Model for vaccine design by prediction of B-epitopes of IEDB given perturbations in peptide sequence, in vivo process, experimental techniques, and source or host organisms.

Perturbation methods add variation terms to a known experimental solution of one problem to approach a solution for a related problem without known exact solution. One problem of this type in immunology is the prediction of the possible action of epitope of one peptide after a perturbation or variation in the structure of a known peptide and/or other boundary conditions (host organism, biological process, and experimental assay). However, to the best of our knowledge, there are no reports of general-purpose perturbation models to solve this problem. In a recent work, we introduced a new quantitative structure-property relationship theory for the study of perturbations in complex biomolecular systems. In this work, we developed the first model able to classify more than 200,000 cases of perturbations with accuracy, sensitivity, and specificity >90% both in training and validation series. The perturbations include structural changes in >50000 peptides determined in experimental assays with boundary conditions involving >500 source organisms, >50 host organisms, >10 biological process, and >30 experimental techniques. The model may be useful for the prediction of new epitopes or the optimization of known peptides towards computational vaccine design.

1. Introduction

National Institute of Allergy and Infectious Diseases (NIAID) supported the launch, in 2004, of the Immune Epitope Database (IEDB), http://www.iedb.org/ [1-4]. The IEDB system withdrew information from approximately 99% of all papers published to date that describe immune epitopes. In doing so, IEDB system analyses over 22 million PubMed abstracts and subsequently curated ≈13 K references, including ≈7 K manuscripts about infectious diseases, ≈1 K about allergy topics, ≈4 K about autoimmunity, and 1 K about transplant/alloantigen topics [5]. IEDB lists a huge amount of information about the molecular structure as well as the experimental conditions (c ) in which different ith molecules were determined to be immune epitopes or not. This explosion of information makes necessary both query/display functions for retrieval of known data from IEDB as well predictive tools for new epitopes. Salimi et al. [5] reviewed advances in epitope analysis and predictive tools available in the IEDB. In fact, IEDB analysis resource (IEDB-AR: http://tools.iedb.org/) is a collection of tools for prediction of molecular targets of T- and B-cell immune responses (i.e., epitopes) [6, 7].

On the other hand, Quantitative Structure-Activity/Property Relationships (QSAR/QSPR) techniques are useful tool to predict new drugs, RNA, drug-protein complexes, and protein-protein complexes. In general, QSAR/QSPR-like methods transform molecular structures into numeric molecular descriptors (λ ) in a first stage and later fit a model to predict the biological process. For example, DRAGON [8-10], CODESSA [11, 12], MOE [13], TOPS-MODE [14-17], TOMOCOMD [18, 19], and MARCH-INSIDE [20] are among the most used softwares to calculate molecular descriptors based on quantum mechanics (QM) and/or graph theory [21-27]. The software STATISTICA [28] and WEKA [29] are often used to perform multivariate statistics and/or machine learning (ML) analysis in order to preprocess data and later fit the final QSAR/QSPR model using techniques like principal component analysis (PCA), linear discriminant analysis (LDA), support vector machine (SVM), or artificial neural networks (ANN) [28].

QSAR/QSPR models are also important in immunoinformatics to predict the propensity of different molecular structures to play different roles in immunological processes. They include skin vaccine adjuvants and sensitizers [30-38], drugs and their activity/toxicity protein targets in the immune system [39], and epitopes [40-49]. Moreover, Reche and Reinherz [50] implemented PEPVAC (promiscuous epitope-based vaccine), a web server for the formulation of multiepitope vaccines that predict peptides binding to five distinct HLA class I supertypes (A2, A3, B7, A24, and B15). PEPVAC can also identify conserved MHC ligands, as well as those with a C-terminus resulting from proteasomal cleavage. The Dana-Farber Cancer Institute hosted the PEPVAC server at the site http://immunax.dfci.harvard.edu/PEPVAC/. To close with a last example, Lafuente and Reche [51] reviewed the available methods for predicting MHC-peptide binding and discussed their most relevant advantages and drawbacks.

In many complex QSPR-like problems in immunoinformatics, like in other areas, we know the exact experimental result (known solution) of the problem, but we are interested in the possible result obtained after a change (perturbation) on one or multiple values of the initial conditions of the experiment (new solution). For instance, we often know, for large collections of ith molecules (m ), organic compounds, drugs, xenobiotics, and/or peptide sequences, the efficiency of the compound ε(c ) as adjuvant, action as epitope, immunotoxicity, and/or the interaction (affinity, inhibition, etc.) with immunological targets. In addition, we often known for each molecule the exact conditions (c ) of assay for the initial experiment including structure of the molecule m (drug, adjuvant, and sequence of the peptide), source organism (so), host organism (ho), immunological process (ip), experimental technique (tq), concentration, temperature, time, solvents, and coadjuvants. This is the case of big data retrieved from very large databases like IEDB [1-4] and CHEMBL [52]. However, we do not know the possible result of the experiment if we change at least one of these conditions (perturbation). We refer to small changes or perturbations in both structure and condition for input or output variables. It means that we include changes in ho, so, ip, and tq, changes of the compound by one analogue compound with similar structure, changes in the sequence of the epitope (artificial by organic synthesis or natural mutations), and polarity of the solvent or coadjuvants. In these cases, we could use a perturbation theory model to solve the QSAR/QSPR problem. Perturbation theory includes methods that add “small” terms to a known solution of a problem in order to approach a solution to a related problem without known solution. Perturbation models have been widely used in all branches of science from QM to astronomy and life sciences including chaos or “butterfly effect,” Bohr's atomic theory, Heisenberg's mechanics, Zeeman's and Stark's effects, and other models with applications in like protein spectroscopy and others [53-57]. In a very recent work Gonzalez-Diaz et al. [58] formulated a general-purpose perturbation theory or model for multiple-boundary QSPR/QSAR problems. However, there is not report in the immunoinformatics literature of a general QSPR perturbation model for IEDB B-epitopes. Here we report the first example of QSPR-perturbation model for B-epitopes reported in IEDB able to predict the probability of occurrence of an epitope after a perturbation in the sequence, the experimental technique, the exposition process, and/or the source or host organisms.

