Backbone Fluctuations Research Articles

Statistical mechanics of protein allostery: Roles of backbone and side-chain structural fluctuations

A statistical mechanical model of allosteric transition of proteins is developed by extending the structure-based model of protein folding to cases that a protein has two different native conformations. Partition function is calculated exactly within the model and free-energy surfaces associated with allostery are derived. In this paper, the model of allosteric transition proposed in a previous paper [Proc. Natl. Acad. Sci. U.S.A 134, 7775 (2010)] is reformulated to describe both fluctuation in side-chain configurations and that in backbone structures in a balanced way. The model is applied to example proteins, Ras, calmodulin, and CheY: Ras undergoes the allosteric transition between guanosine diphosphate (GDP)-bound and guanosine triphosphate (GTP)-bound forms, and the model results show that the GDP-bound form is stabilized enough to prevent unnecessary signal transmission, but the conformation in the GTP-bound state bears large fluctuation in side-chain configurations, which may help to bind multiple target proteins for multiple pathways of signaling. The calculated results of calmodulin show the scenario of sequential ordering in Ca(2+) binding and the associated allosteric conformational change, which are realized though the sequential appearing of pre-existing structural fluctuations, i.e., fluctuations to show structures suitable to bind Ca(2+) before its binding. Here, the pre-existing fluctuations to accept the second and third Ca(2+) ions are dominated by the side-chain fluctuation. In CheY, the calculated side-chain fluctuation of Tyr106 is coordinated with the backbone structural change in the β4-α4 loop, which explains the pre-existing Y-T coupling process in this protein. Ability of the model to explain allosteric transitions of example proteins supports the view that the large entropic effects lower the free-energy barrier of allosteric transition.

Protein folding pathways and state transitions described by classical equations of motion of an elastic network model

Protein topology defined by the matrix of residue contacts has proved to be a fruitful basis for the study of protein dynamics. The widely implemented coarse-grained elastic network model of backbone fluctuations has been used to describe crystallographic temperature factors, allosteric couplings, and some aspects of the folding pathway. In the present study, we develop a model of protein dynamics based on the classical equations of motion of a damped network model (DNM) that describes the folding path from a completely unfolded state to the native conformation through a single-well potential derived purely from the native conformation. The kinetic energy gained through the collapse of the protein chain is dissipated through a friction term in the equations of motion that models the water bath. This approach is completely general and sufficiently fast that it can be applied to large proteins. Folding pathways for various proteins of different classes are described and shown to correlate with experimental observations and molecular dynamics and Monte Carlo simulations. Allosteric transitions between alternative protein structures are also modeled within the DNM through an asymmetric double-well potential.

Structural Origins of High Apparent Dielectric Constants Experienced by Ionizable Groups in the Hydrophobic Core of a Protein

The side chains of Lys66, Asp66, and Glu66 in staphylococcal nuclease are fully buried and surrounded mainly by hydrophobic matter, except for internal water molecules associated with carboxylic oxygen atoms. These ionizable side chains titrate with pKa values of 5.7, 8.8, and 8.9, respectively. To reproduce these pKa values with continuum electrostatics calculations, we treated the protein with high dielectric constants. We have examined the structural origins of these high apparent dielectric constants by using NMR spectroscopy to characterize the structural response to the ionization of these internal side chains. Substitution of Val66 with Lys66 and Asp66 led to increased conformational fluctuations of the microenvironments surrounding these groups, even under pH conditions where Lys66 and Asp66 are neutral. When Lys66, Asp66, and Glu66 are charged, the proteins remain almost fully folded, but resonances for a few backbone amides adjacent to the internal ionizable residues are broadened. This suggests that the ionization of the internal groups promotes a local increase in dynamics on the intermediate timescale, consistent with either partial unfolding or increased backbone fluctuations of helix 1 near residue 66, or, less likely, with increased fluctuations of the charged side chains at position 66. These experiments confirm that the high apparent dielectric constants reported by internal Lys66, Asp66, and Glu66 reflect localized changes in conformational fluctuations without incurring detectable global structural reorganization. To improve structure-based pKa calculations in proteins, we will need to learn how to treat this coupling between ionization of internal groups and local changes in conformational fluctuations explicitly.

