| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Departments of * Computer Science, Bioengineering, and Chemistry, Rice University, Houston, Texas; and Structural and Computational Biology and Molecular Biophysics, Baylor College of Medicine, Houston, Texas
Correspondence: Address reprint requests to Lydia E. Kavraki, Tel.: 713-348-5737; E-mail: kavraki{at}rice.edu; or address reprint requests to Cecilia Clementi, Tel.: 713-348-3485; E-mail: cecilia{at}rice.edu.
 |
ABSTRACT |
|---|
 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSION AND CONCLUSIONACKNOWLEDGEMENTSREFERENCES |
|---|
|
INTRODUCTION |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSION AND CONCLUSIONACKNOWLEDGEMENTSREFERENCES |
|---|
–3). Experiments, simulations, and theory indicate that a detailed description of function (encompassing enzymatic reactions, electron transfer, protein ligand binding, and protein/protein interactions) requires the characterization of a protein's native state as an ensemble of conformations (4–7). Such a characterization involves describing in detail the structural and thermodynamic properties over all conformations of the native state ensemble.
Obtaining this description has proven challenging. While nuclear magnetic resonance (NMR) spectroscopy describes picosecond-millisecond timescale dynamics through relaxation phenomena (1,8,9), the characterization of all the conformations constituting the native state at atomistic detail remains an active area of research (10). Molecular dynamics (MD) and Monte Carlo (MC) methods, especially when combined with enhanced sampling techniques and massive parallelization (11–14) or when conducted in low-dimensional configuration spaces (15–17), are powerful complements to characterize the native state ensemble (18). However, the computational demand of these methods makes it challenging to explore longer timescales (19–21). Efforts to explore native state ensembles with no timescale limitations have recently focused either on obtaining native thermodynamic propensities of amino acids (22) or on generating conformations of the native state ensemble by guiding MD or MC with explicit information from NMR measurements (10,23,24).
In this context, we have recently developed the Protein Ensemble Method (PEM) (25) to exhaustively characterize the native state ensemble of a protein at atomistic detail with no inherent timescale limitations. PEM obtains all-atom conformations of the native state in a multiscale fashion combining geometric and energetic considerations. On the generated conformations, PEM measures thermodynamic averages in a statistical mechanics framework and so allows a direct quantitative comparison with wet-lab experimental measurements. We have shown that PEM is intrinsically parallel, efficient in generating large ensembles, and able to characterize equilibrium fluctuations of both loop segments and polypeptide chains (25,26).
In this work, we show the generality of PEM by using the method to characterize native state ensembles of proteins of different sizes and folds. We present the PEM-obtained native state ensembles of eglin c, the SH3 domain of Fyn tyrosine kinase (FynSH3), the 10th type III domain of fibronectin (FNfn10), and the Peptostreptococcus magnus albumin-binding second GA module of PAB (ALB8-GA). These proteins are 70, 58, 90, and 53 aa long, of 
+ ß, mainly ß, all ß, and all -folds, respectively. We show that for all these proteins the PEM-obtained native fluctuations agree remarkably well with NMR data such as order parameter and three-bond scalar coupling data. In addition, for ALB8-GA, where side-chain NMR data are presently not available, we present our prediction on equilibrium side-chain fluctuations.
|
MATERIALS AND METHODS |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSION AND CONCLUSIONACKNOWLEDGEMENTSREFERENCES |
|---|
).
Generation of native state ensembles
PEM employs the following multi-scaling approach to generate the native state ensemble of a protein:
).
Equilibration of solution structures
For the proteins presented here, an initial native structure is obtained by equilibrating an NMR solution structure. NMR ensembles of solution structures of eglin c (28), FynSH3 (29), FNfn10 (30), and ALB8-GA (31) are available in the PDB (32) under codes 1egl, 1nyg, 1ttf, and 1gab. The solution structure that is reported as the best, representative, or the average of the NMR ensemble for each protein is subjected to a short energy minimization. The average structures of the NMR ensembles of FynSH3, FNfn10, and ALB8-GA are reported under PDB codes 1nyf, 1ttg, and 1prb. When a best, representative, or average structure is not reported in the PDB, which is the case for eglin c, the first structure of the NMR ensemble is chosen to be subjected to an energy minimization procedure.
