Robust Quantitative Modeling of Peptide Binding Affinities for MHC Molecules Using Physical-Chemical Descriptors

Abstract

Major histocompatibility complex (MHC) molecules bind short peptides resulting from intracellular processing of foreign and self proteins, and present them on the cell surface for recognition by T-cell receptors. We propose a new robust approach to quantitatively model the binding affinities of MHC molecules by quantitative structure-activity relationships (QSAR) that use the physical-chemical amino acid descriptors E₁–E₅. These QSAR models are robust, sequence-based, and can be used as a fast and reliable filter to predict the MHC binding affinity for large protein databases.

INTRODUCTION

The ability to distinguish between foreign and self proteins is one of the most important characteristics of the immune system. Short peptides resulting from intracellular processing of foreign and self proteins form a complex with the major histocompatibility complex (MHC) molecules, and T cells recognize the MHC-bound peptides. There are two classes of MHC molecules: (i) MHC class I, which binds and presents to the T cells peptides derived from endogenously expressed proteins that are degraded by cytosolic proteases, usually by the proteasome; and (ii) MHC class II, which presents to the T cells peptides derived mainly from exogenous or transmembrane proteins, but also from cytosolic proteins that are degraded by various proteases which originate from the lysosomal compartment. Peptides that bind to MHC class I have a usual length of 8–12 amino acids, and are transported into the endoplasmic reticulum by the transporter associated with antigen processing (TAP), where they bind to MHC class I molecules. The MHC I molecule with bound peptide on the surface of infected cells and tumor cells can be recognized by a complementary-shaped T cell receptor (TCR) of CD8⁺ cytotoxic T cells (CTL), initiating the destruction of the cell containing the endogenous antigen.

The structural descriptors used in quantitative structure-activity relationships (QSAR) have a substantial contribution to a successful model. Because the present paper advocates a novel group of physical-chemical descriptors [1] for the modeling of the MHC binding, we briefly review the most important descriptors used in MHC QSAR. Lin et al. found that the isotropic surface area, ISA, and the electronic charge index, ECI, are effective descriptors for the QSAR modeling of peptide IC₅₀ for class I MHC HLA-A*0201 [2]. CoMSIA molecular field descriptors were successful in 3D-QSAR for peptide IC₅₀ binding to class I MHC HLA-A*0201 [3; 4], HLA-A2 superfamily [5], HLA-A3 superfamily (A*1101, A*0301, A*3101, and A*6801) [5–7], and mouse class I MHC alleles H2-D^b, H2-K^b, and H2-K^k [8]. In a similar approach, CoMFA molecular field descriptors gave good predictions for the binding to HLA-A*0201 [3]. A series of sequence-based descriptors were evaluated by Guan et al. in QSAR predictions of binding affinities for HLA-A*0201 [9]. The first group of models used 93 amino acid properties from the AAindex database [10], whereas the second approach tested the principal component amino acid indices z₁–z₅ [11]. The study found that the QSAR models obtained with z₁–z₅ have the highest predictivity. Doytchinova et al. compared three classes of descriptors for their ability to predict peptide BL₅₀ for HLA-A*0201 [12], namely a 20-element binary encoding for each amino acid, the z₁–z₅ scale, and a collection of molecular descriptors that included molecular connectivity indices, shape indices, electrotopological state indices, hydrophobicity, polarizability, surface area, and volume. The predictions tests showed that the best results are obtained with the simple 20-element binary encoding, followed by the z₁–z₅ scale, whereas the molecular descriptors did not provide meaningful predictions. The 20-element binary encoding approach [13; 14] was extended to include also cross-interaction terms [5; 15–17], with good results for HLA-A*0201 [18], the HLA-A3 superfamily [19], and MHC class II alleles [20].

The heuristic molecular lipophilicity potential (HMLP) [21] was used by Chou and co-workers to quantify the lipophilicity and hydrophilicity of amino acid side chains [22]. HMLP descriptors were also used to model the binding affinity of class I MHC peptides [23] and for QSAR studies of neuraminidase inhibitors [24]. A support vector machines regression approach in the quantitative modeling of the peptide binding affinity for MHC molecules [25] was applied by Liu et al. to model the peptide IC₅₀ for mouse class I MHC alleles H2-D^b, H2-K^b, and H2-K^k [26]. Each amino acid in a peptide was encoded with 17 physico-chemical properties, such as polarity, isoelectric point, volume, and hydrophobicity. Genetic function approximation and genetic partial least squares were used by Davies et al. to obtain QSAR models for the binding level BL₅₀ of 118 peptides with class I MHC HLA-A*0201 [27]. The QSAR descriptors for BL₅₀ modeling represent peptide-MHC interaction energies computed with AMBER. The average relative binding (ARB) matrix [28] is a quantitative tool that was calibrated for the prediction of binding affinities [29]. Using experimental data from the Immune Epitope Database and Analysis Resource (IEDB) [30], Bui et al. computed 85 matrices for class I MHC alleles and 13 matrices for class II MHC alleles. The ARB matrices were used to model the MHC class I pathway for several alleles [31].

High quality predictions for protein and peptide properties may be obtained only with a proper encoding of the amino acids sequence into a series of structural descriptors. As example of successful amino acids descriptors we mention here the pseudo-amino acid composition indices [32], which were used to model a wide range of bioinformatics problems, such as classification of membrane proteins [33], protease classification [34], protein-protein interactions [35], and protein subcellular location [32]. From the large list of machine learning procedures used in bioinformatics, we mention here k-nearest neighbors classifier [36], partial least squares [8; 13; 18; 27], artificial neural networks (ANN) [37–39], support vector machines (SVM) [33; 40; 41], and LogitBoost [42]. The combination of several machine learning predictions with ensemble, jury or fusion methods proved to be a very efficient strategy in order to obtain robust and predictive models [36; 43–45].

