential, u, typically given by linear combinations of the Wigner functions D₀₀² and (D₀₂² + D_0-2²). Until now, our SRLS analyses provided the tensors, D₁ and D₂, the potential, u, and the geometric link between SRLS and NMR. Here we enhance this description by also examining the SRLS spectral densities obtained by solving the SRLS Smoluchowski equation. In addition, we show that the form of u specified above complies with two NMR-detected potential energy landscapes representing preferential ordering along N-H or C^α-C^α. Pictorial illustrations thereof are provided. The extended SRLS analysis is applied to ¹⁵N-H relaxation from the carbohydrate recognition domain of galectin-3 (Gal3C) in complex with two diastereomeric ligands, S and R. We find that D₂ is isotropic with a principal value, D₂, of 10¹⁰ s^-1 on average, and it is faster in the strands β₃, β₅, and β₈. The potential, u, is strong (∼20 kT); it is slightly rhombic when N-H is the main ordering axis and highly rhombic when C^α-C^α is the main ordering axis. Gal3C-S exhibits primarily preferential ordering along C^α-C^α; Gal3C-R exhibits both types of ordering. The binding-associated polypeptide chain segment of Gal3C-S is homogeneous, whereas that of Gal3C-R is diversified, with regard to D₂ and ordering preference. We associate these features with the previously determined diminished binding constant of Gal3C-R in comparison with Gal3C-S. Thus, the present study enhances the SRLS analysis, in general, and provides new insights into the dynamic structure and binding properties of Gal3C-S and Gal3C-R, in particular.

Aha1 Exhibits Distinctive Dynamics Behavior and Chaperone-Like Activity

Aha1 is the only co-chaperone known to strongly stimulate the ATPase activity of Hsp90. Meanwhile, besides the well-studied co-chaperone function, human Aha1 has also been demonstrated to exhibit chaperoning activity against stress-denatured proteins. To provide structural insights for a better understanding of Aha1's co-chaperone and chaperone-like activities, nuclear magnetic resonance (NMR) techniques were used to reveal the unique structure and internal dynamics features of full-length human Aha1. We then found that, in solution, both the two domains of Aha1 presented distinctive thermal stabilities and dynamics behaviors defined by their primary sequences and three-dimensional structures. The low thermal stability (melting temperature of Aha1^28-162: 54.45 °C) and the internal dynamics featured with slow motions on the µs-ms time scale were detected for Aha1's N-terminal domain (Aha1N). The aforementioned experimental results suggest that Aha1N is in an energy-unfavorable state, which would therefore thermostatically favor the interaction of Aha1N with its partner proteins such as Hsp90's middle domain. Differently from Aha1N, Aha1C (Aha1's C-terminal domain) exhibited enhanced thermal stability (melting temperature of Aha1^204-335: 72.41 °C) and the internal dynamics featured with intermediate motions on the ps-ns time scale. Aha1C's thermal and structural stabilities make it competent for the stabilization of the exposed hydrophobic groove of dimerized Hsp90's N-terminal domain. Of note, according to the NMR data and the thermal shift results, although the very N-terminal region (M1-W27) and the C-terminal relaxin-like factor (RLF) motif showed no tight contacts with the remaining parts of human Aha1, they were identified to play important roles in the recognition of intrinsically disordered pathological α-synuclein.

Bioinformatic Analysis of Structure and Function of LIM Domains of Human Zyxin Family Proteins

Members of the human Zyxin family are LIM domain-containing proteins that perform critical cellular functions and are indispensable for cellular integrity. Despite their importance, not much is known about their structure, functions, interactions and dynamics. To provide insights into these, we used a set of in-silico tools and databases and analyzed their amino acid sequence, phylogeny, post-translational modifications, structure-dynamics, molecular interactions, and functions. Our analysis revealed that zyxin members are ohnologs. Presence of a conserved nuclear export signal composed of LxxLxL/LxxxLxL consensus sequence, as well as a possible nuclear localization signal, suggesting that Zyxin family members may have nuclear and cytoplasmic roles. The molecular modeling and structural analysis indicated that Zyxin family LIM domains share similarities with transcriptional regulators and have positively charged electrostatic patches, which may indicate that they have previously unanticipated nucleic acid binding properties. Intrinsic dynamics analysis of Lim domains suggest that only Lim1 has similar internal dynamics properties, unlike Lim2/3. Furthermore, we analyzed protein expression and mutational frequency in various malignancies, as well as mapped protein-protein interaction networks they are involved in. Overall, our comprehensive bioinformatic analysis suggests that these proteins may play important roles in mediating protein-protein and protein-nucleic acid interactions.