The energy of a structure is measured through the CHARMM all-atom force field (33). The energy minimization procedure involves a conjugate gradient descent in the energy landscape. The minimization of a structure is considered converged if during the last 300 steps of the conjugate gradient descent the improvement in energy is <2.0 kcal/mol. Equilibrated structures of eglin c, FynSH3, FNfn10, and ALB8-GA differ from their corresponding solution structures by all-atom RMSDs of 1.8, 1.7, 2.0, and 2.5 Å, respectively (the effect of the equilibration of PDB-obtained structures on the native state ensembles generated by PEM is discussed in full in Shehu et al. (26)).
PEM divides the polypeptide chain of each of these proteins into segments of 30 aa long with an overlap with each other of 25 aa. The values for the segment length and overlap are chosen by a general and automated procedure. Optimal segment length and overlap result in consistent amino acid fluctuations as measured over the ensembles generated for overlapping segments enclosing each amino acid (see (26) for details and for values to all parameters used by PEM).
Measurement of thermodynamic averages
PEM measures thermodynamic averages over the segment ensembles in a statistical mechanics framework. Each PEM-generated conformation C with energy E(C) is weighted by its Boltzmann probability 
, where Eref is the energy of the equilibrated solution structure (taken as reference), R is the gas constant, and T0 is room temperature of 300 K. The constant Pref is the probability of the reference structure and can be set to 1 without loss of generality. Let Xi(C) indicate the value of an observable X, at position i, measured on conformation C; the thermodynamic average of this quantity over the generated ensemble is measured as 
, where Q refers to the partition function. Averages measured over ensembles of neighboring segments are then combined to obtain structural and thermodynamic observables of the native state. Since a conformation C with energy E(C) higher than 20 kcal/mol from the reference energy Eref has an associated relative Boltzmann probability 
, its contribution to ensemble averages 
Xi
is practically negligible. Therefore, only conformations whose energies are no higher than a cutoff of 20 kcal/mol from the reference energy Eref are considered in the ensembles.
The thermodynamic observables calculated over the PEM-obtained ensembles consist of amide and methyl order parameter (S2) data that measure the reorientational averaging of amide and methyl bonds, respectively, and three-bond scalar coupling (3J) data that measure side-chain rotamer averaging. These average values can be directly compared to the corresponding values measured in NMR experiments and quantify native fluctuations of a protein at varying timescales. While amide S2 data measure picosecond-nanosecond timescale fluctuations, methyl S2 and 3J data can span up to millisecond timescales (1,8,9).
S2 data for a bond are measured by averaging over the distribution of vectors assumed by the bond in a generated ensemble (23). The calculation of S2 data is based on the Lipari-Szabo model-free formalism (34) that does not assume a particular model of internal motions. The model-free formalism allows for a direct comparison of calculated S2 values with experimental order parameters under the assumption that motions of the methyl symmetry axis and of the protons about this axis are decoupled (35). A thorough discussion on the model-free formalism can be found in the literature (34,35). Based on the Lipari-Szabo model-free formalism (34), the order parameter 
for a bond between atoms i and j is calculated through the formula
 |
denote the components of the unit vector along the bond. Since bond lengths remain essentially unchanged from their equilibrium values during PEM's execution, the above formula can be simplified as in Best and Vendruscolo (23) to
 |
refers to the equilibrium length of the bond connecting atoms i and j. The ensemble-averaged S2 for a particular bond is thus obtained by Boltzmann-averaging over the distribution of x, y, z components of vectors assumed by the bond. S2 = 1 indicates no heterogeneity in the distribution of these vectors, whereas S2 = 0 is indicative of a uniform distribution. Similarly, 3J data are measured over the distribution of assumed rotamers (36). The calculation of these quantities and their comparison with NMR data allows us to quantitatively assess the agreement between the PEM-generated and the actual native state ensembles. Additional measurements presented in this work consist of probabilities of contacts and hydrogen bonds, which are similarly Boltzmann-weighted. Two amino acids are considered in contact with one another if the Euclidean distance between two of their atoms is no more than 4.5 Å. A hydrogen bond is considered formed if the OH distance is <2.4 Å and the maximum NHO angle for the hydrogen bond alignment is 2.44 rad.
The computational uncertainty associated with the thermodynamic observables calculated over the PEM-generated ensembles is obtained by measuring differences in the observables when alternative implementation decisions are made in PEM. Therefore, the error bars associated with the PEM-calculated thermodynamic observables measure the inherent error, hence the robustness, of PEM (see (26) for a list of all implementation decisions).
