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Maximum entropy reconstruction of joint φ,ψ-distribution with a coil-library prior: The backbone conformation of the peptide hormone motilin in aqueous solution from φ and ψ-dependent J-couplings
Abstract
In this paper, we present a new method for structure determination of flexible "random-coil" peptides. A numerical method is described, where the experimentally measured 3J(H(alpha)Nalpha) and [3J(H(alpha)Nalpha+1 couplings, which depend on the phi and psi dihedral angles, are analyzed jointly with the information from a coil-library through a maximum entropy approach. The coil-library is the distribution of dihedral angles found outside the elements of the secondary structure in the high-resolution protein structures. The method results in residue specific joint phi,psi-distribution functions, which are in agreement with the experimental J-couplings and minimally committal to the information in the coil-library. The 22-residue human peptide hormone motilin, uniformly 15N-labeled was studied. The 3J(H(alpha)-N(i+1)) were measured from the E.COSY pattern in the sequential NOESY cross-peaks. By employing homodecoupling and an in-phase/anti-phase filter, sharp H(alpha)-resonances (about 5 Hz) were obtained enabling accurate determination of the coupling with minimal spectral overlap. Clear trends in the resulting phi,psi-distribution functions along the sequence are observed, with a nascent helical structure in the central part of the peptide and more extended conformations of the receptor binding N-terminus as the most prominent characteristics. From the phi,psi-distribution functions, the contribution from each residue to the thermodynamic entropy, i.e., the segmental entropies, are calculated and compared to segmental entropies estimated from 15N-relaxation data. Remarkable agreement between the relaxation and J-couplings based methods is found. Residues belonging to the nascent helix and the C-terminus show segmental entropies, of approximately -20 J K(-1) mol(-1) and -12 J K(-1) mol(-1), respectively, in both series. The agreement between the two estimates of the segmental entropy, the agreement with the observed J-couplings, the agreement with the CD experiments, and the assignment of population to sterically allowed conformations show that the phi,psi-distribution functions are indeed meaningful and useful descriptions of the conformational preferences for each residue in this flexible peptide.
... Wells et al. 2008;Shortle and Ackerman 2001;Meier et al. 2007), and J-couplings (e.g. Schwalbe et al. 1997;Massad et al. 2007). The three bond J-couplings of the peptide backbone provide very useful data since they are directly correlated with the distribution of dihedral angles. ...
... The three bond J-couplings of the peptide backbone provide very useful data since they are directly correlated with the distribution of dihedral angles. In particular the 3 J HNHa coupling (corresponding to the u angle) is frequently used in structural characterizations of unfolded proteins (Schwalbe et al. 1997;Meier et al. 2008;Massad et al. 2007). ...
A powerful experiment for the investigation of conformational properties of unstructured states of proteins is presented. The method combines a phase sensitive J-resolved experiment with a (1)H-(15)N SOFAST-HMQC to provide a 3D spectrum with an E.COSY pattern originating from splittings due to (3)J(HNH alpha) and (2)J(NH alpha) couplings. Thereby an effectively homodecoupled (1)H-(15)N correlation spectrum is obtained with significantly improved resolution and greatly reduced spectral overlap compared to standard HSQC and HMQC experiments. The (3)J(HNH alpha) is revealed in three independent ways directly from the peak positions, allowing for internal consistency testing. In addition, the natural H(N) linewidths can easily be extracted from the lineshapes. Thanks to the SOFAST principle, the limited sweep width needed in the J-dimension and the short phase cycle, data accumulation is rapid with excellent sensitivity per time unit. The experiment is demonstrated for the intrinsically unstructured 14 kDa protein alpha-synuclein.
... The restrained simulations should be no more biased by the restraints than is necessary, which is a principle that movitated the alternative maximum entropy method, which seeks a distribution that reproduces the experimental values of the observables and is minimally perturbed from the unbiased distribution [10][11][12][13]. In contrast to restrained ensemble simulations, however, the maximum entropy method constrains every observable to its exact experimental value, thus it does not take into account the measurement uncertainties, which are ubiq-uitous in all experiments. ...
One popular approach to incorporating experimental data into molecular simulations is to restrain the ensemble average of observables to their experimental values. Here I derive equations for the equilibrium distributions generated by restrained ensemble simulations and the corresponding expected values of observables. My results suggest a method to restrain simulations so that they generate distributions that are minimally perturbed from the unbiased distributions while reproducing the experimental values of the observables within their measurement uncertainties.
... We investigated the presence of SSP within CBP-ID4 by comparing experimentally measured heteronuclear chemical shifts (N, C 0 , C a , and C b nuclei) with the corresponding random coil values (55). The obtained differences (Fig. 2) are distributed around zero, consistent with the disordered The 3 J HN-Ha coupling constants (46) (Fig. 3) provide complementary information to detect a contingent residual structural propensity along the polypeptide chain, and therefore are often used in structural characterizations of chemically unfolded proteins or IDPs (76)(77)(78)(79)(80). The obtained average value of~7 Hz is similar to values obtained for flexible proteins and other disordered peptides (79,80). ...
Here, we present a structural and dynamic description of CBP-ID4 at atomic resolution. ID4 is the fourth intrinsically disordered linker of CREB-binding protein (CBP). In spite of the largely disordered nature of CBP-ID4, NMR chemical shifts and relaxation measurements show a significant degree of α-helix sampling in the protein regions encompassing residues 2-25 and 101-128 (1852-1875 and 1951-1978 in full-length CBP). Proline residues are uniformly distributed along the polypeptide, except for the two α-helical regions, indicating that they play an active role in modulating the structural features of this CBP fragment. The two helical regions are lacking known functional motifs, suggesting that they represent thus-far uncharacterized functional modules of CBP. This work provides insights into the functions of this protein linker that may exploit its plasticity to modulate the relative orientations of neighboring folded domains of CBP and fine-tune its interactions with a multitude of partners.
... Technical issues, however, seem to have hindered a practically useful implementation of the method. Although maximum entropy approaches have been explored in certain aspects of X-ray scattering data [41,42] and NMR [43,44], applications in the context of molecular simulation have been surprisingly few. One of the main practical issues is that one needs to numerically determine the optimal values for the Lagrange multiplier corresponding to each constraint. ...
A key component of computational biology is to compare the results of computer modelling with experimental measurements. Despite substantial progress in the models and algorithms used in many areas of computational biology, such comparisons sometimes reveal that the computations are not in quantitative agreement with experimental data. The principle of maximum entropy is a general procedure for constructing probability distributions in the light of new data, making it a natural tool in cases when an initial model provides results that are at odds with experiments. The number of maximum entropy applications in our field has grown steadily in recent years, in areas as diverse as sequence analysis, structural modelling, and neurobiology. In this Perspectives article, we give a broad introduction to the method, in an attempt to encourage its further adoption. The general procedure is explained in the context of a simple example, after which we proceed with a real-world application in the field of molecular simulations, where the maximum entropy procedure has recently provided new insight. Given the limited accuracy of force fields, macromolecular simulations sometimes produce results that are at not in complete and quantitative accordance with experiments. A common solution to this problem is to explicitly ensure agreement between the two by perturbing the potential energy function towards the experimental data. So far, a general consensus for how such perturbations should be implemented has been lacking. Three very recent papers have explored this problem using the maximum entropy approach, providing both new theoretical and practical insights to the problem. We highlight each of these contributions in turn and conclude with a discussion on remaining challenges.