2. Materials and Methods

2.1. Molecular Descriptors for Peptides

We calculated the molecular descriptors of the structure of peptides using the software MARCH-INSIDE (MI) based on the algorithm with the same name [59]. The MI approach uses a Markov Chain method to calculate the kth mean values of different physicochemical molecular properties λ(m ) for ith molecules (m). These λ(m ) values are calculated as an average of λ(m ) values for all atoms placed at topological distance d ≤ k; which are in turn the means of atomic properties (λ ) for all atoms in the molecule and its neighbors placed at d = k. For instance, it is possible to derive average estimations of molecular refractivities MR(m ), partition coefficients P(m ), and hardness η(m ) for atoms placed at different topological distances d ≤ k. In this first work, we calculated only one type of λ(m ) values. We calculated for all peptides the average value χ(m ) of all the atomic electronegativities χ for all δ atoms connected to the ith atom (i → j) and their neighbors placed at a distance d ≤ 5 [59]:

We calculate the probabilities p(λ ) for any atomic property including p(χ ) using a Markov Chain model for the gradual effects of the neighboring atoms at different distances in the molecular backbone. This method has been explained in detail in many previous works so we omit the details here [59].

2.2. Electronegativity Perturbation Model for Prediction of B-Epitopes

Very recently Gonzalez-Diaz et al. [58] formulated a general-purpose perturbation theory or model for multiple-boundary QSPR/QSAR problems. We adapted here this new theory or modeling method to approach to the peptide prediction problem from the point of view of perturbation theory. Let be a set of ith peptide molecules denoted as m with a value of efficiency ε as epitopes experimentally determined under a set of boundary conditions c ≡ (c 0, c 1, c 2, c 3,…, c ). We put the main emphasis here on peptides reported in the database IEDB. In this sense, the boundary conditions c used here are the same reported in this database, c 0 = is the specific peptide, c 1 = so, c 2 = ho, c 3 = ip, and c 4 = tq. In general, so is the organism that expresses the peptide (but it can include also artificial peptides, cellular lines, etc.), ho is the host organism exposed to the peptide by means of the bp detected with tq. As our analysis, based on the data reported by IEDB we are unable to work with continuous values of epitope activity ε . Consequently, we have to predict the discrete function of B-epitope efficiency λ(ε ) = 1 for epitopes reported in the conditions c and λ(ε ) = 0, otherwise. Our main aim is to predict the shift or change in a function of the output efficiency Δλ(ε ) = λ(ε )ref − λ(ε )new that takes place after a change, variation, or perturbation (ΔV) in the structure and/or boundary conditions of a peptide of reference. But we know the efficiency of the process of reference λ(ε )ref in addition to the molecular structure and the set of conditions c for initial (reference) and final processes (new). Consequently, to predict Δλ(ε ) we have to predict only λ(ε )new the efficiency function of the new state obtained by a change in the structure of the peptide and/or the boundary conditions. Let ΔV be a perturbation in a function λ; we can define V as the state information function for the reference and new states. According to our recent model [58], we can write V as a function of the conditions and structure of the peptide m as follows. In fact, the variational state functions V have to be written in pairs in order to describe the initial (reference) and final (new) states of a perturbation, as follow:

The state function V is for the ith peptide measured under a set of c boundary conditions in output, final, or new state. The conjugated state function V is for the qth peptide measured under a set of c boundary conditions for the input, initial, or reference state. The difference ΔV between the new (output) state and the reference (input) state is the additive perturbation [58]. Consider

Equation (3) described before opens the door to test different hypothesis. A simple hypotheses is H0: existence of one small and constant value of the perturbation function ΔV = e 0 for all the pairs of peptides and a linear relationship between perturbations of input/output boundary conditions with coefficients a , b , c , and d . Consider

We can use elemental algebraic operations to obtain from these equations an expression for efficiency as epitope of the peptide λ(ε )new. In this case, considering b ≈ d , we can obtain the different expressions; the last may be very useful to solve the QSRR problem for the large datasets formed by IEDB B-epitopes. Consider

3. Results and Discussion

We propose herein, for the first time, a QSRR-perturbation model able to predict variations in the propensity of a peptide to act as B-epitope taking into consideration the propensity of a peptide of reference and the changes in peptide sequence, immunological process, host organism, source organisms, and the experimental technique used. The best QSPR-perturbation model found here with LDA was

The first input term is the value λ(ε )ref is the scoring function λ of the efficiency of the initial process ε (known solution). The function λ(ε )ref = 1 if the ith peptide could experimentally be demonstrated to be a B-epitope in the assay of reference (reference) carried out in the conditions c , λ(ε )ref = 0 otherwise. The variational-perturbation terms ΔΔχ are at the same time terms typical of perturbation theory and moving average (MA) functions used in Box-Jenkin models in time series [60]. These new types of terms account both for the deviation of the electronegativity of all amino acids in the sequence of the new peptide with respect to the peptide of reference and with respect to all boundary conditions. In Table 2, we give the overall classification results obtained with this model. Speck-Planche et al. [61-63] introduced different multitarget/multiplexing QSAR models that incorporate this type of information based on MAs. The results obtained with the present model are excellent compared with other similar models in the literature useful for other problems including moving average models [64, 65] or perturbation models [58]. Notably, this is also the first model combining both perturbation theory and MAs in a QSPR context.

Table 1

Results of QSPR-perturbation model for IEDB B-Epitopes.

Data	Stat.	Pred.	Predicted epitope perturbations
subset	param.	%	λ(ε ij) = 1	λ(ε ij) = 0
λ(ε ij) = 1	Sp	97.0	84607	2660
λ(ε ij) = 0	Sn	93.6	4354	63548
Total train	Ac	95.5
λ(ε ij) = 1	Sp	97.1	28060	840
λ(ε ij) = 0	Sn	93.3	1485	20641
Total cv	Ac	95.4

Bold font is used to highlight the number of cases correctly classified by the model.

