Backbone dynamics of barstar: a (15)N NMR relaxation study

Backbone dynamics of uniformly (15)N-labeled barstar have been studied at 32 degrees C, pH 6.7, by using (15)N relaxation data obtained from proton-detected 2D (1)H-(15)N NMR spectroscopy. (15)N spin-lattice relaxation rate constants (R(1)), spin-spin relaxation rate constants (R(2)), and steady-state heteronuclear (1)H-(15)N NOEs have been determined for 69 of the 86 (excluding two prolines and the N-terminal residue) backbone amide (15)N at a magnetic field strength of 14.1 Tesla. The primary relaxation data have been analyzed by using the model-free formalism of molecular dynamics, using both isotropic and axially symmetric diffusion of the molecule, to determine the overall rotational correlation time (tau(m)), the generalized order parameter (S(2)), the effective correlation time for internal motions (tau(e)), and NH exchange broadening contributions (R(ex)) for each residue. As per the axially symmetric diffusion, the ratio of diffusion rates about the unique and perpendicular axes (D( parallel)/D( perpendicular)) is 0.82 +/- 0.03. The two results have only marginal differences. The relaxation data have also been used to map reduced spectral densities for the NH vectors of these residues at three frequencies: 0, omega(H), and omega(N), where omega(H),(N) are proton and nitrogen Larmor frequencies. The value of tau(m) obtained from model-free analysis of the relaxation data is 5.2 ns. The reduced spectral density analysis, however, yields a value of 5.7 ns. The tau(m) determined here is different from that calculated previously from time-resolved fluorescence data (4.1 ns). The order parameter ranges from 0.68 to 0.98, with an average value of 0.85 +/- 0.02. A comparison of the order parameters with the X-ray B-factors for the backbone nitrogens of wild-type barstar does not show any considerable correlation. Model-free analysis of the relaxation data for seven residues required the inclusion of an exchange broadening term, the magnitude of which ranges from 2 to 9.1 s(-1), indicating the presence of conformational averaging motions only for a small subset of residues.     

NMR structural analysis of a membrane protein: bacteriorhodopsin peptide backbone orientation and motion

In reconstituted vesicles above the lipid phase transition temperature, bacteriorhodopsin (BR) undergoes rotational diffusion about an axis perpendicular to the plane of the bilayer [Cherry, R. J., Muller, U., & Schneider, G. (1977) FEBS Lett. 80, 465]. This diffusion narrows the 13C NMR powder line shape of the BR peptide carbonyls. In contrast, BR in native purple membrane is relatively immobile and exhibits a rigid-lattice powder line shape. By use of the principal values of the rigid-lattice chemical shift tensor and the motionally narrowed line shape from the reconstituted system, the range of Euler angles of the leucine peptide groups relative to the diffusion axis has been calculated. The experimentally observed line shape is inconsistent with those expected for structures which consist entirely of either alpha helix or beta sheet perpendicular to the membrane or beta sheet tilted at angles up to about 60 degrees from the membrane normal. However, for two more complex structural models, the predicted line shapes agree well with the experimental one. These are, first, a structure consisting entirely of alpha1 helices tilted at 20 degrees from the membrane normal and, second, a combination of 60% alpha II helix perpendicular to the membrane plane and 40% antiparallel beta sheet tilted at 10-20 degrees from the membrane normal. The results also indicate that the peptide backbone of bacteriorhodopsin in native purple membrane is extremely rigid even at 40 degrees. The experiments presented here demonstrate a new approach, using solid-state nuclear magnetic resonance (NMR) methods, for structural studies of transmembrane proteins in fluid membrane environments, either natural or reconstituted.(ABSTRACT TRUNCATED AT 250 WORDS)     

Internal bulge and tetraloop of the catalytic domain 5 of a group II intron ribozyme are flexible: implications for catalysis

