Exploring sparsely populated states of macromolecules by diamagnetic and paramagnetic NMR relaxation

Sparsely populated states of macromolecules, characterized by short lifetimes and high free-energies relative to the predominant ground state, often play a key role in many biological, chemical, and biophysical processes. In this review, we briefly summarize various new developments in NMR spectroscopy that permit these heretofore invisible, sparsely populated states to be detected, characterized, and in some instances visualized. Relaxation dispersion spectroscopy yields detailed kinetic information on processes involving species characterized by distinct chemical shifts with lifetimes in the ～50 μs-10 ms range and populations as low as 0.5%. In the fast exchange regime (time scale less than ～250-500 μs), the footprint of sparsely populated states can be observed on paramagnetic relaxation enhancement profiles measured on the resonances of the major species, thereby yielding structural information that is directly related to paramagnetic center-nuclei distances from which it is possible, under suitable circumstances, to compute a structure or ensemble of structures for the minor species. Finally, differential transverse relaxation measurements can be used to detect lifetime broadening effects that directly reflect the unidirectional rates for the conversion of NMR-visible into high-molecular weight NMR-invisible species. Examples of these various approaches are presented.     

Measurement of signs of chemical shift differences between ground and excited protein states: a comparison between H(S/M)QC and <Emphasis Type="Italic">R</Emphasis><Subscript>1<Emphasis Type="Italic">ρ</Emphasis></Subscript> methods

Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion NMR spectroscopy has emerged as a powerful tool for quantifying the kinetics and thermodynamics of millisecond exchange processes between a major, populated ground state and one or more minor, low populated and often invisible ‘excited’ conformers. Analysis of CPMG data-sets also provides the magnitudes of the chemical shift difference(s) between exchanging states (|Δϖ|), that inform on the structural properties of the excited state(s). The sign of Δϖ is, however, not available from CPMG data. Here we present one-dimensional NMR experiments for measuring the signs of ¹H^N and ¹³C^α Δϖ values using weak off-resonance R _1ρ relaxation measurements, extending the spin-lock approach beyond previous applications focusing on the signs of ¹⁵N and ¹H^α shift differences. The accuracy of the method is established by using an exchanging system where the invisible, excited state can be converted to the visible, ground state by altering conditions so that the signs of Δϖ values obtained from the spin-lock approach can be validated with those measured directly. Further, the spin-lock experiments are compared with the established H(S/M)QC approach for measuring the signs of chemical shift differences. For the Abp1p and Fyn SH3 domains considered here it is found that while H(S/M)QC measurements provide signs for more residues than the spin-lock data, the two different methodologies are complementary, so that combining both approaches frequently produces signs for more residues than when the H(S/M)QC method is used alone.     

Equilibrium distribution of conformations for Met5-enkephalin predicted by energy calculation and related to experiment

Results of an extensive theoretical conformational analysis of the opiate pentapeptide Met⁵-enkephalin are compared to spectroscopic data. The comparison enables us to propose a consistent model for the conformational state of Met⁵-enkephalin in solution. The empirical energy calculations suggest that the molecule exists in aqueous solution in a small number of folded and extended families of conformers. The predominance of β_II′-turns at the level of the glycine residues at positions 2 and 3 is the most significant characteristic of folded conformers. A highly populated conformer of Met⁵-enkephalin is shown to possess structural features in common with the very potent narcotic etonitazene.     

