We have used IC₅₀ values, obtained from binding assays of a variety of test peptides to DR1, to construct coefficients to extend the Hammer 9-register matrix 17 (P9) to position 10 of the peptide binding cleft. The protocol is described under Methods. The new extended matrices, P10 and PP10, are validated in regression analysis of predicted values against experimental binding measurements of peptides from glutamic acid decarboxylase (GAD65), islet cell antigens (ICA69) 32 and Varicella-zoster virus (VZV) (unpublished data). We compare these with results using the canonical 9-register matrix for DR1 17. The TEPITOPE virtual matrices for DR1 and other alleles 33 are based on this published matrix according to similarity in the pocket sequence profile. Logarithm of IC₅₀ values are plotted against predicted values and a function is fit to the data. A fitting function is chosen whose coefficients minimize the residuals.

The best fit was found to be a straight line. Higher order polynomial functions were tried but gave worse results. Low IC₅₀ values correspond to good binding and high IC₅₀ values correspond to poor binding, and negative predicted values. A flat fit has no predictive use. Plots for GAD65, ICA69 and VZV are shown in Figures 1 and 2. In all three scoring methods, there are both false positives (upper right quadrant) and false negatives (bottom left quadrant, Figures 1 and 2). False positives can be screened out in validation tests but false negatives are problematic. With these data sets, the scoring matrices show few false negatives. This is a useful property and the matrices can be used to screen large sequences without missing potential epitopes. A high threshold may be set to eliminate falsely predicted peptides.

In all three data sets, GAD65, ICA69 and VZV, for the three matrices tested there is correlation between binding (measured IC₅₀) and predicted values (Figure 1). This indicates predictive value in all three matrices, the two new extended basis matrices P10 and PP10 and the control matrix P9. For GAD65 (Figure 1a), matrices of the original nine-residue matrix (P9) and the extended matrices (P10 and PP10) perform about equally from the fits. Using the slope m as a surrogate measure, PP10 is better than P9 (0.383 vs. 0.352, in absolute values) and P9 is in turn better than matrix P10 (0.352 vs. 0.341). The analysis is summarized in Table 1. For ICA69 (Figure 1b), PP10 and P9 have nearly the same slope (0.327 vs. 0.338) and better predictive power than P10 (0.275). The difference between the respective slopes of P9 and PP10 is not significant but the deviation between 0.327 and 0.338 (PP10 and P9) and 0.275 for P10 appears significant. Using the coarse criterion of slope m for VZV (Figure 1c), P9 is better than P10 (0.252 vs. 0.225). Visual inspection of the graphs supports these assertions (Figure 1). Interestingly, from Table 1, the difference in the absolute slope values between P9 and P10 for GAD65 and ICA69 data sets is 0.011. Difference in peptide-HLA-DR binding assay sensitivity between different antigenic proteins, data sets, individual experiments and the nature of competition assays makes it difficult to establish absolute numbers, and comparison between different data sets is difficult. Comparison within a data set is more valid as revealed by the plots.

Figures 1a, b and 1c show that low binding peptides (IC₅₀ = 100 uM for GAD65 and ICA69 and 10 uM for VZV) are poorly predicted. This marks the limit of sensitivity of the experimental measurement. The analysis is repeated without these points: Figures 2a, b and 2c show the same plots when data points representing poor IC₅₀ values are ignored. It is not clear how significant the difference between P9 and P10 slopes is for GAD65. Nevertheless, the conclusion that PP10 is superior is not changed. The VZV data set further reveals the difference in performance between P9 and P10. The magnitude of the slope used this way calibrates closely the "structure" or "informational potential" within the data; a flat fit signifies random data and has neither "structure" nor predictive potential.