Our approach for the prediction of MHC binding affinity is based on five physical-chemical descriptors E₁–E₅ [1], where each amino acid position in a peptide is encoded by the five descriptors of the amino acid type at that position. The descriptors capture the physical-chemical similarity of amino acids, and are able to encode the peptide sequence more efficiently than previously used representations. Especially our method can still be applied when for certain peptide positions not all 20 amino acids are present in the training set. Most current QSAR models for predicting binding affinities of MHC-binding peptides aim for a high goodness-of-fit criteria in developing the mathematical models. Typically they use the 20 amino acids in a binary code that leads to a large number of variables, 20×n, to encode a peptide of length n. In many practical applications this number exceeds the available data points used as the training set for generating the computational model. High-quality predictions of the MHC-peptide binding affinity depends both on a reliable set of amino acid descriptors and on the use of predictive machine learning and pattern recognition models.

A large variety of methods have been proposed for the prediction of peptide binding affinity to MHC molecules: position specific scoring matrices [46; 47], ANN [37–39], hidden Makov models [48; 49], SVM [40; 41]. In this paper we explore new avenues to find a minimal number of variables in the mathematical modeling of binding affinities of peptides to MHC molecules. We previously demonstrated that our descriptors are a suitable mathematical framework to find sequence similarities between cross-reactive IgE epitopes using a property distance measure (PD value) [50–55]. We show here that the E₁–E₅ descriptors and three multivariate quantitative structure-activity relationships (QSAR) methods (multilinear regression (MLR), partial least squares (PLS), and multi-layer feed-forward artificial neural networks (ANN), can be efficiently used to find robust quantitative models of MHC binding, and to explore the physical-chemical properties that determine the binding interaction between the MHC molecule and ligand peptides. Our new method is illustrated for the binding affinities (IC₅₀) for the class I MHC HLA-A*0201 of a set of 152 nona-peptides [3].

MATERIALS AND METHODS

Data Set

The sequences and binding affinities for class I MHC HLA-A*0201 of 152 nona-peptides (Table 5) were taken from a recent study in which the IC₅₀ of these peptides was modeled with the CoMFA and CoMSIA techniques [3]. We have selected the same set of nona-peptides in order to compare the QSAR value of the E₁–E₅ descriptors [1] with that of well-established QSAR models CoMFA and CoMSIA.

Table 5.

Sequences of the 152 Nona-Peptides, their Experimental pIC₅₀ Values, Calibration and Prediction Values Obtained with the MLR QSAR Model 7 (Table 1), and the Binding Affinities Predicted with BIMAS, SYFPEITHI, and Rankpep Score

