Abstract

Introduction

Although most of the earlier reports on the relation between chemical shift and protein structure focus on 1Ha and 1HN, with the advent of heteronuclear isotopic enrichment additional chemical shifts have become accessible and offer the potential to make the relation between chemical shift and structure more quantitative. The secondary ¹³Ca and ¹³Cb chemical shifts of a given residue were found to correlate closely with its phi and psi torsion angles (Ando et al., 1984; Saito, 1986; Spera and Bax, 1991), and thereby also with secondary structure (Wishart et al., 1991). Methods have been developed to obtain backbone torsion angle restraints and secondary structure information from either ¹Ha and ¹³Ca (Luginbühl et al., 1995), or ¹³Ca, ¹³Cb, ¹³C', and ¹Ha (Wishart and Sykes, 1994). The empirical correlation between phi and psi backbone torsion angles and the ¹³Ca and ¹³Cb chemical shifts also was found useful for identification of N-terminal helix-capping boxes (Gronenborn and Clore, 1994). This same group also introduced an effective method for incorporating the empirical secondary ¹³Ca and ¹³Cb chemical shift profiles into the structure calculation protocol (Kuszewski et al., 1995, Celda et al., 1995). Ab initio calculations (de Dios and Oldfield, 1993) confirm that the backbone phi and psi torsion angles strongly affect ¹³Ca and ¹³Cb shielding, and the use of experimental ¹³Ca, ¹³Cb and ¹Ha shifts, in conjunction with residue-specific chemical shift surfaces from ab initio methods, has been proposed as a tool for structure refinement (Pearson et al. 1995). Beger and Bolton (1997) proposed an approach to obtain the most probable phi and psi angles from correlation maps between backbone chemical shifts of ¹³Ca, ¹³Cb, ¹Ha , ¹HN and ¹⁵N of a given residue and its backbone torsion angles. They also showed that this information considerably improves structural quality when used in cases where only a very small number of NOE restraints is available.

The similarity in secondary chemical shifts in homologous proteins also has been well recognized (Redfield and Robertson, 1991). Wishart et al. (1997) developed an elegant approach to utilize this similarity during the resonance assignment process. However, a minimum of ca 30% sequence identity is quoted as the requirement for making this procedure reliable.

Here, we describe a hybrid approach which utilizes both sequence and chemical shift homology to predict the most likely backbone angles for a given residue. The idea is based on the notion that if a string of adjacent amino acids shows high similarity in secondary chemical shifts with a string of amino acids in a database, the central residues in the two strings are likely to have similar backbone torsion angles. In particular, when qualitative similarity in the residue types of the two strings is used as an additional criterion, the approach becomes remarkably robust. In essence, this is a generalization of the idea that helix-capping boxes can be identified best by combined use of their characteristic patterns of chemical shifts and the residue types involved (Gronenborn & Clore, 1994).