One popular approach to incorporating experimental data into molecular simulations is to restrain the ensemble average of observables to their experimental values. Here, I derive equations for the equilibrium distributions generated by restrained ensemble simulations and the corresponding expected values of observables. My results suggest a method to restrain simulations so that they generate distributions that are minimally perturbed from the unbiased distributions while reproducing the experimental values of the observables within their measurement uncertainties.
The conformational space available to the flexible molecule α-D-Manp-(1-->2)-α-D-Manp-OMe, a model for the α-(1-->2)-linked mannose disaccharide in N- or O-linked glycoproteins, is determined using experimental data and molecular simulation combined with a maximum entropy approach that leads to a converged population distribution utilizing different input information. A database survey of the Protein Data Bank where structures having the constituent disaccharide were retrieved resulted in an ensemble with >200 structures. Subsequent filtering removed erroneous structures and gave the database (DB) ensemble having three classes of mannose-containing compounds, viz., N- and O-linked structures, and ligands to proteins. A molecular dynamics (MD) simulation of the disaccharide revealed a two-state equilibrium with a major and a minor conformational state, i.e., the MD ensemble. These two different conformation ensembles of the disaccharide were compared to measured experimental spectroscopic data for the molecule in water solution. However, neither of the two populations were compatible with experimental data from optical rotation, NMR (1)H,(1)H cross-relaxation rates as well as homo- and heteronuclear (3)J couplings. The conformational distributions were subsequently used as background information to generate priors that were used in a maximum entropy analysis. The resulting posteriors, i.e., the population distributions after the application of the maximum entropy analysis, still showed notable deviations that were not anticipated based on the prior information. Therefore, reparameterization of homo- and heteronuclear Karplus relationships for the glycosidic torsion angles Φ and Ψ were carried out in which the importance of electronegative substituents on the coupling pathway was deemed essential resulting in four derived equations, two (3)J(COCC) and two (3)J(COCH) being different for the Φ and Ψ torsions, respectively. These Karplus relationships are denoted JCX/SU09. Reapplication of the maximum entropy analysis gave excellent agreement between the MD- and DB-posteriors. The information entropies show that the current reparametrization of the Karplus relationships constitutes a significant improvement. The Φ(H) torsion angle of the disaccharide is governed by the exo-anomeric effect and for the dominating conformation Φ(H) = -40 degrees and Ψ(H) = 33 degrees. The minor conformational state has a negative Ψ(H) torsion angle; the relative populations of the major and the minor states are approximately 3 : 1. It is anticipated that application of the methodology will be useful to flexible molecules ranging from small organic molecules to large biomolecules.
1. GPCRs: Importance and Occurrence G protein-coupled receptors (GPCRs) are seven transmembrane helical bundle proteins (Figure 1) found on the surface of all cells.13 They mediate cellular responses to a diverse range of extracellular stimuli, including both endogenous chemical signals and exogenous environmental agents (e.g., light, amino acids, peptides, proteins, small organic molecules such as amines and lipids, nucleosides, nucleotides, metal ions, and pharmaceuticals). Once activated by an extracellular signal, GPCRs activate heterotrimeric G proteins that interact promiscuously with multiple receptors....
How the information content of an unfolded polypeptide sequence directs a protein towards a well-formed three-dimensional structure during protein folding remains one of the fundamental questions in structural biology. Unfolded proteins have recently attracted further interest due to their surprising prevalence in the cellular milieu, where they fulfill not only central regulatory functions, but also are implicated in diseases involving protein aggregation. The understanding of both the protein folding transition and these often natively unfolded proteins hinges on a more detailed experimental characterization of the conformations and conformational transitions in the unfolded state. This description is intrinsically very difficult due to the very large size of the conformational space. In principle, solution NMR can monitor unfolded polypeptide conformations and their transitions at atomic resolution. However, traditional NMR parameters such as chemical shifts, J couplings, and nuclear Overhauser enhancements yield only rather limited and often qualitative descriptions. This situation has changed in recent years by the introduction of residual dipolar couplings and paramagnetic relaxation enhancements, which yield a high number of well-defined, quantitative parameters reporting on the averages of local conformations and long-range interactions even under strongly denaturing conditions. This information has been used to obtain plausible all-atom models of the unfolded state at increasing accuracy. Currently, the best working model is the coil model, which derives amino acid specific local conformations from the distribution of amino acid torsion angles in the nonsecondary structure conformations of the protein data bank. Deviations from the predictions of such models can often be interpreted as increased order resulting from long-range contacts within the unfolded ensemble.
We have studied the conformation of tau protein and Alzheimer paired helical filaments (PHF) by several spectroscopic, scattering, and imaging methods revealing the overall shape and the conformation of the polypeptide backbone. Tau protein behaves in solution as if it were denatured; no evidence for compact folding was detected. The protein is highly extended, there is no defined radius of gyration, and the scattering is best described by that of a random (''Gaussian'') polymer. CD and Fourier transform infrared spectroscopy show only a minimal content of ordered secondary structure (alpha-helix or beta-sheet). Similarly, PHFs from Alzheimer brain tissue show no detectable secondary structure by x-ray diffraction or spectroscopy. It is thus unlikely that the aggregation of tau into Alzheimer PHFs is based on interactions between strands of beta-sheets (a model currently favored for other disease-related polymers such as beta-amyloid fibers of Alzheimer's disease).
The backbone dihedral angle φ in polypeptides is characterized by four different J couplings: 3JHNHα, 3JHNC‘, 3JHNCβ, and 3JHαC‘. E.COSY and quantitative J correlation techniques have been used to measure these couplings in the protein human ubiquitin, uniformly enriched in 13C and 15N. Assuming that the dihedral backbone angles in solution are identical to those in the X-ray structure of this protein and that HN is located in the C‘−N−Cα plane, Karplus relations for 3JHNHα, 3JHαC‘, and 3JHNCβ, have been reparametrized. The root-mean-square (rms) difference between measured values of 3JHNHα, 3JHαC‘, 3JHNCβ, and 3JHNC‘ and their corresponding Karplus curves are 0.53, 0.25, 0.24, and 0.36 Hz, respectively, whereas the precision of these measurements is considerably better. For any given residue, the differences between the four measured J couplings and values predicted by their Karplus curves on the basis of the X-ray structure-derived φ angle are highly correlated with one another. On average, a root-mean-square change of 5.7° in the X-ray derived φ angles is needed to obtain optimal agreement with all four measured J couplings. There is no clear correlation between the φ angle correction needed and the out-of-plane position of the amide proton predicted by ab initio calculations. The small differences in φ angles therefore presumably result from small uncertainties in the atomic positions of the 1.8 Å X-ray structure. However, they may also be caused by genuine differences between the structure of the protein in solution and in the crystalline state or contain a contribution resulting from deviations from the assumption that the HN−N−Cα−Hα dihedral angle equals φ − 60°.