Modeling conformational ensembles of slow functional motions in Pin1-WW

Protein-protein interactions are often mediated by flexible loops that experience conformational dynamics on the microsecond to millisecond time scales. NMR relaxation studies can map these dynamics. However, defining the network of inter-converting conformers that underlie the relaxation data remains generally challenging. Here, we combine NMR relaxation experiments with simulation to visualize networks of inter-converting conformers. We demonstrate our approach with the apo Pin1-WW domain, for which NMR has revealed conformational dynamics of a flexible loop in the millisecond range. We sample and cluster the free energy landscape using Markov State Models (MSM) with major and minor exchange states with high correlation with the NMR relaxation data and low NOE violations. These MSM are hierarchical ensembles of slowly interconverting, metastable macrostates and rapidly interconverting microstates. We found a low population state that consists primarily of holo-like conformations and is a "hub" visited by most pathways between macrostates. These results suggest that conformational equilibria between holo-like and alternative conformers pre-exist in the intrinsic dynamics of apo Pin1-WW. Analysis using MutInf, a mutual information method for quantifying correlated motions, reveals that WW dynamics not only play a role in substrate recognition, but also may help couple the substrate binding site on the WW domain to the one on the catalytic domain. Our work represents an important step towards building networks of inter-converting conformational states and is generally applicable.     

Characterization of the molten globule state of retinol-binding protein using a molecular dynamics simulation approach

Retinol-binding protein transports retinol, and circulates in the plasma as a macromolecular complex with the protein transthyretin. Under acidic conditions retinol-binding protein undergoes a transition to the molten globule state, and releases the bound retinol ligand. A biased molecular dynamics simulation method has been used to generate models for the ensemble of conformers populated within this molten globule state. Simulation conformers, with a radius of gyration at least 1.1 A greater than that of the native state, contain on average 37%beta-sheet secondary structure. In these conformers the central regions of the two orthogonal beta-sheets that make up the beta-barrel in the native protein are highly persistent. However, there are sizable fluctuations for residues in the outer regions of the beta-sheets, and large variations in side chain packing even in the protein core. Significant conformational changes are seen in the simulation conformers for residues 85-104 (beta-strands E and F and the E-F loop). These changes give an opening of the retinol-binding site. Comparisons with experimental data suggest that the unfolding in this region may provide a mechanism by which the complex of retinol-binding protein and transthyretin dissociates, and retinol is released at the cell surface.     

Measurement of the signs of methyl 13C chemical shift differences between interconverting ground and excited protein states by R 1ρ : an application to αB-crystallin

Carr-Purcell-Meiboom-Gill relaxation dispersion (CPMG RD) NMR spectroscopy has emerged as a powerful tool for quantifying the kinetics and thermodynamics of millisecond time-scale exchange processes involving the interconversion between a visible ground state and one or more minor, sparsely populated invisible 'excited' conformational states. Recently it has also become possible to determine atomic resolution structural models of excited states using a wide array of CPMG RD approaches. Analysis of CPMG RD datasets provides the magnitudes of the chemical shift differences between the ground and excited states, Δ?, but not the sign. In order to obtain detailed structural insights from, for example, excited state chemical shifts and residual dipolar coupling measurements, these signs are required. Here we present an NMR experiment for obtaining signs of (13)C chemical shift differences of (13)CH(3) methyl groups using weak field off-resonance R(1ρ) relaxation measurements. The accuracy of the method is established by using an exchanging system where the invisible, excited state can be converted to the visible, ground state by altering sample conditions so that the signs of Δ? values obtained from the spin-lock approach can be validated against those measured directly. Further, the spin-lock experiments are compared with the established H(S/M)QC approach for measuring signs of chemical shift differences and the relative strengths of each method are discussed. In the case of the 650 kDa human αB-crystallin complex where there are large transverse relaxation differences between ground and excited state spins the R(1ρ) method is shown to be superior to more 'traditional' experiments for sign determination.     