Conformational and Oligomeric Effects on the Cysteine pKa of Tryparedoxin Peroxidase

Typical 2-Cys peroxiredoxins (Prxs) are peroxidases which regulate cell signaling pathways, apoptosis, and differentiation. These enzymes are obligate homodimers, and can form decamers in solution. During catalysis, Prxs exhibit cysteine-dependent reactivity which requires the deprotonation of the peroxidatic cysteine (Cp) supported by a lowered pKa in the initial step. We present the results of molecular dynamics simulations combined with pKa calculations on the monomeric, dimeric and decameric forms of one typical 2-Cys Prx, the tryparedoxin peroxidase from Trypanosoma cruzi (PDB id, 1uul). The calculations indicate that Cp (C52) pKa values are highly affected by oligomeric state; an unshifted Cp pKa (∼ 8.3, comparable to the pKa of isolated cysteine) is calculated for the monomer. In the dimers, starting with essentially identical structures, the Cps evolve dynamically asymmetric pKas during the simulations; one subunit's Cp pKa is shifted downward at a time, while the other is unshifted. However, when averaged over time, or multiple simulations, the two subunits within a dimer exhibit the same Cp, showing no preference for a lowered pKa in either subunit. Two conserved pathways that communicate the asymmetric pKas between Cps of different subunits can be identified. In the decamer, all the Cp pKas are shifted downward, with slight asymmetry in the dimers which form the decamers. Structural analyses implicate oli- gomerization effects as responsible for these oligomeric state-dependent Cp pKa shifts. The intra-dimer and the inter-dimer subunit contacts in the decamer restrict the conformations of the side chains of several residues (T49, T54 and E55) calculated to be key in shifting the Cp pKa. In addition, the backbone fluctuations of a few residues (M46, D47 and F48) result in a different electrostatic environment for the Cp in dimers relative to the monomers. These side chain and backbone interactions which contribute to pKa modulation indicate the importance of oligomerization to the function of the typical 2-Cys Prxs.

High‐Resolution Crystal Structure of a Lasso Peptide

Lasso peptides are a group of a growing class of bioactive peptides of microbial origin. The first crystal structure of a member of this family, the glucagon receptor antagonist BI-32169, shows that the fold is built predominantly by regular secondary structural elements and a tight network of hydrogen bonds that are partially shielded from solvent by hydrophobic amino acid side chains. This results in an extraordinary stable structure that is resistant to thermal unfolding or proteolytic digestion, which facilitates its biological function.

Many Local Motions Cooperate to Produce the Adenylate Kinase Conformational Transition

Conformational transitions are functionally important in many proteins. In the enzyme adenylate kinase (AK), two small domains (LID and NMP) close over the larger CORE domain; the reverse (opening) motion limits the rate of catalytic turnover. Here, using double-well Gō simulations of Escherichia coli AK, we elaborate on previous investigations of the AK transition mechanism by characterizing the contributions of rigid-body (Cartesian), backbone dihedral, and contact motions to transition-state (TS) properties. In addition, we compare an apo simulation to a pseudo-ligand-bound simulation to reveal insights into allostery. In Cartesian space, LID closure precedes NMP closure in the bound simulation, consistent with prior coarse-grained models of the AK transition. However, NMP-first closure is preferred in the apo simulation. In backbone dihedral space, we find that, as expected, backbone fluctuations are reduced in the O/C transition in parts of all three domains. Among these “quenching” residues, most in the CORE, especially residues 11–13, are rigidified in the TS of the bound simulation, while residues 42–44 in the NMP are flexible in the TS. In contact space, in both apo and bound simulations, one nucleus of closed-state contacts includes parts of the NMP and CORE; CORE–LID contacts are absent in the TS of the apo simulation but formed in the TS of the bound simulation. From these results, we predict mutations that will perturb the opening and/or closing transition rates by changing the entropy of dihedrals and/or the enthalpy of contacts. Furthermore, regarding allostery, the fully closed structure is populated in the apo simulation, but our contact results imply that ligand binding shifts the preferred O/C transition pathway, thus precluding a simple conformational selection mechanism. Finally, the analytical approach and the insights derived from this work may inform the rational design of flexibility and allostery in proteins.