On Catalytic Kinetics of Enzymes

Classical enzyme kinetic theories are summarized and linked with modern discoveries here. The sequential catalytic events along time axis by enzyme are analyzed at the molecular level, and by using master equations, this writing tries to connect the microscopic molecular behavior of enzyme to kinetic data (like velocity and catalytic coefficient k) obtained in experiment: 1/k = t equals to the sum of the times taken by the constituent individual steps. The relationships between catalytic coefficient k, catalytic rate or velocity, the amount of time taken by each step and physical or biochemical conditions of the system are discussed, and the perspective and hypothetic equations proposed here regarding diffusion, conformational change, chemical conversion, product release steps and the whole catalytic cycle provide an interpretation of previous experimental observations and can be testified by future experiments.

SRLS Analysis of 15N-1H NMR Relaxation from the Protein S100A1: Dynamic Structure, Calcium Binding, and Related Changes in Conformational Entropy

We report on amide (N-H) NMR relaxation from the protein S100A1 analyzed with the slowly relaxing local structure (SRLS) approach. S100A1 comprises two calcium-binding "EF-hands" (helix-loop-helix motifs) connected by a linker. The dynamic structure of this protein, in both calcium-free and calcium-bound form, is described as the restricted local N-H motion coupled to isotropic protein tumbling. The restrictions are given by a rhombic potential, u (∼10 kT), the local motion by a diffusion tensor with rate constant D₂ (∼10⁹ s^-1), and principal axis tilted from the N-H bond at angle β (10-20°). This parameter combination provides a physically insightful picture of the dynamic structure of S100A1 from the N-H bond perspective. Calcium binding primarily affects the C-terminal EF-hand, among others slowing down the motion of helices III and IV approximately 10-fold. Overall, it brings about significant changes in the shape of the local potential, u, and the orientation of the local diffusion axis, β. Conformational entropy derived from u makes an unfavorable entropic contribution to the free energy of calcium binding estimated at 8.6 ± 0.5 kJ/mol. The N-terminal EF-hand undergoes moderate changes. These findings provide new insights into the calcium-binding process. The same data were analyzed previously with the extended model-free (EMF) method, which is a simple limit of SRLS. In that interpretation, the protein tumbles anisotropically. Locally, calcium binding increases ordering in the loops of S100A1 and conformational exchange (R_ex) in the helices of its N-terminal EF-hand. These are very unusual features. We show that they most likely stem from problematic data-fitting, oversimplifications inherent in EMF, and experimental imperfections. R_ex is shown to be mainly a fit parameter. By reanalyzing the experimental data with SRLS, which is largely free of these deficiencies, we obtain-as delineated above-physically-relevant structural, kinetic, geometric, and binding information.

Structure, self-assembly, and properties of a truncated reflectin variant

Naturally occurring and recombinant protein-based materials are frequently employed for the study of fundamental biological processes and are often leveraged for applications in areas as diverse as electronics, optics, bioengineering, medicine, and even fashion. Within this context, unique structural proteins known as reflectins have recently attracted substantial attention due to their key roles in the fascinating color-changing capabilities of cephalopods and their technological potential as biophotonic and bioelectronic materials. However, progress toward understanding reflectins has been hindered by their atypical aromatic and charged residue-enriched sequences, extreme sensitivities to subtle changes in environmental conditions, and well-known propensities for aggregation. Herein, we elucidate the structure of a reflectin variant at the molecular level, demonstrate a straightforward mechanical agitation-based methodology for controlling this variant's hierarchical assembly, and establish a direct correlation between the protein's structural characteristics and intrinsic optical properties. Altogether, our findings address multiple challenges associated with the development of reflectins as materials, furnish molecular-level insight into the mechanistic underpinnings of cephalopod skin cells' color-changing functionalities, and may inform new research directions across biochemistry, cellular biology, bioengineering, and optics.