No	Peptide	pIC50 Exp	MLR Cal	MLR Pre	BIMAS	SYFPEITHI	Rankpep score
1	VALVGLFVL	5.146	5.838	6.445	10.207	23	33.0
2	VCMTVDSLV	5.146	5.611	5.656	2.856	12	44.0
3	HLESLFTAV	5.301	6.398	6.659	0.288	21	85.0
4	LLGCAANWI	5.301	5.681	5.664	97.547	21	51.0
5	GTLVALVGL	5.342	5.553	5.491	2.525	24	35.0
6	SAANDPIFV	5.342	6.069	6.453	5.313	18	34.0
7	TTAEEAAGI	5.380	5.835	5.749	0.594	19	52.0
8	LLSCLGCKI	5.447	6.277	5.958	17.736	23	52.0
9	LQTTIHDII	5.501	5.615	5.840	0.361	9	22.0
10	TLLVVMGTL	5.580	6.282	6.482	23.633	24	76.0
11	LTVILGVLL	5.580	5.574	5.588	0.504	19	25.0
12	AMFQDPQER	5.740	5.881	5.903	0.040	13	18.0
13	HLLVGSSGL	5.792	6.287	6.374	2.687	25	63.0
14	SLHVGTQCA	5.842	5.672	5.656	4.968	20	47.0
15	ALPYWNFAT	5.869	6.181	6.221	43.222	16	29.0
16	LLVVMGTLV	5.869	6.415	6.180	118.238	22	70.0
17	SLNFMGYVI	5.881	5.898	5.869	4.277	21	57.0
18	NLQSLTNLL	6.000	6.319	6.443	21.362	24	82.0
19	GIGILTVIL	6.000	5.665	5.807	1.204	24	52.0
20	FVTWHRYHL	6.025	5.835	6.037	8.598	15	23.0
21	TVILGVLLL	6.072	6.791	6.610	4.299	23	55.0
22	WLEPGPVTA	6.082	7.184	7.216	1.463	21	36.0
23	WTDQVPFSV	6.145	6.706	7.071	10.309	16	27.0
24	QVMSLHNLV	6.170	6.124	6.089	22.517	17	63.0
25	DPKVKQWPL	6.176	5.632	5.593	0.003	9	−19.0
26	AIAKAAAAV	6.176	6.689	6.733	9.563	25	93.0
27	ITSQVPFSV	6.196	6.744	6.811	9.525	18	48.0
28	ALAKAAAAI	6.211	6.601	6.267	10.433	25	102.0
29	GLGQVPLIV	6.301	7.026	6.824	28.516	22	65.0
30	MLDLQPETT	6.335	6.218	6.511	2.483	16	38.0
31	LLSSNLSWL	6.342	6.365	6.240	459.398	26	80.0
32	GLACHQLCA	6.380	5.749	5.758	4.968	18	30.0
33	VLHSFTDAI	6.380	7.086	7.623	33.024	23	82.0
34	AAAKAAAAV	6.398	5.930	5.909	0.966	21	69.0
35	LIGNESFAL	6.415	6.519	6.365	28.962	21	61.0
36	ALAKAAAAV	6.419	6.945	6.866	69.552	27	103.0
37	ILTVILGVL	6.419	6.439	6.458	4.452	25	68.0
38	LLAVGATKV	6.477	5.956	5.904	118.238	28	80.0
39	MLLAVLYCL	6.477	7.087	6.799	309.050	27	77.0
40	KLPQLCTEL	6.484	6.495	6.212	74.768	24	69.0
41	AVAKAAAAV	6.495	6.159	6.354	6.086	21	87.0
42	ALAKAAAAL	6.511	6.293	6.247	21.362	27	99.0
43	WILRGTSFV	6.556	7.094	7.004	895.230	24	58.0
44	IISCTCPTV	6.580	6.640	6.651	16.258	23	57.0
45	AAGIGILTV	6.581	6.051	5.969	2.222	25	40.0
46	FLGGTPVCL	6.623	6.713	6.673	98.267	25	54.0
47	ALIHHNTHL	6.623	5.952	5.846	21.362	24	66.0
48	ILDEAYVMA	6.623	6.499	6.153	20.776	20	62.0
49	NLSWLSLDV	6.639	6.528	6.975	69.552	22	62.0
50	YMIMVKCWM	6.663	6.650	7.122	90.776	16	32.0
51	YLEPGPVTA	6.668	7.061	7.252	1.463	23	47.0
52	VLQAGFFLL	6.682	6.730	6.739	400.203	23	67.0
53	LLWFHISCL	6.682	6.532	6.733	693.274	26	55.0
54	GTLGIVCPI	6.714	6.766	6.697	1.233	21	32.0
55	TLHEYMLDL	6.726	7.283	7.390	201.447	24	81.0
56	VILGVLLLI	6.785	7.756	7.660	20.753	26	75.0
57	VTWHRYHLL	6.793	6.000	5.844	6.280	17	22.0
58	TLDSQVMSL	6.793	6.940	6.874	19.653	26	93.0
59	PLLPIFFCL	6.796	7.761	8.028	19.163	21	48.0
60	TLGIVCPIC	6.815	6.651	6.910	2.037	11	32.0
61	CLTSTVQLV	6.832	7.181	7.358	159.970	23	88.0
62	HLYQGCQVV	6.832	6.928	6.944	3.103	23	71.0
63	ILLLCLIFL	6.845	6.949	6.158	1699.774	28	58.0
64	FLCKQYLNL	6.875	8.128	8.196	147.401	22	65.0
65	FAFRDLCIV	6.886	6.869	6.756	15.504	20	28.0
66	QLFHLCLII	6.886	7.015	7.111	15.827	21	67.0
67	FLEPGPVTA	6.898	6.993	6.971	1.463	22	44.0
68	ALAKAAAAA	6.947	6.816	6.557	4.968	21	83.0
69	ITDQVPFSV	6.947	6.910	6.556	3.810	18	37.0
70	LMAVVLASL	6.954	6.761	6.803	60.325	30	79.0
71	YVITTQHWL	6.983	6.871	7.238	47.291	19	42.0
72	LLCLIFLLV	6.996	7.324	7.262	224.653	23	63.0
73	HLAVIGALL	7.000	6.462	6.529	0.726	24	65.0
74	ALCRWGLLL	7.000	6.948	6.955	21.362	23	55.0
75	ITAQVPFSV	7.020	7.091	7.299	9.525	20	46.0
76	YLEPGPVTL	7.058	7.033	6.703	6.289	29	63.0
77	YTDQVPFSV	7.066	6.849	6.871	10.309	18	38.0
