Correlating structure, dynamics, and function in transmembrane segment VII of the Na/H exchanger isoform 1

We place ¹⁵N nuclear magnetic resonance relaxation analysis and functional mutagenesis studies in the context of our previous structural and mutagenesis work to correlate structure, dynamics and function for the seventh transmembrane segment of the human Na⁺/H⁺ exchanger isoform 1. Although G261-S263 was previously identified as an interruption point in the helical structure of this isolated transmembrane peptide in dodecylphosphocholine micelles, and rapid conformational exchange was implicated in the NOE measurements, the six ¹⁵N labelled residues examined in this study all have similar dynamics on the ps-ns time scale. A mathematical model incorporating chemical exchange is the best fit for residues G261, L264, and A268. This implies that a segment of residues from G261 to A268 samples different conformations on the μs-ms time scale. Chemical exchange on an intermediate time scale is consistent with an alternating-access cycle where E262 is bent away from the cytosol during proton translocation by the exchanger. The functional importance of chemical exchange at G261-A268 is corroborated by the abrogated activity of the full-length exchanger with the bulky and restricting Ile substitutions F260I, G261I, E262I, S263I, and A268I.     

Multiple time scale backbone dynamics of homologous thermophilic and mesophilic ribonuclease HI enzymes

Backbone conformational fluctuations on multiple time scales in a cysteine-free Thermus thermophilus ribonuclease HI mutant (ttRNH(*)) are quantified using (15)N nuclear magnetic spin relaxation. Laboratory-frame relaxation data acquired at 310 K and at static magnetic field strengths of 11.7, 14.1 and 18.8 T are analysed using reduced spectral density mapping and model-free approaches. Chemical exchange line broadening is characterized using Hahn-echo transverse and multiple quantum relaxation data acquired over a temperature range of 290-320 K and at a static magnetic field strength of 14.1 T. Results for ttRNH(*) are compared to previously published data for a mesophilic homologue, Escherichia coli ribonuclease HI (ecRNH). Intramolecular conformational fluctuations on the picosecond-to-nanosecond time scale generally are similar for ttRNH(*) and ecRNH. beta-Strands 3 and 5 and the glycine-rich region are more rigid while the substrate-binding handle region and C-terminal tail are more flexible in ttRNH(*) than in ecRNH. Rigidity in the two beta-strands and the glycine-rich region, located along the periphery of the central beta-sheet, may be associated with the increased thermodynamic stability of the thermophilic enzyme. Chemical exchange line broadening, reflecting microsecond-to-millisecond time scale conformational changes, is more pronounced in ttRNH(*) than in ecRNH, particularly for residues in the handle and surrounding the catalytic site. The temperature dependence of chemical exchange show an increase of approximately 15 kJ/mol in the apparent activation energies for ttRNH(*) residues in the handle compared to ecRNH. Increased activation barriers, coupled with motion between alpha-helices B and C not present in ecRNH, may be associated with the reduced catalytic activity of the thermophilic enzyme at 310 K.     

Ligand-induced changes in dynamics in the RT loop of the C-terminal SH3 domain of Sem-5 indicate cooperative conformational coupling

We report the effects of peptide binding on the (15)N relaxation rates and chemical shifts of the C-SH3 of Sem-5. (15)N spin-lattice relaxation time (T(1)), spin-spin relaxation time (T(2)), and ((1)H)-(15)N NOE were obtained from heteronuclear 2D NMR experiments. These parameters were then analyzed using the Lipari-Szabo model free formalism to obtain parameters that describe the internal motions of the protein. High-order parameters (S(2) > 0.8) are found in elements of regular secondary structure, whereas some residues in the loop regions show relatively low-order parameters, notably the RT loop. Peptide binding is characterized by a significant decrease in the (15)N relaxation in the RT loop. Concomitant with the change in dynamics is a cooperative change in chemical shifts. The agreement between the binding constants calculated from chemical shift differences and that obtained from ITC indicates that the binding of Sem-5 C-SH3 to its putative peptide ligand is coupled to a cooperative conformational change in which a portion of the binding site undergoes a significant reduction in conformational heterogeneity.     