The Pearson correlation R2 and reduced 
2 are used to quantify the agreement between calculated and experimental thermodynamic averages. They are measured as defined in Bevington and Robinson (37).
Computational cost
For each of the proteins in this study, 
13,000 conformations with energy within 20 kcal/mol from the reference structure are generated for each 30 aa segment. Of these, 5000 conformations per segment have energies no higher than 5 kcal/mol from the energy of the equilibrated solution structure used as reference. All results presented here were obtained on the Rice University Terascale cluster of 900 MHz Intel Itanium2 processors (Intel, Santa Clara, CA) and on the Rice University ADA cluster of 2.2 GHz AMD Opteron processors. The calculations for each protein required <100 CPU hours.
|
RESULTS |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSION AND CONCLUSIONACKNOWLEDGEMENTSREFERENCES |
|---|
and 3Jcalc) and the NMR S2 and 3J data (
and 3Jexp) are >92%. This result is particularly significant when considering the low correlations, 37–50%, between the , 3Jexp data and the corresponding quantities measured over the NMR ensembles (28–31) available for these proteins. Results for each protein are discussed in the following.
|
|
|
|
data corresponding to the amide bonds of the loop's amino acids.
The entire amide and methyl data computed over the ensemble obtained for eglin c are shown in Fig. 1 b. Fig. 1 b shows that agree with data (38) with a Pearson correlation of 95% and reduced 2 of 0.98. Methyl data measured over the generated native state ensemble of eglin c are on average as low as 0.49. This is mostly due to the disordered Thr1-Gly15 N-terminus.
Analysis of PEM-generated native state ensemble of Fyn SH3
The obtained native state ensemble of FynSH3 is shown in Fig. 2 a. In contrast to the ensemble obtained for eglin c, Fig. 2 a shows that the obtained equilibrium fluctuations for FynSH3 are prevalently small-scale. The largest fluctuations are located in the N-Src loop, which encompasses amino acids Asn113-Trp119. Interestingly, the N-Src loop discriminates between class I and class II ligands binding to FynSH3 (29). Of all this loop's amino acids, its central amino acid, Glu116 is the most mobile.
The obtained equilibrium fluctuations of FynSH3 are validated by comparing data to the corresponding NMR data (39). Fig. 2 b shows that and data (39) for FynSH3 agree with a Pearson correlation of 93% and reduced 2 of 0.77. The small-scale fluctuations qualitatively shown in Fig. 2 a are reflected in the data: amide and methyl data have high averages of 0.84 and 0.72. This result agrees with experimental findings that large amplitude microsecond-millisecond motions are unlikely in the FynSH3 native state (39).
An interesting instance is represented by amino acid Leu112, located at the border between a ß-sheet and the beginning of the N-Src loop. The methyl values associated with the 1 and 2 angles of Leu112 are the lowest in the whole protein, even though the backbone fluctuations at this position are limited. Fig. 3 shows the distribution of the side-chain 1 and 2 angles in Leu112 and reveals that the low methyl data result from averaging over multiple rotameric states populated by the side chain of Leu112 in the ensemble.
|
). In particular, the most mobile amino acids, Val27, Ser43, and Arg78, are located in the BC, CC', and FG loops. Interestingly, the FG loop, which includes the RGD cell-adhesion motif, encompassing amino acids Arg78-Asp80 (40), is the most flexible of all the surface loops in FNfn10.
Fig. 4, b and c, show that and 3Jcalc for FNfn10 agree with and 3Jexp data (41) with Pearson correlations of 97% and 93%, and reduced 2s of 1.21 and 0.86, respectively. Amide S2 data with a high average of 0.86 indicate small-scale fluctuations and a practically rigid hydrophobic core. This result agrees with the findings reported in Carr et al. (40), where microsecond-millisecond motions in FNfn10 are not observed.
While most side chains have a single staggered rotamer, Val4, Val11, and Val50 have unusually low 3J values, indicative of rotamer averaging. Distributions of the side-chain 
1 and 2 angles in these amino acids are measured over the obtained native state ensemble of FNfn10 and shown in Fig. 5. Fig. 5 confirms that Val4, Val11, and Val50, while preferring one rotamer, are found on average in 4–5 rotamers.
|
measured over the obtained ensemble. Amide and data (42) for ALB8-GA agree with a Pearson correlation of 92% and reduced 2 of 1.12. Since NMR methyl S2 data are currently not available for comparison, in Fig. 6 b we show our prediction of methyl S2 data as obtained by PEM.