78	NLYVSLLLL	7.114	6.967	6.670	157.227	26	77.0
79	NLGNLNVSI	7.119	6.528	7.061	10.433	23	74.0
80	ILHNGAYSL	7.127	6.962	6.621	36.316	27	73.0
81	HLYSHPIIL	7.131	7.064	7.299	0.953	21	70.0
82	SIISAVVGI	7.159	7.100	7.124	3.299	27	83.0
83	VVMGTLVAL	7.174	6.858	7.162	27.042	25	74.0
84	ITFQVPFSV	7.179	7.422	7.435	35.242	19	42.0
85	YLEPGPVTI	7.187	6.852	6.739	3.071	27	66.0
86	FTDQVPFSV	7.212	6.857	6.586	10.309	17	35.0
87	GLSRYVARL	7.248	7.148	7.169	49.134	28	87.0
88	LLAQFTSAI	7.301	6.915	6.675	67.396	26	96.0
89	YMLDLQPET	7.310	7.673	8.002	375.567	21	41.0
90	VLLDYQGML	7.328	7.645	7.368	71.619	25	70.0
91	YLEPGPVTV	7.342	7.103	7.369	20.476	29	67.0
92	RLMKQDFSV	7.342	8.027	8.032	1492.586	23	74.0
93	ILSPFMPLL	7.347	7.337	7.394	317.403	26	77.0
94	KLHLYSHPI	7.352	7.483	7.503	36.515	21	61.0
95	YLSPGPVTA	7.383	7.405	7.372	22.853	24	55.0
96	ALAKAAAAM	7.398	6.547	6.697	4.968	21	93.0
97	IIDQVPFSV	7.398	7.841	7.928	37.718	22	60.0
98	ITMQVPFSV	7.398	7.035	6.966	35.242	19	47.0
99	YMNGTMSQV	7.398	7.234	7.381	531.455	23	80.0
100	SVYDFFVWL	7.444	6.939	6.853	973.849	21	51.0
101	ITWQVPFSV	7.463	7.538	7.773	79.056	19	37.0
102	KIFGSLAFL	7.478	7.766	7.865	481.186	28	69.0
103	ITYQVPFSV	7.480	7.246	7.568	30.479	19	44.0
104	GLYSSTVPV	7.481	7.791	7.816	222.566	26	84.0
105	VMGTLVALV	7.553	6.937	6.787	196.407	26	79.0
106	LLLCLIFLL	7.585	7.279	7.033	1792.489	29	65.0
107	SLDDYNHLV	7.585	7.186	7.033	114.065	25	70.0
108	ALVGLFVLL	7.585	7.070	7.550	40.589	27	78.0
109	YLSPGPVTV	7.642	7.560	7.349	319.939	30	75.0
110	VLIQRNPQL	7.644	7.705	7.609	36.316	24	67.0
111	SLYADSPSV	7.658	7.823	7.588	222.566	26	82.0
112	RLLQETELV	7.682	7.300	7.266	126.098	24	83.0
113	ILSQVPFSV	7.699	8.070	8.106	685.783	24	81.0
114	GLYSSTVPV	7.699	7.791	7.816	222.566	26	84.0
115	IMDQVPFSV	7.719	7.770	7.705	198.115	22	60.0
116	QLFEDNYAL	7.764	6.963	6.884	324.068	25	64.0
117	ALMDKSLHV	7.770	7.882	7.897	1055.104	26	85.0
118	YLYPGPVTA	7.772	8.000	7.982	73.129	25	51.0
119	YAIDLPVSV	7.796	7.835	7.965	18.219	24	44.0
120	YLAPGPVTV	7.818	7.583	7.642	319.939	32	73.0
121	FVWLHYYSV	7.824	7.419	7.563	348.534	19	42.0
122	MLGTHTMEV	7.845	6.966	6.867	118.238	24	87.0
123	VVLGVVFGI	7.845	8.072	7.974	76.598	22	59.0
124	LLFGYPVYV	7.886	8.162	8.223	2406.151	28	71.0
125	ILKEPVHGV	7.921	7.836	7.810	39.025	30	66.0
126	MMWYWGPSL	7.921	7.789	7.662	217.695	21	34.0
127	YLMPGPVTV	7.932	7.932	7.926	1183.775	31	74.0
128	WLDQVPFSV	7.939	8.139	7.978	742.259	22	60.0
129	ILAQVPFSV	7.939	8.077	7.996	685.783	26	79.0
130	KTWGQYWQV	7.955	7.829	7.416	315.701	18	25.0
131	ALMPLYACI	8.000	7.325	7.765	57.902	26	77.0
132	YLAPGPVTA	8.032	7.442	7.459	22.853	26	53.0
133	WLSLLVPFV	8.048	7.543	7.852	4047.231	26	63.0
134	YLYPGPVTV	8.051	8.058	8.114	1023.805	31	71.0
135	FLLSLGIHL	8.053	7.372	7.427	363.588	24	65.0
136	LLMGTLGIV	8.097	7.694	7.983	53.631	29	78.0
137	YLWPGPVTV	8.125	8.133	8.103	2655.495	31	64.0
138	ILMQVPFSV	8.125	8.187	8.061	2537.396	25	80.0
139	FLLTRILTI	8.149	8.180	8.134	408.402	28	85.0
140	GLLGWSPQA	8.237	7.921	8.215	18.382	20	46.0
141	YLFPGPVTV	8.237	8.103	8.184	1183.775	31	69.0
142	ILYQVPFSV	8.310	8.226	8.178	2194.505	25	77.0
143	GILTVILGV	8.347	7.879	7.641	81.385	27	67.0
144	YLMPGPVTA	8.367	7.846	7.873	84.555	25	54.0
145	NMVPFFPPV	8.398	8.168	8.204	362.675	22	50.0
146	ILDQVPFSV	8.481	7.968	7.782	274.313	24	70.0
147	YLFPGPVTA	8.495	8.055	8.035	84.555	25	49.0
148	YLWPGPVTA	8.495	8.093	8.048	189.678	25	44.0
149	YLDQVPFSV	8.638	8.086	7.955	742.259	24	71.0
150	FLDQVPFSV	8.658	8.043	7.737	742.259	23	68.0
151	ILFQVPFSV	8.699	8.240	8.351	2537.396	25	75.0
152	ILWQVPFSV	8.770	8.249	8.190	5691.997	25	70.0