Histidine side-chain dynamics and protonation monitored by 13C CPMG NMR relaxation dispersion

The use of ¹³C NMR relaxation dispersion experiments to monitor micro-millisecond fluctuations in the protonation states of histidine residues in proteins is investigated. To illustrate the approach, measurements on three specifically ¹³C labeled histidine residues in plastocyanin (PCu) from Anabaena variabilis (A.v.) are presented. Significant Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion is observed for ¹³C^ε1 nuclei in the histidine imidazole rings of A.v. PCu. The chemical shift changes obtained from the CPMG dispersion data are in good agreement with those obtained from the chemical shift titration experiments, and the CPMG derived exchange rates agree with those obtained previously from ¹⁵N backbone relaxation measurements. Compared to measurements of backbone nuclei, ¹³C^ε1 dispersion provides a more direct method to monitor interchanging protonation states or other kinds of conformational changes of histidine side chains or their environment. Advantages and shortcomings of using the ¹³C^ε1 dispersion experiments in combination with chemical shift titration experiments to obtain information on exchange dynamics of the histidine side chains are discussed.     

Off-resonance rotating-frame amide proton spin relaxation experiments measuring microsecond chemical exchange in proteins

NMR spin relaxation in the rotating frame (R_1ρ) is a unique method for atomic-resolution characterization of conformational (chemical) exchange processes occurring on the microsecond time scale. Here, we use amide ¹H off-resonance R_1ρ relaxation experiments to determine exchange parameters for processes that are significantly faster than those that can be probed using ¹⁵N or ¹³C relaxation. The new pulse sequence is validated using the E140Q mutant of the C-terminal domain of calmodulin, which exhibits significant conformational exchange contributions to the transverse relaxation rates. The ¹H off-resonance R_1ρ data sample the entire relaxation dispersion profiles for the large majority of residues in this protein, which exchanges between conformations with a time constant of approximately 20 μs. This is in contrast to the case for ¹⁵N, where additional laboratory-frame relaxation data are required to determine the exchange parameters reliably. Experiments were performed on uniformly ¹⁵N-enriched samples that were either highly enriched in ²H or fully protonated. In the latter case, dipolar cross-relaxation with aliphatic protons were effectively decoupled to first order using a selective inversion pulse. Deuterated and protonated samples gave the same results, within experimental errors. The use of deuterated samples increases the sensitivity towards exchange contributions to the ¹H transverse relaxation rates, since dipolar relaxation is greatly reduced. The exchange correlation times determined from the present ¹H off-resonance R_1ρ experiments are in excellent agreement with those determined previously using a combination of ¹⁵N laboratory-frame and off-resonance R_1ρ relaxation data, with average values of and 21 ± 3 μs, respectively.     

Probing Slow Backbone Dynamics in Proteins Using TROSY-Based Experiments to Detect Cross-Correlated Time-Modulation of Isotropic Chemical Shifts

The difference in the relaxation rates of zero-quantum (ZQ) and double-quantum (DQ) coherences is the result of three principal mechanisms. These include the cross-correlation between the chemical shift anisotropies of the two participating nuclei, dipolar interactions with remote protons as well as interference effects due to the time-modulation of their isotropic chemical shifts as a consequence of slow micros-ms dynamics. The last effect when present, dominates the others resulting in large differences between the relaxation rates of ZQ and DQ coherences. We present here four sets of TROSY-based (Salzmann et al., 1998) experiments that measure this effect for several pairs of backbone nuclei including (15)N, (13)C(alpha) and (13)C'. These experiments allow the detection of the presence of slow dynamic processes in the protein backbone including correlated motion over two and three bonds. Further, we define a new parameter chi which represents the extent of correlated motion on the slow (micros-ms) timescale. This methodology has been applied to (15)N,(13)C,REDPRO-(2)H-labeled (Shekhtman et al., 2002) human ubiquitin. The ubiquitin backbone is seen to exhibit extensive dynamics on the slow timescale. This is most pronounced in several residues in the N-terminal region of the alpha-helix and in the loop connecting the strands beta(4) and beta(5). These residues which include Glu24, Asn25, Glu51 and Asp 52 form a continuous surface. As an additional benefit, the measured rates confirm the dependence of the (13)C(alpha) chemical shift tensor on local secondary structure of the protein backbone.     