The Karplus relations for vicinal J couplings, which relate the peptide backbone angles phi and psi to (3)J(H(a)lpha-N) and (3)J(H-N-C'), have been reparametrized on the basis of measurements made on uniformly C-13/N-15-enriched human ubiquitin and backbone angles derived from the 1.8 Angstrom X-ray structure of this protein (Vijay-Kumar, S.; Bugg, C. E.; Cook, W. J. J. Mol. Biol. 1987, 194, 531-544). For (3)J(H(a)lpha-N), values measured using an E.COSY-type HCACO experiment fall in the -1.9 to 0.1 Hz range and are described by the following: (3)J(H(a)lpha-N) = -0.88 cos(2)(psi + 60 degrees) - 0.61 cos(psi + 60 degrees) - 0.27. The root-mean-square difference (rmsd) between measured values and the Karplus relation is 0.16 Hz. Values measured for (3)J(H-N-C') using an E.COSY-type HNCA experiment fall in the -0.4 to 3.6 Hz range, are described by 4.0 cos(2)(phi) + 1.1 cos(phi) + 0.1, and fit the observed J couplings with an rmsd of 0.45 Hz.
Protein folding and unfolding are coupled to a range of biological phenomena, from the regulation of cellular activity to
the onset of neurodegenerative diseases. Defining the nature of the conformations sampled in nonnative proteins is crucial
for understanding the origins of such phenomena. We have used a combination of nuclear magnetic resonance (NMR) spectroscopy
and site-directed mutagenesis to study unfolded states of the protein lysozyme. Extensive clusters of hydrophobic structure
exist within the wild-type protein even under strongly denaturing conditions. These clusters involve distinct regions of the
sequence but are all disrupted by a single point mutation that replaced residue Trp62 with Gly located at the interface of the two major structural domains in the native state. Thus, nativelike structure in
the denatured protein is stabilized by the involvement of Trp62 in nonnative and long-range interactions.
We consider Thomas Bayes's famous Scholium--his argument in defence of an a priori uniform distribution for an unknown probability, and argue that critics (R. A. Fisher) and friends (Karl Pearson, Harold Jeffreys) alike have misinterpreted the argument as an appeal to the principle of insufficient reason, and that Bayes's actual argument is free from the principal defect it has been charged with. True "Bayesian Inference" is found to differ considerably from and perhaps be logically preferable to modern perceptions of it.
NMR has unique potential for detailed structural characterization of denatured states of proteins, provided that workable spectral resolution and sequence-specific assignments can be obtained in spite of the lack of conformation-dependent dispersion of the 1 H chemical shifts. Structures can be determined in the presence of dynamic conformational polymorphism. This has recently been achieved for urea-unfolded bacteriophage 434 repressor, and NMR assignments were determined for urea-unfolded FK 506-binding protein.
The solution structure of the 22-residue peptide hormone motilin has been studied by circular dichroism and two-dimensional ¹H nuclear magnetic resonance spectroscopy. Circular dichroism spectra indicate the presence of α-helical secondary structure in aqueous solution, and the secondary structure can be stabilized with hexafluoro-2-propanol. Sequence-specific assignments of the proton NMR spectrum of porcine motilin in 30% hexafluoro-2-propanol have been made by using two-dimensional NMR techniques. All backbone proton resonances (NH and αCH) and most of the side-chain resonances have been assigned by using double-quantum-filtered COSY, RELAYED-COSY, and NOESY experiments. Simulations of NOESY cross-peak intensities as a function of mixing time indicate that spin diffusion has a relatively small effect in peptides the size of motilin, thereby allowing the use of long mixing times to confidently make assignments and delineate secondary structure. Sequential αCH-NH and NH-NH NOESY connectivities were observed over a significant portion of the length of the peptide. The intensities of selected NOESY cross-peaks relative to corresponding diagonal peaks were used to estimate a rotational correlation time of approximately 2.5 ns for the peptide, indicating that the peptide exists as a monomer in solution under the conditions used here.
Using the Maximum Entropy principle, we find probability distribution of torsion angles in proteins. We estimate parameters of this distribution numerically, by implementing the conjugate gradient method in Polak-Ribiere variant. We investigate practical approximations of the theoretical distribution. We discuss the information content of these approximations and compare them with standard histogram method. Our data are pairs of main chain torsion angles for a selected subset of high resolution non-homologous protein structures from Protein Data Bank.
The valence‐bond theory for the contact electron‐spin coupling of nuclear magnetic moments is used to calculate the proton‐proton, proton‐fluorine, and fluorine‐fluorine coupling constants in ethanic and ethylenic molecules. A considerable simplification is introduced into the theory by approximations which reduce the problem to one involving only a small number of electrons and canonical structures. The agreement between calculated and experimental values is such as to demonstrate that the mechanism considered is the one of primary importance for the nuclear coupling in the compounds studied. Of particular interest is the theoretical confirmation of the observation that in ethylenic compounds the trans coupling between nuclei (HH, HF, FF) is considerably larger than cis coupling.
PFG-NMR methods were used to measure the translational diffusion coefficients for the Aβ peptide involved in Alzheimer's disease and also for a series of fragments of this peptide. The peptides ranged from a pentamer to the full length Aβ(1–40). They were studied at 25° C and physiological pH in aqueous solution. The measured diffusion coefficients, including those of known monomeric peptides, were fitted without systematic deviations to a scaling law function of the molecular mass. We concluded that under these conditions Aβ(1–40) is in monomeric form. From the diffusion coefficient data, hydrodynamic radii rH were evaluated for the peptides. When combining our results on non- or weakly structured peptides with previously reported results on denatured proteins, we found that the hydrodynamic radii for the combined dataset could be well described by the same scaling law relating them to the molecular weight. The same law would even encompass data on single amino acids and di- and tripeptides measured by classical methods. From the above-mentioned experimental data, scaling law parameters were determined. The relation between the measured hydrodynamic radius (rH) and the molecular weight of the polypeptide chain (Mr) for amino acids, peptides and denatured proteins is rH = 0.27Mr0.50 Å. There is a remarkably good fit to this function for the measured hydrodynamic radii in a large range, almost three orders of magnitude, of molecular weights. The numerical value of the exponent, 0.5, is an indication that these polymers behave as Gaussian chains. Copyright © 2002 John Wiley & Sons, Ltd.