Materials and Methods

When using collections of chemical shifts of proteins reported by different groups, it is critical to ensure that the same chemical shift referencing convention is used for all these proteins. This is particularly important for ¹³C and ¹⁵N, where a wide variety of direct and indirect referencing methods have been used. Rather than relying on the information supplied with the deposited chemical shift data, we evaluate the need for applying a correction to these shifts by calculating how much, on average, the secondary shifts (calculated by subtracting the random coil shifts of Spera and Bax, 1991) deviate from the corresponding secondary chemical shifts predicted by the (phi,psi)-surfaces of Spera and Bax. These averages are conveniently calculated with a routine added to the X-PLOR program (Brünger, 1993) by Kuszewski et al. (1995), and intended for use of the secondary ¹³Ca and ¹³Cb shifts during structure calculation. We apply a chemical shift correction only if the average deviation for a given protein exceeds by more than a factor of three the expected random variation in this average [i.e., the standard error of ca 1 ppm (Spera and Bax, 1991) divided by the square root of the number of shifts used]. This manner of correcting the deposited chemical shifts ensures that all secondary shifts are defined in the same manner, and corresponds to subtraction of the random coil ¹³Ca and ¹³Cb shifts of Spera and Bax (1991) and ¹³C' (Wishart et al., 1995a) from experimentally determined shifts relative to internal trimethylsilyl propionate (TSP). Note that TSP resonates upfield from the IUPAC-recommended standard (Markley et al., 1998), dimethylsilapentane-5-sulfonic acid or DSS, by an insignificant amount (0.12 ppm at pH 7) (Wishart et al., 1995b). The same correction procedure must be used for all other new proteins added to the database. Only a small fraction of the proteins required the above correction procedure. For ¹⁵N, the chemical shift reference standard is liquid ammonia at 25 degrees C, and the need for application of a correction was evaluated by calculating the average ¹⁵N chemical shifts for all non-Gly, non-Ser, non-Thr residues in alpha-helical and beta-strand regions of the protein and comparing them with the database averages (119.47 ppm for a-helices and 122.38 ppm for b-strands). Whenever the average of the a-helix and b-strand ¹⁵N chemical shift deviations (weighted according to the number of residues used for each type of secondary structure) is larger than 1 ppm, a correction to the chemical shifts needs to be applied. Alphalytic protease was the only protein for which such ¹⁵N chemical shift adjustment (by -2.26 ppm) needed to be used. For ¹H, where historically chemical shift referencing has been much less of a problem, no such corrections were applied.

To investigate whether the ¹³C' chemical shift is strongly influenced by the hydrogen bond length, hydrogens were added to the 1.1 Å crystal structure of basic pancreatic trypsin inhibitor (Wlodawer et al., 1984) with the program X-PLOR (Brünger, 1993) . For the 24 carbonyls involved in stable backbone-backbone hydrogen bonds, no significant correlation was found between the lengths of the backbone-backbone hydrogen bonds, calculated from this structure, and the corresponding ¹³C' secondary shifts. This result suggests that the ¹³C' secondary shift is primarily a function of the backbone geometry, in agreement with its previously reported correlation with secondary structure (Kricheldorf and Muller, 1983; Wishart et al., 1991). Therefore, we decided to include the ¹³C' shift information in the evaluation, even while for several proteins no ¹³C' shifts have been reported in the database.

Although the ¹⁵N chemical shift is known to be influenced by hydrogen bonding (de Dios et al., 1993), it is also influenced by backbone geometry and therefore is included as an input parameter in the torsion angle prediction procedure. However, as discussed below, optimization of the torsion angle prediction program results in a relatively low weighting factor for this chemical shift.

Results and Discussion

TALOS reads the experimental protein chemical shift tables and converts them to secondary chemical shifts before entering them in the database. In its current implementation, TALOS evaluates the similarity in amino acid sequence and secondary shifts for a string of three sequential amino acids relative to all triplets of sequential residues contained in the database. Although we expect that further improvement in performance might be attainable for string lengths longer than three, the number of residues in the database is presently too small to yield a sufficient sampling for such longer strings. For each query triplet of consecutive residues, the similarity to a triplet with center-residue j in the database is evaluated by computing a similarity factor, S (i,j), given by:

S (i,j) = Sn=-1 [k0n DResType2 + k1n(DdCai+n-DdCaj+n)2 + k2n(DdNi+n-DdNj+n)2 +

k3n(DdCbi+n-DdCbj+n)2 + k4n(DdC¢i+n-DdC¢j+n)2 + k5n(DdHai+n-DdHaj+n)2] (1)

and the value of S(i,j) is evaluated for all triplets j in the database. Dd denotes the secondary shifts of the ¹³Ca, ¹³Cb, ¹³C', ¹Ha and ¹⁵N nuclei. For Gly residues, ¹Ha shifts are calculated as the average of ¹Ha2 and ¹Ha3. Values for the weighting factors, k0n through k5n are optimized as described below and are given in Table 2; the residue-type similarity matrix ascribes a number to how similar two types of amino acids are and this 20 ¥ 20 matrix is shown in Table 3. The composition of this similarity matrix is largely based on empirical knowledge that, for example, Gly frequently has a positive phi angle, Pro has a very restricted range of phi angles, and Cb-branched residues are frequently found in beta-sheets. There has been some empirical adjustment of the similarity matrix during the process of optimizing the performance of the TALOS program, but results were not found to be particularly sensitive to small changes (by ±1) in the Table 3 matrix elements. Using the empirical k values of Table 2, and DResType of Table 3, S(i,j) values typically range from 5 to 600.