RNA molecules have an inherent flexibility that enables recognition of other interacting partners through potential disorder-order transitions, yet studies to quantify such motional dynamics remain few. With an increasing database of three-dimensional structures of biologically important RNA molecules, quantifying such motions becomes important to link structural deformations with function. One such system studied intensely is domain 5 (D5) from the self-splicing group II introns, which is at the heart of its catalytic machinery. We report the dynamics of a 36 nucleotide D5 from the Pylaiella littoralis group II intron in the presence and absence of magnesium ions, and at a range of temperatures (298K-318 K). Using high-resolution NMR experiments of heteronuclear nuclear Overhauser enhancement (NOE), spin-lattice (R(1)), and spin-spin (R(2)) (13)C relaxation rates, we determined the rotational diffusion tensor of D5 using the ROTDIF program modified for RNA dynamic analysis (ROTDIF_RNA). The D5 rotational diffusion tensor has an axial symmetric ratio (D(||)/D(perpendicular)) of 1.7+/-0.3, consistent with an estimated overall rotational correlation time of tau(m)=(2D(||)+4D(perpendicular))(-1) of 6.1(+/-0.3) ns at 298 K and 4.1(+/-0.2) ns at 318 K. The measured relaxation data were analyzed with the reduced spectral density mapping formalism using assumed values of the chemical shift anisotropy of the (13)C spins. Both the relaxation data and the values of the spectral density function reveal that the functional groups in D5 implicated in magnesium ion binding and catalysis (catalytic triad, internal bulge, and tetraloop regions) exhibit thermally induced motion on a wide variety of timescales. Because these motions parallel those observed in the intramolecular stem-loop of the U6 element within the spliceosome, we hypothesize that such extensive dynamic disorder likely facilitates D5 engaging both binding and catalytic regions of the ribozyme, and these may be a conserved feature of the catalytic machinery essential for catalysis.     

15N NMR relaxation studies of backbone dynamics in free and steroid-bound Delta 5-3-ketosteroid isomerase from Pseudomonas testosteroni

The backbone dynamics of Delta(5)-3-ketosteroid isomerase (KSI) from Pseudomonas testosteroni has been studied in free enzyme and its complex with a steroid ligand, 19-nortestosterone hemisuccinate (19-NTHS), by (15)N relaxation measurements. The relaxation data were analyzed using the model-free formalism to extract the model-free parameters (S(2), tau(e), and R(ex)) and the overall rotational correlation time (tau(m)). The rotational correlation times were 19.23 +/- 0.08 and 17.08 +/- 0.07 ns with the diffusion anisotropies (D( parallel)/D( perpendicular)) of 1.26 +/- 0.03 and 1.25 +/- 0.03 for the free and steroid-bound KSI, respectively. The binding of 19-NTHS to free KSI causes a slight increase in the order parameters (S(2)) for a number of residues, which are located mainly in helix A1 and strand B4. However, the majority of the residues exhibit reduced order parameters upon ligand binding. In particular, strands B3, B5, and B6, which have most of the residues involved in the dimer interaction, have the reduced order parameters in the steroid-bound KSI, indicating the increased high-frequency (pico- to nanosecond) motions in the intersubunit region of this homodimeric enzyme. Our results differ from those of previous studies on the backbone dynamics of monomeric proteins, in which high-frequency internal motions are typically restricted upon ligand binding.     

Backbone dynamics measurements on leukemia inhibitory factor, a rigid four-helical bundle cytokine