Multifrequency Electron Spin Resonance Study of the Dynamics of Spin Labeled T4 Lysozyme

An extensive set of electron spin resonance spectra was obtained over a wide range of frequencies (9, 95, 170, and 240 GHz) and temperatures (2 to 32 degrees C) to explore the dynamic modes of nitroxide-labeled T4 lysozyme in solution. A commonly used nitroxide side chain (R1), or a methylated analogue with hindered internal motion (R2), was substituted for the native side chain at solvent-exposed helical sites, 72 or 131. The spectra at all four frequencies were simultaneously fit with the slowly relaxing local structure (SRLS) model. Good fits were achieved at all the temperatures. Two principle dynamic modes are included in the SRLS model, the global tumbling of the protein and the internal motion consisting of backbone fluctuations and side chain isomerizations. Three distinct spectral components were required for R1 and two for R2 to account for the spectra at all temperatures. One is a highly ordered and slow motional component, which is observed in the spectra of both R1 and R2; it may correspond to conformers stabilized by interaction with the protein surface. The fraction of this component decreases with increasing temperature and is more populated in the R2 spectra, possibly arising from stronger interaction of the nitroxide ring with the protein surface due to the additional methyl group. The other two components of R1 and the second component of R2 are characterized by fast anisotropic diffusion and relatively low ordering, most likely corresponding to conformers having little or no interactions with nearby residues. Ficoll of different concentrations was added to increase the solution viscosity, thereby slowing down the global tumbling of the protein. A significant effect of Ficoll on the internal motion of an immobilized component was apparent in R2 but not in R1. The ability of such multifrequency studies to separate the effects of faster internal modes of motion from slower overall motions is clearly demonstrated, and its utility in future studies is considered.

Solvent-induced backbone fluctuations and the collective librational dynamics of lysozyme studied by terahertz spectroscopy

THz spectroscopy is used to investigate the dynamics of the globular protein hen egg white lysozyme under varying hydration and temperature conditions. An analysis of the experimental spectra has revealed that the amount of solvent in the hydration shell has a strong influence on the low-frequency protein conformational dynamics and also the arrangement of hydrogen bonds in the protein secondary structure. Furthermore at a hydration level >0.2 we identify collective backbone fluctuations in the protein secondary structure that are not present at low hydration. It is possible that these solvent induced modes are important for the biological function of the protein.

Direct Evidence of the Amino Acid Side Chain and Backbone Contributions to Protein Anharmonicity

Elastic incoherent neutron scattering has been used to study the temperature dependence of the mean-square displacements of nonexchangeable hydrogen atoms in powders of a series of homomeric polypeptides (polyglycine, polyalanine, polyphenylalanine and polyisoleucine) in comparison with myoglobin at the same hydration level (h = 0.2). The aim of the work was to measure the dynamic behavior of different amino acid residues separately and assess the contribution of each type of side chain to the anharmonic dynamics of proteins. The results provide direct experimental evidence that the first anharmonic activation, at approximately 150 K, is largely due to methyl group rotations entering the time window of the spectrometer used; however, contributions on the order of 10-20% from the motions of other groups (e.g., the phenolic ring and the methylene groups) are present. Our data also indicate that the dynamical transition occurring at approximately 230 K can be attributed, at least at the hydration level investigated, mainly to motions involving backbone fluctuations.

Millisecond timescale fluctuations in dihydrofolate reductase are exquisitely sensitive to the bound ligands