For all database triplets, j, that yield a S(i,j) value lower than an adjustable threshold (typically ~150), TALOS reports the corresponding X-ray crystal structure phi and psi angles of residue j, together with the S(i,j) value. The threshold is set sufficiently large to obtain a minimum of at least 10 matches for each residue i.

Optimization of the 15 chemical shift weighting factors made use of a scheme which finds all triplets of residues in the database for which the central residue has phi/psi angles within 15 degrees of those of a query residue. We then calculate the average and the standard deviation of the secondary chemical shifts for each of the 15 types of chemical shifts (5 nuclei for residue i-1, i, and i+1) over this ensemble of triplets. The rms value of all database secondary chemical shifts of a given type of nucleus, divided by the standard deviation derived in the above described manner, provides a measure for how useful a given type of secondary chemical shift (e.g., DdNi-1) is at providing information on the phi/psi angles of residue i. This ratio was calculated 183 times, each time using a different cutinase residue as the query residue. The chemical shift weighting factors listed in Table 2 are derived from the averages of these respective ratios, after scaling to compensate for the intrinsically different widths of the secondary shift distributions of the types of atoms involved (i.e., using the root-mean-square (rms) values of the ¹⁵N, ¹Ha,¹³Ca, ¹³Cb and ¹³C' secondary chemical shift values in the entire database).

The relative weight of the residue type homology versus secondary shifts in the S(i,j) formula (k0n factors in eq 1) was optimized empirically, by searching for k0n factors that minimize the number of erroneous predictions, using all residues present in the database for test purposes.

If a particular chemical shift is missing, the corresponding secondary chemical shift difference between the query and the corresponding database chemical shift is set to 1.5 times the rms value of the corresponding secondary chemical shift (rms values are 4.56 ppm for 15N, 2.49 ppm for 13Ca, 0.51 ppm for ¹Ha, 2.01 ppm for ¹³Cb, and 2.02 ppm for ¹³C'). This way of dealing with incomplete assignments decreases the likelihood that database residues with incomplete assignments contribute to the phi/psi output of TALOS, but does not exclude them altogether.

To date, the database used by TALOS contains only 20 structures for which both a high-resolution X-ray structure and nearly complete resonance assignments are available. The reason we felt it is not warranted to include proteins for which a high-resolution NMR structure but no crystal structure is available is that, as discussed below, the agreement between the phi and psi angles of most NMR structures and the output of TALOS is considerably lower than for the high-resolution crystal structures in the database.

The TALOS output for the phi and psi backbone angles of the center residue in each string consists of the average of the corresponding angles in the 10 strings in the database with the highest degree of similarity (cf eq 1). In a first, fully automated but very conservative mode of analysis, the program classifies only those predictions for which at least nine out of ten predictions fall in the same populated (gray shaded) region of the Ramachandran map (Figure 2), and none of the center residues in the 10 strings has a positive f angle. If a single residue falls well outside the Ramachandran region in which the remaining 9 residues are located, its f/y values are excluded from calculating the average and rmsd. This procedure typically results in predictions for only about 40% of the residues.

A subsequent interactive inspection of the results, using the graphical interface described below, permits additional predictions to be made. For example, if several predictions fall just outside the most populated region of the Ramachandran map, but generally cluster well with the other phi/psi predictions, the prediction should be accepted. In some cases, there is one center-residue in the ensemble of 10 most similar triplets for which either f or y deviates by more than 2 standard deviations from the average value for that angle. Empirical testing indicates that it is safe to remove (at most) one such triplet from the ensemble of 10 (TALOS then recalculates the new average phi and psi angles and their rmsd), provided that the outlier does not have its f angle in the 0 degrees < phi < +150 degrees range, and the average S(i,j) value is less than 80. When the TALOS output for a given query residue yields a cluster where at least 9 residues have positive f angles, this prediction also should be accepted.