The backbone dynamics of the four-helical bundle cytokine leukemia inhibitory factor (LIF) have been investigated using 15N NMR relaxation and amide proton exchange measurements on a murine-human chimera, MH35-LIF. For rapid backbone motions (on a time scale of 10 ps to 100 ns), as probed by 15N relaxation measurements, the dynamics parameters were calculated using the model-free formalism incorporating the model selection approach. The principal components of the inertia tensor of MH35-LIF, as calculated from its NMR structure, were 1:0.98:0.38. The global rotational motion of the molecule was, therefore, assumed to be axially symmetric in the analysis of its relaxation data. This yielded a diffusion anisotropy D(parallel)/D(perpendicular) of 1.31 and an effective correlation time (4D(perpendicular) + 2D(parallel))(-1) of 8.9 ns. The average values of the order parameters (S2) for the four helices, the long interhelical loops, and the N-terminus were 0.91, 0.84, and 0.65, respectively, indicating that LIF is fairly rigid in solution, except at the N-terminus. The S2 values for the long interhelical loops of MH35-LIF were higher than those of their counterparts in short-chain members of the four-helical bundle cytokine family. Residues involved in LIF receptor binding showed no consistent pattern of backbone mobilities, with S2 values ranging from 0.71 to 0.95, but residues contributing to receptor binding site III had relatively lower S2 values, implying higher amplitude motions than for the backbone of sites I and II. In the relatively slow motion regime, backbone amide exchange measurements showed that a number of amides from the helical bundle exchanged extremely slowly, persisting for several months in 2H2O at 37 degrees C. Evidence for local unfolding was considered, and correlations among various structure-related parameters and the backbone amide exchange rates were examined. Both sets of data concur in showing that LIF is one of the most rigid four-helical bundle cytokines.     

Domain flexibility in ligand-free and inhibitor-bound Escherichia coli adenylate kinase based on a mode-coupling analysis of 15N spin relaxation

Adenylate kinase from Escherichia coli (AKeco), consisting of a 23.6-kDa polypeptide chain folded into domains CORE, AMPbd, and LID catalyzes the reaction AMP + ATP <--> 2ADP. The domains AMPbd and LID execute large-amplitude movements during catalysis. Backbone dynamics of ligand-free and AP(5)A-inhibitor-bound AKeco is studied with slowly relaxing local structure (SRLS) (15)N relaxation, an approach particularly suited when the global (tau(m)) and the local (tau) motions are likely to be coupled. For AKeco tau(m) = 15.1 ns, whereas for AKeco*AP(5)A tau(m) = 11.6 ns. The CORE domain of AKeco features an average squared order parameter, , of 0.84 and correlation times tau(f) = 5-130 ps. Most of the AKeco*AP(5)A backbone features = 0.90 and tau(f) = 33-193 ps. These data are indicative of relative rigidity. Domains AMPbd and LID of AKeco, and loops beta(1)/alpha(1), alpha(2)/alpha(3), alpha(4)/beta(3), alpha(5)/beta(4), and beta(8)/alpha(7) of AKeco*AP(5)A, feature a novel type of protein flexibility consisting of nanosecond peptide plane reorientation about the C(i-1)(alpha)-C(i)(alpha) axis, with correlation time tau(perpendicular) = 5.6-11.3 ns. The other microdynamic parameters underlying this dynamic model include S(2) = 0.13-0.5, tau(parallel) on the ps time scale, and a diffusion tilt beta(MD) ranging from 12 to 21 degrees. For the ligand-free enzyme the tau(perpendicular) mode was shown to represent segmental domain motion, accompanied by conformational exchange contributions R(ex) < or = 4.4 s(-1). Loop alpha(4)/beta(3) and alpha(5)/beta(4) dynamics in AKeco*AP(5)A is related to the "energetic counter-balancing of substrate binding" effect apparently driving kinase catalysis. The other flexible AKeco*AP(5)A loops may relate to domain motion toward product release.     

Dynamics of an integral membrane peptide: a deuterium NMR relaxation study of gramicidin.