The predictive potential is more accurately captured in terms of variance ("bandwidth") and residuals ("noise"). Residuals for the three data sets were calculated. A typical plot is shown in Figure 3 for GAD65 data set. The sum of the square of the residual values is calculated for each prediction matrix P9, P10 or PP10. Finally, the quality of the fit is assessed through the r-square value:

r 2 = ( 1 − J S ) MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xI8qiVKYPFjYdHaVhbbf9v8qqaqFr0xc9vqFj0dXdbba91qpepeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaemOCai3aaWbaaSqabeaacqaIYaGmaaGccqGH9aqpdaqadaqaaiabigdaXiabgkHiTKqbaoaalaaabaGaemOsaOeabaGaem4uamfaaaGccaGLOaGaayzkaaaaaa@3619@

J is the sum of the square terms of the residual error and S is the variance of the data. The analyses incorporating the slope m of the fitting function, residuals J, and r² are shown in Table 1. r² values range from 0.25 to 0.54 for the full data and 0.21 to 0.57 for the pruned set. The corresponding range for the magnitude of the slope is 0.22 to 0.38 for the full set and 0.24 to 0.41 for the edited set. The slopes shadow closely the respective r² values (Table 1).

From r² values, prediction method PP10 again works the best in both GAD65 and ICA69 data sets: PP10 performs better than the control matrix P9 and is superior to the other extended basis matrix P10. P10 is better than the control P9 matrix in GAD65 (r² of 0.45 versus 0.37) but not in ICA69 (0.25 versus 0.33). The ordering and conclusions are unchanged with filtered data. PP10 matrix has superior discrimination potential in terms of the slope m and also in terms of r². PP10 shows marked improvement over matrix P9 and PP10 is also better than P10. While extended matrix P10 makes better prediction than P9 in GAD65 it is worse than P9 in the edited ICA69 data set. In VZV, matrix P10 shows no improvement over P9 in either the filtered or unfiltered data sets, according to r². Overall, average r² values of the raw data sets (Table 1) are 0.36, 0.34 and 0.44 respectively for P9, P10 and PP10. For comparison, reported average r² value of a large-scale evaluation of class II molecules using similar quantitative matrices is 0.2534.

To gain structural insight into epitope prediction, and why matrix PP10 performs better than P9, we examined peptides that bind well according to IC₅₀ binding measurements. The best experimental binding measurement is for peptide 54 from GAD65 (GDKVNFFRMVISNPAATHQD, pIC₅₀ = 2.15; Supplementary table, Additional file 1). The same register FRMVISNPA(A) is predicted as a strong binder for both matrices, P9 (predicted score = 3.05) and PP10 (predicted score = 3.58). Anchor residues at dominant pockets p1, p4, p6 and p9 are as expected for DR1 12. Ala at position p10 is also predicted to contribute to favourable binding. Incidentally, matrix P10 is in agreement: the same binding frame is predicted and Ala at the extended position is also predicted to interact with the shallow shelf at position p10 for enhanced binding. The added contribution of Ala is given greater weight in matrix P10 (1.05 units) than in PP10 (0.53 units). Competition binding assay of the peptides used for the libraries shows that Ala is a preferred residue at p10 for HLA-DR1.

A unanimous binding frame (in bold letters) is also predicted from peptide 9 (Supplementary table, Additional file 1) SCSKVDVNYAFLHATDLLPA, another strong binder. Leucine at position p10 is predicted to contribute to greater binding affinity, in agreement with experiment. Matrices P9 and PP10 predict the same frame (in bold letters) in peptide 4, QVAQKFTGGIGNKLCALLYG (Supplementary table, Additional file 1). Strong peptide anchor residues at p1 and p9 (F and L, respectively) compensate for poor anchors (G) at p4 and p6, and the contribution of cysteine at position p10 is predicted to enhance binding from matrix PP10. The predicted binding frame in matrix P10, however, differs – IGNKLCALLY.

Another example shows how the extended position changes the predicted binding frame between matrices P9 and PP10: in SHFSLKKGAAALGIGTDSVI (peptide 28), LKKGAAALG is predicted to bind best by matrix P9 while FSLKKGAAAL is predicted by the two extended basis matrices. LKKGAAALG (predicted by P9) has a good leucine anchor at p1 but three poor anchors at p4, p6 and p9. For matrices P10 and PP10, a strong phenylalanine anchor at position p1 in the peptide predicted combines with lysine at p4 and the auxiliary leucine anchor at position 10 to improve the score.