The standard deviations and the range of (f,y) values in the 10 (or 9) most similar database strings provide a measure for the uncertainty in these averages. When this standard deviation exceeds 45s, the prediction must be deemed "ambiguous", and it is recommended that the result of the prediction not be used without careful further inspection of other data, such as the daN(i-1,i)/daN(i,i) NOE intensity ratio (which provides information on the y angle), the 3JHNHa coupling (f angle), and 1JCaHa (primarily for identifying positive f angles; Vuister et al., 1992, 1993). Not including such cases where NOE or J coupling information is needed, the above described protocol typically allows a definitive prediction of the phi and psi angles to be made for about two thirds of the residues.

Because the number of proteins for which complete NMR assignments and high resolution crystal structures are available is still very limited, the TALOS database usually contains insufficient entries for unambiguous identification of residues with positive f angles. However, testing indicates that if the center-residue of a query triplet has a positive f angle, this frequently results in a significant fraction of center-residues which also have positive f angles in the ten most similar database triplets. These positive f angle triplets typically yield the lowest S(i,j) values, suggesting that the program will successfully predict most of the positive f angles once the database becomes sufficiently large. For now, unambiguous identification of such positive f angles in most cases requires additional experimental data, such as a very small 1JCaHa (<136 Hz) (Vuister et al., 1992, 1993), or the presence of an exceptionally strong intraresidue HN-Ha NOE.

A graphical interface for inspecting and interactively updating the TALOS output is available. An example of its use is shown in Figure 2 for the HIV protease. The interface consists of three windows: the sequence display, the prediction display, and the Ramachandran display.

The sequence display lists the residues in the protein whose backbone angles are being predicted. The residues are color-coded according to whether the overall prediction for a given residue was designated as good, ambiguous, or bad. In the initial display, before interactive analysis, residues are color-coded as green (prediction accepted in automated mode) and gray (requires inspection). If the true f/y angles are known, residues for which a wrong prediction was accepted can be classified as bad (red), which is convenient for testing purposes. All residues for which TALOS has made predictions which meet the criteria listed above, are highlighted in green. Residues shaded in yellow are those for which no firm prediction can be made, but which nevertheless may contain useful information. For example, if for a given residue 5 out of the 10 triplets show a positive f angle, this suggests that there is a high likelihood that the center residue of the query triplet has a positive f angle.

When a given residue is selected in the sequence display (K20 in Figure 2), the f, y, and S(i,j) parameters are listed in the prediction display, together with the residue numbers and the names of the proteins from which the triplets were taken. The ten f/y pairs are graphed in the Ramachandran display, which also shows the most populated areas of the entire database, shaded in gray. If a reference or trial structure for the query protein is available, its f/y angles will also be graphed on the Ramachandran display (blue square). By clicking on an individual match in the Ramachandran display, it is possible to include or remove this entry from the overall prediction, which is based on the average and standard deviations of the selected matches.

The final results are summarized in an ASCII text table which gives the average f/y angles and their standard deviations for each residue. Versions of the TALOS program are available for most types of UNIX platforms.

Figure 3 plots the predicted phi and psi angles of ubiquitin versus those of the high resolution crystal structure. As can be seen from this plot, TALOS does considerably more than classifying residues by their type of secondary structure, and there is a good correlation between predicted and crystallographic torsion angles, even when considering only the residues with a positive y angle, for example.

Figure 4 shows the predicted phi and psi angles as a function of residue number, together with the corresponding crystallographically determined angles. The error bars correspond to the standard deviation from the average angle for the center-residue of the 10 (or 9) best fitting triplets in the database. No result is shown if this standard deviation exceeds 45s, or if any (but less than 9) of the f angles of the center-residues have a positive f angle.