The ensemble drawn in Fig. 6 a shows that the second -helix of ALB8-GA, 2, is tightly packed between the other two helices, 1 and 3. Fig. 6 b shows that obtained backbone fluctuations of 2 are small (amide S2 data >0.8). This result supports the loss of conformational flexibility resulting from selective pressure on 2, which has evolved to bind human serum albumin with high affinity (42).
In contrast, we observe disorder in the N-terminus of 1. We find that amino acids Leu7-Lys11 located at the beginning of the 1 helix of the solution structure of ALB8-GA (31) are highly mobile. These amino acids' high fluctuations can be seen in Fig. 6 b. Moreover, we find that Leu7-Lys11 can populate both helical and coil configurations. Indeed, while occasionally populating helical configurations in the PEM-obtained ensemble, these amino acids have a high probability to visit unfolded coil-like configurations.
The low helical content of these amino acids in the PEM-generated ensemble can be seen in Fig. 7 a. Fig. 7 a shows a square symmetric matrix where a blue square at position (i, j) indicates the presence of a contact between amino acid i and amino acid j, and a red square indicates the formation of a hydrogen bond between amino acids i and j. Fig. 7 a contrasts the contacts and hydrogen bond network as present in the PEM-generated ensemble, shown top left, with the network present in the representative NMR structure of ALB8-GA, shown bottom right. The bottom right half of the map reveals that in the NMR structure hydrogen bonds are present for amino acids Leu7-Lys11 to be in helical configurations. On the other hand, the top left half of the map shows both the scarcity and the low probabilities for hydrogen bonds in this region, indicating that amino acids Leu7-Lys11 visit coil-like configurations in the PEM-generated ensemble with high probability.
|
). The measured probabilities are shown in Table 1(b). We have compared these probabilities with the helicity scores produced by Agadir (44), a program that predicts the helical behavior of polypeptide chains given only amino acid sequence information. The complete amino acid sequence of Leu7-Ala21 is shown in Table 1(a). The helicity scores predicted by Agadir are shown in Table 1(c).
|
1 have lower probabilities of being found in helical configurations in the native state of ALB8-GA compared to amino acids Lys12-Lys19. This can be seen in Fig. 7 b, where we plot and correlate the probabilities measured over the PEM-obtained ensemble with the Agadir-predicted scores. Although the comparison with the Agadir-predicted scores can only be interpreted at a qualitative level (the two data sets measure different quantities), the Pearson correlation with these scores is interestingly high, 82%. This agreement further supports our claim that these five amino acids (Leu7-Lys11) at the beginning of the 1 helix in ALB8-GA have indeed a high probability to visit unfolded configurations under native conditions.
Since helix/coil transitions happen on timescales longer than nanoseconds (45), the unfolding observed for amino acids Leu7-Lys11 cannot be detected by the NMR amide data (42). The native state ensemble obtained by PEM for ALB8-GA may contain additional information to what is present in the available NMR data. It would be interesting to devise wet-lab experiments that can observe native fluctuations of 1 over longer timescales. In this particular case, by capturing helix-coil transitions, such experiments could allow to test our prediction of low helical content for Leu7-Lys11.
|
DISCUSSION AND CONCLUSION |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSION AND CONCLUSIONACKNOWLEDGEMENTSREFERENCES |
|---|
Unlike in trajectory-based simulation techniques, the native conformations obtained by PEM are not correlated to one another. It is this feature that gives PEM its inherent lack of timescale limitations and makes the method intrinsically parallel. The massive parallelism together with the efficient sampling and geometric techniques employed to generate each all-atom conformation of the native state, make PEM an efficient method to obtain extensive native state ensembles of thousands of conformations.
It is worth stressing that the agreement obtained between PEM-calculated and experimental order parameter and scalar coupling data is still a challenge for MD or MC simulation techniques, since slow side-chain rotations may take up to milliseconds (46). In addition, the rotameric averaging measured in the scalar couplings may take from picoseconds to few hundredths of a second (47).
As a sampling-based approach with no inherent timescale limitations, PEM can complement current simulation techniques in highlighting structural and thermodynamic properties of the native state. In particular, as demonstrated for ALB8-GA, PEM can also complement experimental techniques and formulate hypotheses that can be tested through wet-lab experiments.