The peptide VETFRHRAISDTWLTVNRME from ICA69 is another example where the extended matrix PP10 predicts a frame (FRHRAISDTW, score = 0.27) different from that predicted by P9 (VETFRHRAI, score = -1.15). The better score predicted by PP10 may arise from an aromatic hydrophobic anchor in pocket 1 versus a relatively small aliphatic p1 anchor, valine, predicted by matrix P9. In the latter, phenylalanine is disfavoured in pocket 4, and likewise histidine in pocket 6, in the frame predicted by matrix P9. The other extended matrix P10 predicts the same frame as PP10 but with a much worse score (-1.75). This implies a predicted negative contribution of tryptophan at position p10 for matrix P10 but a positive contribution of tryptophan for PP10. Experimental binding measurements support a positive contribution of tryptophan at pocket 10. The binding frame predicted by matrix PP10 is structurally consistent with the measured binding affinity.

In peptide 117, the ICA69 peptide QCRTEYRGALLWMKDVSQEL (Supplementary table, Additional file 1) is predicted to bind in a different frame (CRTEYRGAL, score = -0.52) than that predicted for PP10 (YRGALLWMKD, score = -1.15). Non-ideal anchors (Cys at p1 and Glu at p4) predicted by matrix P9 are compensated by good anchors (Arg at p6 and Leu at p9). The frame predicted by PP10 possesses a large and favourable hydrophobic anchor (Tyr) at p1, a favoured small residue (Ala) at p4 but Leu and Lys at pockets p6 and p9, respectively. Leu and Lys are disfavoured in these positions. The contribution at position p10 does not overcome these hindrances.

AIHESFKGYQPYEFTTLKSL and RKESSSFKTEDGKSILSALD (peptides 126 and 132; Supplementary table, Additional file 1) are predicted as strong binders, in agreement with experimental data, and in the expected registers, FKGYQPYEF(T) and FKTEDGKSI(L), for all three matrices. In peptide 126, polar threonine is not favoured at position p10; this reduces the score slightly in both extended matrices. On the other hand, in peptide 132, hydrophobic leucine anchor at p10 in the predicted fragment enhances the interaction between DR1 and the peptide ligand to give a slightly higher score for both extended matrices P10 and PP10.

And in another example, the predicted register is shifted one position between matrices P9 and PP10 for peptide SVVNKMQQRYWETKQAFIKA (peptide 103; Supplementary table, Additional file 1): VNKMQQRYW and VVNKMQQRYW (p1, p4, p6 and p9 anchors are in bold). The added basis in PP10, the increased number of parameters, has allowed better prediction accuracy.

Finally, all three matrices unanimously select the same best frame YGAFDPLLA(V) from overlapping peptides 33 and 34 (Supplementary table, Additional file 1). The experimental pIC50 values are 0.05 (peptide 33) and -0.70 (peptide 34) compared to predicted scores of 0.68, 0.33 and 0.45 for P9, P10 and PP10, respectively. Similarly, the same frame FRKVQTQVRL is unanimously selected by the three matrices for peptides 119 and 120 (Supplementary table, Additional file 1). pIC50 values are 0.22 (peptide 119) and 0.00 (peptide 120). Predicted scores are 0.15, 0.90 and 1.42 for P9, P10 and PP10, respectively, for the unanimously predicted best frame for the two peptides. In the former pair of peptides, the experimental values are far apart while the computational scores are relatively close. In the latter set, the experimental values are close but the predicted scores show a big spread.

Statistics for predicted scores are easy to obtain but similar statistics for binding measurements are difficult to obtain as little statistical data is given along with the experimental data. As is typical of such measurements, baseline values are determined on a case by case basis.