The other input terms are the following. The first Δχ seq = χ(m )ref − χ(m )new is the perturbation term for the variation or in the mean value of electronegativity for all amino acids in the sequence of the peptide of reference. The remnant input variables of the model ΔΔχ = Δχ − Δχ = [χ(m )ref − *χ(c )ref]−[χ(m )new − *χ(c )new] quantify values of the conditions of the new assay cj-new that represent perturbations with respect to the initial conditions c -ref of the assay of reference. The quantities *χ(c ) and *χ(c ) are the average values of the mean electronegativity values χ(m ) and χ(m ) for all new and reference peptides in IEDB that are epitopes under the jth or rth boundary condition. The values of these terms have been tabulated for >500 source organisms, >50 host organisms, >10 biological process, and >30 experimental techniques. We must substitute the values of χ(m ) and χ(m ) of the new and reference peptides and the tabulated values of *χ(c ) and *χ(c ) for all combinations of boundary conditions to predict the perturbations of the action as epitope of peptides. In doing so we can found the optimal sequence and boundary conditions towards the use of the peptide in the development of a vaccine. In Table 2 we give some of these values of *χ(c ) and *χ(c ).

Table 2

Average values and count of input-output cases for different organisms, process, and techniques.

Source organism (so)	N in	N out	*χ
Homo sapiens	38920	39274	2.685
Plasmodium falciparum	10669	9446	2.704
Hepatitis C virus	9935	10239	2.683
Bos taurus	5671	5780	2.690
Canine parvovirus	5655	5637	2.693
Foot-mouth disease virus	4062	4176	2.676
Triticum aestivum	3769	3887	2.703
Bacillus anthracis	3602	3600	2.699
Human papillomavirus	3316	3414	2.693
Human herpesvirus	3026	3132	2.684
Gallus gallus	2850	2829	2.689
Arachis hypogaea	2648	2670	2.687
Mycobacterium tuberculosis	2637	2593	2.688
Clostridium botulinum	2588	2722	2.685
SARS coronavirus	2550	2704	2.686
Mus musculus	2334	2287	2.682
Hepatitis B virus	2007	2066	2.680
Helicobacter pylori	1958	1796	2.695
Hevea brasiliensis	1938	1958	2.697
Hepatitis E virus	1928	1941	2.685
Shigella flexneri	1878	1701	2.699
Dengue virus 2	1767	1828	2.679
Staphylococcus aureus	1757	1661	2.694
Treponema pallidum	1739	1755	2.691
Escherichia coli	1721	1678	2.689
Murine hepatitis virus	1575	1603	2.692
Haemophilus influenzae	1545	1587	2.695
Streptococcus mutans	1523	1537	2.697
Puumala virus (strain)	1505	1574	2.689
Chlamydia trachomatis	1402	1546	2.704
Human respiratory  virus	1347	1398	2.682
Borrelia burgdorferi	1228	1237	2.698
Hepatitis delta virus	1182	1199	2.690
Streptococcus pyogenes	1181	1251	2.697
Porphyromonas gingivalis	1143	1085	2.688
Human enterovirus	1106	1132	2.689
Influenza A virus	1085	1086	2.687
Mycoplasma hyopneumoniae	1044	1024	2.695
Rattus norvegicus	1025	1039	2.689
Bordetella pertussis	1011	960	2.685
Human T-lymphotropic virus	996	1031	2.680
Anaplasma marginale	977	857	2.707
Measles virus strain	804	810	2.688
Fasciola hepatica	803	857	2.685
Neisseria meningitidis	789	853	2.696
Human poliovirus	766	780	2.690
Tityus serrulatus	764	775	2.680
Torpedo californica	752	788	2.687
Cryptomeria japonica	719	794	2.680
Mycobacterium bovis	717	733	2.688
Trypanosoma cruzi	691	777	2.704
Andes virus CHI-7913	679	687	2.690
Bovine papillomavirus	672	665	2.692
Human hepatitis	670	696	2.688
Leishmania infantum	659	735	2.688
Human parvovirus	649	691	2.683
Poa pratensis	648	664	2.692
Aspergillus fumigatus	642	709	2.677