Dilute aqueous solutions of glucagon were investigated by high-resolution 1H nuclear magnetic resonance at 360 MHz. Monomeric glucagon was found to adopt predominantly an extended flexible conformation which contains, however, a local non-random spatial structure involving the fragment -Phe-22-Val-23-Gln-24-Trp-25-. This local conformation is preserved in the partial sequence 22–26 and could thus be characterized in detail. Two interesting conclusions resulted from these experiments. One is that the local spatial structure in the fragment 22–25 of glucagon is identical to that observed in the fragment 20–23 of the human parathyroid hormone. Secondly, the backbone conformation in the C-terminal fragment of glucagon in solution must be different from the α-helical structure observed in single crystals of glucagon. These new structural data are analyzed with regard to relationships with glucagon binding to the target cells.
Geometrical validation around the Cα is described, with a new Cβ measure and updated Ramachandran plot. Deviation of the observed Cβ atom from ideal position provides a single measure encapsulating the major structure-validation information contained in bond angle distortions. Cβ deviation is sensitive to incompatibilities between sidechain and backbone caused by misfit conformations or inappropriate refinement restraints. A new ϕ,ψ plot using density-dependent smoothing for 81,234 non-Gly, non-Pro, and non-prePro residues with B < 30 from 500 high-resolution proteins shows sharp boundaries at critical edges and clear delineation between large empty areas and regions that are allowed but disfavored. One such region is the γ-turn conformation near +75°,−60°, counted as forbidden by common structure-validation programs; however, it occurs in well-ordered parts of good structures, it is overrepresented near functional sites, and strain is partly compensated by the γ-turn H-bond. Favored and allowed ϕ,ψ regions are also defined for Pro, pre-Pro, and Gly (important because Gly ϕ,ψ angles are more permissive but less accurately determined). Details of these accurate empirical distributions are poorly predicted by previous theoretical calculations, including a region left of α-helix, which rates as favorable in energy yet rarely occurs. A proposed factor explaining this discrepancy is that crowding of the two-peptide NHs permits donating only a single H-bond. New calculations by Hu et al. [Proteins 2002 (this issue)] for Ala and Gly dipeptides, using mixed quantum mechanics and molecular mechanics, fit our nonrepetitive data in excellent detail. To run our geometrical evaluations on a user-uploaded file, see MOLPROBITY (http://kinemage.biochem.duke.edu) or RAMPAGE (http://www-cryst.bioc.cam.ac.uk/rampage). Proteins 2003;50:437–450. © 2003 Wiley-Liss, Inc.
A new strategy is described for the production of peptides enriched with stable isotopes. Peptides of interest are expressed in Escherichia coli (E. coli) cells as recombinant fusion proteins with Saccharomyces cerevisiae ubiquitin. This method yields as much as 30–100 mg/l of isotope-enriched fusion proteins in minimal media. A decahistidine tag attached to the N-terminus of ubiquitin enables a one-step purification of the fusion protein via Ni2+-chelating affinity chromatography. The ubiquitin moiety is then easily and specifically cleaved off by a protease, yeast ubiquitin hydrolase. Since this enzyme is also expressed at a high level in E. coli cells and can be purified in one step, the presented strategy has an advantage in view of costs over others that use commercially available proteases. In addition, since ubiquitin fusion proteins easily refold, the fusion protein can be expressed either in a soluble form or as inclusion bodies. This flexibility enables us to prepare peptides that are unstable in a soluble state in E. coli cells. As an example, the expression and the uniform stable isotope enrichment with 15N and/or13 C are described for mastoparan-X, a tetradecapeptide known to activate GTP-binding regulatory proteins. An amide group at the C-terminus of this peptide can also be formed by our method. The presented system is considered powerful for the stable isotope enrichment of short peptides with proton resonances that are too severely overlapped to be analyzed solely by proton NMR.
Treatment of the predictive aspect of statistical mechanics as a form of statistical inference is extended to the density-matrix formalism and applied to a discussion of the relation between irreversibility and information loss. A principle of "statistical complementarity" is pointed out, according to which the empirically verifiable probabilities of statistical mechanics necessarily correspond to incomplete predictions. A preliminary discussion is given of the second law of thermodynamics and of a certain class of irreversible processes, in an approximation equivalent to that of the semiclassical theory of radiation. It is shown that a density matrix does not in general contain all the information about a system that is relevant for predicting its behavior. In the case of a system perturbed by random fluctuating fields, the density matrix cannot satisfy any differential equation because rho˙(t) does not depend only on rho(t), but also on past conditions The rigorous theory involves stochastic equations in the type rho(t)=G(t, 0)rho(0), where the operator G is a functional of conditions during the entire interval (0-->t). Therefore a general theory of irreversible processes cannot be based on differential rate equations corresponding to time-proportional transition probabilities. However, such equations often represent useful approximations.
A new approach to the interpretation of nuclear magnetic resonance relaxation experiments on macromolecules in solution is presented. This paper deals with the theoretical foundations and establishes the range of validity of this approach, and the accompanying paper demonstrates how a wide variety of experimental relaxation data can be successfully analyzed by using this approach. For both isotropic and anisotropic overall motion, it is shown that the unique imformation on fast internal motions contained in relaxation experiments can be completely specified by two model-independent quantities; (1) a generalized order parameter, S, which is a measure of the spatial restriction of the motion, and (2) an effective correlation time, T/sub e/, which is a measure of the rate of motion. A simple expression for the spectral density involving these two parameters is derived and is shown to be exact when the internal (but not overall) motions are in the extreme narrowing limit. The model-free approach (so called because S² and T/sub e/ have model-independent significance) consists of using the above spectral density to least-squares fit relaxation data by treating S² and T/sub e/ as adjustable parameters. The range of validity of this approach is illustrated by analyzing error-free relaxation data generated by using sophisticated dynamical models. Empirical rules are presented that allow one to estimate the of S² and T/sub e/ extracted by using the model-free approach by considering their numerical values, the resonance frequencies, and the parameters for the overall motion. For fast internal motions, it is unnecessary to use approaches based on complicated spectral densities derived within the framework of a model because all models that can give the correct value of S² work equally well.
