Folding rates of small single-domain proteins that fold through simple two-state kinetics can be estimated from details of the three-dimensional protein structure. Previously, predictions of secondary structure had been exploited to predict folding rates from sequence. Here, we estimate two-state folding rates from predictions of internal residue–residue contacts in proteins of unknown structure. Our estimate is based on the correlation between the folding rate and the number of predicted long-range contacts normalized by the square of the protein length. It is well known that long-range order derived from known structures correlates with folding rates. The surprise was that estimates based on very noisy contact predictions were almost as accurate as the estimates based on known contacts. On average, our estimates were similar to those previously published from secondary structure predictions. The combination of these methods that exploit different sources of information improved performance. It appeared that the combined method reliably distinguished fast from slow two-state folders.

Keywords: two-state proteins; folding rate; long-range order; contact predictions

Abbreviations used: LRO, long-range order; PROFcon, system for prediction of residue–residue contact in single-chain proteins (unpublished results); PDB, Protein Data Bank; PROFphd, system for prediction of 1D structure; L, length of protein, i.e. number of its residues; LRO_pred, number of long-range contacts predicted by method introduced here; k_f, experimental folding rate; two-state folders, proteins that fold without intermediates; multi-state folders, proteins that fold through intermediate states

Article Outline

Multi-state folding rate inversely proportional to protein length

Two-state folding rates correlate with secondary structure

Two-state folding rates correlate with long-range order (LRO)

PROFcon accurately predicts the LRO from sequence

Data set and parameter optimization

Predicted long-range order correlates with folding rates

Results statistically significant

Predictions more accurate for short proteins

Implications for understanding folding?

Conclusions

Acknowledgements

References

Multi-state folding rate inversely proportional to protein length

Advances in the experimental and theoretical study of the dynamics of protein folding have improved our understanding of the phenomenon over the last few years.¹ Various theories and simulations suggest a surprisingly simple relation between the number of residues in a protein, its length L, and the rate at which it folds.^{2, 3, 4, 5 and 6} Basically, this relation is of the form:

log(kf)C1LC2

(1)

Two-state folding rates correlate with secondary structure

In solution, native secondary structure such as helices can form even in the unfolded state.¹⁰ This implies that regular secondary structure might be a key player in determining the rate of folding. Indeed, two recent methods estimate folding rates directly from secondary structure content. George Rose and collaborators¹¹ observed that folding rates correlate very well with the overall secondary structure composition in three states (helix, strand, other) assigned from 3D co-ordinates through the programs DSSP¹² and PROSS.¹¹ Ivankov & Finkelstein¹³ have introduced the concept of an “effective length of a folding chain” that is defined as the length of the protein L minus the number of residues in helical conformation, plus the number of helices; more precisely:¹³

(2)

Two-state folding rates correlate with long-range order (LRO)

Here, we introduce a new approach to the prediction of two-state protein folding rates from sequence alone. Our method relies on predictions of residue–residue contacts to tap into another correlation, first reported by Gromiha & Selvaraj,¹⁵ namely that between folding rates and the long-range order (LRO).¹⁵ LRO is defined as:

(3)

PROFcon accurately predicts the LRO from sequence

PROFcon is a neural network trained to predict intra-chain residue–residue contacts.¹⁶ For each pair of internal residues ij, PROFcon predicts the probability that i and j are in spatial contact (closer than 0.8 nm for C^β atoms). One remarkable and unexpected feature of PROFcon is that it can predict the overall number of contacts in a protein more accurately than any simple function (our unpublished results). In order to achieve this, we consider all the N(T) contacts predicted above a threshold of T, i.e. the N(T) most probable predictions (Figure 1; PROFcon is available online through PredictProtein†¹⁷). Using this protein-specific threshold in predicting contact maps also improves the contact predictions directly.¹⁶ In the context of two-state folding rates, the relevant finding is that our predictions allow the distinction between two proteins that both have L residues but differ in their numbers of contacts. The difference between predicting the number of contacts in a protein through its length^{18, 19, 20 and 21} and our method is crucial in this context because protein length correlates very poorly with two-state folding rates.⁹ The next step was to combine our prediction for the number of contacts with the correlation between the observed number of long-range contacts in two-state folders (LRO) and their folding rates. We defined the following quantity:

(4)

(48K)

Figure 1. Sketch of underlying method. (a) PROFcon predicts the probability of a spatial contact between each pair of residues ij in the protein. The output of PROFcon is a number between 0 and 1, with scores closer to 1 indicating a higher probability for the pair to be in contact. Iterating over all possible residue pairs in the protein produces a list (b) of scores. By fixing a cut-off on the output score (we used 0.45), all pairs ranking below the cut-off were discarded. Next, pairs with sequence separations ≤14 were eliminated. The remaining number of pairs divided by L² (L is the protein length) was our estimate for the number of long-range contacts (LRO_pred; equation (4)).