Enzyme catalysis can be described as progress over a multi-dimensional energy landscape where ensembles of interconverting conformational substates channel the enzyme through its catalytic cycle. We applied NMR relaxation dispersion to investigate the role of bound ligands in modulating the dynamics and energy landscape of Escherichia coli dihydrofolate reductase to obtain insights into the mechanism by which the enzyme efficiently samples functional conformations as it traverses its reaction pathway. Although the structural differences between the occluded substrate binary complexes and product ternary complexes are very small, there are substantial differences in protein dynamics. Backbone fluctuations on the micros-ms timescale in the cofactor binding cleft are similar for the substrate and product binary complexes, but fluctuations on this timescale in the active site loops are observed only for complexes with substrate or substrate analog and are not observed for the binary product complex. The dynamics in the substrate and product binary complexes are governed by quite different kinetic and thermodynamic parameters. Analogous dynamic differences in the E:THF:NADPH and E:THF:NADP(+) product ternary complexes are difficult to rationalize from ground-state structures. For both of these complexes, the nicotinamide ring resides outside the active site pocket in the ground state. However, they differ in the structure, energetics, and dynamics of accessible higher energy substates where the nicotinamide ring transiently occupies the active site. Overall, our results suggest that dynamics in dihydrofolate reductase are exquisitely "tuned" for every intermediate in the catalytic cycle; structural fluctuations efficiently channel the enzyme through functionally relevant conformational space.

Interaction and conformational dynamics of membrane-spanning protein helices.

Within 1 or 2 decades, the reputation of membrane-spanning alpha-helices has changed dramatically. Once mostly regarded as dull membrane anchors, transmembrane domains are now recognized as major instigators of protein-protein interaction. These interactions may be of exquisite specificity in mediating assembly of stable membrane protein complexes from cognate subunits. Further, they can be reversible and regulatable by external factors to allow for dynamic changes of protein conformation in biological function. Finally, these helices are increasingly regarded as dynamic domains. These domains can move relative to each other in different functional protein conformations. In addition, small-scale backbone fluctuations may affect their function and their impact on surrounding lipid shells. Elucidating the ways by which these intricate structural features are encoded by the amino acid sequences will be a fascinating subject of research for years to come.

Backbone Dynamics of Alamethicin Bound to Lipid Membranes: Spin-Echo Electron Paramagnetic Resonance of TOAC-Spin Labels

Alamethicin F50/5 is a hydrophobic peptide that is devoid of charged residues and that induces voltage-dependent ion channels in lipid membranes. The peptide backbone is likely to be involved in the ion conduction pathway. Electron spin-echo spectroscopy of alamethicin F50/5 analogs in which a selected Aib residue (at position n=1, 8, or 16) is replaced by the TOAC amino-acid spin label was used to study torsional dynamics of the peptide backbone in association with phosphatidylcholine bilayer membranes. Rapid librational motions of limited angular amplitude were observed at each of the three TOAC sites by recording echo-detected spectra as a function of echo delay time, 2τ. Simulation of the time-resolved spectra, combined with conventional EPR measurements of the librational amplitude, shows that torsional fluctuations of the peptide backbone take place on the subnanosecond to nanosecond timescale, with little temperature dependence. Associated fluctuations in polar fields from the peptide could facilitate ion permeation.

TraR auto-inducer enhances protein backbone fluctuations in DNA binding domain

The bacterium Agrobacterium tumefaciens mediates quorum sensing via TraR, a N-3-oxo-octanoyl- l-homoserine lactone (OOHL) signaling transcription factor. TraR consists of an N-terminal Per-Arnt-Sim domain (PAS-domain) containing OOHL and a C-terminal helix-turn-helix motif (HTF-motif) binding DNA, thus comprising a complete signaling pathway. Using Molecular Dynamics, we investigate the influence of OOHL on the dynamics of the protein. The OOHL binding pocket is in contact with water, leading to dynamic changes in OOHL–protein interactions. These rearrangements increase fluctuations in the PAS-domain, and, interestingly, also enhance fluctuations in the HTF-motif. Our results imply OOHL in inducing fluctuations in TraR that may facilitate DNA binding.

Normal Mode Analysis of Polytheonamide B

Polytheonamide B is a linear 48-residue peptide which forms a single β-helix structure with alternating D- and L-amino acids and contains methylated and hydroxy variants of proteinogenic amino acids. To investigate the dynamical properties of polytheonamide B we perform the normal mode analysis. Root-mean-square displacements of all backbone atoms, root-mean-square fluctuations of the backbone dihedral angles (Φ, ψ), and correlation factors for the C α atom fluctuations and for the dihedral angle fluctuations are calculated. The normal mode analysis reveals that polytheonamide B shows the elastic rod behavior in the very low-frequency regions and that librational motions of backbone amide planes have the modes with relatively low frequencies, which is relevant to the function of polytheonamide B. In addition, these librational motions occur almost independently and weakly anticorrelate with those of the hydrogen-bonded neighboring amide planes. Calculations of the backbone fluctuations show that the flexibility of polytheonamide B is roughly uniform over the entire helix. We compare our results with those of gramicidin A, the analogue of polytheonamide B, to discuss the structures and functions, and obtain some common features in the flexibilities and dynamics of the backbone atoms. These results present important clues for clarifying the function of polytheonamide B at the atomic level.