Fast transverse relaxation of 1H, 15N, and 13C by dipole-dipole coupling (DD) and chemical shift anisotropy (CSA) modulated by rotational molecular motions has a dominant impact on the size limit for biomacromolecular structures that can be studied by NMR spectroscopy in solution. Transverse relaxation-optimized spectroscopy (TROSY) is an approach for suppression of transverse relaxation in multidimensional NMR experiments, which is based on constructive use of interference between DD coupling and CSA. For example, a TROSY-type two-dimensional 1H,15N-correlation experiment with a uniformly 15N-labeled protein in a DNA complex of molecular mass 17 kDa at a 1H frequency of 750 MHz showed that 15N relaxation during 15N chemical shift evolution and 1HN relaxation during signal acquisition both are significantly reduced by mutual compensation of the DD and CSA interactions. The reduction of the linewidths when compared with a conventional two-dimensional 1H,15N-correlation experiment was 60% and 40%, respectively, and the residual linewidths were 5 Hz for 15N and 15 Hz for 1HN at 4°C. Because the ratio of the DD and CSA relaxation rates is nearly independent of the molecular size, a similar percentagewise reduction of the overall transverse relaxation rates is expected for larger proteins. For a 15N-labeled protein of 150 kDa at 750 MHz and 20°C one predicts residual linewidths of 10 Hz for 15N and 45 Hz for 1HN, and for the corresponding uniformly 15N,2H-labeled protein the residual linewidths are predicted to be smaller than 5 Hz and 15 Hz, respectively. The TROSY principle should benefit a variety of multidimensional solution NMR experiments, especially with future use of yet somewhat higher polarizing magnetic fields than are presently available, and thus largely eliminate one of the key factors that limit work with larger molecules.
The organization of the internal contents of bovine adrenal chromaffin granules has been studied using nuclear magnetic resonance spectroscopy. The method permits an examination of the interactions between adenosine triphosphate, metal ions, adrenaline and the chromogranin proteins. Particular advantage accrues when the naturally occurring cations, magnesium and calcium are replaced by manganese cations, since, as shown here, the manganous ion is an effective perturbing probe of structure. The nuclear magnetic resonance spectrum of the protein in the vesicles is compared with that of the isolated proteins.The results show that there is a loose network of interactions between the various components. The major part of the network is the interaction of the chromogranin protein, shown to have approximately a random coil conformation, with the adenosine triphosphate and the adrenaline. The purpose of the organized loose structure would appear to be to lower osmotic pressure without hindering rapid release of the vesicle contents on breaking the membrane.
A recent systematic study of porcine motilin fragments has clearly shown that biological activity resides in the amino-terminal end. The amino-terminal tetradecapeptide retains more than 90% of the potency of the full molecule. We now examined the effect of replacement of residues 1 through 11 by either their D-isomer or by alanine in [Leu13]pMOT(1-14). Peptides were synthesized using Fmoc solid phase methodology, purified by HPLC, and assayed for their ability to displace bound motilin (rabbit antral smooth muscle homogenate) and to induce contractions (isolated rabbit duodenal segments). The negative logarithm of the concentration displacing 50% of the tracer (pIC50), or producing 50% of the maximal contractile response (pEC50), was determined. All compounds were still full agonists. A reduction in potency of more than two log units was seen for the compounds in which residues 1 (Phe), 4 (Ile), and 7 (Tyr) were replaced by Ala and residues 3 (Pro), 4 (Ile), and 6 (Thr) by their D-isomer. The largest drop was noted for the analogs substituted at position 4. For all compounds there was an almost perfect correlation between the pIC50 and the pEC50 values (r = 0.96), although the pEC50 was consistently smaller. These results show that the biological activity of motilin is mainly determined by the first seven residues. The pharmacophore consists of the aromatic rings from Phe1 and Tyr7 and the aliphatic side chains from Val2 and Ile4. Pro3, Phe5, and Thr6 may stabilize the bioactive conformation.
Several peptide fragments representing N-terminal, C-terminal, and internal sequences of [Leu13]porcine motilin ([Leu13]pMOT) were synthesized using Fmoc solid phase methodology. Peptides were assayed for motilin receptor binding activity in a rabbit antrum smooth muscle preparation and for stimulation of contractile activity in segments of rabbit duodenum. In vitro activity was directly correlated with motilin receptor binding affinity for all [Leu13]pMOT fragments examined. N-Terminal fragments of just over half the length of the native peptide are nearly equipotent as full-length motilin. These results suggest that the N-terminal segment, together with residues from the mid-portion of the molecule, constitutes the bioactive portion of pMOT. The C-terminal segment, in contrast, contributes little to receptor binding affinity or in vitro activity.
Using small-angle X-ray scattering and Fourier transform infrared spectroscopy, we have determined that the thermally denatured state of native ribonuclease A is on average a compact structure having residual secondary structure. Under strongly reducing conditions, the protein further unfolds into a looser structure with larger dimensions but still retains a comparable amount of secondary structure. The dimensions of the thermally and chemically denatured states of the reduced protein are different but both are more compact than is predicted for a random coil of the same length. These results demonstrate that thermal denaturation in ribonuclease A is not a simple two-state transition from a native to a completely disordered random coil state.
The "random coil" conformational problem is examined by comparison of vibrational CD (VCD) spectra of various polypeptide model systems with that of proline oligomers [(Pro)n] and poly(L-proline). VCD, ir and uv CD spectra of blocked L-proline oligopeptides [(Pro)n, n = 2-12] in different solvents are reported and compared to the spectra of poly(L-proline) II, poly(L-glutamic acid), and unblocked proline oligomers. Based on the chain-length dependence of the VCD and electronic CD (ECD) spectra of proline oligomers, it is established that VCD spectra are dominated by short-range interactions. The VCD of random coil model polypeptides is shown to be identical in shape but smaller in magnitude than poly(L-proline) II and of similar magnitude to that of (Pro)n (n = 3, 4). Based on the spectral evidence, it is concluded that the "random coil" conformation has a large fraction of helical regions, conformationally similar to the left-handed, 3(1) polyproline II helix, as was previously suggested by Krimm and co-workers. This conclusion is further supported by studies of effects of salt (CaCl2, LiBr, LiClO4), temperature (5-75 degrees C), and pH on the VCD spectra of L-proline oligomers, poly(L-proline) II, and poly(L-glutamic acid). These show that, after each of these perturbations, a significant local ordering remains in the oligomers and polymers studied, and that charged polypeptides such as poly(L-glutamic acid) are more flexible than are polyproline or even L-proline oligomers.
A model of the structure of the 22 amino acid residue gastrointestinal peptide hormone motilin in 30% hexafluoro-2-propanol has been obtained by using distance constraints obtained from two-dimensional nuclear Overhauser enhancements. A set of initial structures have been generated by using the distance geometry program DIANA, and 10 of these structures have been refined by using restrained molecular dynamics (AMBER). The resulting structures are virtually indistinguishable in terms of constraint violations and energies and display less than 0.5-A root mean square deviations (RMSD) of the backbone atom positions from Tyr7 to Lys20. A comparison of back-calculated and experimental NOE intensities indicates that RMSD's are not the best indicators of the goodness of fit or of the precision with which the structure is defined. The structure was further refined by fitting the experimental NOE data using an iterative full relaxation matrix analysis. The mean error between the observed and calculated backbone NOE intensities for the final refined structure was 0.23 for the full length of the molecule, 0.18 for the region from Glu9 to Lys20, and 0.29 for the region from Phe1 to Gly8. R factors for the same regions were 0.27, 0.19, and 0.43, respectively. All of the NOE-determined structures consistently display an alpha-helix which extends from Glu9 to Lys20. Considerable lack of definition of structure exists at the amino and carboxyl ends of the molecule and also in the vicinity of Thr6-Tyr7-Gly8. A tendency to form a wide turn appears to exist over the sequence Pro3-Ile4-Phe5-Thr6, but the structure in this region is not well defined by the NOE data.