There are two free parameters to be chosen in our number of predicted long-range contacts (LRO_pred; equation (4)), the sequence separation S and the threshold T in the probability of our PROFcon for considering long-range contacts. In this case, we simply chose S=12 in analogy to the optimal value found for the LRO¹⁵ (equation (3)), and T=0.5, i.e. considered all residue pairs for which the PROFcon prediction for contact was higher than the prediction for non-contact. The number of long-range contacts predicted in this way (LRO_pred) correlated with the long-range order (LRO; Table 1). This correlation was significantly higher for shorter proteins. Different choices of S and T gave qualitatively similar results, i.e. the correlation was robust with our ad hoc choice. PROFcon performs better for shorter than for longer proteins; this may be the reason why the correlation between LRO_pred and LRO was higher for shorter proteins. Since most proteins experimentally known to fold directly (two-state transition) are short, this problem is not severely limiting our ability to estimate two-state folding rates.

Table 1.

Correlation between predicted long-range contacts and long-range order

L	Nprot	R(LROpred, LRO)
≤150	199	0.69
150–250	211	0.53
250–400	226	0.49

Scores: L, sequence length (number of residues in protein) interval chosen to group data; N_prot, number of proteins in a sequence-unique subset of proteins from the PDB within the given length interval; R(LRO_pred, LRO), correlation between predicted long-range contacts and long-range order (S=12 and T=0.5; equation (4)). Data set: taken from the EVA version of the largest sequence-unique subset as of December 2003.^{39 and 40} All proteins in the set have X-ray structures at resolutions <0.25 nm. No pair in the set has levels of sequence similarity with HSSP values>0^{22 and 23} to any other protein (this corresponds to <20% sequence identity for long alignments).

Data set and parameter optimization

We used the set of 37 two-state folders introduced by Ivankov & Finkelstein.¹³ These proteins are not sequence-unique, in fact, at HSSP values<0,^{22, 23 and 24} this set is reduced to 31 proteins. The results for the correlation are similar for the entire and the sequence-unique subset. Furthermore, homologous proteins may differ in their folding rates. For example, the SH3 domain in human Fyn (PDB^{25 and 26} identifier, 1shf:A²⁷) and the SH3 domain of the p85 alpha subunit of phosphatidylinositol 3-kinase (1pnj²⁸) have similar sequence (HSSP value=0.27); however, their folding rates differ substantially: for 1shf_A log(k_f)=2.0, and for 1pnj log(k_f)=−0.5 (k_f is the experimentally derived folding rate). In order to simplify the comparison to the previous results,¹³ we therefore reported our performance on the full data set. It is also important to note that one protein (acylphosphatase, 2acy²⁹) was used to train PROFcon; 13 others were sequence-similar to proteins used for training. Removing all these proteins from our set of two-state folders did not alter any of the results discussed below (data not shown). Note, furthermore, that our re-capitulation of the method introduced by Ivankov & Finkelstein (; Table 2) was based on our secondary structure predictions from PROFphd^{30, 31 and 32} rather than on those from PSIPRED¹⁴ and ALB³³ used by Ivankov & Finkelstein. Again, this technical detail appeared not to have altered any results, since the PROFphd predictions yielded results similar to those obtained by the methods used previously¹³ (data not shown). The reported optimal estimates from LRO_pred were obtained for the following choices of the parameters: S=14 and T=0.45. For (equation (2)), we used P=0.1 and C₃=1.

Table 2.