Solid state deuterium (2H) NMR inversion-recovery and Jeener-Broekaert relaxation experiments were performed on oriented multilamellar dispersions consisting of 1,2-dilauroyl-sn-glycero-3-phosphatidylcholine and 2H exchange-labeled gramicidin D, at a lipid to protein molar ratio (L/P) of 15:1, in order to study the dynamics of the channel conformation of the peptide in a liquid crystalline phase. Our dynamic model for the whole body motions of the peptide includes diffusion of the peptide around its helix axis and a wobbling diffusion around a second axis perpendicular to the local bilayer normal in a simple Maier-Saupe mean field potential. This anisotropic diffusion is characterized by the correlation times, tau R parallel and tau R perpendicular. Aligning the bilayer normal perpendicular to the magnetic field and graphing the relaxation rate, 1/T1Z, as a function of (1-S2N-2H), where S2N-2H represents the orientational order parameter, wer were able to estimate the correlation time, tau R parallel, for rotational diffusion. Although in the quadrupolar splitting, which varies as (3 cos2 theta D-1), has in general two possible solutions to theta D in the range 0 < or = theta D < or = 90 degrees, the 1/T1Z vs. (1-S2N-2H) curve can be used to determine a single value of theta D in this range. Thus, the 1/T1Z vs. (1-S2N-2H) profile can be used both to define the axial diffusion rate and to remove potential structural ambiguities in the splittings. The T1Z anisotropy permits us to solve for the two correlation times (tau R parallel = 6.8 x 10(-9) s and tau R perpendicular = 6 x 10(-6) s). The simulated parameters were corroborated by a Jeener-Broekaert experiment where the bilayer normal was parallel to the principal magnetic field. At this orientation the ratio, J2(2 omega 0)/J1(omega 0) was obtained in order to estimate the strength of the restoring potential in a model-independent fashion. This measurement yields the rms angle, <theta 2>1/2 (= 16 +/- 2 degrees at 34 degrees C), formed by the peptide helix axis and the average bilayer normal.     

Anisotropic rotational diffusion in model-free analysis for a ternary DHFR complex

Model-free analysis has been extensively used to extract information on motions in proteins over a wide range of timescales from NMR relaxation data. We present a detailed analysis of the effects of rotational anisotropy on the model-free analysis of a ternary complex for dihydrofolate reductase (DHFR). Our findings show that the small degree of anisotropy exhibited by DHFR (D_||/D=1.18) introduces erroneous motional models, mostly exchange terms, to over 50% of the NH spins analyzed when isotropic tumbling is assumed. Moreover, there is a systematic change in S², as large as 0.08 for some residues. The significant effects of anisotropic rotational diffusion on model-free motional parameters are in marked contrast to previous studies and are accentuated by lowering of the effective correlation time using isotropic tumbling methods. This is caused by the preponderance of NH vectors aligned perpendicular to the principal diffusion tensor axis and is readily detected because of the high quality of the relaxation data. A novel procedure, COPED (COmparison of Predicted and Experimental Diffusion tensors) is presented for distinguishing genuine motions from the effects of anisotropy by comparing experimental relaxation data and data predicted from hydrodynamic analyses. The procedure shows excellent agreement with the slow motions detected from the axially symmetric model-free analysis and represents an independent procedure for determining rotational diffusion and slow motions that can confirm or refute established procedures that rely on relaxation data. Our findings show that neglect of even small degrees of rotational diffusion anisotropy can introduce significant errors in model-free analysis when the data is of high quality. These errors can hinder our understanding of the role of internal motions in protein function.     

Backbone dynamics of the calcium-signaling protein apo-S100B as determined by 15N NMR relaxation