Duck hepatitis	587	603	2.688
Olea europaea	571	577	2.692
Porcine reproductive	515	514	2.681
Fagopyrum esculentum	509	497	2.685
Juniperus ashei	505	568	2.672
Mycobacterium leprae	489	542	2.690
Glycine max	477	509	2.685
D. pteronyssinus	455	464	2.680
Plasmodium vivax	453	446	2.690
Chlamydophila pneumoniae	446	462	2.690
Pseudomonas aeruginosa	443	454	2.691
Vibrio cholera	427	426	2.694
Streptococcus sp.	426	425	2.691
Mycobacterium avium	425	415	2.689
Dermatophagoides farinae	410	390	2.693
Human coxsackievirus	406	392	2.694
Equine infectious  virus	404	419	2.688
Babesia equi	383	371	2.696
Prunus dulcis	383	379	2.708
Human adenovirus	375	405	2.686
Theileria parva	366	371	2.713
Candida albicans	365	370	2.690
Porcine endogenous	355	351	2.692
Ovis aries	352	350	2.683
Chironomus thummi	347	338	2.691
Sus scrofa	343	362	2.686
Bovine leukemia virus	333	329	2.676
Ricinus communis	329	314	2.692
Androctonus australis	322	357	2.685
Renibacterium salmoninarum	319	350	2.690
Orientia tsutsugamushi	309	372	2.705
Anacardium occidentale	293	306	2.693
Conus geographus	289	295	2.660
Host organism (ho)	N in	N out	*χ
Homo sapiens	257293	91093	2.6856
Mus musculus	107867	51466	2.6873
Oryctolagus cuniculus	65053	31433	2.6900
Bos taurus	15333	2072	2.6909
Rattus norvegicus	9450	3562	2.6876
Aotus sp.	9044	3933	2.6879
Sus scrofa	7725	3464	2.6873
Gallus gallus	7507	997	2.6790
Canis lupus	6604	3334	2.6906
Macaca mulatta	5261	2569	2.6993
Ovis aries	3953	1653	2.6836
Equus caballus	3943	2099	2.6842
Cavia porcellus	3458	1688	2.6833
Capra hircus	2182	1127	2.6830
Aotus nancymaae	1659	852	2.6837
Pan troglodytes	1614	732	2.6757
Marmota monax	1100	509	2.7011
Felis catus	901	279	2.6838
Myodes glareolus	814	388	2.6863
Anas platyrhynchos	688	342	2.6880
Homo sapiens  (human)	508	270	2.6851
Trichosurus vulpecula	456	126	2.6921
Mesocricetus auratus	438	104	2.6909
Macaca cyclopis	382	193	2.6871
O. tshawytscha	333	159	2.6929
Macaca fuscata	188	100	2.6667
Cricetulus migratorius	171	142	2.7008
Camelus dromedarius	171	89	2.6886
Dicentrarchus labrax	121	55	2.6759
Macaca fascicularis	96	52	2.6793
Saimiri sciureus	92	44	2.6900
Canis familiaris	77	42	2.6850
Rattus rattus	72	31	2.6760
Callithrix pygmaea	67	30	2.6920
Chinchilla lanigera	41	24	2.6729
Aotus lemurinus	30	19	2.6860
Papio cynocephalus	27	13	2.7267
Aotus griseimembra	26	12	2.7000
Mustela vison	18	10	2.7000
Chlorocebus aethiops	15	10	2.6875
Bos indicus	13	4	2.6925
Oncorhynchus mykiss	10	4	2.6700
M. macquariensis	9	6	2.6600
Cricetulus griseus	8	4	2.6900
Aotus trivirgatus	7	4	2.7000
Process type (pt)	N in	N out	*χ
AID	111197	108536	2.6876
OOID	32419	32617	2.6868
OAID	19210	18954	2.6801
OOA	15863	16303	2.6902
NI	13430	15206	2.6845
EWEIR	4818	4864	2.6843
EEE	3113	3546	2.6906
OOD	2806	2799	2.6887
AICD	1077	1095	2.6812
EWED	696	686	2.6879
DEWED	280	337	2.6804
TT	260	215	2.6806
OOC	153	137	2.6800
Technique (tq)	N in	N out	*χ
ELISA	133458	135109	2.6871
WI	33627	33292	2.6887
ACAbB	7780	9068	2.6862
PhDIP	7450	4496	2.6771
RIA	5241	5218	2.6858
IFAIH	4454	4581	2.6879
NIAA	4222	4316	2.6892
FIA	2255	2276	2.6897
PAC	1312	1219	2.6837
IP	1127	1089	2.6886
SPR	758	639	2.6860
FACS	608	647	2.6907
Other	502	495	2.6813
SAC	484	393	2.6878
ELISPOT	396	412	2.6979
RDAT	366	323	2.6859
EDAT	284	330	2.6800
XRC	231	227	2.6880
MS	209	179	2.6849
PFF	171	153	2.6820
AbDPO	162	295	2.6968
CdC	146	205	2.6895
IAbBA	144	183	2.6940
IOT	124	106	2.6835
HAGGI	115	122	2.6834
IgMHR	89	90	2.6929
EAAA	84	139	2.6922
HS	82	67	2.6791
AbdCC	73	118	2.6897
AGG	50	60	2.6980
CM	50	57	2.6863