Correlation between estimated and experimental folding rates

Nprot	R(, Kf)	D(, Kf)	R(LRO, Kf)	D(LRO, Kf)	R(LROpred, Kf)	D(LROpred, Kf)
37	0.70 (−0.74)	0.96	0.78 (−0.80)	0.81	0.61 (−0.68)	0.98
36	0.68 (−0.74)	0.99	0.78 (−0.81)	0.80	0.74 (−0.78)	0.86

Scores: N_prot, number of proteins; K_f=log(k_f), logarithm of the folding rate k_f; R(x,K_f) correlations between estimated (x) and observed (K_f) logarithm of folding rate; D(x,K_f) average differences from the actual K_f, e.g. , where N_prot was the overall number of proteins in the dataset under consideration. Methods: (equation (2)) is our implementation of Ivankov & Finkelstein,¹³ x=LRO the long-range order (equation (3)), and x=LRO_pred our prediction of long-range contacts. Data set: all proteins were taken from a previous work;¹³ lower rows give results for subsets of the first set. Values in parentheses are for back-check correlation, i.e. the values obtained by the fit using all proteins, rather than by determining the parameters from the fit on different proteins and testing on a protein left out (jack-knife). Note that values in parentheses most likely over-estimate performance; they are given for comparison with other work only.

Predicted long-range order correlates with folding rates

The “effective length” (; equation (2)) predicted the folding rates remarkably well with a correlation of 0.70 in the jack-knife test, which was almost as high from sequence alone as the correlation between LRO and folding rates from 3D structures (Table 2). Note for comparison that the back-check, i.e. the value obtained after fitting to all experimental rates, was −0.74 as reported.¹³ The correlation between our predicted long-range contacts LRO_pred and the folding rate was markedly lower (0.61 for jack-knife and −0.68 for back-check; Table 2). However, when considering the sum over the differences between estimate and predictions as a measure for the performance instead of the correlation then both the predicted effective length, , and the predicted long-range contacts, LRO_pred, reached rather similar levels (Table 2). For the 37 proteins the correlation between LRO_pred and reached 0.47; we observed a similar number (0.45) when testing the correlation between the two on a much larger data set of 199 proteins shorter than 150 residues that had been used to test our contact prediction method PROFcon¹⁶ (same set as used for Table 1).

Results statistically significant

In order to establish that the correlation achieved by our method was not due to the small data set, we carried out two different tests. Firstly, we calculated the probability that a correlation of −0.68 (Figure 2) could be achieved by chance. Toward this end, we randomly assigned the 37 values of the LRO_pred to the 37 experimental folding rates (taken as logarithms) and calculated the correlation between these two sets (i.e. the random pairs of prediction/observation). We repeated this operation 10⁶ times; the correlation was >|0.68| only five times (absolute values). By this model, the probability for a correlation to exceed 0.68 in our data set therefore is 5×10⁻⁶. Secondly, we estimated the standard error in our estimate for the correlation between our prediction and the observed folding rates by bootstrapping³⁴ the 37 pairs of predicted/observed rates. The average was −0.67 with a standard deviation of 0.12. Even the lower limit (the average minus standard plus the deviation, i.e. −0.67+0.12=−0.55) had a chance of being random of <4.6×10⁻⁴. Clearly then, the correlation between predicted and experimental folding rates was statistically significant.

(51K)

Figure 2. Regression line for the comparison of the predicted number of long-range contacts (LRO_pred; S=14 and T=0.45; equation (4)) and the logarithm of the observed two-state folding rates on a set of 37 two-state folders. The overall correlation coefficient was R=−0.68. The green circle labels the outlier, antigen Vlse (1l8w³⁵).

Predictions more accurate for short proteins

The Lyme disease antigen Vlse of Borrelia burgdorferi (1l8w³⁵) was an extreme outlier in the distribution of our predictions (Figure 2). This 341 residue protein is by far the longest protein in our dataset; the next longest was cyclophilin A (1lop³⁶) with 164 residues, and the average over the entire set was 84 residues. Obviously, our method failed for proteins much longer than the average domain length (around 100 residues^{37 and 38}). Excluding this outlier left us with 36 proteins for which the LRO_pred (predicted long-range contacts) predicted folding rates more accurately than the (effective length) measured both by correlation and mean deviation (Table 2, in bold). In fact, for these proteins our estimates from sequence alone were almost as accurate as the estimates from the full details of 3D structures (LRO). Although the helical content and LRO are related, we observed some degree of non-redundancy between the predictions based on contacts (LRO_pred) and those based on secondary structure (). By simply compiling the arithmetic average over both, we improved the estimate of folding rates to a jack-knife correlation of 0.73 (for all 37 proteins) and to a deviation sum of 0.89. In other words, the performance was better than that of any of the two individual methods that predicted two-state folding rates from sequence alone.