The solution structure of the 22-residue peptide hormone motilin has been studied by circular dichroism and two-dimensional 1H nuclear magnetic resonance spectroscopy. Circular dichroism spectra indicate the presence of alpha-helical secondary structure in aqueous solution, and the secondary structure can be stabilized with hexafluoro-2-propanol. Sequence-specific assignments of the proton NMR spectrum of porcine motilin in 30% hexafluoro-2-propanol have been made by using two-dimensional NMR techniques. All backbone proton resonances (NH and alpha CH) and most of the side-chain resonances have been assigned by using double-quantum-filtered COSY, RELAYED-COSY, and NOESY experiments. Simulations of NOESY cross-peak intensities as a function of mixing time indicate that spin diffusion has a relatively small effect in peptides the size of motilin, thereby allowing the use of long mixing times to confidently make assignments and delineate secondary structure. Sequential alpha CH-NH and NH-NH NOESY connectivities were observed over a significant portion of the length of the peptide. A number of medium-range NOESY cross-peaks indicate that the peptide is folded into alpha-helix from Glu9 to Lys20, which agrees favorably with the 50% helical content determined from CD measurements. The intensities of selected NOESY cross-peaks relative to corresponding diagonal peaks were used to estimate a rotational correlation time of approximately 2.5 ns for the peptide, indicating that the peptide exists as a monomer in solution under the conditions used here.
Publisher Summary This chapter deals with the recent developments regarding the description and nature of the conformation of proteins and polypeptides with special reference to the stereochemical aspects of the problem. This chapter considers the parameters that are required for an adequate description of a polypeptide chain. This chapter focuses the attention on what may be called “internal parameters”—that is, those which can be defined in terms of the relationships among atoms or units that form the building blocks of the polypeptide chains. This chapter also provides an account of the mathematical method of utilizing these parameters for calculating the coordinates of all the atoms in a suitable frame of reference, so that all the interatomic distances, and bond angles, can be calculated and their consequences worked out. This chapter observes conformations in amino acids, peptides, polypeptides, and proteins.
It has been indicated that amino acids have various intrinsic phi and psi propensities, as demonstrated from the comparison between experimental secondary structure propensities and their relative statistical distribution in the protein database for the appropriate region of the Ramachandran plot. However, this does not eliminate the possibility that these experimental propensities are the result of context effects due to the secondary structure environment of the mutated position. To demonstrate that there are at least real intrinsic phi propensities, independent of context effects, we have used two different nuclear magnetic resonance parameters related to the phi dihedral angle (J3 alpha HN coupling constants and the chemical shift of the C alpha H proton), determined in random-coil tetra- and pentapeptides, and/or in proteins. Comparison of the experimentally determined values for these parameters with the theoretical ones determined from the analysis by different empirical and theoretical equations of the phi dihedral angle statistical distribution of the amino acids in the protein database, supports the idea that each amino acid has, at least, different phi intrinsic propensities. Consideration of all conformations, or only coil conformations, in the protein database produces similar results. The reasonable correlation between these experimental and theoretical data and the hydrogen-exchange data in random-coil peptides suggests that maximisation of hydrophobic surface-buried and hydrogen-bond formation with the solvent could be responsible for these different random-coil conformational preferences. Analysis of the intrinsic propensities for beta-strand, alpha-helix and polyproline II dihedral angles of the 20 amino acids in coil conformations, indicates that the side-chain of the amino acids is mainly determining the relative preferences for the phi angle.
The backbone dynamics of the C-terminal SH2 domain of phospholipase C gamma 1 have been investigated. Two forms of the domain were studied, one in complex with a high-affinity binding peptide derived from the platelet-derived growth factor receptor and the other in the absence of this peptide. 2-D 1H-15N NMR methods, employing pulsed field gradients, were used to determine steady-state 1H-15N NOE values and T1 and T2 15N relaxation times. Backbone dynamics were characterized by the overall correlation time (tau m), order parameters (S2), effective correlation times for internal motions (tau e), and, if required, terms to account for motions on a microsecond-to-millisecond-time scale. An extended two-time-scale formalism was used for residues having relaxation data and that could not be fit adequately using a single-time-scale formalism. The overall correlation times of the uncomplexed and complexed forms of SH2 were found to be 9.2 and 6.5 ns, respectively, suggesting that the uncomplexed form is in a monomer-dimer equilibrium. This was subsequently confirmed by hydrodynamic measurements. Analysis of order parameters reveals that residues in the so-called phosphotyrosine-binding loop exhibited higher than average disorder in both forms of SH2. Although localized differences in order parameters were observed between the uncomplexed and complexed forms of SH2, overall, higher order parameters were not found in the peptide-bound form, indicating that on average, picosecond-time-scale disorder is not reduced upon binding peptide. The relaxation data of the SH2-phosphopeptide complex were fit with fewer exchange terms than the uncomplexed form. This may reflect the monomer-dimer equilibrium that exists in the uncomplexed form or may indicate that the complexed form has lower conformational flexibility on a microsecond-to-millisecond-time scale.
Many different factors contribute to secondary structure propensities, including phi, psi preferences, side-chain interactions, steric effects and hydrophobic tertiary contacts. To deconvolute these competing factors, we have adopted a novel approach which quantifies the intrinsic phi, psi propensities for residues in coil regions (that is, residues not in alpha-helix and not in beta-strand). Comparisons of intrinsic phi, psi propensities with their equivalent secondary structure propensities show that while correlations for helix are relatively weak, those for strand are much stronger. This paper describes our new phi, psi propensities and provides an explanation for the variations observed.
The picosecond time-resolved fluorescence decay data of nine single-tryptophan (trp) proteins and two multi-trp proteins in their native and denatured states were analyzed by the maximum entropy method (MEM). In the denatured state (6 M guanidine hydrochloride) a majority of the single-trp proteins show bimodal (at 25 degrees C) and trimodal (at 85 degrees C) distributions with similar patterns and similar values for average lifetimes. In the native state of the proteins the lifetime distributions were bimodal or trimodal. These results (multimodal distributions) are contradictory to the unimodal Lorentzian distribution of lifetimes reported for some proteins in the native and denatured states. MEM analysis gives a unimodal distribution of lifetimes only when the signal-to-noise ratio is poor in the time-resolved fluorescence decay data. The unimodal distribution model is therefore not realistic for proteins in the native and denatured states. The fluorescence decay components of the bi- or trimodal distribution are associated with the rotamer structures of the indole moiety when the protein is in the random coil state.