Side-chain interactions in the folding pathway of a Fyn SH3 domain mutant studied by relaxation dispersion NMR spectroscopy

A major challenge to the study of protein folding is the fact that intermediate states along the reaction pathway are generally unstable and thus difficult to observe. Recently developed NMR relaxation dispersion experiments present an avenue to accessing such states, providing kinetic, thermodynamic, and structural information for intermediates with small (greater than or equal to approximately 1%) populations at equilibrium. We have employed these techniques to study the three-state folding reaction of the G48M Fyn SH3 domain. Using (13)C-, (1)H-, and (15)N-based methods, we have characterized backbone and side-chain interactions in the folded, unfolded, intermediate, and transition states, thereby mapping the energy landscape of the protein. We find that the intermediate, populated to approximately 1%, contains nativelike structure in a central beta-sheet, and is disordered at the amino and carboxy termini. The intermediate is stabilized by side-chain van der Waals contacts, yet (13)C chemical shifts indicate that methyl-containing residues remain disordered. This state has a partially structured backbone and a collapsed yet mobile hydrophobic core and thus closely resembles a molten globule. Nonpolar side-chain contacts are formed in the unfolded-intermediate transition state; these interactions are disrupted in the intermediate-folded transition state, possibly allowing side chains to rearrange as they adopt the native packing configuration. This work illustrates the power of novel relaxation dispersion experiments in characterizing excited states that are "invisible" in even the most sensitive of NMR experiments.     

Hydrogen exchange: the modern legacy of Linderstrøm-Lang.

This discussion, prepared for the Protein Society's symposium honoring the 100th anniversary of Kaj Linderstrøm-Lang, shows how hydrogen exchange approaches initially conceived and implemented by Lang and his colleagues some 50 years ago are contributing to current progress in structural biology. Examples are chosen from the active protein folding field. Hydrogen exchange methods now make it possible to define the structure of protein folding intermediates in various contexts: as tenuous molten globule forms at equilibrium under destabilizing conditions, in kinetic intermediates that exist for less than one second, and as infinitesimally populated excited state forms under native conditions. More generally, similar methods now find broad application in studies of protein structure, energetics, and interactions. This article considers the rise of these capabilities from their inception at the Carlsberg Labs to their contemporary role as a significant tool of modern structural biology.     

Backbone dependency further improves side chain prediction efficiency in the Energy‐based Conformer Library (bEBL)

Side chain optimization is an integral component of many protein modeling applications. In these applications, the conformational freedom of the side chains is often explored using libraries of discrete, frequently occurring conformations. Because side chain optimization can pose a computationally intensive combinatorial problem, the nature of these conformer libraries is important for ensuring efficiency and accuracy in side chain prediction. We have previously developed an innovative method to create a conformer library with enhanced performance. The Energy‐based Library (EBL) was obtained by analyzing the energetic interactions between conformers and a large number of natural protein environments from crystal structures. This process guided the selection of conformers with the highest propensity to fit into spaces that should accommodate a side chain. Because the method requires a large crystallographic data‐set, the EBL was created in a backbone‐independent fashion. However, it is well established that side chain conformation is strongly dependent on the local backbone geometry, and that backbone‐dependent libraries are more efficient in side chain optimization. Here we present the backbone‐dependent EBL (bEBL), whose conformers are independently sorted for each populated region of Ramachandran space. The resulting library closely mirrors the local backbone‐dependent distribution of side chain conformation. Compared to the EBL, we demonstrate that the bEBL uses fewer conformers to produce similar side chain prediction outcomes, thus further improving performance with respect to the already efficient backbone‐independent version of the library. Proteins 2014; 82:3177–3187. © 2014 Wiley Periodicals, Inc.     

Minimal ensembles of side chain conformers for modeling protein–protein interactions

The goal of this article is to reduce the complexity of the side chain search within docking problems. We apply six methods of generating side chain conformers to unbound protein structures and determine their ability of obtaining the bound conformation in small ensembles of conformers. Methods are evaluated in terms of the positions of side chain end groups. Results for 68 protein complexes yield two important observations. First, the end‐group positions change less than 1 Å on association for over 60% of interface side chains. Thus, the unbound protein structure carries substantial information about the side chains in the bound state, and the inclusion of the unbound conformation into the ensemble of conformers is very beneficial. Second, considering each surface side chain separately in its protein environment, small ensembles of low‐energy states include the bound conformation for a large fraction of side chains. In particular, the ensemble consisting of the unbound conformation and the two highest probability predicted conformers includes the bound conformer with an accuracy of 1 Å for 78% of interface side chains. As more than 60% of the interface side chains have only one conformer and many others only a few, these ensembles of low‐energy states substantially reduce the complexity of side chain search in docking problems. This approach was already used for finding pockets in protein–protein interfaces that can bind small molecules to potentially disrupt protein–protein interactions. Side‐chain search with the reduced search space will also be incorporated into protein docking algorithms. Proteins 2012. © 2011 Wiley Periodicals, Inc.     