Implications for understanding folding?

Two-state folding rates are closely related to the content in local, regular secondary structure,¹¹ in particular to that in α-helices.¹³ Our results seem to suggest that although the α-helical content is crucial for determining two-state folding rates, some other mechanisms might play an important role. The extreme argument in point is highlighted by the observation that, when considering two-state folders that have a significant content of beta strands (i.e. all-beta; alpha/beta and alpha+beta; 27 proteins in our dataset) the correlation between the effective length (equation (2)) and the folding rate becomes insignificant (0.13 in a jack-knife experiment), while the correlation between the long-range order and the folding rates remains considerable (>0.5 in a jack-knife experiment) for both the lookup from 3D structures (equation (3)) and for the prediction from sequence (equation (4)). Do our results then favor any model of folding over any other? We believe that our evidence was not clear and conclusive enough to answer that question in the affirmative.

Conclusions

We did not find new evidence concerning the question of what are the determinants of two-state folding rates. However, we have shown that estimates from local secondary structure and long-range contacts both somehow contribute independent information in a predictive sense. Our estimates are based on contact predictions that in turn rely mostly on local sequence features. Therefore, our results do not clearly falsify the assumption that folding rates are determined largely by local factors. Most importantly, even methods that predict internal residue–residue contacts at seemingly low levels of accuracy contain enough relevant information to predict two-state folding rates almost as well as the entirely correct experimentally observed contact map. We therefore challenge the suggestion that de novo predictions of inter-residue contact maps have been significantly under-appreciated.

Acknowledgements

Thanks to Jinfeng Liu and Megan Restuccia (both Columbia) for computer assistance, to Guy Yachdav (Columbia) for integrating the program into an Internet server, and to Dariusz Przybylski (Columbia) and Murad Nayal (Columbia) for important discussions. Thanks to Dmitry N. Ivankov and Alexey V. Finkelstein (both Institute of Protein Research, Pushchino) for providing us with crucial data. This work was supported by the grants RO1-GM64633-01 from the National Institutes of Health (NIH) and RO1-LM07329-01 from the National Library of Medicine (NLM). Last, but not least, thanks to all those who deposit their experimental data in public databases, and to those who maintain these databases.

References

1 L. Mirny and E. Shakhnovich, Protein folding theory: from lattice to all-atom models, Annu. Rev. Biophys. Biomol. Struct. 30 (2001), pp. 361–396. Abstract-EMBASE | Abstract-Elsevier BIOBASE | Abstract-MEDLINE   | Full Text via CrossRef

2 A.V. Finkelstein and A. Badretdinov, Rate of protein folding near the point of thermodynamic equilibrium between the coil and the most stable chain fold, Fold. Des. 2 (1997), pp. 115–121. Abstract-MEDLINE  

3 O.V. Galzitskaya, D.N. Ivankov and A.V. Finkelstein, Folding nuclei in proteins, FEBS Letters 489 (2001), pp. 113–118. SummaryPlus | Full Text + Links | PDF (169 K)

4 D. Thirumalai, From minimal models to real proteins:time scales for protein folding kinetics, J. Phys. 5 (1995), pp. 1457–1469.

5 A.M. Gutin, V.V. Abkevich and E.I. Shakhnovich, Chain length scaling of protein folding time, Phys. Rev. Letters 77 (1996), pp. 5433–5436. Abstract-INSPEC | Abstract-INSPEC   | APS full text | Full Text via CrossRef

6 N. Koga and S. Takada, Roles of native topology and chain-length scaling in protein folding: a simulation study with a Go-like model, J. Mol. Biol. 313 (2001), pp. 171–180. SummaryPlus | Full Text + Links | PDF (453 K)

7 J.J. Ewbank and T.E. Creighton, Protein folding by stages, Curr. Opin. Struct. Biol. 2 (1992), pp. 347–349. SummaryPlus | Full Text + Links | PDF (461 K)

8 J.J. Ewbank, T. Creighton, M.K. Hayer-Hartl and F.U. Hartl, What is the molten globule?, Nature Struct. Biol. 2 (1995), p. 10. Abstract-MEDLINE   | Full Text via CrossRef