The indicates that quantities like χ is the average value of the mean electronegativity (m ) for all the peptides in IEDB that are epitopes for the same boundary condition.

In Table 3 we depict the sequences and input-output boundary conditions for top perturbations present in IEDB. All these perturbations have observed value of λ(ε )new = 1 and predicted value also equal to 1 with a high probability. See Supplementary Material available online at http://dx.doi.org/10.1155/2014/768515 file contains a full list of >200,000 cases of perturbations.

Table 3

Top100 values of p1 for positive perturbations in training series.

New experiment						Experiment of reference						Input perturbation terms
IDE	Sequence	ho	so	ip	tq	IDE	Sequence	ho	so	ip	tq	Δχ	ΔΔχ ho	ΔΔχ so	ΔΔχ ip	ΔΔχ tq
115153	MKGVVCTRIYEKV	Homo sapiens	Homo sapiens	OAID	ELISA	115155	NNQRKKAKNTPFNMLKRERN	Mus musculus	Dengue virus 2	AID	WI	0.01	0.012	0.004	0.017	0.012
52124	QQQPP	Homo sapiens	Triticum aestivum	OOA	ELISA	52128	QQQQGGSQSQKGKQQ	Homo sapiens	Glycine max	OOA	WI	0	0	−0.018	0	0.002
3639	APLGVT	Homo sapiens	Hepatitis E virus	EWEIR	ELISA	3652	APLTRGSCRKRNRSPER	Homo sapiens	Human herpesvirus	OOID	ELISA	0.04	0.04	0.039	0.043	0.04
135959	LTRAYAKDVKFG	Homo sapiens	Homo sapiens	OAID	ELISA	135963	NGQEEKAGVVSTGLIGGG	Mus musculus	MD	AID	ELISA	−0.04	−0.038	−0.047	−0.033	−0.04
108075	PREPQVY	Homo sapiens	Homo sapiens	OAID	ELISA	108078	PTSPSGVEEWIVTQVVPGVA	Oryctolagus cuniculus	Homo sapiens	AID	ACAbB	−0.01	−0.006	−0.01	−0.003	−0.011
25113	HVVDLP	Homo sapiens	Hepatitis E virus	EWEIR	ELISA	25126	HWGNHSKSHPQR	Mus musculus	MD	AID	ELISA	0.02	0.022	0.013	0.023	0.02
48780	PPFSPQ	Homo sapiens	Hepatitis delta virus	OOID	ELISA	48782	PPFTSAVGGVDHRS	Mus musculus	MD	AID	SAC	0.02	0.022	0.008	0.021	0.021
40988	LYVVAYQA	Mus musculus	Viscum album	AID	ELISA	41004	MAARLCCQLDPARDV	Homo sapiens	Hepatitis B virus	OOID	ELISA	0.02	0.018	0.006	0.019	0.02
50439	QDAYNAAG	Mus musculus	Mycobacterium scrofulaceum	AID	ELISA	50445	QDCNCSIYPGHASGHRMAWD	Homo sapiens	Hepatitis C virus	OOID	ELISA	0.04	0.038	0.028	0.039	0.04
98849	KIPAVFKIDA	Homo sapiens	Bos taurus	DEWED	WI	98850	KKGSEEEGDITNPIN	Homo sapiens	Arachis hypogaea	OOA	IFAIH	−0.05	−0.05	−0.053	−0.04	−0.051
116171	TQDQDPBBHFFKNIVTPR	Homo sapiens	Homo sapiens	OAID	ACAbB	116286	CGKGLSATVTGGQKGRGSR	Oryctolagus cuniculus	Mus musculus	AID	MS	0.01	0.014	0.008	0.017	0.009
123442	LLKDLRKN	Homo sapiens	Borna disease virus	EWEIR	WI	123443	LLTEHRMTWDPAQPPRDLTE	Homo sapiens	Homo sapiens	OOID	ELISA	−0.02	−0.02	−0.025	−0.017	−0.022
47858	PHVVDL	Homo sapiens	Hepatitis E virus	EWEIR	ELISA	47860	PHWIKKPNRQGLGYYS	Capra hircus	Human T-lymphotropic virus	AID	ACAbB	0.01	0.007	0.005	0.013	0.009
61783	STNKAVVSLS	Bos taurus	Bovine respiratory	AID	ELISA	61792	STNPKPQRKTKRNTNRRPQD	Homo sapiens	Hepatitis C virus	OOID	ELISA	0.03	0.025	0.019	0.029	0.03
118210	VMLYQISEE	Homo sapiens	Homo sapiens	OAID	WI	118217	VTKYITKGWKEVH	Oryctolagus cuniculus	Homo sapiens	AID	ELISA	0.05	0.054	0.05	0.057	0.048
130944	LFKHS	Oryctolagus cuniculus	Rattus norvegicus	AID	ELISA	130956	LPPRVTPKWSLDAWSTWR	Homo sapiens	MD	OOD	WI	0.01	0.006	−0.002	0.011	0.012
23028	GVKYA	Homo sapiens	MD	OAID	WI	23032	GVLAKDVRFSQV	Homo sapiens	MD	OOID	ELISA	0	0	0	0.007	−0.002
51199	QKKAIE	Oryctolagus cuniculus	Vibrio cholerae	AID	ELISA	51204	QKKNKRNTNRRPQDV	Homo sapiens	Hepatitis C virus	OOID	ELISA	0.03	0.026	0.018	0.029	0.03
144783	SHVVTMLDNF	Homo sapiens	Homo sapiens	NI	ELISA	144786	SMNRGRGTHPSLIWM	Mus musculus	MD	AID	ACAbB	0.03	0.032	0.023	0.033	0.029
134343	DLYIK	Mus musculus	Human papillomavirus	AID	NIAA	134344	DMAQVTVGPGLLGVSTL	Mus musculus	Homo sapiens	AID	WI	0	0	−0.009	0	0
38321	LNQLAGRM	Anas platyrhynchos	Duck hepatitis	AID	ELISA	38323	LNQTARAFPDCAICWEPSPP	Oryctolagus cuniculus	Bovine leukemia virus	AID	ACAbB	−0.01	−0.008	−0.022	−0.01	−0.011
144657	GQITVDMMYG	Homo sapiens	Homo sapiens	OAID	ELISA	144661	GREGYPADGGCAWPACYC	Oryctolagus cuniculus	MD	AID	WI	0.02	0.024	0.013	0.027	0.022
21084	GLQN	Mus musculus	Chlamydia trachomatis	AID	ELISA	21093	GLRAQDDFSGWDINTPAFEW	Mus musculus	Mycobacterium tuberculosis	AID	WI	0.03	0.03	0.013	0.03	0.032