Peptide-sandwiched protoporphyrin compounds mimicking hemoprotein structures in solution

A series of covalently bound peptide-protoporphyrin-peptide compounds, also carrying naphthalene (N) to allow a photophysical investigation, were synthesized. Their general formula is P(nN)(2), where P refers to protoporphyrin IX, and n to the number of amino acids in the sequence Boc-Leu-Leu-Lys-(Ala)(x) -Leu-Leu-Lys-OtBu of each backbone chain (x = 0-3; n = x + 6). Their structural features in methanol solution were investigated by ir and CD spectra, and by steady-state and time resolved fluorescence experiments as well. The ir spectra indicate that intramolecularly H-bonded conformations form, and CD data in both methanol and water-methanol mixture suggest the presence of alpha-helix structure. Quenching of excited naphthalene takes place by electronic energy transfer from singlet N* to P ground state. Fluorescence decays coupled with molecular mechanics calculations indicate that two conformers for each dimeric peptide are the major contributors to the observed phenomena. These conformers are characterized by a globular, protein-like structure, where the protoporphyrin resides in a central pocket, while the two N groups are externally situated. Of the four N linkages in the two conformers, three of them attain a very similar steric arrangement around the central P molecule, in terms of both center-to-center distance and mutual orientation, while the fourth experiences a different steric disposition as compared to the others. Experimental photophysical parameters satisfactorily compare with those obtained by theoretical calculations, within the F?rster mechanism for long-range energy transfer, only when the mutual orientation of the chromophores was also taken into account. This implies that interconversion among conformational substates of probes linkages is slow on the time scale of the energy transfer process.     

Potential transition-state analogs for glycosyltransferases. Design and DFT calculations of conformational behavior

The structure of a previously calculated transition state (TS) was used to design the [tetrahydro-2-(methylthio)furan-2-yl]methyl phosphate dianion (1) as a new scaffold for transition-state analogs of reactions catalyzed by the inverting glycosyltransferases. This scaffold contains relevant features of the donor and acceptor and represents a new type of potential inhibitors for these enzymes. Available conformational space of 1 was explored using DFT quantum chemical methods by means of two-dimensional potential-energy maps calculated as a function of Phi, Psi, and omega dihedral angles at the B3LYP/6-31+G* level. The calculated potential energy surfaces revealed the existence of several low-energy domains. Structures from these regions were refined at the 6-311++G** level and led to 14 conformers. The stability of conformers is influenced by their environment, and in aqueous solution two conformers dominate the equilibrium. A superposition of calculated conformers with the predicted TS structure revealed that the preferred conformers in solution nicely mimic structural features of the TS. These results imply that 1 has structural properties required to mimic the TS and therefore can be used as a scaffold for further development of TS-analog inhibitors for retaining glycosyltransferases.     