It is worth stressing that PEM is primarily intended for application on proteins with nonconcerted motions, as for instance the proteins studied in this article. By obtaining conformations of one segment at a time while maintaining the rest of the protein in a reference conformation, as a first-order approximation method, PEM does consider the possibility of correlated motions of segments far away in sequence. We are currently investigating higher-order approximations (25) to extend PEM to proteins with concerted motions and, more generally, to larger and more complex systems. The results presented in this work lead us to believe that PEM represents a significant first step toward improving our characterization and understanding of protein function at a microscopic scale.
|
ACKNOWLEDGEMENTS |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSION AND CONCLUSIONACKNOWLEDGEMENTSREFERENCES |
|---|
Submitted on July 31, 2006; accepted for publication November 13, 2006.
|
REFERENCES |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSION AND CONCLUSIONACKNOWLEDGEMENTSREFERENCES |
|---|
2. Karplus, M., and J. Kuriyan. 2005. Molecular dynamics and protein function. Proc. Natl. Acad. Sci. USA. 102:6679–6685.
3. Eisenmesser, E. Z., O. Millet, W. Labeikovsky, D. M. Korzhnev, M. Wolf-Watz, D. A. Bosco, J. J. Skalicky, L. E. Kay, and D. Kern. 2005. Intrinsic dynamics of an enzyme underlies catalysis. Nature. 438:117–121.[CrossRef][Medline]
4. Peters, G. H., T. M. Frimurer, and O. H. Olsen. 1999. Molecular dynamics simulations of protein-tyrosine phosphatase 1B. I. Ligand-induced changes in the protein motions. Biophys. J. 77:505–515.
5. Balabin, I. A., and J. N. Onuchic. 2000. Dynamically controlled protein tunneling paths in photosynthetic reaction centers. Science. 290:114–117.
6. Schnell, J. R., H. J. Dyson, and P. E. Wright. 2004. Structure, dynamics, and catalytic function of dihydrofolate reductase. Annu. Rev. Biophys. Biomol. Struct. 33:119–140.[CrossRef][Medline]
7. Smith, G. R., M. J. E. Sternberg, and P. A. Bates. 2005. The relationship between the flexibility of proteins and their conformational states on forming protein-protein complexes with an application to protein-protein docking. J. Mol. Biol. 347:1077–1101.[CrossRef][Medline]
8. Igumenova, T. I., K. K. Frederick, and A. J. Wand. 2006. Characterization of the fast dynamics of protein amino acid side chains using NMR relaxation in solution. Chem. Rev. 106:1672–1699.[CrossRef][Medline]
9. Lee, A. L., and A. J. Wand. 2006. Microscopic origins of entropy, heat capacity and the glass transition in proteins. Nature. 411:501–504.
10. Lindorff-Larsen, K., R. B. Best, M. A. DePristo, C. M. Dobson, and M. Vendruscolo. 2005. Simultaneous determination of protein structure and dynamics. Nature. 433:128–132.[CrossRef][Medline]
11. Okamoto, Y. 2004. Generalized-ensemble algorithms: enhanced sampling techniques for Monte Carlo and molecular dynamics simulations. J. Mol. Graph. Model. 22:425–439.[CrossRef][Medline]
12. Singhal, N., C. D. Snow, and V. S. Pande. 2004. Using path sampling to build better Markovian state models: predicting the folding rate and mechanism of a tryptophan zipper beta hairpin. J. Chem. Phys. 121:415–425.[CrossRef][Medline]
13. Jayachandran, G., V. Vishal, and V. S. Pande. 2006. Using massively parallel simulation and Markovian models to study protein folding: examining the dynamics of the villin headpiece. J. Chem. Phys. 124:164902–164914.[CrossRef][Medline]
14. Chen, J., and C. L. Brooks III. 2005. Application of torsion angle molecular dynamics for efficient sampling of protein conformations. J. Comput. Chem. 26:1565–1578.[CrossRef][Medline]
15. Bahar, I., and A. J. Rader. 2005. Coarse-grained normal mode analysis in structural biology. Curr. Opin. Struct. Biol. 15:1–7.[CrossRef]
16. Tai, K., T. Shen, U. Boerjesson, M. Philippopulos, and J. A. McCammon. 2001. Analysis of a 10-ns molecular dynamics simulation of mouse acetylcholinesterase. Biophys. J. 81:715–724.