Matrix coefficients to extend the binding register to position p10 are derived following the method described previously 17. A designed peptide carrying the test amino acid residue at position p10 is used in competitive human leukocyte antigen binding assays with purified DR1 allele. The peptide library was designed after the human integrin β3 peptide AWCSDEALPLGSPRC, a natural ligand of HLA-DR52a (DRA/DRB3*0101), and altered to incorporate anchor residues favourable to HLA-DR1, Y, Q, T and L, as deduced from the known peptide binding motif 30. The first series called PP10 is AAYSDQATPLLXSPR; anchor residues, at positions 1, 4, 6 and 9 (p1, p4, p6 and p9) in bold, and X represents one of the twenty natural L amino acids. In order to obtain coefficients for a residue X at p10, the amino acid at that position within the peptide is varied and the IC₅₀ value is measured (described below). The IC₅₀ value is normalized with the IC₅₀ value of the Ala-substitution at position p10 for each residue X. The logarithm of the reciprocal value of normalization is obtained as:

log ⁡ ( I C 50 A l a I C 50 X ) MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xI8qiVKYPFjYdHaVhbbf9v8qqaqFr0xc9vqFj0dXdbba91qpepeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGagiiBaWMaei4Ba8Maei4zaC2aaeWaaKqbagaadaWcaaqaaiabdMeajjabdoeadjabiwda1iabicdaWmaaBaaabaGaemyqaeKaemiBaWMaemyyaegabeaaaeaacqWGjbqscqWGdbWqcqaI1aqncqaIWaamdaWgaaqaaiabdIfaybqabaaaaaGccaGLOaGaayzkaaaaaa@3FC4@

Another peptide library is constructed based on the peptide AAYSDQATLLLXSPR, P10. Proline has been replaced with leucine to avoid the backbone restriction and conformational heterogeneity of the pyrrolidine ring that are associated with proline. The extended matrix coefficients are calculated independently for pocket 10 with no assumption of neighbouring pockets or peptide positions. The free energy of binding of a peptide is approximated by the sum of individual side chain contribution within the binding register, the Independent Binding of Side Chains 16.

The affinity of test peptides of the peptide library to HLA-DR1 was determined in standard competition binding experiments. 25 nM of the unliganded class II molecule was incubated with an equimolar amount of the probe, biotinylated influenza virus HA [306–318] peptide and unlabelled competitor peptide; the amount of the competitor peptide used is varied for each assay. The assay mixture is incubated in 50 mM NaCl, 100 mM Na₃PO₄, pH = 5.5, a cocktail giving final concentration 1 mg/ml PMSF, 37 ug/ml iodoacetamide, 10 mM EDTA, 0.02% NaN₃ and 0.5 mg/ml octylglucoside at 37°C until equilibrium is reached after 3 days. This was followed by immunoassay using the anti-HLA-DR1 antibody LB3.1 in streptavidin to detect the bound biotinylated HA [306–318] peptide. IC₅₀ values are deduced for each peptide from fluorescence values with respect to a range of concentration of the competitor peptide 31.

The performance of the extended matrices was evaluated in prediction against experimental binding measurements of peptides derived from 65 kDa glutamic acid decarboxylase (GAD65) 32, 69 kDa islet cell antigens (ICA69) 32 and Varicella-zoster virus (VZV) (unpublished data). GAD65 and ICA69 data consist of 20-mer peptides overlapping by 10 amino acids and covering the complete sequence of the proteins. VZV peptides contain a variety of 15-mer through 27-mer peptides also overlapping by 10 amino acids and covering the entire range of the sequence.

For each data set, a dependent variable was derived from experimental IC₅₀ values through a logarithmic transform. This is correlated with predicted peptide scores through a fitted function by regression. Linear and nonlinear functions are used and evaluated based on the residual. The predicted scores are further evaluated through the r² (R-square) function. Regression analysis was carried out using MATLAB http://www.mathworks.com. Predictions were carried out within the in-house MHC epitope prediction tool PREDICT (CSP, unpublished).