We have studied the conformation of tau protein and Alzheimer paired helical filaments (PHF) by several spectroscopic, scattering, and imaging methods revealing the overall shape and the conformation of the polypeptide backbone. Tau protein behaves in solution as if it were denatured; no evidence for compact folding was detected. The protein is highly extended, there is no defined radius of gyration, and the scattering is best described by that of a random ("Gaussian") polymer. CD and Fourier transform infrared spectroscopy show only a minimal content of ordered secondary structure (alpha-helix or beta-sheet). Similarly, PHFs from Alzheimer brain tissue show no detectable secondary structure by x-ray diffraction or spectroscopy. It is thus unlikely that the aggregation of tau into Alzheimer PHFs is based on interactions between strands of beta-sheets (a model currently favored for other disease-related polymers such as beta-amyloid fibers of Alzheimer's disease).
Formation of local structure and overall chain dimensions in the 124-residue, four-disulfide protein bovine pancreatic ribonuclease A (RNase A) under conditions favoring either the native or partially folded states have been studied by nonradiative excitation energy transfer measurements. Three RNase A derivatives, doubly labeled with 2-naphthylalanine amide (fluorescent donor) at the C-terminus of each and 7-carboxymethylamino-4-methyl-coumarin (fluorescent acceptor) at the epsilon-amino group of lysine 1, 61, and 104, respectively [(1-124)RNase A, (61-124)RNase A, and (104-124)Rnase A], were prepared. RNase A was modified by a two-step labeling strategy involving prior modification of the C-terminus with the donor probe by enzymatic methods, followed by modification of lysine epsilon-amino groups with the coumarin derivative. The derivatives were purified by liquid chromatography and characterized by tryptic mapping. The mono-labeled donor derivative (without acceptor) undergoes a reversible thermal folding transition (Tm = 48.3 degrees C; native RNase A, Tm = 54.4 degrees C), and all labeled derivatives retain enzymatic activity (activities against the substrate cCMP relative to native are 87 +/- 5%, 94 +/- 6.5%, 79 +/- 10%, and 207 +/- 15% for the donor-only and doubly-labeled derivatives with the acceptor at Lys 104, 61, and 1, respectively), supporting the suitability of these derivatives for protein folding studies. Time-resolved fluorescence measurements were used to determine the extent of nonradiative excitation energy transfer between donor and acceptor probes, which allowed recovery of parameters describing the distribution of interprobe distances and the diffusion coefficient of the ends of the segments defined by the pairs of sites labeled by the probes. Use of a donor with a relatively long intrinsic fluorescence decay rate allowed greater precision in the recovery of the interprobe diffusion coefficients compared with earlier studies using donors with shorter intrinsic decay rates, and this parameter provides an important measure of the extent of folding and degree of packing of the chain segments. Analyses for each derivative were carried out under solution conditions favoring native (pH 5.0, 22 degrees C, < 0.7 M guanidinium hydrochloride) or denatured (> 6 M guanidinium hydrochloride) chain conformations, both with and without intact disulfide bonds (in the absence or presence of dithiothreitol, respectively).(ABSTRACT TRUNCATED AT 400 WORDS)
Using a data base of 85 high resolution protein crystal structures the distributions of main chain torsion angles, both in secondary structure and in coil regions where no secondary structure is present, have been analysed. These torsion angle distributions have been used to predict NMR homonuclear and heteronuclear coupling constants for residues in secondary structure using known Karplus relationships. For α helices, 310helices and β strands mean predicted3JHNαcoupling constants are 4.8, 5.6 and 8.5 Hz, respectively. These values differ significantly from those expected for the ideal 7φ angles (3.9, 3.0 and 8.9 Hz; φ=−57 °, −49 °, −139 ° for α and 310helices and β strands (antiparallel), respectively) in regular secondary structure, but agree well with available experimental NMR data for nine proteins. The crystallographic data set has also been used to provide a basis for interpreting coupling constants measured for peptides and denatured proteins. Using a model for a random coil, in which all residues adopt distributions of φ, ψ angles equivalent to those seen for residues in the coil regions of native folded proteins, predicted3JHNαvalues for different residue types have been found to range from 5.9 Hz and 6.1 Hz for glycine and alanine, respectively, to 7.7 Hz for valine. A good correlation has been found between the predicted3JHNαcoupling constants for this model and experimental values for a set of peptides that other evidence suggest are highly unstructured. For other peptides, however, deviations from the predictions of the model are clear and provide evidence for additional interactions within otherwise disordered states. The values of homonuclear and heteronuclear coupling constants derived from the protein data base listed here therefore provide a basis not only for analysing the secondary structure of native proteins in solution but for assessing and interpreting the extent of structure present in peptides and non-native states of proteins.
Established NMR methods are increasingly being applied to the non-native states of proteins. For small denatured proteins, full assignment of proton, 15N and 13C resonances is often straightforward. Sensitive methods exist for detecting fractionally populated alpha helices and beta strands, but defining transient interactions among side chains is proving more problematic. The non-native states of several small proteins are being intensively investigated to address a number of questions about protein folding.
The relation between order parameters derived from NMR spin relaxation experiments and the contribution to conformational entropy from ns-ps timescale bond vector dynamics is investigated by considering a number of simple models describing bond vector motion. In a few cases both classical and quantum mechanical derivations are included to establish the validity of obtaining order parameter-entropy relations using classical mechanics only. For these cases it is found that classical and quantum mechanical derivations give very similar results so long as the square of the order parameter of the bond vector is less than approximately 0.95. For a given change in order parameter, the change in conformational entropy is sensitive to the model employed, with the absolute value of the entropy change increasing with the number of degrees of freedom in the model. The entropy-order parameter profile calculated from a 1.12 ns molecular dynamics trajectory of fully hydrated Escherichia coli ribonuclease HI is well fit using a simple expression based on a model assuming bond vector diffusion in a cone, suggesting that it may well be possible to extract meaningful entropy changes reflecting changes in ps-ns time scale motions from changes in NMR-derived order parameters. Contributions to the conformational entropy change associated with a folding-unfolding transition of an SH3 domain and calculated from changes in rapid N-HN backbone dynamics are presented.
Non-native states of proteins are of increasing interest because of their relevance to issues such as protein folding, translocation and stability. A framework for interpreting the wealth of experimental data for non-native states emerging from rapid advances in experimental techniques involves comparison with a "random coll' state, which possesses no structure except that inherent in the local interactions. We review here the concept of a random coil, from its global to its local properties. In particular, we focus on the description of a random coil in terms of statistical distributions in psi, phi space. We show that such a model, in combination with experimental data, provides insight into the structural properties of polypeptide chains and has significance for understanding protein folding and for molecular design.