9 O.V. Galzitskaya, S.O. Garbuzynskiy, D.N. Ivankov and A.V. Finkelstein, Chain length is the main determinant of the folding rate for proteins with three-state folding kinetics, Proteins: Struct. Funct. Genet. 51 (2003), pp. 162–166. Abstract-EMBASE | Abstract-Elsevier BIOBASE | Abstract-MEDLINE   | Full Text via CrossRef

10 J. Prieto and L. Serrano, C-capping and helix stability: the Pro C-capping motif, J. Mol. Biol. 274 (1997), pp. 276–288. SummaryPlus | Full Text + Links | PDF (391 K)

11 H. Gong, D.G. Isom, R. Srinivasan and G.D. Rose, Local secondary structure content predicts folding rates for simple, two-state proteins, J. Mol. Biol. 327 (2003), pp. 1149–1154. SummaryPlus | Full Text + Links | PDF (244 K)

12 W. Kabsch and C. Sander, Dictionary of protein secondary structure: pattern recognition of hydrogen-bonded and geometrical features, Biopolymers 22 (1983), pp. 2577–2637. Abstract-MEDLINE   | Full Text via CrossRef

13 D.N. Ivankov and A.V. Finkelstein, Prediction of protein folding rates from the amino acid sequence-predicted secondary structure, Proc. Natl Acad. Sci. USA 101 (2004), pp. 8942–8944. Abstract-EMBASE | Abstract-MEDLINE   | Full Text via CrossRef

14 D.T. Jones, Protein secondary structure prediction based on position-specific scoring matrices, J. Mol. Biol. 292 (1999), pp. 195–202. SummaryPlus | Full Text + Links | PDF (221 K)

15 M.M. Gromiha and S. Selvaraj, Comparison between long-range interactions and contact order in determining the folding rate of two-state proteins: application of long-range order to folding rate prediction, J. Mol. Biol. 310 (2001), pp. 27–32. SummaryPlus | Full Text + Links | PDF (140 K)

16 M. Punta and B. Rost, Toward good 2D predictions in proteins, Bioinformatics (2005) In the press.

17 B. Rost, G. Yachdav and J. Liu, The PredictProtein server, Nucl. Acids Res. 32 (2004), pp. W321–W326. Abstract-EMBASE | Abstract-Elsevier BIOBASE | Abstract-MEDLINE  

18 U. Goebel, C. Sander, R. Schneider and A. Valencia, Correlated mutations and residue contacts in proteins, Proteins: Struct. Funct. Genet. 18 (1994), pp. 309–317.

19 O. Olmea and A. Valencia, Improving contact predictions by the combination of correlated mutations and other sources of sequence information, Fold. Des. 2 (1997), pp. S25–S32. Abstract-MEDLINE  

20 O. Olmea, B. Rost and A. Valencia, Effective use of sequence correlation and conservation in fold recognition, J. Mol. Biol. 293 (1999), pp. 1221–1239. SummaryPlus | Full Text + Links | PDF (1186 K)

21 P. Fariselli, O. Olmea, A. Valencia and R. Casadio, Progress in predicting inter-residue contacts of proteins with neural networks and correlated mutations, Proteins: Struct. Funct. Genet. Suppl (2001), pp. 157–162. Abstract-EMBASE | Abstract-Elsevier BIOBASE | Abstract-MEDLINE   | Full Text via CrossRef

22 C. Sander and R. Schneider, Database of homology-derived structures and the structural meaning of sequence alignment, Proteins: Struct. Funct. Genet. 9 (1991), pp. 56–68. Abstract-EMBASE | Abstract-MEDLINE  

23 B. Rost, Twilight zone of protein sequence alignments, Protein Eng. 12 (1999), pp. 85–94. Abstract-EMBASE | Abstract-MEDLINE   | Full Text via CrossRef

24 S. Mika and B. Rost, UniqueProt: creating representative protein sequence sets, Nucl. Acids Res. 31 (2003), pp. 3789–3791. Abstract-Elsevier BIOBASE | Abstract-MEDLINE   | Full Text via CrossRef

25 F.C. Bernstein, T.F. Koetzle, G.J.B. Williams, E.F. Meyer, M.D. Brice and J.R. Rodgers et al., The Protein Data Bank: a computer based archival file for macromolecular structures, J. Mol. Biol. 112 (1977), pp. 535–542. Abstract-EMBASE | Abstract-MEDLINE  