The effects of cosolutes on protein dynamics: The reversal of denaturant‐induced protein fluctuations by trimethylamine N‐oxide

The protein stabilizing effects of the small molecule osmolyte, trimethylamine N-oxide, against chemical denaturant was investigated by NMR spin-relaxation measurements and model-free analysis. In the presence of 0.7 M guanidine hydrochloride increased picosecond-nanosecond dynamics are observed in the protein ribonuclease A. These increased fluctuations occur throughout the protein, but the most significant increases in flexibility occur at positions believed to be the first to unfold. Addition of 0.35 M trimethylamine N-oxide to this destabilized form of ribonuclease results in significant rigidification of the protein backbone as assessed by (1)H-(15)N order parameters. Statistically, these order parameters are the same as those measured in native ribonuclease indicating that TMAO reduces the amplitude of backbone fluctuations in a destabilized protein. These data suggest that TMAO restricts the bond vector motions on the protein energy landscape to resemble those motions that occur in the native protein and points to a relation between stability and dynamics in this enzyme.

Repeat Motions and Backbone Flexibility in Designed Proteins with Different Numbers of Identical Consensus Tetratricopeptide Repeats

The tetratricopeptide repeat (TPR) is a 34-residue helix-turn-helix motif that occurs as three or more tandem repeats in a wide variety of proteins. We have determined the repeat motions and backbone fluctuations of proteins containing two or three consensus TPR repeats (CTPR2 and CPTR3, respectively) using 15N NMR relaxation measurements. Rotational diffusion tensors calculated from these data for each repeat within each TPR protein indicate that there is a high degree of motional correlation between different repeats in the same protein. This is consistent with the prevailing view that repeat proteins, such as CTPR2 and CTPR3, behave as single cooperatively folded domains. The internal motions of backbone NH groups were determined using the Lipari-Szabo model-free formalism. For most residues, there was a clear separation between the influence of internal motion and the influence of global rotational tumbling on the observed magnetic relaxation. The local internal motions are highly restricted in most of the helical elements, with slightly greater flexibility in the linker elements. Comparisons between CTPR2 and CTPR3 indicate that an addition of a TPR repeat to the C-terminus (before the solvation helix) of CTPR2 slightly reduces the flexibility of the preceding helix.

Sizing Backbone Internet Links

One of the distinguishing features of a backbone link is that it is designed to carry traffic from a large number of end users. This results in a Normal distribution for the number of bytes or packets that arrive in a fixed-length time interval. Based on this observation, which is substantiated by data analysis, we present a simple model for the steady-state loss probability that can be solved in closed form. This model assumes that there is no buffer, so that issues raised by the correlation of counts that is characteristic of packet traffic are bypassed. The longest interval that captures the relevant statistical fluctuations of backbone traffic is one second. Data collection on live commercial networks is costly, so byte and packet counts are usually collected over much longer time intervals; five minutes is a lower bound. This creates no problem in estimating the mean of the Normal distribution, but it makes direct estimation of the variance for one-second counts infeasible. Routers collect flow data; flows are analogous to “calls” in telephony. By modeling the number of active flows as an M/G/∞ queue and assuming that packets in a flow are spread uniformly in time, an equation for the variance of (say) one-second counts in terms of measured quantities is derived. The efficacy of this formula is demonstrated by applying it to data.