NMR investigation of the dynamics of tryptophan side-chains in hemoglobins

NMR relaxation measurements of 15N spin-lattice relaxation rate (R(1)), spin-spin relaxation rate (R(2)), and heteronuclear nuclear Overhauser effect (NOE) have been carried out at 11.7T and 14.1T as a function of temperature for the side-chains of the tryptophan residues of 15N-labeled and/or (2H,15N)-labeled recombinant human normal adult hemoglobin (Hb A) and three recombinant mutant hemoglobins, rHb Kempsey (betaD99N), rHb (alphaY42D/betaD99N), and rHb (alphaV96W), in the carbonmonoxy and the deoxy forms as well as in the presence and in the absence of an allosteric effector, inositol hexaphosphate (IHP). There are three Trp residues (alpha14, beta15, and beta37) in Hb A for each alphabeta dimer. These Trp residues are located in important regions of the Hb molecule, i.e. alpha14Trp and beta15Trp are located in the alpha(1)beta(1) subunit interface and beta37Trp is located in the alpha(1)beta(2) subunit interface. The relaxation experiments show that amino acid substitutions in the alpha(1)beta(2) subunit interface can alter the dynamics of beta37Trp. The transverse relaxation rate (R(2)) for beta37Trp can serve as a marker for the dynamics of the alpha(1)beta(2) subunit interface. The relaxation parameters of deoxy-rHb Kemspey (betaD99N), which is a naturally occurring abnormal human hemoglobin with high oxygen affinity and very low cooperativity, are quite different from those of deoxy-Hb A, even in the presence of IHP. The relaxation parameters for rHb (alphaY42D/betaD99N), which is a compensatory mutant of rHb Kempsey, are more similar to those of Hb A. In addition, TROSY-CPMG experiments have been used to investigate conformational exchange in the Trp residues of Hb A and the three mutant rHbs. Experimental results indicate that the side-chain of beta37Trp is involved in a relatively slow conformational exchange on the micro- to millisecond time-scale under certain experimental conditions. The present results provide new dynamic insights into the structure-function relationship in hemoglobin.     

CPMG sequences with enhanced sensitivity to chemical exchange

Improved relaxation-compensated Carr–Purcell–Meiboom-Gill pulse sequences are reported for studying chemical exchange of backbone ¹⁵N nuclei. In contrast to the original methods [J. P. Loria, M. Rance, and A. G. Palmer, J. Am. Chem. Soc. 121, 2331–2332 (1999)], phenomenological relaxation rate constants obtained using the new sequences do not contain contributions from ¹H-¹H dipole-dipole interactions. Consequently, detection and quantification of chemical exchange processes are facilitated because the relaxation rate constant in the limit of fast pulsing can be obtained independently from conventional ¹⁵N spin relaxation measurements. The advantages of the experiments are demonstrated using basic pancreatic trypsin inhibitor.     

A hydrogen bond regulates slow motions in ubiquitin by modulating a β-turn flip

Proteins exist as conformational ensembles composed of multiple interchanging substates separated by kinetic barriers. Interconverting conformations are often difficult to probe, owing to their sparse population and transient nature. Here, we report the identification and characterization of a subset of conformations in ubiquitin that participate in microsecond-to-millisecond motions in the amides of Ile23, Asn25, and Thr55. A novel side chain to the backbone hydrogen bond that regulates these motions has also been identified. Combining our NMR studies with the available X-ray data, we have unearthed the physical process underlying slow motions—the interconversion of a type I into a type II β-turn flip at residues Glu51 through Arg54. Interestingly, the dominant conformer of wild-type ubiquitin observed in solution near neutral pH is only represented by about 22% of the crystal structures. The conformers generated as a result of the dynamics of the hydrogen bond appear to be correlated to ligand recognition by ubiquitin.     

Backbone dynamics of free barnase and its complex with barstar determined by 15N NMR relaxation study

Backbone dynamics of uniformly ¹⁵N-labeled free barnase and its complex with unlabelled barstar have been studied at 40°C, pH 6.6, using ¹⁵N relaxation data obtained from proton-detected 2D {¹H}-¹⁵N NMR spectroscopy. ¹⁵N spin-lattice relaxation rate constants (R₁), spin-spin relaxation rate constants (R₂), and steady-state heteronuclear {¹H}-¹⁵N NOEs have been measured at a magnetic field strength of 14.1 Tesla for 91 residues of free barnase and for 90 residues out of a total of 106 in the complex (excluding three prolines and the N-terminal residue) backbone amide ¹⁵N sites of barnase. The primary relaxation data for both the cases have been analyzed in the framework of the model-free formalism using both isotropic and axially symmetric models of the rotational diffusion tensor. As per the latter, the overall rotational correlation times (_m) are 5.0 and 9.5 ns for the free and complexed barnase, respectively. The average order parameter is found to be 0.80 for free barnase and 0.86 for the complex. However, the changes are not uniform along the backbone and for about 5 residues near the binding interface there is actually a significant decrease in the order parameters on complex formation. These residues are not involved in the actual binding. For the residues where the order parameter increases, the magnitudes vary significantly. It is observed that the complex has much less internal mobility, compared to free barnase. From the changes in the order parameters, the entropic contribution of NH bond vector motion to the free energy of complex formation has been calculated. It is apparent that these motions cause significant unfavorable contributions and therefore must be compensated by many other favorable contributions to effect tight complex formation. The observed variations in the motion and their different locations with regard to the binding interface may have important implications for remote effects and regulation of the enzyme action.     