Backbone dynamics of homodimeric apo-S100B were studied by (15)N nuclear magnetic resonance relaxation at 9.4 and 14.1 T. Longitudinal relaxation (T(1)), transverse relaxation (T(2)), and the (15)N-[(1)H] NOE were measured for 80 of 91 backbone amide groups. Internal motional parameters were determined from the relaxation data using the model-free formalism while accounting for diffusion anisotropy. Rotational diffusion of the symmetric homodimer has moderate but statistically significant prolate axial anisotropy (D( parallel)/D( perpendicular) = 1.15 +/- 0.02), a global correlation time of tau(m) = 7.80 +/- 0.03 ns, and a unique axis in the plane normal to the molecular symmetry axis. Of 29 residues at the dimer interface (helices 1 and 4), only one has measurable internal motion (Q71), and the order parameters of the remaining 28 were the highest in the protein (S(2) = 0.80 to 0.91). Order parameters in the typical EF hand calcium-binding loop (S(2) = 0.73 to 0.87) were slightly lower than in the pseudo-EF hand (S(2) = 0.75 to 0.89), and effective internal correlation times, tau(e), distinct from global tumbling, were detected in the calcium-binding loops. Helix 3, which undergoes a large, calcium-induced conformational change necessary for target-protein binding, does not show evidence of interchanging between the apo and Ca(2+)-bound orientations in the absence of calcium but has rapid motion in several residues throughout the helix (S(2) = 0.78 to 0.88; 10 < or = tau(e) < or = 30 ps). The lowest order parameters were found in the C-terminal tail (S(2) = 0.62 to 0.83). Large values for chemical exchange also occur in this loop and in regions nearby in space to the highly mobile C-terminal loop, consistent with exchange broadening effects observed.     

Characterization of the overall and local dynamics of a protein with intermediate rotational anisotropy: Differentiating between conformational exchange and anisotropic diffusion in the B3 domain of protein G

Because the overall tumbling provides a major contribution to protein spectral densities measured in solution, the choice of a proper model for this motion is critical for accurate analysis of protein dynamics. Here we study the overall and backbone dynamics of the B3 domain of protein G using ¹⁵N relaxation measurements and show that the picture of local motions is markedly dependent on the model of overall tumbling. The main difference is in the interpretation of the elevated R ₂ values in the -helix: the isotropic model results in conformational exchange throughout the entire helix, whereas no exchange is predicted by anisotropic models that place the longitudinal axis of diffusion tensor almost parallel to the helix axis. Due to small size (fast tumbling) of the protein, the T ₁ values have low sensitivity to NH bond orientation. The diffusion tensor derived from orientation dependence of R ₂/R ₁ is anisotropic (D _par/D _perp=1.4), with a small rhombic component. In order to distinguish the correct picture of motion, we apply model-independent methods that are sensitive to conformational exchange and do not require knowledge of protein structure or assumptions about its dynamics. A comparison of the CSA/dipolar cross-correlation rate constants with ¹⁵N relaxation rates and the estimation of R _ex terms from relaxation data at 9.4 and 14.1 T indicate no conformational exchange in the helix, in support of the anisotropic models. The experimentally derived diffusion tensor is in excellent agreement with theoretical predictions from hydrodynamic calculations; a detailed comparison with various hydrodynamic models revealed optimal parameters for hydrodynamic calculations.     

Recurrent alpha beta loop structures in TIM barrel motifs show a distinct pattern of conserved structural features.

A systematic survey of seven parallel alpha/beta barrel protein domains, based on exhaustive structural comparisons, reveals that a sizable proportion of the alpha beta loops in these proteins--20 out of a total of 49--belong to either one of two loop types previously described by Thornton and co-workers. Six loops are of the alpha beta 1 type, with one residue between the alpha-helix and beta-strand, and 13 are of the alpha beta 3 type, with three residues between the helix and the strand. Protein fragments embedding the identified loops, and termed alpha beta connections since they contain parts of the flanking helix and strand, have been analyzed in detail revealing that each type of connection has a distinct set of conserved structural features. The orientation of the beta-strand relative to the helix and loop portions is different owing to a very localized difference in backbone conformation. In alpha beta 1 connections, the chain enters the beta-strand via a residue adopting an extended conformation, while in alpha beta 3 it does so via a residue in a near alpha-helical conformation. Other conserved structural features include distinct patterns of side chain orientation relative to the beta-sheet surface and of main chain H-bonds in the loop and the beta-strand moieties. Significant differences also occur in packing interactions of conserved hydrophobic residues situated in the last turn of the helix. Yet the alpha-helix surface of both types of connections adopts similar orientations relative to the barrel sheet surface. Our results suggest furthermore that conserved hydrophobic residues along the sequence of the connections, may be correlated more with specific patterns of interactions made with neighboring helices and sheet strands than with helix/strand packing within the connection itself. A number of intriguing observations are also made on the distribution of the identified alpha beta 1 and alpha beta 3 loops within the alpha/beta-barrel motifs. They often occur adjacent to each other; alpha beta 3 loops invariably involve even numbered beta-strands, while alpha beta 1 loops involve preferentially odd beta-strands; all the analyzed proteins contain at least one alpha beta 3 loop in the first half of the eightfold alpha/beta barrel. Possible origins of all these observations, and their relevance to the stability and folding of parallel alpha/beta barrel motifs are discussed.     