A Two-Dimensional Infrared Study of Localization, Structure, and Dynamics of a Dipeptide in Membrane Environment

Using methods of time-resolved two-dimensional infrared (2D-IR) spectroscopy, we approach the problem of the structural characterization of small polypeptide systems in a membrane environment. The 2D-IR spectra recorded for a model dipeptide in different environments demonstrated a significant change in the homogeneous and inhomogeneous broadenings of the amide I resonances when the molecule inserts either into a surfactant or a phospholipid membrane. Besides the change in the diagonal features in the 2D-IR response, we observe both intramolecular and intermolecular crosspeaks between the carbonyls of the dipeptide and the phospholipid. Considering the character of the diagonal peaks and the presence of the crosspeaks, we discuss the localization of the dipeptide moieties in the membrane. Using both the anisotropy and relative intensity of the observed intramolecular crosspeaks between the two amide I modes, we provide observables that help to determine the ϕ/ ψ-dihedral angles for the backbone of the dipeptide. Time dependent studies revealed slower conformational fluctuations of the dipeptide backbone in a membrane as compared to that in an aqueous environment.

A Multifrequency Electron Spin Resonance Study of T4 Lysozyme Dynamics Using the Slowly Relaxing Local Structure Model

Electron spin resonance (ESR) spectra were obtained at 250 and 9 GHz for nitroxide-labeled mutants of the protein T4 lysozyme in aqueous solution over a range of temperatures from 2 to 37.5 °C. Two mutants labeled at sites 72 and 131 were studied and compared. The mutant sites are solvent exposed and free of tertiary interactions with other side chains, but the former is at the center of a 5 turn helix, whereas the latter site is on a small two and a half turn helix. The 250 GHz ESR spectra, because of their “fast time scale”, are rather insensitive to the slow overall tumbling motion of the protein. Thus, they are qualitatively different for the two mutants, implying that there are different local dynamics at the two sites. The 9 GHz spectra, which are significantly affected by the overall tumbling and are less sensitive to the internal dynamics, do not show such marked differences between the two sites. The 250 and 9 GHz spectra for each mutant and temperature were simultaneously fit to the slowly relaxing local structure (SRLS) model for slow-motional ESR, using newly developed software. The SRLS model explicitly accounts for the overall tumbling of the protein and the internal modes of motion, which include the motion of the nitroxide side chain (expected to be the same for both mutants) and backbone fluctuations. Very good simultaneous fits are obtained. Whereas two conformers (or spectral components) are typically detected at the lower temperatures, only a single component is observed at the higher temperatures. The significant differences in the high-frequency spectra for the two mutants are readily attributed mainly to a difference in their respective local ordering. That is, site 72 exhibits significantly greater local ordering than does site 131, which is expected from the greater rigidity of the larger helix on which the 72 site is located. The results of this multifrequency study are compared with a previous 9 GHz study. A description of the application of the SRLS model in such a multifrequency study is provided.

Mapping backbone dynamics in solution with site-directed spin labeling: GCN4-58 bZip free and bound to DNA.

In site-directed spin labeling, a nitroxide-containing side chain is introduced at selected sites in a protein. The EPR spectrum of the labeled protein encodes information about the motion of the nitroxide on the nanosecond time scale, which has contributions from the rotary diffusion of the protein, from internal motions in the side chain, and from backbone fluctuations. In the simplest model for the motion of noninteracting (surface) side chains, the contribution from the internal motion is sequence independent, as is that from protein rotary diffusion. Hence, differences in backbone motions should be revealed by comparing the sequence-dependent motions of nitroxides at structurally homologous sites. To examine this model, nitroxide side chains were introduced, one at a time, along the GCN4-58 bZip sequence, for which NMR (15)N relaxation experiments have identified a striking gradient of backbone mobility along the DNA-binding region [Bracken et al. (1999) J. Mol. Biol. 285, 2133]. Spectral simulation techniques and a simple line width measure were used to extract dynamical parameters from the EPR spectra, and the results reveal a mobility gradient similar to that observed in NMR relaxation, indicating that side chain motions mirror backbone motions. In addition, the sequence-dependent side chain dynamics were analyzed in the DNA/protein complex, which has not been previously investigated by NMR relaxation methods. As anticipated, the backbone motions are damped in the DNA-bound state, although a gradient of motion persists with residues at the DNA-binding site being the most highly ordered, similar to those of helices on globular proteins.