Identification of a collapsed intermediate with non-native long-range interactions on the folding pathway of a pair of Fyn SH3 domain mutants by NMR relaxation dispersion spectroscopy

Recent 15N and 13C spin-relaxation dispersion studies of fast-folding mutants of the Fyn SH3 domain have established that folding proceeds through a low-populated on-pathway intermediate (I) where the central beta-sheet is at least partially formed, but without interactions between the NH2- and COOH-terminal beta-strands that exist in the folded state (F). Initial studies focused on mutants where Gly48 is replaced; in an effort to establish whether this intermediate is a general feature of Fyn SH3 folding a series of 15N relaxation experiments monitoring the folding of Fyn SH3 mutants N53P/V55L and A39V/N53P/V55L are reported here. For these mutants as well, folding proceeds through an on-pathway intermediate with similar features to those observed for G48M and G48V Fyn SH3 domains. However, the 15N chemical shifts extracted for the intermediate indicate pronounced non-native contacts between the NH2 and COOH-terminal regions not observed previously. The kinetic parameters extracted for the folding of A39V/N53P/V55L Fyn SH3 from the three-state folding model F<-->I<-->U are in good agreement with folding and unfolding rates extrapolated to zero denaturant obtained from stopped-flow experiments analyzed in terms of a simplified two-state folding reaction. The folding of the triple mutant was studied over a wide range of temperatures, establishing that there is no difference in heat capacities between F and I states. This confirms a compact folding intermediate structure, which is supported by the 15N chemical shifts of the I state extracted from the dispersion data. The temperature-dependent relaxation data simplifies data analysis because at low temperatures (< 25 degrees C) the unfolded state (U) is negligibly populated relative to I and F. A comparison between parameters extracted at low temperatures where the F<-->I exchange model is appropriate with those from the more complex, three-state model at higher temperatures has been used to validate the protocol for analysis of three-site exchange relaxation data.     

Gated electron transfers and electron pathways in azurin: a NMR dynamic study at multiple fields and temperatures

Dynamic properties of electron transfer pathways in a small blue copper cupredoxin are explored using an extensive 15N NMR relaxation study of reduced Pseudomonas aeruginosa azurin at four magnetic fields (500-900 MHz) and at two temperatures chosen well below the melting point of the protein. Following a careful model-free analysis, several protein regions with different dynamic regimes are identified. Nanosecond time-scale mobility characterizes various residues of the hydrophobic surface patch believed to mark the natural entry point for electrons, notably the surface-exposed copper-ligand His117. These findings are consistent with a gated electron transfer process according to the "dynamic docking" model. Residues 47-49 along intramolecular pathways of electrons show rigidity that is remarkably conserved when increasing the temperature. Three different conformational exchange processes were observed in the millisecond range, one near the only disulfide bridge in the molecule and two near the copper ion. The latter two processes are consistent with previous data such as crystal structures at various pH values and NMR relaxation dispersion experiments; they may indicate an additional gated electron transfer mechanism at slower time-scales.     

Tautomerism,acid-base equilibria,and H-bonding of the six histidines in subtilisin BPN' by NMR