Fluorescence depolarization study of lamellar liquid crystalline to inverted cylindrical micellar phase transition of phosphatidylethanolamine.

The orientational order and rotational dynamics of 2-[3-(diphenyl-hexatrienyl) propanoyl]-3-palmitoyl-L-alpha- phosphatidylcholine (DPH-PC) embedded in dioleoylphosphatidyl-ethanolamine (DOPE) were studied by fluorescence depolarization technique. Upon increasing the temperature, the calculated wobbling diffusion constant D perpendicular of the fluorescent probe was found to decrease at the lamellar (L alpha) to inverted cylindrical (H II) phase transition (10 degrees C). This suggested that the increased gauche rotamers of the alkene chains in the HII phase imposes a constraint in the wobbling motion of the fluorophore. The calculated ratio of order parameter in the L alpha phase to that in the HII phase was 1.7 and different from the theoretical value of 2.0 as predicted from the change in packing symmetry. This result can be explained by a slightly higher local order parameter of the fluorophore or by the fast rotational diffusion motion of the fluorophore around the symmetry axis of the cylindrical tubes in the HII phase.     

Association of the cystic fibrosis transmembrane regulator with CAL: structural features and molecular dynamics

The association of the cystic fibrosis transmembrane regulator (CFTR) with two PDZ-containing molecular scaffolds (CAL and EBP50) plays an important role in CFTR trafficking and membrane maintenance. The CFTR-molecular scaffold interaction is mediated by the association of the C-terminus of the transmembrane regulator with the PDZ domains. Here, we characterize the structure and dynamics of the PDZ of CAL and the complex formed with CFTR employing high-resolution NMR. On the basis of NMR relaxation data, the alpha2 helix as well as the beta2-beta3 loop of CAL PDZ domain undergoes rapid dynamics. Molecular dynamics simulations suggest a concerted motion between the alpha2 helix and the beta1-beta2 and beta2-beta3 loops, elements which define the binding pocket, suggesting that dynamics may play a role in PDZ-ligand specificity. The C-terminus of CFTR binds to CAL with the final four residues (-D(-)(3)-T-R-L(0)) within the canonical PDZ-binding motif, between the beta2 strand and the alpha2 helix. The R(-)(1) and D(-)(3) side chains make a number of contacts with the PDZ domain; many of these interactions differ from those in the CFTR-EBP50 complex, suggesting sites that can be targeted in the development of PDZ-selective inhibitors that may help modulate CFTR function.     

Self-consistent residual dipolar coupling based model-free analysis for the robust determination of nanosecond to microsecond protein dynamics