Tests of the accuracy of TALOS predictions were made by eliminating each protein from the database and using the program to predict its backbone angles (Table 4). We found that for about 2% of the residues in the database (i.e., 3% of the predictions made) TALOS predicts the wrong torsion angles. Some examples are:1.Thr45 in cutinase: Predicted y = -4 ± 10s; X-ray y = 163s. Although the B factor is not unusually high, 15N relaxation data indicate this residue is located in the middle of a flexible loop which differs in conformation relative to the crystal structure (Prompers et al., 1997).

2. Asp159 of beta-hydroxydecanoyl thiol ester dehydrase: Predicted f = -57 ± 7s, y = -36 ±10s; X-ray f = 56s, y = 52s.

3. Asp19 of staphylococcal nuclease: Predicted f = -90 ± 12s; y = 8 ±11s; X-ray f = -156s, y= -166s.Both for Asp159 and Asp19 there is no doubt regarding the similarity in backbone angles in solution and in the crystalline state, but TALOS fails to predict the unusual backbone angles of these residues. The user therefore should be aware that a small fraction of the TALOS predictions may be in error. However, as shown below, for the vast majority of cases, the output of TALOS is highly accurate. When listing the rms differences between the predicted f/y angles and those of the crystal structure, the small fraction of erroneous predictions are not included.

For ubiquitin, TALOS yields 53 f/y angle predictions (76 % of its database residues) and the rms differences between the predicted f/y angles and those of the crystal structure are 12s/9s. Similarly, for cutinase f/y predictions are made for 127 residues (69%, including 5 bad predictions, but excluding the disordered N-terminal tail), with rmsds of 12s/12s relative to the crystallographically determined f and y angles.

BPTI yielded the worst performance of all proteins tested. Only 32 f/y predictions (65%, 4 bad predictions) were made, which agree to within rmsds of 16s and 17s with the 1.1 Å crystal structure. Differences relative to the solution structure (Berndt et al., 1992) are slightly larger (18/19s). For the same set of phi and psi angles, the rms differences between the average solution structure and crystal structure are 14s and 12s, respectively.

For human thioredoxin the NMR data have been derived for a mutant which differs from the sequence used for the crystal structure. The f angles predicted by TALOS are nevertheless in very good agreement with those of the crystal structure (Supplementary Material), with 80 (78%) f/y predictions (rmsds of 15s and 12s from the X-ray structure, respectively), including one erroneous prediction. For reference, the rmsds relative to the solution structure for the same group of phi and psi angles are 20s and 22s, respectively. The pairwise rmsd between the crystal structure and solution structure angles is 16s (f) and 20s (y).

Use of TALOS output in structure calculation.

Three sets of calculations were performed: (A) using only 273 NOEs, randomly taken from the total set of 2727 NOE cross peaks, peak-picked from 3D and 4D NOESY spectra (J.L. Marquardt, unpublished results); (B) additionally using TALOS-f/y constraints for the 53 residues for which a (correct) prediction had been made; (C) as B, but deliberately introducing two serious errors in the f/y constraints by interchanging the TALOS-derived angles of Ala46 (TALOS: f = 54±7s, y = 39±9s; X-ray: f = 48s, y = 46s) with those of Arg54 (TALOS: f = -102±22s, y = 150±17s; X-ray: f = -85s, y = 165s). Starting from a fully extended strand and using an X-PLOR based simulated annealing protocol (Nilges et al, 1988), set A yielded convergence for 9 out of 30 calculated structures. The backbone rmsd (residues 2-70) from the average was 1.52 Å, and the backbone rmsd displacement between the average of these NMR structures and the crystal structure was 1.36 Å. For set B, f- and y-constraints were included as "harmonic-well" potentials with zero energy over the range fTALOS ± SD and yTALOS ± SD, where SD is the standard deviation in the set of 10 (or 9) residues from which fTALOS and yTALOS were derived. Outside the well, the energy increased quadratically with 200 kcal/rad2. With 13 out of 30 calculations converging, the yield was 50% higher than in the absence of TALOS constraints. Moreover, the rmsd from the average was also considerably lower (0.75 Å), as was the difference relative to the X-ray structure (0.89 Å). For set C, which includes the erroneous backbone constraints, convergence was worst (7 out of 30), but the rmsd from the average (0.87 Å) and between the averaged NMR and crystal structure (1.04 Å) were intermediate. The errors introduced in the NMR structure by the wrong TALOS constraints were highly localized.