We have determined by (15)N, (1)H, and (13)C NMR, the chemical behavior of the six histidines in subtilisin BPN' and their PMSF and peptide boronic acid complexes in aqueous solution as a function of pH in the range of from 5 to 11, and have assigned every (15)N, (1)H, C(epsilon 1), and C(delta2) resonance of all His side chains in resting enzyme. Four of the six histidine residues (17, 39, 67, and 226) are neutrally charged and do not titrate. One histidine (238), located on the protein surface, titrates with pK(a) = 7.30 +/- 0.03 at 25 degrees C, having rapid proton exchange, but restricted mobility. The active site histidine (64) in mutant N155A titrates with a pK(a) value of 7.9 +/- 0.3 and sluggish proton exchange behavior, as shown by two-site exchange computer lineshape simulation. His 64 in resting enzyme contains an extremely high C(epsilon 1)-H proton chemical shift of 9.30 parts per million (ppm) owing to a conserved C(epsilon 1)-H(.)O=C H-bond from the active site imidazole to a backbone carbonyl group, which is found in all known serine proteases representing all four superfamilies. Only His 226, and His 64 at high pH, exist as the rare N(delta1)-H tautomer, exhibiting (13)C(delta1) chemical shifts approximately 9 ppm higher than those for N(epsilon 2)-H tautomers. His 64 in the PMSF complex, unlike that in the resting enzyme, is highly mobile in its low pH form, as shown by (15)N-(1)H NOE effects, and titrates with rapid proton exchange kinetics linked to a pK(a) value of 7.47 +/- 0.02.     

Biophysical characterization of elongin C from Saccharomyces cerevisiae

Elongin C (ELC) is an essential component of the mammalian CBC(VHL) E3 ubiquitin ligase complex. As a step toward understanding the role of ELC in assembly and function of CBC-type ubiquitin ligases, we analyzed the quaternary structure and backbone dynamics of the highly homologous Elc1 protein from Saccharomyces cerevisiae. Analytical ultracentrifugation experiments in conjunction with size exclusion chromatography showed that Elc1 is a nonglobular monomer over a wide range of concentrations. Pronounced line broadening in (1)H,(15)N-HSQC NMR spectra and failure to assign peaks corresponding to the carboxy-terminal helix 4 of Elc1 indicated that helix 4 is conformationally labile. Measurement of (15)N NMR relaxation parameters including T(1), T(2), and the (1)H-(15)N nuclear Overhauser effect revealed (i) surprisingly high flexibility of residues 69-77 in loop 5, and (ii) chemical exchange contributions for a large number of residues throughout the protein. Addition of 2,2,2-trifluoroethanol (TFE) stabilized helix 4 and reduced chemical exchange contributions, suggesting that stabilization of helix 4 suppresses the tendency of Elc1 to undergo conformational exchange on a micro- to millisecond time scale. Binding of a peptide representing the major ELC binding site of the von Hippel-Lindau (VHL) tumor suppressor protein almost completely eliminated chemical exchange processes, but induced substantial conformational changes in Elc1 leading to pronounced rotational anisotropy. These results suggest that elongin C interacts with various target proteins including the VHL protein by an induced fit mechanism involving the conformationally flexible carboxy-terminal helix 4.     

Identification of a residue critical for maintaining the functional conformation of BPTI

The effects of amino acid replacements on the backbone dynamics of bovine pancreatic trypsin inhibitor (BPTI) were examined using 15N NMR relaxation experiments. Previous studies have shown that backbone amide groups within the trypsin-binding region of the wild-type protein undergo conformational exchange processes on the micros time scale, and that replacement of Tyr35 with Gly greatly increases the number of backbone atoms involved in such motions. In order to determine whether these mutational effects are specific to the replacement of this residue with Gly, six additional replacements were examined in the present study. In two of these, Tyr35 was replaced with either Ala or Leu, and the other four were single replacements of Tyr23, Phe33, Asn43 or Asn44, all of which are highly buried in the native structure and conserved in homologous proteins. The Y35A and Y35L mutants displayed dynamic properties very similar to those of the Y35G mutant, with the backbone segments including residues 10-19 and 32-44 undergoing motions revealed by enhanced 15N transverse relaxation rates. On the other hand, the Y23L, N43G and N44A substitutions caused almost no detectable changes in backbone dynamics, on either the ns-ps or ms-micros time scales, even though each of these replacements significantly destabilizes the native conformation. Replacement of Phe33 with Leu caused intermediate effects, with several residues that have previously been implicated in motions in the wild-type protein displaying enhanced transverse relaxation rates. These results demonstrate that destabilizing amino acid replacements can be accommodated in a native protein with dramatically different effects on conformational dynamics and that Tyr35 plays a particularly important role in defining the conformation of the trypsin-binding site of BPTI.     