The Role of Conformational Dynamics in the Recognition and Regulation of Ubiquitination

The ubiquitination pathway is central to many cell signaling and regulatory events. One of the intriguing aspects of the pathway is the combinatorial sophistication of substrate recognition and ubiquitin chain building determinations. The abundant structural and biological data portray several characteristic protein folds among E2 and E3 proteins, and the understanding of the combinatorial complexity that enables interaction with much of the human proteome is a major goal to developing targeted and selective manipulation of the pathway. With the commonality of some folds, there are likely other aspects that can provide differentiation and recognition. These aspects involve allosteric effects and conformational dynamics that can direct recognition and chain building processes. In this review, we will describe the current state of the knowledge for conformational dynamics across a wide timescale, address the limitations of present approaches, and illustrate the potential to make new advances in connecting dynamics with ubiquitination regulation.

Dynamically encoded reactivity of Ras enzymes: opening new frontiers for drug discovery

Decoding molecular flexibility in order to understand and predict biological processes-applying the principles of dynamic-structure-activity relationships (DSAR)-becomes a necessity when attempting to design selective and specific inhibitors of a protein that has overlapping interaction surfaces with its upstream and downstream partners along its signaling cascade. Ras proteins are molecular switches that meet this definition perfectly. The close-lying P-loop and the highly flexible switch I and switch II regions are the site of nucleotide-, assisting-, and effector-protein binding. Oncogenic mutations that also appear in this region do not cause easily characterized overall structural changes, due partly to the inherent conformational heterogeneity and pliability of these segments. In this review, we present an overview of the results obtained using approaches targeting Ras dynamics, such as nuclear magnetic resonance (NMR) measurements and experiment-based modeling calculations (mostly molecular dynamics (MD) simulations). These methodologies were successfully used to decipher the mutant- and isoform-specific nature of certain transient states, far-lying allosteric sites, and the internal interaction networks, as well as the interconnectivity of the catalytic and membrane-binding regions. This opens new therapeutic potential: the discovered interaction hotspots present hitherto not targeted, selective sites for drug design efforts in diverse locations of the protein matrix.

Dynamic 15N{1H} NOE measurements: a tool for studying protein dynamics

Intramolecular motions in proteins are one of the important factors that determine their biological activity and interactions with molecules of biological importance. Magnetic relaxation of 15N amide nuclei allows one to monitor motions of protein backbone over a wide range of time scales. 15N{1H} nuclear Overhauser effect is essential for the identification of fast backbone motions in proteins. Therefore, exact measurements of NOE values and their accuracies are critical for determining the picosecond time scale of protein backbone. Measurement of dynamic NOE allows for the determination of NOE values and their probable errors defined by any sound criterion of nonlinear regression methods. The dynamic NOE measurements can be readily applied for non-deuterated or deuterated proteins in both HSQC and TROSY-type experiments. Comparison of the dynamic NOE method with commonly implied steady-state NOE is presented in measurements performed at three magnetic field strengths. It is also shown that improperly set NOE measurement cannot be restored with correction factors reported in the literature.