E₁–E₅ Physical-Chemical Descriptors

Numerous amino acids properties were developed for predicting a wide range of protein proteins, such as secondary structure, fold type, or subcellular localization. However, these scales numerically encode similar or related amino acids property, such as hydrophobicity or polarity. In order to cluster together related numerical scales, the principal components-like amino acids descriptors E₁–E₅ were developed [1]. Starting from 237 physical-chemical properties for all 20 naturally occurring amino acids, multidimensional scaling was used to condense the structural information into five descriptors. The mathematical procedure used in deriving these five descriptors ensures that the main variations of all 237 properties for the 20 amino acids are reflected by E₁–E₅. Every position in a nona-peptide was characterized by five E₁–E₅ descriptors of the corresponding amino acid, giving a vector with 45 components for each peptide. Similarly with the computation of IgE epitopes sequence similarity index PD [50; 52], each E component was weighted with the square root of the corresponding eigenvalue.

Strategies to Find a Robust MLR Model

To find a robust MLR QSAR model of the binding affinities, standard multiple linear regression methods were then applied by progressively reducing the number of parameters from 45 to 9 in blocks of 9. The model with all 45 components was used as a reference model. Two different strategies were tested in this reduction process: (1) a position independent strategy where in each round 9 descriptors with the lowest absolute correlation coefficient to the IC₅₀ values were discarded and (2) a position dependent strategy where we eliminated in each round the descriptors with the lowest absolute correlation coefficient IC₅₀ of each position in the nona-peptide.

Software

The PLS models were computed with Unscrambler (CAMO Inc., Corvalis, OR, http://www.camo.com), while MLR and ANN models were obtained with in-house developed C programs.

Artificial Neural Networks

The present study uses multilayer feed-forward neural networks provided with a single hidden layer. The number of neurons in the hidden layer was selected on the basis of systematic empirical trials in which ANNs with increasing number of hidden neurons were trained to predict the experimental pIC₅₀ binding affinities. Each network was provided with a bias neuron connected to all neurons in the hidden and output layers, and with one output neuron providing the calculated pIC₅₀ value.

Activation Functions

The most commonly used activation function in biological applications of neural networks has a sigmoidal shape and takes values between 0 and 1. For large negative arguments its value is close to 0, and practice demonstrated that ANN training is difficult in such conditions. To overcome this deficiency of the sigmoid function, the hyperbolic tangent (tanh) which takes values between −1 and 1 was used in the present study for the hidden and output layers.

Preprocessing of the Data

Each component of the input (PLS factors) and output (pIC₅₀ binding affinities) patterns was linearly scaled between −0.9 and 0.9. For the tanh output activation function the scaling is required by the range of values of the function, while for the linear function experiments showed that a linear scaling improves the learning process.

Learning Method

The training of the ANNs was performed with the Polack-Ribiere method, for 2000 epochs. One epoch corresponds to the presentation of one complete set of examples. The patterns were presented randomly to the network, and the weights were updated after the presentation of each pattern. Random values between −0.1 and 0.1 were used as initial weights.

Performance Indicators

The performances of the neural networks were evaluated both for the model calibration and prediction. The quality of model calibration is estimated by comparing the calculated pIC₅₀ during the training phase (pIC_50calc) with the target values (pIC_50exp), while the predictive quality was estimated by a cross-validation method by comparing the predicted (pIC_50pr) and experimental values. In order to compare the performance of the ANN models with the statistical results of the MLR models, we have used the correlation coefficient r and the standard deviation s of the linear correlation between experimental and calibration or prediction pIC₅₀: pIC_50exp = A + B·pIC_50calc/pr. In order to evaluate the effect of random initial weights, each ANN was trained 10 times, and in each case we obtained the same values for the QSAR statistical indices, at the precision reported in this paper.

Cross-Validation

Because the scope of our study is to develop quantitative models that can offer reliable predictions for the pIC₅₀ of nona-peptides not used in the calibration of the QSAR model, we have estimated the prediction power of the MLR and ANN models with the leave-one-out (LOO) and leave-10%-out (L10%O) cross-validation methods. The LOO (or the “jackknife test”) test is a rigorous and objective method to evaluate the accuracy of a statistical prediction method, as shown in a comprehensive review [56] and in numerous bioinformatics applications [36; 43–45; 57]. In the L10%O algorithm 10% of the patterns are selected from the complete data set and form the prediction set. In the following step the QSAR model is calibrated with a learning set consisting of the remaining 90% of the data and the neural model obtained in the calibration phase is used to predict the pIC₅₀ values for the patterns in the prediction set. This procedure is repeated ten times, until all patterns are selected for prediction once and only once. In order to compare the QSAR models obtained with MLR, PLS and ANN, we will give the correlation coefficient and standard deviation between experimental and calculated pIC₅₀ for calibration/training/fitting (r_cal and s_cal) and for the cross-validation prediction (r_pre and s_pre). Some QSAR studies, including the CoMFA and CoMSIA models for the class I MHC HLA-A*0201 binding of the 152 nona-peptides [3], use as prediction parameter the leave-one-out q² statistics:

$$q^2=1-\frac{{\displaystyle \sum _i{({\text{pIC}}_{50\text{pr},i}-{\text{pIC}}_{50\exp ,i})}^2}}{{\displaystyle \sum _i{({\text{pIC}}_{50\exp ,i}-{\text{pIC}}_{50\mathrm{m}ean})}^2}}$$

In order to compare our E₁–E₅ MLR and ANN models with the CoMFA and CoMSIA results, we will report also the q² statistics for LOO and L10%O cross-validation experiments.

RESULTS

Linear Regression Model

In the first set of experiments we have used linear regression to evaluate the contribution of the quantitative descriptors and individual positions in a nona-peptide to the binding affinity. In Fig. (1) we present the plots of the correlation coefficient r for each E descriptor across the nona-peptides length. From these plots it is apparent that the structure-activity correlation is distributed among the five E descriptors and across the nine positions in the ligands. Each position has a small but significant contribution to the overall binding, with different physical-chemical properties determining the affinity. The most important descriptors for each position will be discussed below, when we present our main QSAR model.

Figure 1.

Correlation coefficients between E₁–E₅ and pIC₅₀ for each position of the 152 nona-peptides.