17. Jacobs, D. J., A. J. Rader, L. A. Kuhn, and M. F. Thorpe. 2001. Protein flexibility predictions using graph theory. Proteins Struct. Funct. Genet. 44:150–165.[CrossRef][Medline]
18. Rod, T. H., J. L. Radkiewicz, and C. L. Brooks III. 2003. Correlated motion and the effect of distal mutations in dihydrofolate reductase. Proc. Natl. Acad. Sci. USA. 100:6980–6985.
19. Daggett, V. 2000. Long timescale simulations. Curr. Opin. Struct. Biol. 10:160–164.[CrossRef][Medline]
20. Price, D. J., and C. L. Brooks III. 2002. Modern protein force fields behave comparably in molecular dynamics simulations. J. Comput. Chem. 23:1045–1057.[CrossRef][Medline]
21. Hansson, T., C. Oostenbrink, and W. F. van Gunsteren. 2002. Molecular dynamics simulations. Curr. Opin. Struct. Biol. 12:190–196.[CrossRef][Medline]
22. Wrabl, J. O., S. A. Larson, and V. J. Hilser. 2001. Thermodynamic propensities of amino acids in the native state ensemble: implications for fold recognition. Protein Sci. 10:1032–1045.
23. Best, R. B., and M. Vendruscolo. 2004. Determination of ensembles of structures consistent with NMR order parameters. J. Am. Chem. Chem. Soc. 126:8090–8091.[CrossRef][Medline]
24. Chen, J., H. S. Won, W. Im, H. J. Dyson, and C. L. Brooks III. 2005. Generation of native-like protein structures from limited NMR data, modern force fields and advanced conformational sampling. J. Biomol. NMR. 31:59–64.[CrossRef][Medline]
25. Shehu, A., C. Clementi, and L. E. Kavraki. 2006. Computing protein conformations from a single structure: modeling protein flexibility at equilibrium. Algorithmica. In press.
26. Shehu, A., C. Clementi, and L. E. Kavraki. 2006. Modeling protein conformational ensembles: From missing loops to equilibrium fluctuations. Proteins Struct. Funct. Bioinf. 65:164–179.[CrossRef]
27. Canutescu, A. A., and R. L. Dunbrack, Jr. 2003. Cyclic Coordinate Descent: a robotics algorithm for protein loop closure. Protein Sci. 12:963–972.
28. Hyberts, S. G., M. S. Goldberg, and G. Wagner. 1992. The solution structure of eglin c based on measurements of many NOEs and coupling constants and its comparison with x-ray structures. Protein Sci. 1:736–751.[Abstract]
29. Morton, C. J., D. J. R. Pugh, E. L. J. Brown, J. D. Kahmann, D. A. Renzoni, and I. D. Campbell. 1996. Solution structure and peptide binding of the SH3 domain from human Fyn. Struct. Fold. Des. 4:705–714.[Medline]
30. Main, A. L., T. S. Harvey, M. J. Baron, and I. D. Campbell. 1992. The three-dimensional structure of the tenth type III module of fibronectin: an insight into RGD-mediated interactions. Cell. 71:671–678.[CrossRef][Medline]
31. Johansson, M. U., M. de Château, M. Wikström, S. Forsén, T. Drakenberg, and L. Björck. 1997. Solution structure of the albumin-binding GA module: a versatile bacterial protein domain. J. Mol. Biol. 266:859–865.[CrossRef][Medline]
32. Berman, H. M., J. Westbrook, Z. Feng, G. Gilliand, T. N. Bhat, H. Weissig, I. N. Shindyalov, and P. E. Bourne. 2000. The Protein Data Bank. Nucleic Acids Res. 28:235–242.