Although preliminary and clearly incomplete, the above results for ubiquitin are quite encouraging. They suggest that a substantial improvement in quality of the structure can be obtained by including the TALOS-derived f/y-restraints, particularly when the number of NOEs per residue is low. The introduction of two serious errors in the TALOS-derived torsion angle restraints decreases the quality of the structure, but it remains better than in the absence of the TALOS-derived constraints. Nevertheless, it is recommended that the constraints are used with care, keeping in mind that they may contain errors. Thus, if either a TALOS- or NOE-constraint (or both) is violated consistently during structure calculations, it is essential to recheck the quality of the constraint(s) involved. In this respect, an erroneous TALOS-derived restraint is no different from a wrongly assigned NOE connectivity.

Concluding Remarks

At the outset of developing this approach, we anticipated being able to obtain c1 angle predictions too. However, these c1 results so far appear insufficiently reliable for general use. Three possible reasons for this are that (1) chemical shifts of the backbone nuclei are not sufficiently sensitive to c1, (2) in the crystal structures it is not possible to reliably and routinely separate residues with a single c1 conformation from those which undergo c1 rotameric averaging, and (3) there are practical difficulties in comparing c1 angles for residues with different types of sidechains, i.e., a Cb-branched residue such as Thr with a non-branched residue. Although it may be feasible to develop criteria which yield useful TALOS c1 predictions, it is expected that it will be difficult to make predictions that are more reliable than those based on residue type and a residue's own backbone angles, as implemented by Kuszewski et al. (1997).

Our results indicate that concerted use of 15N, 13Ca, 1Ha, 13Cb and 13C¢ chemical shifts of triplets of adjacent residues can be used to predict the backbone torsion angles for the majority of residues in assigned proteins. When using the crystal structure as the standard, the accuracy of the TALOS prediction appears to exceed that of even some of the best solution structures calculated on the basis of NOEs and J couplings. In principle, one could possibly argue that, as the angles in the database are all derived from crystal structures, one might expect the TALOS output to be closer to the crystal structure than to the solution structure. However, this argument is clearly invalid as it would require a systematic (as opposed to a random) difference between torsion angles in crystal structures and in solution. Second, when comparing the TALOS output for ubiquitin with a solution structure calculated by including a large number of 13Ca-1Ha, 13Ca-13C¢, 1H-15N, 13C¢-15N and 13Ca-13Cb dipolar couplings (Tjandra and Bax, 1997; Marquardt et al., unpublished results) the agreement of the TALOS-predicted angles with the solution structure is actually better than with the crystal structure, with rmsd's of 10s (solution) and 12s (X-ray) for f and 8s (solution) and 9s (X-ray) for y. The rmsd between crystal structure and solution structure torsion angles is 7s for both phi and psi.

The 3% fraction of TALOS predictions which are found to be in disagreement with the crystal structure includes residues which may adopt a different conformation in the solution and crystal structures (e.g., Thr45 in cutinase, discussed above), although most of these regions where differences occur are excluded by the B-factor criterion (see Materials and Methods). For most proteins used in our database, no high resolution solution structure is available, and it therefore was not possible to exclude these residues from the database. A set of residues in the database for which the solution backbone angles differ strongly from those in the crystalline state does not increase the number of errors when TALOS is applied to a new protein. Instead, if their chemical shifts match those of the query triplet, they result in an outlier in the display of Figure 2. The same is true if a small fraction of residues in the database is wrongly assigned.