98453	SGFSGSVQFV	Oryctolagus cuniculus	Neisseria meningitidis	AID	ELISA	98456	SICSNNPTCWAICKRIPNKK	Mus musculus	Human respiratory virus	AID	IFAIH	0.04	0.037	0.027	0.04	0.041
98453	SGFSGSVQFV	Mus musculus	Neisseria meningitidis	AID	ELISA	98456	SICSNNPTCWAICKRIPNKK	Mus musculus	Human respiratory virus	AID	IFAIH	0.04	0.04	0.027	0.04	0.041
107107	EAIQP	Rattus norvegicus	Homo sapiens	AID	ELISA	107110	EKERRPSPIGTATLL	Homo sapiens	MD	OOA	ELISA	0.05	0.048	0.043	0.053	0.05
110857	FTGEAYSYWSAK	Homo sapiens	Mycoplasma penetrans	EWEIR	ELISA	110859	GEESRISLPLPNFSSLNLRE	Mus musculus	Homo sapiens	AID	FIA	0	0.002	−0.017	0.003	0.003
36315	LGSAYP	Mus musculus	Mycobacterium leprae	MD	ELISA	36317	LGSGAFGTIYKG	Mus musculus	Avian erythroblastosis virus	AID	ACAbB	0.01	0.01	0	0.011	0.009
122034	WNPAD	Rattus norvegicus	Torpedo californica	AID	ELISA	122035	WNPADYGGIKWNPADYGGIK	Rattus norvegicus	MD	AID	RIA	0.01	0.01	0.001	0.01	0.009
25013	HVADIDKLID	Mus musculus	Puumala virus Kazan	AID	ELISA	25021	HVAPTHYVTESDASQRVTQL	Homo sapiens	Hepatitis C virus	OOID	ELISA	0	−0.002	−0.014	−0.001	0
36162	LGIHE	Oryctolagus cuniculus	Candida albicans	AID	ELISA	36166	LGIMGEYRGTPRNQDLYDAA	Mus musculus	Human respiratory  virus	AID	RIA	0	−0.003	−0.007	0	−0.001
67253	TWEVLH	Mus musculus	Plasmodium vivax	AID	ELISA	67257	TWGENETDVLLLNNTRPPQ	Homo sapiens	Hepatitis C virus	OOID	ACAbB	−0.02	−0.022	−0.027	−0.021	−0.021
50990	QGYRVSSYLP	Homo sapiens	Hevea brasiliensis	OOA	WI	50998	QHEQDRPTPSPAPSRPFSVL	Homo sapiens	Hepatitis E virus	OOID	ELISA	0.01	0.01	−0.002	0.007	0.008
100458	RDVLQLYAPE	Mus musculus	Bacillus anthracis	AID	ELISA	100462	RFSTRYGNQNGRIRVLQRFD	Homo sapiens	Arachis hypogaea	EWED	ELISA	0.03	0.028	0.018	0.03	0.03
111036	TESTFTGEAYSV	Homo sapiens	Mycoplasma penetrans	EWEIR	ELISA	111039	TGVPIDPAVPDSSIVPLLES	Bos taurus	Bovine papillomavirus	AID	ELISA	0.03	0.035	0.02	0.033	0.03
117919	IFIEME	Homo sapiens	Homo sapiens	OAID	WI	117921	IGIIDLIEKRKFNQ	Mus musculus	Homo sapiens	AID	WI	0.03	0.032	0.03	0.037	0.03
7127	CTDTDKLF	Oryctolagus cuniculus	Shigella flexneri	AID	ELISA	7128	CTDVSTAIHADQLTPAW	Homo sapiens	SARS coronavirus	OOID	ELISA	0.01	0.006	−0.003	0.009	0.01
112253	PGQSPKL	Homo sapiens	Homo sapiens	OAID	ELISA	112255	PIRALVGDEVELPCRISPGK	Mus musculus	Homo sapiens	AID	ELISA	0.01	0.012	0.01	0.017	0.01
122034	WNPAD	Rattus norvegicus	Torpedo californica	AID	ELISA	122038	WNPDDYGGVKWNPDDYGGVK	Rattus norvegicus	MD	AID	RIA	0	0	−0.009	0	−0.001
131878	FLMLVGGSTL	Homo sapiens	Homo sapiens	OAID	ACAbB	131879	FLVAHTRARAPSAGERARRS	Mus musculus	Mus musculus	AID	NIAA	0.03	0.032	0.028	0.037	0.033
70664	VQVVYDYQ	Homo sapiens	Treponema pallidum	OOID	ELISA	70667	VQWMNRLIAFAFAGNHVSP	Homo sapiens	Hepatitis C virus	OOID	ELISA	0.05	0.05	0.041	0.05	0.05
71545	VTV	Homo sapiens	Helicobacter pylori	OOID	ELISA	71559	VTVRGGLRILSPDRK	Homo sapiens	Arachis hypogaea	OOA	WI	0.04	0.04	0.032	0.043	0.042
127856	TDVRYKD	Mus musculus	Mus musculus	AID	ACAbB	127857	TDVRYKDDMYHFFCPAIQAQ	Mus musculus	Mus musculus	AID	PFF	0.01	0.01	0.01	0.01	0.006
112149	GVGWIRQ	Homo sapiens	Homo sapiens	OAID	ELISA	112152	HHPARTAHYGSLPQKSHGRT	Homo sapiens	Homo sapiens	AID	ELISA	0	0	0	0.007	0
119581	FSCSVMHE	Homo sapiens	Homo sapiens	OAID	ELISA	119582	GLQLIQLINVDEVNQI	Mus musculus	Homo sapiens	AID	RIA	−0.01	−0.008	−0.01	−0.003	−0.011
144657	GQITVDMMYG	Homo sapiens	Homo sapiens	OAID	ELISA	144659	GREGYPADGGAAGYCNTE	Oryctolagus cuniculus	MD	AID	WI	−0.01	−0.006	−0.017	−0.003	−0.008
25013	HVADIDKLID	Mus musculus	Puumala virus Kazan	AID	ELISA	25022	HVAPTHYVVESDASQRVTQV	Homo sapiens	Hepatitis C virus	OOID	ELISA	0	−0.002	−0.014	−0.001	0
144652	GMRGMKGLVY	Homo sapiens	Homo sapiens	OAID	ELISA	144654	GPHPTLEVVPMGRGS	Mus musculus	MD	AID	ELISA	−0.02	−0.018	−0.027	−0.013	−0.02
104515	HDCRPKKI	Mus musculus	La Crosse virus	AID	IFAIH	104521	IGTLKKILDETVKDKIAKEQ	Rattus norvegicus	Streptococcus pyogenes	AID	ELISA	−0.04	−0.04	−0.053	−0.04	−0.041
7367	CYGDWA	Homo sapiens	Triticum aestivum	OOA	ELISA	7374	CYGLPDSEPTKTNGK	Mus musculus	Tityus serrulatus	AID	WI	−0.02	−0.018	−0.043	−0.023	−0.018