Activity-dependent interdomain dynamics of matrix metalloprotease-1 on fibrin

The roles of protein conformational dynamics and allostery in function are well-known. However, the roles that interdomain dynamics have in function are not entirely understood. We used matrix metalloprotease-1 (MMP1) as a model system to study the relationship between interdomain dynamics and activity because MMP1 has diverse substrates. Here we focus on fibrin, the primary component of a blood clot. Water-soluble fibrinogen, following cleavage by thrombin, self-polymerize to form water-insoluble fibrin. We studied the interdomain dynamics of MMP1 on fibrin without crosslinks using single-molecule Forster Resonance Energy Transfer (smFRET). We observed that the distance between the catalytic and hemopexin domains of MMP1 increases or decreases as the MMP1 activity increases or decreases, respectively. We modulated the activity using (1) an active site mutant (E219Q) of MMP1, (2) MMP9, another member of the MMP family that increases the activity of MMP1, and (3) tetracycline, an inhibitor of MMP1. We fitted the histograms of smFRET values to a sum of two Gaussians and the autocorrelations to an exponential and power law. We modeled the dynamics as a two-state Poisson process and calculated the kinetic rates from the histograms and autocorrelations. Activity-dependent interdomain dynamics may enable allosteric control of the MMP1 function.

Recent advances in solid-state relaxation dispersion techniques

This review describes two rotating-frame (R_1ρ) relaxation dispersion methods, namely the Bloch-McConnell Relaxation Dispersion and the Near-rotary Resonance Relaxation Dispersion, which enable the study of microsecond time-scale conformational fluctuations in the solid state using magic-angle-spinning nuclear magnetic resonance spectroscopy. The goal is to provide the reader with key ideas, experimental descriptions, and practical considerations associated with R_1ρ measurements that are needed for analyzing relaxation dispersion and quantifying conformational exchange. While the focus is on protein motion, many presented concepts can be equally well adapted to study the microsecond time-scale dynamics of other bio- (e.g. lipids, polysaccharides, nucleic acids), organic (e.g. pharmaceutical compounds), or inorganic molecules (e.g., metal organic frameworks). This article summarizes the essential contributions made by recent theoretical and experimental solid-state NMR studies to our understanding of protein motion. Here we discuss recent advances in fast MAS applications that enable the observation and atomic level characterization of sparsely populated conformational states which are otherwise inaccessible for other experimental methods. Such high-energy states are often associated with protein functions such as molecular recognition, ligand binding, or enzymatic catalysis, as well as with disease-related properties such as misfolding and amyloid formation.

Allosteric Communications between Domains Modulate the Activity of Matrix Metalloprotease-1

An understanding of the structure-dynamics relationship is essential for understanding how a protein works. Prior research has shown that the activity of a protein correlates with intradomain dynamics occurring at picosecond to millisecond timescales. However, the correlation between interdomain dynamics and the function of a protein is poorly understood. Here, we show that communications between the catalytic and hemopexin domains of matrix metalloprotease-1 (MMP1) on type 1 collagen fibrils correlate with its activity. Using single-molecule Förster resonance energy transfer, we identified functionally relevant open conformations in which the two MMP1 domains are well separated, which were significantly absent for catalytically inactive point mutant (E219Q) of MMP1 and could be modulated by an inhibitor or an enhancer of activity. The observed relevance of open conformations resolves the debate about the roles of open and closed MMP1 structures in function. We fitted the histograms of single-molecule Förster resonance energy transfer values to a sum of two Gaussians and the autocorrelations to an exponential and power law. We used a two-state Poisson process to describe the dynamics and calculate the kinetic rates from the fit parameters. All-atom and coarse-grained simulations reproduced some of the experimental features and revealed substrate-dependent MMP1 dynamics. Our results suggest that an interdomain separation facilitates opening up the catalytic pocket so that the collagen chains come closer to the MMP1 active site. Coordination of functional conformations at different parts of MMP1 occurs via allosteric communications that can take place via interactions mediated by collagen even if the linker between the domains is absent. Modeling dynamics as a Poisson process enables connecting the picosecond timescales of molecular dynamics simulations with the millisecond timescales of single-molecule measurements. Water-soluble MMP1 interacting with water-insoluble collagen fibrils poses challenges for biochemical studies that the single-molecule tracking can overcome for other insoluble substrates. Interdomain communications are likely important for multidomain proteins.