It also should be pointed out that a database approach such as the one described here tends to predict torsion angles that fall closer to the most commonly occupied regions of the Ramachandran map than the true value. This is a direct result of the fact that TALOS angles are derived from a set of triplets with the most similar chemical shifts: First, if the true backbone angles of a given center-residue position it somewhere on the edge of the most populated region of the Ramachandran map, there statistically will be a larger number of "hits" inside than outside the most populated region, simply because the density of residues is higher in the most populated region. This effect is visible in Figure 3B, for example, where for residues with X-ray y angles in the -25s to +25s range the predicted y angles are shifted in the direction of the a-helical region of the Ramachandran map. Similarly, for residues with unusually large y angles in the X-ray structure, the predicted values consistently are shifted slightly towards the more populated region near y = 130s. Second, in rare cases where residues are located far outside the populated region of the Ramachandran map (such as Asp19 in Staphylococcal nuclease), no other triplet with such unusual angles may be present in the database. If TALOS finds a cluster of triplets which accidentally match the shifts and residue types of the query triplet, it is likely that the torsion angles in this cluster fall in the highly populated region of the Ramachandran map. Both these types of problems will be alleviated when the database becomes larger.

It is important to realize that the TALOS-derived f/y-values are empirical in nature. In a conservative approach, deviations between these f/y-values and those in structures calculated on the basis of regular experimental restraints can be used for "trouble-shooting" purposes. Alternatively, in cases where an insufficient number of regular experimental constraints is available, preliminary results on ubiquitin suggest that incorporation of the TALOS-derived f/y-values can enhance structural quality considerably. Collecting a large number of NOEs can be particularly difficult in larger proteins, which require extensive deuteration. It is expected that the use of TALOS-derived torsion angle restraints, when combined with one-bond dipolar couplings measured in dilute liquid crystalline media (Bax and Tjandra, 1997; Clore et al, 1998; Hansen et al., 1998; Bewley et al., 1998; Wang et al., 1998), will make it possible to obtain reliable backbone structures for such larger systems, even if only a limited number of NOEs is available.

Software availability

Acknowledgements

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Tables

n = -1, 0, 1), for weighting the relative importance of a given chemical shift or residue type in determining the similarity score, S(i,j) of eq 1.

Res. Homology 15N 1Ha13C¢13Ca13Cb

n = -1 0.74 0.16 14.66 1.15 0.72 0.76

n = 0 1.48 0.18 17.54 1.21 0.99 0.91

n = 1 0.74 0.20 15.25 1.04 0.72 0.70
 

  Table 3. Residue similarity factors, DResType, used by TALOS in eq 1.
 
 

Residue	A	R	D	N	C	Q	E	G	H	I	L	K	M	F	P	S	T	W	Y	V
A	0	1	1	1	1	1	1	2	1	2	1	1	1	2	3	1	2	2	2	2
R	1	0	1	1	1	1	1	2	1	2	1	0	1	1	3	1	2	1	1	2
D	1	1	0	0	1	1	1	2	1	2	1	1	1	1	3	1	2	1	1	2
N	1	1	0	0	1	1	1	2	1	2	1	1	1	1	3	1	2	1	1	2
C	1	1	1	1	0	1	1	2	1	2	1	1	1	1	3	1	2	1	1	2
Q	1	1	1	1	1	0	1	2	1	2	1	1	1	1	3	1	2	1	1	2
E	1	1	1	1	1	1	0	2	1	2	2	2	1	1	3	1	2	1	1	2
G	2	2	2	2	2	2	2	0	3	3	3	3	3	3	3	3	3	3	3	3
H	1	1	1	1	1	1	1	3	0	2	1	2	2	1	3	2	2	1	1	2
I	2	2	2	2	2	2	2	3	2	0	1	2	2	2	3	2	1	2	2	0
L	1	1	1	1	1	1	2	3	1	1	0	1	1	1	3	2	2	1	1	2
K	1	0	1	1	1	1	2	3	2	2	1	0	1	2	3	1	2	2	2	2
M	1	1	1	1	1	1	1	3	2	2	1	1	0	2	3	1	2	2	2	2
F	2	1	1	1	1	1	1	3	1	2	1	2	2	0	3	2	2	0	0	1
P	3	3	3	3	3	3	3	3	3	3	3	3	3	3	0	3	3	3	3	3
S	1	1	1	1	1	1	1	3	2	2	2	1	1	2	3	0	1	2	2	2
T	2	2	2	2	2	2	2	3	2	1	2	2	2	2	3	1	0	1	1	1
W	2	1	1	1	1	1	1	3	1	2	1	2	2	0	3	2	1	0	0	1
Y	2	1	1	1	1	1	1	3	1	2	1	2	2	0	3	2	1	0	0	1
V	2	2	2	2	2	2	2	3	2	0	2	2	2	1	3	2	1	1	1	0