Multilinear Regression Model

In order to identify a robust MLR model with good prediction statistics, we have pursued two strategies, a position independent and a position dependent strategy, as described in the Methods part. As a reference we used the MLR model with all 45 E₁–E₅ descriptors (Table 1, model 1), with the following statistics: calibration r_cal = 0.866 and s_cal = 0.510, LOO r_pre = 0.685 and s_pre = 0.625, L10%O r_pre = 0.676 and s_pre = 0.633. In the first position independent strategy (Table 1, models 2–5) we eliminated in each round 9 descriptors that have the lowest absolute correlation coefficient with pIC₅₀. The statistical indices for these for MLR models show that their prediction ability is lower than in the case when all 45 E₁–E₅ descriptors are used in an MLR model. However, in the second position dependent strategy, where we kept for each position the same number of best descriptors, the predictive capability determined by r_pre, increases to a maximum for model 7 with 27 position best descriptors (r_cal = 0.825 and s_cal = 0.534, LOO r_pre = 0.709 and s_pre= 0.605, L10%O r_pre= 0.700 and s_pre= 0.613). This MLR model with 27 E₁–E₅ has better prediction statistics than the reference model 1 with all 45 E₁–E₅ descriptors, showing that the eliminated descriptors are not important in modeling the binding affinity. The plot of experimental vs. calculated pIC₅₀, and experimental vs. L10%O predicted pIC₅₀ obtained with the best MLR model (Table 1, model 7) do not show any particular clustering of data or regions with abnormal high prediction errors, as can be seen from Fig. (2).

Table 1.

Calibration and Prediction (Leave-10%-out and Leave-one-out Cross-Validation) Statistics for the MLR QSAR Models. Model 1 was Obtained with all 45 E₁–E₅ Descriptors, Models 2–5 were Obtained by Eliminating in Each Step 9 Descriptors with the Lowest Correlation Coefficient, and Models 6–9 were Obtained by Eliminating in Each Step and for each Position in a Nona-Peptide the Descriptor with Minimum Correlation Coefficient

Model	Descriptors				L10%O			LOO
		rcal	scal	rpre	spre	q2	rpre	spre	q2
1	all 45 E1–E5	0.866	0.510	0.676	0.633	0.377	0.685	0.625	0.403
2	overall best 36 E1–E5	0.839	0.534	0.665	0.641	0.396	0.664	0.642	0.385
3	overall best 27 E1–E5	0.786	0.583	0.644	0.657	0.380	0.634	0.664	0.363
4	overall best 18 E1–E5	0.716	0.636	0.590	0.693	0.324	0.591	0.692	0.330
5	overall best 9 E1–E5	0.659	0.664	0.599	0.687	0.355	0.595	0.690	0.350
6	position best 36 X	0.838	0.535	0.666	0.641	0.396	0.668	0.639	0.395
7	position best 27 X	0.825	0.534	0.700	0.613	0.467	0.709	0.605	0.484
8	position best 18 X	0.717	0.636	0.596	0.689	0.335	0.591	0.693	0.328
9	position best 9 X	0.664	0.680	0.602	0.685	0.359	0.599	0.687	0.354

Figure 2.

MLR calibration and prediction (leave-10%-out cross-validation) results obtained with 27 E₁–E₅ descriptors (the best three E₁–E₅ descriptors for each position in a nona-peptide, model 7 in Table 2). (a) Calibrated versus experimental pIC₅₀ values; (b) Predicted versus experimental pIC₅₀ values.

Neural Network Model

Artificial neural networks form a class of computational models that can explore non-linear relationships between structural descriptors and biological activities, with many applications in drug design. The ANN hidden neurons, that have non-linear transfer functions, can model both the interactions between the input descriptors and the non-linear relationships between input and output variables. We have used ANN models to investigate the non-linear relationships between the E₁–E₅ descriptors and pIC₅₀, and the cross-interaction between the input descriptors. In preliminary tests we have determined that the optimum number of hidden neurons is two, because a larger number of hidden neurons gives lower prediction statistics. In Table 2 we give the statistics of the ANN models obtained with the same sets of descriptors as the MLR models in Table 1. While the fitting (calibration) statistics are better than those of the corresponding MLR models, the LOO and L10%O prediction tests show a drastic decrease, indicating that the neural networks are over-fitted and give less reliable prediction, compared with those obtained with MLR models. One explanation for the poor prediction performance of the ANN models is the larger number of parameters for optimization. When all 45 E1–E₅ descriptors are used as input for the ANN, each nona-peptide is described by a 45 elements vector and 45 input neurons are required. For an ANN with 2 hidden neurons and one output neuron, the number of network connections (parameters to optimize) is (45 +1)×2 + (2 + 1)×1 = 95. In this case, the ratio between the number of experimental data and the number of network connections is too small (ρ = 152/95 = 1.6), compared to the MLR model (ρ = 152/46 = 3.3). Another explanation comes from the nature of the pIC₅₀ data, which are affected by experimental errors. When these errors are large, the non-linear mapping of the ANN model gives erroneous predictions. The plot of experimental vs. calculated pIC₅₀, and experimental vs. L10%O predicted pIC₅₀ obtained with the best ANN model (Table 2, model 7), shown in Fig. (3), indicate that the neural model is over-fitted, compared with the corresponding MLR QSAR.

Table 2.