33. MacKerell, J. A. D., D. Bashford, M. Bellot, R. L. Dunbrack, Jr., J. D. Evanseck, M. J. Field, S. Fischer, J. Gao, H. Guo, S. Ha, D. Joseph-McCarthy, L. Kuchnir, K. Kuczera, F. T. K. Lau, C. Mattos, S. Michnick, T. Ngo, D. T. Nguyen, B. Prodhom, W. E. Reiher III, B. Roux, B. Schlenkrich, J. C. Smith, R. H. Stote, J. Straub, J. Wiórkiewicz-Kuczera, D. Yin, and M. Karplus. 1998. All-atom empirical potential for molecular modeling and dynamics studies of proteins. J. Phys. Chem. B. 102:3586–3616.[CrossRef]
34. Lipari, G., and A. Szabo. 1982. Model-free approach to the interpretation of nuclear magnetic resonance relaxation in macromolecules. 1. Theory and range of validity. J. Am. Chem. Soc. 104:4546–4559.[CrossRef]
35. Lipari, G., and A. Szabo. 1982. Protein dynamics and NMR relaxation: comparison of simulations with experiment. Nature. 300:197–198.[CrossRef]
36. Chou, J. J., D. A. Case, and A. Bax. 2003. Insights into the mobility of methyl-bearing side chains in proteins from 3JCC and 3JCN couplings. J. Am. Chem. Soc. 125:8959–8966.[CrossRef][Medline]
37. Bevington, P. R., and D. K. Robinson. 2002. Data Reduction and Error Analysis for the Physical Sciences, 3rd Ed. D. Bruflodt and S. J. Cotkin, editors. McGraw-Hill, New York, NY.
38. Clarkson, M. W., and A. L. Lee. 2004. Long-range dynamic effects of point mutations propagate through side chains in the serine protease inhibitor eglin c. Biochemistry. 43:12448–12458.[CrossRef][Medline]
39. Mittermaier, A., and L. E. Kay. 2004. The response of internal dynamics to hydrophobic core mutations in the SH3 domain from the Fyn tyrosine kinase. Protein Sci. 13:1088–1099.
40. Carr, P. A., H. P. Erickson, and A. G. Palmer III. 1997. Backbone dynamics of homologous fibronectin type III cell adhesion domains from fibronectin and tenascin. Struct. Fold. Des. 5:949–959.[Medline]
41. Best, R. B., T. J. Rutherford, S. M. V. Freund, and J. Clarke. 2004. Backbone dynamics of homologous fibronectin type III cell adhesion domains from fibronectin and tenascin. Biochemistry. 43:1145–1155.[CrossRef][Medline]
42. Johansson, M. U., H. Nilson, J. Evenäs, S. Forsén, T. Drakenberg, L. Björck, and M. Wikström. 2002. Differences in backbone dynamics of two homologous bacterial albumin-binding modules: implications for binding specificity and bacterial adaptation. J. Mol. Biol. 316:1036–1099.
43. Frishman, D., and P. Argos. 1995. Knowledge-based protein secondary structure assignment. Proteins Struct. Funct. Genet. 23:566–579.[CrossRef][Medline]
44. Muñoz, V., and L. Serrano. 1997. Development of the multiple sequence approximation within the Agadir model of -helix formation. Comparison with Zimm-Bragg and Lifson-Roig formalisms. Biopolymers. 41:495–509.[CrossRef][Medline]
45. Doshi, U. R., and V. Muñoz. 2004. The principles of -helix formation: explaining complex kinetics with nucleation-elongation theory. J. Phys. Chem. B. 108:8497–8506.[CrossRef]
46. Ming, D., and R. Brueschweiler. 2004. Prediction of methyl side-chain dynamics in proteins. J. Biomol. NMR. 29:363–368.[CrossRef][Medline]
47. Bax, A., G. W. Vuister, S. Grzesiek, F. Delaglio, A. C. Wang, R. Tschudin, and G. Zhu. 1994. Measurement of homo- and heteronuclear J couplings from quantitative J correlation. Meth. Enzymol. 239:79–105.[Medline]
48. Humphrey, W., A. Dalke, and K. Schulten. 1996. VMD—Visual Molecular Dynamics. J. Mol. Graph. 14:33–38.[CrossRef][Medline]
This article has been cited by other articles:
 |
|
 |
|
  R. W. Alston, M. Lasagna, G. R. Grimsley, J. M. Scholtz, G. D. Reinhart, and C. N. Pace Tryptophan Fluorescence Reveals the Presence of Long-Range Interactions in the Denatured State of Ribonuclease Sa Biophys. J., March 15, 2008; 94(6): 2288 - 2296. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 A. Shehu, L. E. Kavraki, and C. Clementi Unfolding the fold of cyclic cysteine-rich peptides Protein Sci., March 1, 2008; 17(3): 482 - 493. [Abstract] [Full Text] [PDF]
|
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
and 
(3Jcalc on the y axis) are compared to NMR 3J data (3Jexp on the x axis). (b and c) The dashed black line indicates the linear least-squares regression fit on the data sets. The continuous line is the identity line.
and the 
bonds, respectively) for Leu112 in FynSH3 reveal that Leu112 prefers more than one rotameric state.