Energy functions for protein design: adjustment with protein-protein complex affinities, models for the unfolded state, and negative design of solubility and specificity

The development of the EGAD program and energy function for protein design is described. In contrast to most protein design methods, which require several empirical parameters or heuristics such as patterning of residues or rotamers, EGAD has a minimalist philosophy; it uses very few empirical factors to account for inaccuracies resulting from the use of fixed backbones and discrete rotamers in protein design calculations, and describes the unfolded state, aggregates, and alternative conformers explicitly with physical models instead of fitted parameters. This approach unveils important issues in protein design that are often camouflaged by heuristic-emphasizing methods. Inter-atom energies are modeled with the OPLS-AA all-atom forcefield, electrostatics with the generalized Born continuum model, and the hydrophobic effect with a solvent-accessible surface area-dependent term. Experimental characterization of proteins designed with an unmodified version of the energy function revealed problems with under-packing, stability, aggregation, and structural specificity. Under-packing was addressed by modifying the van der Waals function. By optimizing only three parameters, the effects of >400 mutations on protein-protein complex formation were predicted to within 1.0 kcal mol(-1). As an independent test, this modified energy function was used to predict the stabilities of >1500 mutants to within 1.0 kcal mol(-1); this required a physical model of the unfolded state that includes more interactions than traditional tripeptide-based models. Solubility and structural specificity were addressed with simple physical approximations of aggregation and conformational equilibria. The complete energy function can design protein sequences that have high levels of identity with their natural counterparts, and have predicted structural properties more consistent with soluble and uniquely folded proteins than the initial designs.     

Anion-induced folding of rabbit muscle pyruvate kinase: existence of multiple intermediate conformations at low pH

Structural and functional characteristics of rabbit muscle pyruvate kinase (PK), a tetrameric enzyme having identical subunits, were investigated under neutral as well as acidic conditions by using enzymatic activity measurements and a combination of optical methods, such as circular dichroism, fluorescence, and ANS binding. At low pH and low ionic strength, pyruvate kinase exists in a partially unfolded state (UA state) retaining half of the secondary structure and no tertiary interactions along with a strong binding to the hydrophobic dye, ANS. Addition of anions, like NaCl, KCl, and Na2SO4, to the acid-unfolded state induces refolding, resulting structural propensities similar to that of native tetramer. When anion concentration exceeds a critical limit (0.7 M KCl), a sudden loss of secondary structure and decrease in fluorescence intensity with a redshift in the emission maximum are seen which may be due to the aggregation of the protein, probably due to the intermolecular association. The anion-refolded state is more stable than the UA state, and its stability is nearly equal to that of native protein toward chemical-induced unfolding by Gu-HCl and urea. Moreover, at low concentrations, Gu-HCl behaves like an anion, by inducing refolding of the acid-unfolded state with structural features equivalent to that of native molecule. These observations support a model of protein folding where certain conformations of low free energy prevail and are populated under non-native conditions with different stability.     

Structural diversity of domain superfamilies in the CATH database

The CATH database of domain structures has been used to explore the structural variation of homologous domains in 294 well populated domain structure superfamilies, each containing at least three sequence diverse relatives. Our analyses confirm some previously detected trends relating sequence divergence to structural variation but for a much larger dataset and in some superfamilies the new data reveal exceptional structural variation. Use of a new algorithm (2DSEC) to analyse variability in secondary structure compositions across a superfamily sheds new light on how structures evolve. 2DSEC detects inserted secondary structures that embellish the core of conserved secondary structures found throughout the superfamily. Analysis showed that for 56% of highly populated superfamilies (>9 sequence diverse relatives), there are twofold or more increases in the numbers of secondary structures in some relatives. In some families fivefold increases occur, sometimes modifying the fold of the domain. Manual inspection of secondary structure insertions or embellishments in 48 particularly variable superfamilies revealed that although these insertions were usually discontiguous in the sequence they were often co-located in 3D resulting in a larger structural motif that often modified the geometry of the active site or the surface conformation promoting diverse domain partnerships and protein interactions. These observations, supported by automatic analysis of all well populated CATH families, suggest that accretion of small secondary structure insertions may provide a simple mechanism for evolving new functions in diverse relatives. Some layered domain architectures (e.g. mainly-beta and alpha-beta sandwiches) that recur highly in the genomes more frequently exploit these types of embellishments to modify function. In these architectures, aggregation occurs most often at the edges, top or bottom of the beta-sheets. Information on structural variability across domain superfamilies has been made available through the CATH Dictionary of Homologous Structures (DHS).     