7367	CYGDWA	Homo sapiens	Triticum aestivum	OOA	ELISA	7374	CYGLPDSEPTKTNGK	Mus musculus	Tityus serrulatus	AID	WI	−0.02	−0.018	−0.043	−0.023	−0.018
144610	DFFTYK	Mus musculus	Porcine transmissible	AID	WI	144611	DFNGSFDMNGTITA	Oryctolagus cuniculus	Escherichia coli	AID	ELISA	−0.01	−0.007	−0.018	−0.01	−0.012
112047	ASTRESG	Homo sapiens	Homo sapiens	OAID	ELISA	112048	ATASTMDHARHGFLPRHRDT	Homo sapiens	Homo sapiens	AID	ELISA	0.05	0.05	0.05	0.057	0.05
36136	LGGVFT	Homo sapiens	Dengue virus 2	OOID	ELISA	36137	LGGWKLQSDPRAYAL	Homo sapiens	Ambrosia artemisiifolia	OOA	RIA	0.01	0.01	0.007	0.013	0.009
115256	FRELKDLKGY	Homo sapiens	Bos taurus	DEWED	WI	115261	GDLEILLQKWENGECAQKKI	Homo sapiens	Bos taurus	OOA	FIA	−0.01	−0.01	−0.01	0	−0.009
129024	KADQLYK	Homo sapiens	Homo sapiens	OAID	ELISA	129026	KAKKPAAAAGAKKAKS	Oryctolagus cuniculus	Homo sapiens	AID	ELISA	0.03	0.034	0.03	0.037	0.03
148481	YTRDLVYK	Rattus norvegicus	Homo sapiens	AID	WI	148483	YVPIVTFYSEISMHSSRAIP	Oryctolagus cuniculus	MD	AID	ELISA	0	0.002	−0.007	0	−0.002
150850	GY	Mus musculus	Human papillomavirus	AID	ELISA	150853	HIGGLSILDPIFGVL	Homo sapiens	Dermatophagoides farinae	OOA	ACAbB	0.04	0.038	0.04	0.043	0.039
107366	FPPKPKD	Homo sapiens	Homo sapiens	OAID	ELISA	107376	GDRSGYSSPGSPG	Mus musculus	Homo sapiens	AID	ACAbB	−0.03	−0.028	−0.03	−0.023	−0.031
114859	ICGTDGVTYT	Homo sapiens	Gallus gallus	OOA	WI	114865	IVERETRGQSENPLWHALRR	Rattus norvegicus	Human herpesvirus	AID	ELISA	0.04	0.042	0.035	0.037	0.038
62149	SVHLF	Homo sapiens	MD	OAID	WI	62150	SVIALGSQEGALHQALAGAI	Equus caballus	West Nile virus	AID	IFAIH	−0.02	−0.021	−0.012	−0.013	−0.021
98455	SGSVQFVPIQ	Mus musculus	Neisseria meningitidis	AID	ELISA	98456	SICSNNPTCWAICKRIPNKK	Mus musculus	Human respiratory  virus	AID	IFAIH	0.04	0.04	0.027	0.04	0.041
61783	STNKAVVSLS	Bos taurus	Bovine respiratory	AID	ELISA	61791	STNPKPQRKTKRNTNRRPQ	Homo sapiens	Hepatitis C virus	EWEIR	ACAbB	0.04	0.035	0.029	0.037	0.039
100318	NAPKTFQFIN	Mus musculus	Bacillus anthracis	AID	ELISA	100319	NASSELHLLGFGINAENNHR	Homo sapiens	Arachis hypogaea	EWED	ELISA	0	−0.002	−0.012	0	0
118947	PFSAPPPA	Homo sapiens	Homo sapiens	OAID	ELISA	118948	PGAIEQGPADDPGEGPSTGP	Homo sapiens	Human herpesvirus	NI	ACAbB	−0.04	−0.04	−0.041	−0.036	−0.041
78323	YSFRD	Mus musculus	Bluetongue virus 1	AID	ELISA	78341	AALTAENTAIKKRNADAKA	Homo sapiens	Streptococcus mutans	EEE	ELISA	0.01	0.008	0.007	0.013	0.01
145831	IPLGTRP	Mus musculus	Human papillomavirus	AID	ELISA	145841	KEDFRYAISSTNEIGLLGA	Sus scrofa	Classical swine	AID	PAC	−0.04	−0.04	−0.045	−0.04	−0.043
119592	HTFPAVLQ	Homo sapiens	Homo sapiens	OAID	ELISA	119596	IHIPSEKIWRPDLVLY	Mus musculus	Homo sapiens	AID	RIA	0.01	0.012	0.01	0.017	0.009
58780	SKAANLSIIK	MD	Beet necrotic	MD	WI	58783	SKAFSNCYPYDVPDYASL	Oryctolagus cuniculus	Influenza A virus	AID	RIA	−0.01	−0.004	−0.014	−0.009	−0.013
115153	MKGVVCTRIYEKV	Homo sapiens	Homo sapiens	NI	ELISA	115155	NNQRKKAKNTPFNMLKRERN	Mus musculus	Dengue virus 2	AID	ELISA	0.01	0.012	0.004	0.013	0.01
133629	LPLRF	Oryctolagus cuniculus	Gallus gallus	AID	ACAbB	133630	LPPGLHVFPLASNRS	Mus musculus	MD	AID	SPR	−0.01	−0.013	−0.021	−0.01	−0.01
96215	EEEEAEDKED	Homo sapiens	Homo sapiens	OAID	ELISA	96216	EEEGLLKKSADTLWNMQK	Mus musculus	Mus musculus	AID	ELISA	0.08	0.082	0.078	0.087	0.08
39782	LTAASV	Homo sapiens	Triticum aestivum	OOA	ELISA	39788	LTAELKIYSVIQAEINKHL	Oryctolagus cuniculus	Yersinia pestis	AID	ACAbB	0.01	0.014	−0.001	0.007	0.009
107479	KFNWYVD	Homo sapiens	Homo sapiens	OAID	ELISA	107482	KGEPGLPGRGFPGFP	Mus musculus	Homo sapiens	AID	ACAbB	0	0.002	0	0.007	−0.001
63569	TETVNSDI	Macaca mulatta	Shigella flexneri	AID	ELISA	63573	TEVELKERKHRIEDAVRNAK	Homo sapiens	Mycobacterium leprae	OOID	ELISA	0.05	0.036	0.041	0.049	0.05
134028	DDTIS	Mus musculus	Homo sapiens	AID	NIAA	134029	DEDENQSPRSFQKKTR	Oryctolagus cuniculus	Homo sapiens	AID	ELISA	0.05	0.053	0.05	0.05	0.048
23028	GVKYA	Homo sapiens	MD	OAID	WI	23032	GVLAKDVRFSQV	Homo sapiens	MD	EWEIR	ACAbB	0	0	0	0.004	−0.003
115293	IMCVKKILDK	Homo sapiens	Bos taurus	DEWED	WI	115295	INPSKENLCSTFCKEVVRNA	Homo sapiens	Bos taurus	OOA	FIA	−0.03	−0.03	−0.03	−0.02	−0.029