Residual dipolar couplings (RDCs) provide information about the dynamic average orientation of inter-nuclear vectors and amplitudes of motion up to milliseconds. They complement relaxation methods, especially on a time-scale window that we have called supra-tau(c) (tau(c) < supra-tau(c) < 50 micros). Here we present a robust approach called Self-Consistent RDC-based Model-free analysis (SCRM) that delivers RDC-based order parameters-independent of the details of the structure used for alignment tensor calculation-as well as the dynamic average orientation of the inter-nuclear vectors in the protein structure in a self-consistent manner. For ubiquitin, the SCRM analysis yields an average RDC-derived order parameter of the NH vectors 0.72 +/- 0.02 compared to = 0.778 +/- 0.003 for the Lipari-Szabo order parameters, indicating that the inclusion of the supra-tau(c) window increases the averaged amplitude of mobility observed in the sub-supra-tau(c) window by about 34%. For the beta-strand spanned by residues Lys48 to Leu50, an alternating pattern of backbone NH RDC order parameter S2(rdc)(NH) = (0.59, 0.72, 0.59) was extracted. The backbone of Lys48, whose side chain is known to be involved in the poly-ubiquitylation process that leads to protein degradation, is very mobile on the supra-tau(c) time scale (S2(rdc)(NH) = 0.59 +/- 0.03), while it is inconspicuous (S2(LS)(NH)= 0.82) on the sub-tau(c) as well as on micros-ms relaxation dispersion time scales. The results of this work differ from previous RDC dynamics studies of ubiquitin in the sense that the results are essentially independent of structural noise providing a much more robust assessment of dynamic effects that underlie the RDC data.     

Dynamical properties of phospholipid bilayers from computer simulation

We present the results of a 10-ns molecular dynamics simulation of a dipalmitoylphosphatidylcholine/water system. The main emphasis of the present study is on the investigation of the stability over a long time and the dynamic properties of the water/membrane system. The motion of the lipid molecules is characterized by the center of mass movement and the displacement of individual atom groups. Because of the slow movement of the headgroup atoms, their contributions to the dipole potential vary slowly and with a large amplitude. Nevertheless, the water molecules compensate the strong fluctuations and maintain an almost constant total dipole potential. From the lateral displacement of the center of masses, we calculate the lateral diffusion coefficient to be Dlat = (3 +/- 0.6) x 10(-7) cm2/s, in agreement with neutron scattering results. The rotational motion is also investigated in our simulations. The calculated value for the rotational diffusion coefficient parallel to the molecular long axis, D = (1.6 +/- 0.1) x 10(8) s-1, is in good agreement with the experiment.     

Comprehensive analysis of the helix-X-helix motif in soluble proteins

Alpha-helices are the most common secondary structures found in globular proteins. In this report, we analyze the stereochemical and sequence properties of helix-X-helix (HXH) motifs in which two alpha-helices are linked by a single residue, in search of characteristic structures and sequence signals. The analysis is carried out on a database of 837 nonredundant HXH motifs. The kinks are characterized by the bend angle between the axes of the N-terminal and C-terminal helices and the wobble angle corresponding to the rotation of C-terminal helix axis on the plane perpendicular to the N-terminal one. The phi-psi dihedral angles of the linker residue are clustered in six distinct areas of the Ramachandran plot: two areas are located in the additional allowed alpha region (alpha(1) and alpha(2)), two areas are in the additional allowed beta region (beta(1) and beta(2)) and two areas have positive phi values (alpha(L) and beta(M)). Each phi/psi region corresponds to characteristic bend and wobble angles and amino acid distributions. Bend angles can vary from 0 degrees to 160 degrees. Most wobble angles correspond to a counter-clockwise rotation of the C-terminal helix. Proline residues are rigorously excluded from the linker position X but have a high propensity at position X+1 of the beta(1) and beta(2) motifs (12 and 7, respectively) and at position X+3 of the alpha(1) motifs (9). Glycine linkers are located either in the alpha(L) region (20%) or in the beta(M) region (80%). This latter conformation is characterized by a marked bend angle (124 degrees +/- 18 degrees) and a clockwise wobble. Among other amino acids, Asn is remarkable for its high propensity (>3) at the linker position of the alpha(2), beta(1), and beta(2) motifs. Stabilization of HXH motifs by H-bonds between polar side chains of the linker and polar groups of the backbone is determined. A method based on position-specific scoring matrices is developed for conformational prediction. The accuracy of the predictions reaches 80% when the method is applied to proline-induced kinks or to kinks with bend angles in the 50 degrees-100 degrees range.     