The solution structure of the porcine gastrointestinal peptide hormone motilin was determined in the presence of sodium dodecyl sulfate (SDS) micelles at 28 degrees C using 1H nuclear magnetic resonance, full relaxation matrix analysis, and structure calculations based on restrained molecular dynamics. The structure of motilin in SDS micelles is described by a reverse gamma-turn and a beta-turn of type II in the N terminal end, an alpha-helical region in the middle of the molecule, and an extended structure at the C terminus. The position of the motilin molecule relative to the SDS micelles was probed by adding spin-labeled stearic acids, containing 12-doxyl or 5-doxyl spin-labels. We observed selective broadening of the proton resonances of residues 3-5 and concluded that they must be located in the interior of the micelle. These experiments suggest a structural model in which the hydrophobic N terminus consists of two well-defined turns buried in the interior of the micelle, whereas the amphiphilic alpha-helical part is located at the surface of the micelle. Spectral density mapping using a 13C label on the alphaC of Leu10 gave overall rotational correlation times taum of 6.6 and 4.5 ns at 35 and 45 degrees C, respectively. The long correlation time in combination with a high order parameter (S = 0.92) indicates that motilin has a rigid structure in the complex with the SDS micelle.
Analysis of residues in coil regions of protein structures presents a novel approach to deconvoluting the various competing factors which determine the intrinsic phi,psi propensities of amino acids free from the regular interactions associated with beta-strands and alpha-helices. We have considered the role of context on phi,psi preferences by examining the effects of neighbouring residues in modulating coil propensities within a data base of 512 high-resolution, low-homology structures. In the general case, when flanking residues are beta-branched or aromatic (Val, Ile, Tyr and Phe) the beta-propensity (Pbeta) increases significantly, largely due to steric effects between flanking residues. More subtle residue-specific effects are apparant when Pbeta values are examined in detail, showing "random coil" conformations to be highly sequence-dependent. The effects of flanking residues on phi distributions have been used to calculate context-dependent average 3JNH-Halpha coupling constants. We have examined these findings in the context of the folding of a model 16-residue beta-hairpin peptide, "mutant" hairpin (VSI-->KSK sequence change) and the isolated C-terminal beta-strand fragments of both hairpins. We find a better correlation between 3JNH-Halpha values derived from the data base model and those determined experimentally when context-dependent phi distributions are considered. The individual C-terminal beta-strand sequences (GKKITVSI versus GKKITKSK) of the two hairpins are predisposed to different extents to formation of an extended beta-like conformation. Conformational "predisposition" in this context may contribute significantly to beta-hairpin stability.
A major challenge in the post-genome era will be determination of the functions of the encoded protein sequences. Since it is generally assumed that the function of a protein is closely linked to its three-dimensional structure, prediction or experimental determination of the library of protein structures is a matter of high priority. However, a large proportion of gene sequences appear to code not for folded, globular proteins, but for long stretches of amino acids that are likely to be either unfolded in solution or adopt non-globular structures of unknown conformation. Characterization of the conformational propensities and function of the non-globular protein sequences represents a major challenge. The high proportion of these sequences in the genomes of all organisms studied to date argues for important, as yet unknown functions, since there could be no other reason for their persistence throughout evolution. Clearly the assumption that a folded three-dimensional structure is necessary for function needs to be re-examined. Although the functions of many proteins are directly related to their three-dimensional structures, numerous proteins that lack intrinsic globular structure under physiological conditions have now been recognized. Such proteins are frequently involved in some of the most important regulatory functions in the cell, and the lack of intrinsic structure in many cases is relieved when the protein binds to its target molecule. The intrinsic lack of structure can confer functional advantages on a protein, including the ability to bind to several different targets. It also allows precise control over the thermodynamics of the binding process and provides a simple mechanism for inducibility by phosphorylation or through interaction with other components of the cellular machinery. Numerous examples of domains that are unstructured in solution but which become structured upon binding to the target have been noted in the areas of cell cycle control and both transcriptional and translational regulation, and unstructured domains are present in proteins that are targeted for rapid destruction. Since such proteins participate in critical cellular control mechanisms, it appears likely that their rapid turnover, aided by their unstructured nature in the unbound state, provides a level of control that allows rapid and accurate responses of the cell to changing environmental conditions.
Experimental methods have demonstrated that when a protein unfolds, not all of its structure is lost. Here we report measurement
of residual dipolar couplings in denatured forms of the small protein staphylococcal nuclease oriented in strained polyacrylamide
gels. A highly significant correlation among the dipolar couplings for individual residues suggests that a native-like spatial
positioning and orientation of chain segments (topology) persists to concentrations of at least 8 molar urea. These data demonstrate
that long-range ordering can occur well before a folding protein attains a compact conformation, a conclusion not anticipated
by any of the standard models of protein folding.
An efficient new method is presented for the characterization of motional correlations derived from a set of protein structures without requiring the separation of overall and internal motion. In this method, termed isotropically distributed ensemble (IDE) analysis, each structure is represented by an ensemble of isotropically distributed replicas corresponding to the situation found in an isotropic protein solution. This leads to a covariance matrix of the cartesian atomic positions with elements proportional to the ensemble average of scalar products of the position vectors with respect to the center of mass. Diagonalization of the covariance matrix yields eigenmodes and amplitudes that describe concerted motions of atoms, including overall rotational and intramolecular dynamics. It is demonstrated that this covariance matrix naturally distinguishes between "rigid" and "mobile" parts without necessitating a priori selection of a reference structure and an atom set for the orientational alignment process. The method was applied to the analysis of a 5-ns molecular dynamics trajectory of native ubiquitin and a 40-ns trajectory of a partially folded state of ubiquitin. The results were compared with essential dynamics analysis. By taking advantage of the spherical symmetry of the IDE covariance matrix, more than a 10-fold speed up is achieved for the computation of eigenmodes and mode amplitudes. IDE analysis is particularly suitable for studying the correlated dynamics of flexible and large molecules.
The experimental material accumulated in the literature on the conformational behavior of intrinsically unstructured (natively unfolded) proteins was analyzed. Results of this analysis showed that these proteins do not possess uniform structural properties, as expected for members of a single thermodynamic entity. Rather, these proteins may be divided into two structurally different groups: intrinsic coils, and premolten globules. Proteins from the first group have hydrodynamic dimensions typical of random coils in poor solvent and do not possess any (or almost any) ordered secondary structure. Proteins from the second group are essentially more compact, exhibiting some amount of residual secondary structure, although they are still less dense than native or molten globule proteins. An important feature of the intrinsically unstructured proteins is that they undergo disorder-order transition during or prior to their biological function. In this respect, the Protein Quartet model, with function arising from four specific conformations (ordered forms, molten globules, premolten globules, and random coils) and transitions between any two of the states, is discussed.
The recent suggestion that the classical structure-function paradigm should be extended to proteins and protein domains whose native and functional state is intrinsically unstructured has received a great deal of support. There is ample evidence that the unstructured state, common to all living organisms, is essential for basic cellular functions; thus it deserves to be recognized as a separate functional and structural category within the protein kingdom. In this review, recent findings are surveyed to illustrate that this novel but rapidly advancing field has reached a point where these proteins can be comprehensively classified on the basis of structure and function.