Calibration and Prediction (Leave-10%-Out and Leave-one-out Cross-Validation) Statistics for the ANN QSAR Models. See Table 1 Caption for a Description of the Experiments

Model	Descriptors				L10%O			LOO
		rcal	scal	rpre	spre	q2	rpre	spre	q2
1	all 45 E1–E5	0.968	0.215	0.489	0.749	−0.045	0.540	0.722	0.014
2	overall best 36 E1–E5	0.960	0.239	0.514	0.736	−0.113	0.573	0.703	0.081
3	overall best 27 E1–E5	0.904	0.367	0.536	0.725	0.023	0.623	0.671	0.249
4	overall best 18 E1–E5	0.838	0.469	0.426	0.776	0.013	0.435	0.773	−0.043
5	overall best 9 E1–E5	0.767	0.551	0.476	0.755	0.093	0.444	0.769	0.068
6	position best 36 X	0.958	0.246	0.509	0.739	−0.218	0.532	0.727	0.024
7	position best 27 X	0.929	0.317	0.561	0.710	0.112	0.446	0.768	−0.091
8	position best 18 X	0.865	0.431	0.439	0.771	−0.074	0.599	0.688	0.259
9	position best 9 X	0.727	0.589	0.496	0.745	0.148	0.498	0.744	0.168

Figure 3.

ANN calibration and prediction (leave-10%-out cross-validation) results obtained with 27 E₁–E₅ descriptors (the best three E₁–E₅ descriptors for each position in a nona-peptide, model 7 in Table 3). (a) Calibrated versus experimental pIC50 values; (b) Predicted versus experimental pIC₅₀ values.

Partial Least Squares Model

Because the physical-chemical information from the 45 E₁–E₅ descriptors is correlated, we have used PLS to extract principal components and develop a regression model (Table 3). The first group of experiments tried to estimate the importance of each individual E descriptor (Table 3, models 1–5), while in the second group of experiments the descriptors were added step-wise (Table 3, models 6–9). Based on L10%O cross-validation results, a PLS QSAR with three principal components gives best predictions, with r_cal= 0.795, s_cal= 0.517, r_pre= 0.696, and s_pre= 0.616. Both calibration and prediction statistics are slightly lower than those from the best MLR QSAR (Table 1, model 7), showing that the data compression into PLS components does not improve the predictive power of the QSAR model.

Table 3.

Calibration and Prediction Statistics for PLS QSAR Models Obtained with Various Combinations of E₁-E₅ Descriptors

Model	E1	E2	E3	E4	E5	rcal	scal	rpre	spre	PC
1	1	0	0	0	0	0.631	0.662	0.569	0.704	3
2	0	1	0	0	0	0.480	0.748	0.338	0.814	6
3	0	0	1	0	0	0.436	0.768	0.396	0.784	1
4	0	0	0	1	0	0.370	0.792	0.206	0.845	1
5	0	0	0	0	1	0.534	0.721	0.458	0.761	2
6	1	1	0	0	0	0.645	0.652	0.560	0.709	2
7	1	1	1	0	0	0.735	0.578	0.644	0.657	3
8	1	1	1	1	0	0.752	0.562	0.657	0.656	3
9	1	1	1	1	1	0.795	0.517	0.696	0.616	3

DISCUSSION

After comparing a wide range of QSAR models (MLR, PLS, and ANN) we found that the MLR model with 27 E₁–E₅ descriptors (the best three E₁–E₅ descriptors for each position in a nona-peptide, model 7 in Table 1) has the best prediction statistics and the lowest difference between calibration and prediction statistics. This shows that the MLR model is more robust and more predictive than the PLS or ANN QSAR models. It is also of interest to compare the results from our sequence-based MLR prediction of MHC peptide binding affinities with the 3D-QSAR models for the same dataset [3] but which are more difficult to compute and cannot be done automatically. The CoMSIA model has calibration r² = 0.870 and LOO q² = 0.542. Our best MLR model, with LOO q² = 0.484, is slightly lower in predictive power. However, the CoMSIA model requires a 3D modeling of all peptides, a computational intensive step that also requires human assistance, whereas our QSAR model is fast, sequence-based, and can be easily applied to an automatic screening of large protein databases.

The peptides affinity for the MHC class I HLA-A*0201 may be also predicted with several servers, such as BIMAS (http://bimas.dcrt.nih.gov/molbio/hla_bind/) [58], SYFPEITHI (http://www.syfpeithi.de/) [59], and Rankpep (http://bio.dfci.harvard.edu/Tools/rankpep.html) [47; 60]. All 152 nonapeptides from the dataset were submitted to these three servers, and the predictions are collected in Table 5. Our aim is to compare the predictions obtained with our MLR QSAR model with those computed with BIMAS, SYFPEITHI, and Rankpep, and we use the predictions of the MLR model 7 (Table 1) as a benchmark. The predictions obtained with BIMAS, SYFPEITHI, and Rankpep are compared with the experimental pIC₅₀ in Fig. (4). To compare all these methods, a linear regression was performed between the predicted binding affinity and experimental pIC₅₀ values, and the correlation coefficient is used to evaluate the predictions. We selected this test because the predictions are not on the same scale with the pIC₅₀ values used to develop the QSAR models. The correlation coefficients for all four predictions are as follows: r = 0.823 for MLR QSAR, r = 0.428 for BIMAS, r = 0.445 for SYFPEITHI, and r = 0.258 for Rankpep. It is obvious from this comparison that the MLR QSAR model outperforms other algorithms that predict the peptides affinity for the MHC class I HLA-A*0201.

Figure 4.

Comparison between experimental pIC₅₀ and predictions with three servers: (a) BIMAS, (b) SYFPEITHI, and (c) Rankpep.