Allosteric Regulation at the Crossroads of New Technologies: Multiscale Modeling, Networks, and Machine Learning

Allosteric regulation is a common mechanism employed by complex biomolecular systems for regulation of activity and adaptability in the cellular environment, serving as an effective molecular tool for cellular communication. As an intrinsic but elusive property, allostery is a ubiquitous phenomenon where binding or disturbing of a distal site in a protein can functionally control its activity and is considered as the "second secret of life." The fundamental biological importance and complexity of these processes require a multi-faceted platform of synergistically integrated approaches for prediction and characterization of allosteric functional states, atomistic reconstruction of allosteric regulatory mechanisms and discovery of allosteric modulators. The unifying theme and overarching goal of allosteric regulation studies in recent years have been integration between emerging experiment and computational approaches and technologies to advance quantitative characterization of allosteric mechanisms in proteins. Despite significant advances, the quantitative characterization and reliable prediction of functional allosteric states, interactions, and mechanisms continue to present highly challenging problems in the field. In this review, we discuss simulation-based multiscale approaches, experiment-informed Markovian models, and network modeling of allostery and information-theoretical approaches that can describe the thermodynamics and hierarchy allosteric states and the molecular basis of allosteric mechanisms. The wealth of structural and functional information along with diversity and complexity of allosteric mechanisms in therapeutically important protein families have provided a well-suited platform for development of data-driven research strategies. Data-centric integration of chemistry, biology and computer science using artificial intelligence technologies has gained a significant momentum and at the forefront of many cross-disciplinary efforts. We discuss new developments in the machine learning field and the emergence of deep learning and deep reinforcement learning applications in modeling of molecular mechanisms and allosteric proteins. The experiment-guided integrated approaches empowered by recent advances in multiscale modeling, network science, and machine learning can lead to more reliable prediction of allosteric regulatory mechanisms and discovery of allosteric modulators for therapeutically important protein targets.

Maturation of the functional mouse CRES amyloid from globular form

The epididymal lumen contains a complex cystatin-rich nonpathological amyloid matrix with putative roles in sperm maturation and sperm protection. Given our growing understanding for the biological function of this and other functional amyloids, the problem still remains: how functional amyloids assemble including their initial transition to early oligomeric forms. To examine this, we developed a protocol for the purification of nondenatured mouse CRES, a component of the epididymal amyloid matrix, allowing us to examine its assembly to amyloid under conditions that may mimic those in vivo. Herein we use X-ray crystallography, solution-state NMR, and solid-state NMR to follow at the atomic level the assembly of the CRES amyloidogenic precursor as it progressed from monomeric folded protein to an advanced amyloid. We show the CRES monomer has a typical cystatin fold that assembles into highly branched amyloid matrices, comparable to those in vivo, by forming β-sheet assemblies that our data suggest occur via two distinct mechanisms: a unique conformational switch of a highly flexible disulfide-anchored loop to a rigid β-strand and by traditional cystatin domain swapping. Our results provide key insight into our understanding of functional amyloid assembly by revealing the earliest structural transitions from monomer to oligomer and by showing that some functional amyloid structures may be built by multiple and distinctive assembly mechanisms.

Membrane Proteins Have Distinct Fast Internal Motion and Residual Conformational Entropy

The internal motions of integral membrane proteins have largely eluded comprehensive experimental characterization. Here the fast side-chain dynamics of the α-helical sensory rhodopsin II and the β-barrel outer membrane protein W have been investigated in lipid bilayers and detergent micelles by solution NMR relaxation techniques. Despite their differing topologies, both proteins have a similar distribution of methyl-bearing side-chain motion that is largely independent of membrane mimetic. The methyl-bearing side chains of both proteins are, on average, more dynamic in the ps-ns timescale than any soluble protein characterized to date. Accordingly, both proteins retain an extraordinary residual conformational entropy in the folded state, which provides a counterbalance to the absence of the hydrophobic effect. Furthermore, the high conformational entropy could greatly influence the thermodynamics underlying membrane-protein functions, including ligand binding, allostery, and signaling.