Effect of single amino acid replacements on the folding and stability of dihydrofolate reductase from Escherichia coli

The role of the secondary structure in the folding mechanism of dihydrofolate reductase from Escherichia coli was probed by studying the effects of amino acid replacements in two alpha helices and two strands of the central beta sheet on the folding and stability. The effects on stability could be qualitatively understood in terms of the X-ray structure for the wild-type protein by invoking electrostatic, hydrophobic, or hydrogen-bonding interactions. Kinetic studies focused on the two slow reactions that are thought to reflect the unfolding/refolding of two stable native conformers to/from their respective folding intermediates [Touchette, N. A., Perry, K. M., & Matthews, C. R. (1986) Biochemistry 25, 5445-5452]. Replacements at three different positions in helix alpha B selectively alter the relaxation time for unfolding while a single replacement in helix alpha C selectively alters the relaxation time for refolding. This behavior is characteristic of mutations that change the stability of the protein but do not affect the rate-limiting step. In striking contrast, replacements in strands beta F and beta G can affect both unfolding and refolding relaxation times. This behavior shows that these mutations alter the rate-limiting step in these native-to-intermediate folding reactions. It is proposed that the intermediates have an incorrectly formed beta sheet whose maturation to the structure found in the native conformation is one of the slow steps in folding.     

Set theory formulation of the model-free problem and the diffusion seeded model-free paradigm

Model-free analysis of NMR relaxation data, which describes the motion of individual atoms, is a problem intricately linked to the Brownian rotational diffusion of the macromolecule. The diffusion tensor parameters strongly influence the optimisation of the various model-free models and the subsequent model selection between them. Finding the optimal model of the dynamics of the system among the numerous diffusion and model-free models is hence quite complex. Using set theory, the entirety of this global problem has been encapsulated by the universal set Ll, and its resolution mathematically formulated as the universal solution Ll. Ever since the original Lipari and Szabo papers the model-free dynamics of a molecule has most often been solved by initially estimating the diffusion tensor. The model-free models which depend on the diffusion parameter values are then optimised and the best model is chosen to represent the dynamics of the residue. Finally, the global model of all diffusion and model-free parameters is optimised. These steps are repeated until convergence. For simplicity this approach to Ll will be labelled the diffusion seeded model-free paradigm. Although this technique suffers from a number of problems many have been solved. All aspects of the diffusion seeded paradigm and its consequences, together with a few alternatives to the paradigm, will be reviewed through the use of set notation.     

Cooperative effects in hydrogen-bonding of protein secondary structure elements: a systematic analysis of crystal data using Secbase

A systematic analysis of the hydrogen-bonding geometry in helices and beta sheets has been performed. The distances and angles between the backbone carbonyl O and amide N atoms were correlated considering more than 1500 protein chains in crystal structures determined to a resolution better than 1.5 A. They reveal statistically significant trends in the H-bond geometry across the different secondary structural elements. The analysis has been performed using Secbase, a modular extension of Relibase (Receptor Ligand Database) which integrates information about secondary structural elements assigned to individual protein structures with the various search facilities implemented into Relibase. A comparison of the mean hydrogen-bond distances in alpha helices and 3(10) helices of increasing length shows opposing trends. Whereas in alpha helices the mean H-bond distance shrinks with increasing helix length and turn number, the corresponding mean dimension in 3(10) helices expands in a comparable series. Comparing similarly the hydrogen-bond lengths in beta sheets there is no difference to be found between the mean H-bond length in antiparallel and parallel beta sheets along the strand direction. In contrast, an interesting systematic trend appears to be given for the hydrogen bonds perpendicular to the strands bridging across an extended sheet. With increasing number of accumulated strands, which results in a growing number of back-to-back piling hydrogen bonds across the strands, a slight decrease of the mean H-bond distance is apparent in parallel beta sheets whereas such trends are obviously not given in antiparallel beta sheets. This observation suggests that cooperative effects mutually polarizing spatially well-aligned hydrogen bonds are present either in alpha helices and parallel beta sheets whereas such influences seem to be lacking in 3(10) helices and antiparallel beta sheets.