26 H.M. Berman, T. Battistuz, T.N. Bhat, W.F. Bluhm, P.E. Bourne and K. Burkhardt et al., The Protein Data Bank, Acta Crystallog. sect. D 58 (2002), pp. 899–907. Abstract-Elsevier BIOBASE | Abstract-MEDLINE   | Full Text via CrossRef

27 M.E. Noble, A. Musacchio, M. Saraste, S.A. Courtneidge and R.K. Wierenga, Crystal structure of the SH3 domain in human Fyn; comparison of the three-dimensional structures of SH3 domains in tyrosine kinases and spectrin, EMBO J. 12 (1993), pp. 2617–2624. Abstract-EMBASE | Abstract-MEDLINE  

28 G.W. Booker, I. Gout, A.K. Downing, P.C. Driscoll, J. Boyd, M.D. Waterfield and I.D. Campbell, Solution structure and ligand-binding site of the SH3 domain of the p85 alpha subunit of phosphatidylinositol 3-kinase, Cell 73 (1993), pp. 813–822. SummaryPlus | Full Text + Links | PDF (3639 K)

29 M.M. Thunnissen, N. Taddei, G. Liguri, G. Ramponi and P. Nordlund, Crystal structure of common type acylphosphatase from bovine testis, Structure 5 (1997), pp. 69–79. SummaryPlus | Full Text + Links | PDF (927 K)

30 B. Rost, How to use protein 1D structure predicted by PROFphd. In: J.E. Walker, Editor, The Proteomics Protocols Handbook, Humana, Totowa, NJ (2005), pp. 879–908.

31 B. Rost, Protein secondary structure prediction continues to rise, J. Struct. Biol. 134 (2001), pp. 204–218. Abstract | Abstract + References | PDF (233 K)

32 B. Rost, PHD: predicting one-dimensional protein structure by profile based neural networks, Methods Enzymol. 266 (1996), pp. 525–539. Abstract-EMBASE | Abstract-MEDLINE  

33 O.B. Ptitsyn and A.V. Finkelstein, Theory of protein secondary structure and algorithm of its prediction, Biopolymers 22 (1983), pp. 15–25. Abstract-MEDLINE   | Full Text via CrossRef

34 Efron, B.; & Tibshirani, R.J. (1993). An Introduction to the Bootstrap, Chapman & Hall/CRC, Boca Raton, FL.

35 C. Eicken, V. Sharma, T. Klabunde, M.B. Lawrenz, J.M. Hardham, S.J. Norris and J.C. Sacchettini, Crystal structure of Lyme disease variable surface antigen VlsE of Borrelia burgdorferi, J. Biol. Chem. 277 (2002), pp. 21691–21696. Abstract-EMBASE | Abstract-Elsevier BIOBASE | Abstract-MEDLINE   | Full Text via CrossRef

36 M. Konno, M. Ito, T. Hayano and N. Takahashi, The substrate-binding site in Escherichia coli cyclophilin A preferably recognizes a cis-proline isomer or a highly distorted form of the trans isomer, J. Mol. Biol. 256 (1996), pp. 897–908. Abstract | PDF (899 K)

37 J. Liu and B. Rost, CHOP proteins into structural domains, Proteins: Struct. Funct. Genet. 55 (2004), pp. 678–688. Abstract-EMBASE | Abstract-Elsevier BIOBASE | Abstract-MEDLINE   | Full Text via CrossRef

38 J. Liu, H. Hegyi, T.B. Acton, G.T. Montelione and B. Rost, Automatic target selection for structural genomics on eukaryotes, Proteins: Struct. Funct. Genet. 56 (2005), pp. 188–200.

39 V. Eyrich, M.A. Martí-Renom, D. Przybylski, A. Fiser, F. Pazos and A. Valencia et al., EVA: continuous automatic evaluation of protein structure prediction servers, Bioinformatics 17 (2001), pp. 1242–1243. Abstract-MEDLINE   | Full Text via CrossRef

40 I.Y.Y. Koh, V.A. Eyrich, M.A. Marti-Renom, D. Przybylski, M.S. Madhusudhan and E. Narayanan et al., EVA: evaluation of protein structure prediction servers, Nucl. Acids Res. 31 (2003), pp. 3311–3315. Abstract-Elsevier BIOBASE | Abstract-MEDLINE   | Full Text via CrossRef