Conformational analysis of methyl 6-O-[(R)- and (S)-1-carboxyethyl]-α-D-galactopyranoside by MM and Langevin dynamics simulations

The conformational space of methyl 6-O-[(R)- and (S)- 1-carboxyethyl]-α-D-galactopyranoside has been investigated. A grid search employing energy minimization at each grid point over the three major degrees of freedom, namely φ, ψ and ω, identified low energy regions. The R-isomer shows five low energy conformers within ca. 1 kcal mol−1 of the global energy minimum. The S-isomer has two conformers within a few tenths of a kcal mol−1 of the global energy minimum. Langevin dynamics simulations have been have been performed at 300 K for 30 ns of each isomer. The φ dihedral angle has as its major conformer (g−1) for the R-isomer whereas it is the (g+) conformer for the S-isomer. For the ψ dihedral angle the (t) conformer has the highest population for both isomers. The dihedral angle ω has the (g+) conformer most highly populated, both for the R- and S-isomer. The above five and two conformational states for the R- and S-isomers, respectively, make up 90% in each case of the populated states during the Langevin dynamics (LD) simulations. Rate constants for the ω dihedral angle have been calculated based on a number correlation function. Three bond homo- and heteronuclear, i.e. proton and carbon-13, coupling constants have been calculated from the dynamics trajectories for comparison to experimental values. The heteronuclear coupling constant H2′,C6 has been measured for the S-isomer and found to be 3.3 Hz. The J value calculated from the LD simulations, namely 2.6 Hz, is in fair agreement with experiment. A comparison to the X-ray structure of the R-isomer shows that the conformation of the crystalline compound occupies the low energy region most highly populated as a single R-conformer (30%) during the LD simulations. This revised version was published online in August 2006 with corrections to the Cover Date.     

The Intramolecular Impact to the Sequence Specificity of B→A Transition: Low Energy Conformational Variations in AA/TT and GG/CC Steps

Abstract It is well known, that local B→A transformation in DNA is involved in several biological processes. In vitro B?A transition is sequence-specific. The physical basis of this specificity is not known yet. Here we analyze the effect of intramolecular interactions on the structural behavior of the GG/CC and AA/TT steps. These steps exemplify sequence specific bias to the B- or A-form structure. Optimization of potential energy of the molecular systems composed of an octanucle-otide, neutralized by Na(+) and solvated with TIP3P water molecules in rectangular box with periodic boundary conditions gives the statistically representative sets of low energy structures for GG/CC and AA/TT steps in the middle of the diverse flanking sequences. Permissible 3D variations of GG/CC and AA/TT, and correlation of the relative motion of base pairs in these steps were analyzed. AA/TT step permits high variability for low energy conformers in the B-form DNA and small variability for low energy conformers in the A-form DNA. In contrast GG/CC step permits high variability for low energy conformers in the A-form DNA and small variability for low energy conformers in the B-form DNA. The relative motion of base pairs in GG/CC step is high correlated, while in AA/TT step this correlation is notably less. Atom-atom interactions inside-the-step always favors the B-form and their component - stacking interactions (atomatom interactions between nucleic bases) is crucial for the duplex stabilization. Formation of the A-form for both steps is a result of interactions with the flanking sequences and water-cation environment in the box. The average energy difference between conformations presenting B-form and A-form for the GG/CC step is high, while for the AA/TT step it is rather low. Thus, intramolecular interactions in GG/CC and AA/TT steps affect the possible conformational diversity ("conformational entropy") of the A- and B- type structures of DNA step. This determines the known bias of the A-form DNA depending on the enrichment of sequences with GG/CC. If structural tuning during the process of protein-DNA complex formation lead to the local B→A transformation of DNA, it is largely directed by high conformational diversity of GG/CC step in the A-form. In such a case the presence in the target site of both kinds of examined steps ensures the reversible character of ligand binding.