Transverse relaxation optimized triple-resonance NMR experiments for nucleic acids

Triple resonance HCN and HCNCH experiments are reliable methods of establishing sugar-to-base connectivity in the NMR spectra of isotopicaly labeled oligonucleotides. However, with larger molecules the sensitivity of the experiments is drastically reduced due to relaxation processes. Since the polarization transfer between ¹³C and ¹⁵N nuclei relies on rather small heteronuclear coupling constants (11–12 Hz), the long evolution periods (up to 30–40 ms) in the pulse sequences cannot be avoided. Therefore any effort to enhance sensitivity has to concentrate on manipulating the spin system in such a way that the spin–spin relaxation rates would be minimized. In the present paper we analyze the efficiency of the two known approaches of relaxation rate control, namely the use of multiple-quantum coherence (MQ) and of the relaxation interference between chemical shift anisotropy and dipolar relaxation – TROSY. Both theoretical calculations and experimental results suggest that for the sugar moiety (H1-C1-N1/9) the MQ approach is clearly preferable. For the base moiety (H6/8-C6/8-N1/9), however, the TROSY shows results superior to the MQ suppression of the dipole–dipole relaxation at moderate magnetic fields (500 MHz) and the sensitivity improvement becomes dramatically more pronounced at very high fields (800 MHz). The pulse schemes of the triple-resonance HCN experiments with sensitivity optimized performance for unambiguous assignments of intra-residual sugar-to-base connectivities combining both approaches are presented.     

The folding pathway of an FF domain: characterization of an on-pathway intermediate state under folding conditions by (15)N, (13)C(alpha) and (13)C-methyl relaxation dispersion and (1)H/(2)H-exchange NMR spectroscopy

The FF domain from the human protein HYPA/FBP11 folds via a low-energy on-pathway intermediate (I). Elucidation of the structure of such folding intermediates and denatured states under conditions that favour folding are difficult tasks. Here, we investigated the millisecond time-scale equilibrium folding transition of the 71-residue four-helix bundle wild-type protein by (15)N, (13)C(alpha) and methyl(13)C Carr-Purcell-Meiboom-Gill (CPMG) NMR relaxation dispersion experiments and by (1)H/(2)H-exchange measurements. The relaxation data for the wild-type protein fitted a simple two-site exchange process between the folded state (F) and I. Destabilization of F in mutants A17G and Q19G allowed the detection of the unfolded state U by (15)N CPMG relaxation dispersion. The dispersion data for these mutants fitted a three-site exchange scheme, U<-->I<-->F, with I populated higher than U. The kinetics and thermodynamics of the folding reaction were obtained via temperature and urea-dependent relaxation dispersion experiments, along with structural information on I from backbone (15)N, (13)C(alpha) and side-chain methyl (13)C chemical shifts, with further information from protection factors for the backbone amide groups from (1)H/(2)H-exchange. Notably, helices H1-H3 are at least partially formed in I, while helix H4 is largely disordered. Chemical shift differences for the methyl (13)C nuclei suggest a paucity of stable, native-like hydrophobic interactions in I. These data are consistent with Phi-analysis of the rate-limiting transition state between I and F. The combination of relaxation dispersion and Phi data can elucidate whole experimental folding pathways.     

Temperature-dependent dynamics of the villin headpiece helical subdomain,an unusually small thermostable protein

(15)N spin relaxation experiments were used to measure the temperature-dependence of protein backbone conformational fluctuations in the thermostable helical subdomain, HP36, of the F-actin-binding headpiece domain of chicken villin. HP36 is the smallest domain of a naturally occurring protein that folds cooperatively to a compact native state. Spin-lattice, spin-spin, and heteronuclear nuclear Overhauser effect relaxation data for backbone amide (15)N spins were collected at five temperatures in the range of 275-305 K. The data were analyzed using a model-free formalism to determine generalized order parameters, S, that describe the distribution of N-H bond vector orientations in a molecular reference frame. A novel parameter, Lambda=dln(1-S)/dln T is introduced to characterize the temperature-dependence of S. An average value of Lambda=4.5 is obtained for residues in helical conformations in HP36. This value of Lambda is not reproduced by model potential energy functions commonly used to parameterize S. The maximum entropy principle was used to derive a new model potential function that reproduces both S and Lambda. Contributions to the entropy, S(r), and heat capacity, C(r)(p), from reorientational conformational fluctuations were analyzed using this potential energy function. Values of S(r) show a qualitative dependence on S similar to that obtained for the diffusion-in-a-cone model; however, quantitative differences of up to 0.5k, in which k is the Boltzmann constant, are observed. Values of C(r)(p) approach zero for small values of S and approach k for large values of S; the largest values of C(r)(p) are predicted to occur for intermediate values of S. The results suggest that backbone dynamics, as probed by relaxation measurements, make very little contribution to the heat capacity difference between folded and unfolded states for HP36.