Table 4. Summary of TALOS results when applied to predicting backone angles of proteins included in the database. Listed are the number of "Good" predictions, and the percentage relative to the total number of residues with acceptable B factors (Avail.), the number of "Bad" predictions, and the number of residues for which no predictions could be made (Ambig.), plus the total number of residues (All).

Name Good (%) Bad (%) Ambig. (%) Avail. All

HIV-1protease 65 67.0 1 1.0 31 32.0 97 99
III-glc 87 61.7 4 2.8 50 35.5 141 168
Alpha-lytic protease 101 54.6 3 1.6 81 43.8 185 198
BPTI 32 58.2 4 7.3 19 34.5 55 58
Calbindin 48 72.7 0 0.0 18 27.3 66 75
Calmodulin 107 84.9 0 0.0 19 15.1 126 148
Calmodulin/M13 98 80.3 0 0.0 24 19.7 122 148
Cutinase 122 66.7 5 2.7 56 30.6 183 214
Cyanovirin-N 55 61.1 1 1.1 34 37.8 90 101
Cyclophilin 87 54.0 5 3.1 69 42.9 161 165
Dehydrase 91 62.7 3 2.1 51 35.2 145 171
HCA I 149 60.3 7 2.8 91 36.9 247 260
Interleukin-1b 75 61.0 3 2.4 45 36.6 123 153
Lactamase 137 66.2 4 1.9 66 31.9 207 232
Serine protease PB 92 161 62.7 8 3.1 88 34.2 257 269
D-MBP 217 62.0 5 1.4 128 36.6 350 370
Profilin 72 67.9 0 0.0 34 32.1 106 125
Staph nuclease 81 67.5 4 3.3 35 29.2 120 141
Human thioredoxin 79 76.7 1 1.0 23 22.3 103 105
Ubiquitin 53 75.7 0 0.0 17 24.3 70 76
 
 

Total:

predictions: 2910
correct: 1920 (65.3%)
incorrect: 58 (2.0%)

Figure 1. Flow chart of the TALOS program.
 

Figure 2. Graphical display of TALOS output for HIV protease. The lower right window shows the amino acid sequence, with predictions for each residue designated as "good" (green), "ambiguous" (yellow), or "bad" (red). The prediction data for the selected residue, K20, are listed in the prediction display (top right) and graphed in the Ramachandran display (left). The 10 individual matches from the database are indicated as small green squares in the Ramachandran display, and for reference purposes, the known f/y position from the HIV protease X-ray structure (blue square) is also shown. Clicking on any of the squares highlights the corresponding triplet in the prediction display.

Figure 3. Plots of the backbone angles (A) phi, and (B) psi predicted by TALOS, versus those observed in the crystal structure, for ubiquitin.

Figure 4. Predicted backbone angles (A) phi, and (B) psi of ubiquitin. The length of the error bars represents the standard deviation from the average of the dihedral angles of the 10 residues from the database having the highest chemical shift and sequence similarity with the query residues. Triangles correspond to the angles observed in the crystal structure.

Figure 5. (Supplementary Figure) Predicted backbone angles (A) phi, and (B) psi for the reduced form of human thioredoxin. The length of the error bars represents the standard deviation from the average of the dihedral angles of the 10 residues from the database having the highest chemical shift and sequence similarity with the query residues. Triangles correspond to the angles observed in the crystal structure.