The MLR QSAR model based on physical chemical descriptors can also provide guidance in the design of high-affinity peptides, similar as 3D-QSAR models do. The MLR QSAR for the modeling of the MHC binding affinity (Table 1, model 7) is presented in Table 4. An inspection of the partial correlation coefficients r and MLR coefficients for individual E descriptors can offer an insight for the preferences for a particular amino acid type at each of the nine positions in a nona-peptide.

Table 4.

Statistical indices for the MLR Model 7 from Table 1 (E Descriptors, Individual Statistics r, s and F, and MLR Model Coefficients)

No		r	s	F	MLR Coef
0					6.251572
1	E1,1	−0.1618	0.847	4.0	−0.007284
2	E2,1	−0.1340	0.851	2.7	−0.008691
3	E3,1	0.2955	0.820	14.3	0.014139
4	E1,2	−0.2395	0.833	9.1	−0.038484
5	E2,2	−0.2062	0.840	6.7	−0.025657
6	E5,2	0.1948	0.842	5.9	0.042089
7	E1,3	−0.1935	0.842	5.8	−0.028070
8	E2,3	0.2157	0.838	7.3	0.009419
9	E3,3	0.2410	0.833	9.2	0.026485
10	E1,4	0.3719	0.797	24.1	0.025164
11	E3,4	−0.2343	0.834	8.7	−0.000594
12	E5,4	0.3194	0.813	17.0	0.036336
13	E3,5	0.2034	0.840	6.5	0.022777
14	E4,5	−0.1260	0.851	2.4	−0.049741
15	E5,5	−0.1951	0.842	5.9	−0.012579
16	E2,6	0.1753	0.845	4.8	0.013265
17	E3,6	−0.3681	0.798	23.5	−0.000668
18	E4,6	−0.2343	0.834	8.7	−0.049334
19	E1,7	−0.2816	0.824	12.9	−0.012053
20	E4,7	0.1490	0.849	3.4	0.008458
21	E5,7	0.1258	0.852	2.4	0.062446
22	E1,8	0.3035	0.818	15.2	0.014795
23	E3,8	0.2017	0.841	6.4	0.010158
24	E5,8	0.2358	0.834	8.8	0.008948
25	E2,9	0.2920	0.821	14.0	0.080997
26	E4,9	0.0993	0.854	1.5	0.039239
27	E5,9	−0.2091	0.839	6.9	−0.000990

Position 1

The negative correlation with E_1,1 (mainly correlated with hydrophobicity) favors Ile, Phe and Val for position 1. Similarly, the negative correlation with E_2,1 (mainly correlated with side chain size) indicates that Arg, Lys, and Glu are favored. The positive correlation with E_3,1 indicates a preference for α-helix breaking residues, such as Tyr, Pro, and Trp.

Position 2

Amino acids with large hydrophobic side chains are preferred for position 2 (E_1,2 and E_2,2 have negative correlations with pIC₅₀). The positive correlation with E_5,2 points out that β-strand breakers (Pro, Glu, Trp) are also favored here.

Position 3

The statistical results suggest that for this position the binding affinity of the peptides is enhanced by hydrophobic (negative correlation with E_1,3), small side-chain (positive correlation with E_2,3; Gly, Pro, or Ser are favored), or α-helix breaking residues (positive correlation with E_3,3).

Position 4

The binding affinity is increased by polar and charged residues (positive correlation with E_1,4; Asp, Asn, or Lys are favored), β-strand breakers (positive correlation with E_5,4), and by residues with high α-helix forming propensity (negative correlation with E_3,4; Ala, Glu, or Leu are favored).

Position 5

The MLR model indicates that the binding affinity is enhanced by the presence in position 5 of α-helix breaking residues (positive correlation with E_3,5), most abundant residues (negative correlation with E_4,5; Lys, Leu, or Arg are favored), or β-strand forming residues (negative correlation with _E5,5; Cys, Arg, or Val are favored).

Position 6

IC₅₀ for a peptide increases when position 6 is occupied by small side-chain residues (positive correlation with E_2,6), most abundant residues (negative correlation with E_4,5), or α-helix forming residues (negative correlation with E_3,6).

Position 7

Binding affinity increases when position 7 corresponds to by hydrophobic residues (negative correlation with E_1,7), less abundant residues (positive correlation with E_4,7; Cys, Met, or His are favored), or β-strand breakers (positive correlation with E_5,7).

Position 8

The statistical correlation suggests that peptide binding increases when position 8 is occupied by polar and charged residues (positive correlation with E_1,8), α-helix breaking residues (positive correlation with E_3,8), or β-strand breakers (positive correlation with E_5,8).

Position 9

The C-terminal residue increases the peptide binding affinity when it corresponds to a small side-chain residue (positive correlation with E_2,9), less abundant residue (positive correlation with E_4,9), or to β-strand forming residues (negative correlation with E_5,9).

CONCLUSIONS

In this paper we presented a successful QSAR application of the amino acids E₁–E₅ descriptors [1] for the modeling of the binding affinities of 152 nona-peptides for class I MHC HLA-A*0201. After a comparative modeling with multiple linear regression, partial least squares, and artificial neural networks, we found that the MLR model has the highest predictive power. The predictions of the MLR model are as good as those obtained with CoMSIA [3], and much better than the predictions of BIMAS, SYFPEITHI, and Rankpep. The MLR QSAR based on the E₁–E₅ descriptors has several advantages over the CoMSIA method, because CoMSIA requires a 3D modeling of all peptides, a computational intensive step that also requires human assistance. In contrast, the E₁–E₅ MLR model is sequence-based, fast, and can be easily applied to an automatic screening of large protein databases.