Structure and Molecular Recognition Mechanism of IMP-13 Metallo-β-Lactamase

Multidrug resistance among Gram-negative bacteria is a major global public health threat. Metallo-β-lactamases (MBLs) target the most widely used antibiotic class, the β-lactams, including the most recent generation of carbapenems. Interspecies spread renders these enzymes a serious clinical threat, and there are no clinically available inhibitors. We present the crystal structures of IMP-13, a structurally uncharacterized MBL from the Gram-negative bacterium Pseudomonas aeruginosa found in clinical outbreaks globally, and characterize the binding using solution nuclear magnetic resonance spectroscopy and molecular dynamics simulations. The crystal structures of apo IMP-13 and IMP-13 bound to four clinically relevant carbapenem antibiotics (doripenem, ertapenem, imipenem, and meropenem) are presented. Active-site plasticity and the active-site loop, where a tryptophan residue stabilizes the antibiotic core scaffold, are essential to the substrate-binding mechanism. The conserved carbapenem scaffold plays the most significant role in IMP-13 binding, explaining the broad substrate specificity. The observed plasticity and substrate-locking mechanism provide opportunities for rational drug design of novel metallo-β-lactamase inhibitors, essential in the fight against antibiotic resistance.

Protein Dynamics revealed by NMR Relaxation Methods

Structural biology often focuses primarily on three-dimensional structures of biological macromolecules, deposited in the Protein Data Bank (PDB). This resource is a remarkable entity for the world-wide scientific and medical communities, as well as the general public, as it is a growing translation into three-dimensional space of the vast information in genomic databases, e.g. GENBANK. There is, however, significantly more to understanding biological function than the three-dimensional coordinate space for ground-state structures of biomolecules. The vast array of biomolecules experiences natural dynamics, interconversion between multiple conformational states, and molecular recognition and allosteric events that play out on timescales ranging from picoseconds to seconds. This wide range of timescales demands ingenious and sophisticated experimental tools to sample and interpret these motions, thus enabling clearer insight into functional annotation of the PDB. NMR spectroscopy is unique in its ability to sample this range of timescales at atomic resolution and in physiologically relevant conditions using spin relaxation methods. The field is constantly expanding to provide new creative experiments, to yield more detailed coverage of timescales, and to broaden the power of interpretation and analysis methods. This review highlights the current state of the methodology and examines the extension of analysis tools for more complex experiments and dynamic models. The future for understanding protein dynamics is bright, and these extended tools bring greater compatibility with developments in computational molecular dynamics, all of which will further our understanding of biological molecular functions. These facets place NMR as a key component in integrated structural biology.

Entropy Hotspots for the Binding of Intrinsically Disordered Ligands to a Receptor Domain

Proline-rich motifs (PRMs) are widely used for mediating protein-protein interactions with weak binding affinities. Because they are intrinsically disordered when unbound, conformational entropy plays a significant role for the binding. However, residue-level differences of the entropic contribution in the binding of different ligands remain not well understood. We use all-atom molecular dynamics simulation and the maximal information spanning tree formalism to analyze conformational entropy associated with the binding of two PRMs, one from the Abl kinase and the other from the nonstructural protein 1 of the 1918 Spanish influenza A virus, to the N-terminal SH3 (nSH3) domain of the CrkII protein. Side chains of the stably folded nSH3 experience more entropy change upon ligand binding than the backbone, whereas PRMs involve comparable but heterogeneous entropy changes among the backbone and side chains. In nSH3, two conserved nonpolar residues forming contacts with the PRM experience the largest side-chain entropy loss. In contrast, the C-terminal charged residues of PRMs that form polar contacts with nSH3 experience the greatest side-chain entropy loss, although their "fuzzy" nature is attributable to the backbone that remains relatively flexible. Thus, residues that form high-occupancy contacts between nSH3 and PRM do not reciprocally contribute to entropy loss. Furthermore, certain surface residues of nSH3 distal to the interface with PRMs gain entropy, indicating a nonlocal effect of ligand binding. Comparing between the PRMs from cAbl and nonstructural protein 1, the latter involves a larger side-chain entropy loss and forms more contacts with nSH3. Consistent with experiments, this indicates stronger binding of the viral ligand at the expense of losing the flexibility of side chains, whereas the backbone experiences less entropy loss. The entropy "hotspots" as identified in this study will be important for tuning the binding affinity of various ligands to a receptor.