65105	TLTPENTL	Mus musculus	Shigella flexneri	AID	ELISA	65110	TLTSGSDLDRCTTFDDV	Oryctolagus cuniculus	SARS coronavirus	AID	ELISA	0.01	0.013	−0.003	0.01	0.01
134471	PKPEQ	Mus musculus	Streptococcus pneumoniae	AID	FACS	134472	PLLPGTSTTSTGPCKT	Homo sapiens	Hepatitis B virus	AID	ELISA	0.02	0.018	0.019	0.02	0.016
142228	LYCYEQLNDSSE	Homo sapiens	Human papillomavirus	NI	ELISA	142250	NWGDEPSKRRDRSNSRGRKN	Felis catus	Feline infectious	AID	ELISA	0.07	0.068	0.071	0.073	0.07
21549	GNYDFWYQS	Homo sapiens	Staphylococcus aureus	OOID	ELISA	21553	GNYNYKYRYLRHGKLRPFER	Mus musculus	SARS coronavirus	AID	ELISA	0.03	0.032	0.021	0.031	0.03
21549	GNYDFWYQS	Homo sapiens	Staphylococcus aureus	OOID	ELISA	21553	GNYNYKYRYLRHGKLRPFER	Oryctolagus cuniculus	SARS coronavirus	AID	ELISA	0.03	0.034	0.021	0.031	0.03
34908	LAPLGE	Homo sapiens	Hepatitis E virus	EWEIR	ELISA	34914	LAPSTLRSLRKRRLSSP	Homo sapiens	Human herpesvirus	OOID	ELISA	0.06	0.06	0.059	0.063	0.06
130454	CLFPNNSYC	Mus musculus	MD	AID	NIAA	130456	CRPQVNNPKEWSCAAC	Homo sapiens	MD	OOD	ACAbB	0.01	0.008	0.01	0.011	0.007
19644	GFVPSM	Homo sapiens	Hepatitis delta virus	OOID	ELISA	19647	GFVSASIFGFQAEVGPNNTR	Oryctolagus cuniculus	Vaccinia virus WR	AID	ELISA	−0.01	−0.006	−0.013	−0.009	−0.01
20678	GKRPE	Mus musculus	Streptococcus pyogenes	AID	WI	20680	GKSKRDAKNNAAKLAVDKLL	Mus musculus	Vaccinia virus WR	AID	WI	0.01	0.01	0.001	0.01	0.01
123278	GYLKDLPTT	Ovis aries	Fasciola hepatica	AID	ELISA	123282	HACQKKLLKFEALQQEEGEE	Rattus norvegicus	Gallus gallus	AID	PFF	−0.02	−0.016	−0.016	−0.02	−0.025
141067	PLSLEPDP	Mus musculus	Homo sapiens	AID	FACS	141073	REGVRWRVMAIQ	Mus musculus	Homo sapiens	AID	ELISA	0.06	0.06	0.06	0.06	0.056
139248	SFAGTVIE	Mus musculus	Classical swine	AID	WI	139305	TAAQITQRKWEAAREAEQRR	Oryctolagus cuniculus	Homo sapiens	AID	IP	0.03	0.033	0.026	0.03	0.03
104515	HDCRPKKI	Mus musculus	La Crosse virus	AID	IFAIH	104520	IAKEQENKETIGTLKKILDE	Rattus norvegicus	Streptococcus pyogenes	AID	ELISA	−0.06	−0.06	−0.073	−0.06	−0.061
113517	HLYADGLTD	Mus musculus	Human papillomavirus	AID	IFAIH	113518	HNKIQAIELEDLLRYSKLYR	Mus musculus	Homo sapiens	AID	ELISA	0.02	0.02	0.011	0.02	0.019
156970	VERHQ	Homo sapiens	Homo sapiens	OAID	ELISA	156975	WSSTVLRVSPTRTVP	Mus musculus	MD	AID	ELISA	0.01	0.012	0.003	0.017	0.01
78252	PVQNLT	Mus musculus	Porphyromonas gingivalis	AID	WI	78253	QGGCGRGWAFSATGAIEA	Mus musculus	Glycine max	AID	ELISA	0.02	0.02	0.017	0.02	0.018
6068	CCPDKNKS	Mus musculus	Human herpesvirus	AID	WI	6074	CCRHKQKDVGDVKQTLPPS	Ovis aries	MD	AID	ELISA	0.01	0.006	0.004	0.01	0.008
53109	RAGVCY	Homo sapiens	Triticum aestivum	OOA	ELISA	53116	RAILTAFSPAQDIWGTS	Oryctolagus cuniculus	SARS coronavirus	AID	ELISA	−0.02	−0.016	−0.037	−0.023	−0.02
147041	IPEQ	Homo sapiens	Triticum aestivum	OOA	WI	147064	KHQGAQYVWNRTA	Homo sapiens	Bos taurus	OOID	WI	0.06	0.06	0.047	0.057	0.06
70664	VQVVYDYQ	Oryctolagus cuniculus	Treponema pallidum	AID	ELISA	70667	VQWMNRLIAFAFAGNHVSP	Homo sapiens	Hepatitis C virus	OOID	ELISA	0.05	0.046	0.041	0.049	0.05
134343	DLYIK	Mus musculus	Human papillomavirus	AID	PhDIP	134344	DMAQVTVGPGLLGVSTL	Mus musculus	Homo sapiens	AID	PhDIP	0	0	−0.009	0	0

4. Conclusions

It is possible to develop general models for vaccine design able to predict the results of multiple input-output perturbations in peptide sequence and experimental assay boundary conditions using ideas of QSPR analysis, perturbation theory, and Box and Jenkins MA operators. The electronegativity values calculated with MARCH-INSIDE seem to be good molecular descriptors for this type of QSPR-perturbation models.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

Supplementary Material includes the sequences of peptides obtained from IEDB, boudary conditions (source organisms, host organisms, techniques, biological process) as well as the values of the input/output variables of the models calculated for all the cases present in the dataset used. These values have been obtained for all the input-output boundary conditions for the perturbations.

Click here for additional data file.