BIOINF 3360 Computational Immunomics

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1 BIOINF 3360 Computational Immunomics Oliver Kohlbacher Summer Design of Epitope Based Vaccines Outline Vaccine Design Types of vaccines Epitope based vaccines Vaccine Design as an Optimization Problem Basic problem formulation Heuristics for vaccine design Linear and integer linear programming OptiTope Formulation of epitope selection as an ILP Formalization of immunological constraints Results OptiTope web server 3 Vaccines Many different approaches to develop vaccines, e.g.: Whole organism vaccines: Killed or inactivated organism Purified antigens: inactivated exotoxins, capsular polysaccharides, recombinant microbial antigens DNA vaccines: plasmid DNA directly injected into the muscle of the recipient Synthetic peptide vaccines: priming of DC cells or other delivery mechanisms Common: an epitope is being presented Difference: mechanism leading to epitope generation 4 1

2 Peptide Based Vaccines MHC binding peptides can be used as vaccines Two basic types Prophylactic vaccines: protection from an infective agent Therapeutic vaccines: reduce or arrest disease progression Identification of MHC binding peptides for vaccine development is a major goal of computational immunomics 5 Vaccine Design As discussed earlier, most vaccines are based on attenuated pathogens Recently, epitope based vaccines have become an interesting alternative 6 Peptide Based Vaccines Delivery Immunostimulating complexes (ISCOM) are lipid-conjugated complexes of antigens DNA-based vaccines contain the DNA sequence encoding the antigen 7 2

3 String of Beads vs. Peptide Mix Peptides can be administered as Peptide mixtures (A) Concatenated into a polypeptide (B) Combined with spacers ensuring proper cleavage into a polypeptide (C) B and C are so called string of beads (or beads on astring) vaccines as the epitopes are strung together like beads on a string B and C consist of only one component A allows a simpler synthesis and combination of individual peptides 8 Advantages of EBVs Absence of infectious material Production of chemically well characterized peptides can be done efficiently and economically Peptide preparations can be stored freeze dried, which avoids the need for cold storage In contrast to attenuated vaccines, no risk of reversion and thus pathogenicity Well established peptide analytics allows for better quality control... Purcell et al., Nature Rev. Drug Discov., 2007, 6: Epitope Based Vaccines Key idea of epitope based vaccines is the rational selection of individual epitopes In contrast to attenuated vaccines, only these epitopes are used instead of whole pathogens or sets of antigens Key goals are to make the vaccine as simple as possible (small number of components) as effective as possible (high immunogenicity) as broadly applicable as possible (cover a wide range of the population) 10 3

4 MHC Allele Frequencies Different populations have very different allele frequencies! Saisiat (Taiwan) Zulu (South Africa) 20 0 A*01 A*02 A*03 A*11 A*23 A*24 A*26 A*29 A*30 A*34 A*68 A*74 Data from 11 Population Optimized Vaccines A vaccine effective in Africa does not need to be effective in Europe or Asia due to different predominant MHC alleles Epitope driven vaccines should be designed with an appropriate choice of epitopes to cover the right population Goal Vaccine should be effective for a sufficiently large percentage of a given population At the same time: minimize the number of epitopes contained in the vaccine (problematic for approval, quality control, pricing, ) Design of population optimized vaccines represents an interesting optimization problem not yet solved! 12 Personalized Medicine Personalized Medicine (PM) aims to deliver a tailor made therapy optimal for a specific patient Requires diagnostic tests (here: immunotyping) to classify and predict the patient s response to specific treatments Personalized vaccines must be designed dto the specific MHC allele l set present in a the patient Different patients have differing MHC allele combinations These present differing peptide repertoires Personalized vaccine 13 4

5 Optimization Problem Selecting the best epitopes for an EBV can be formulated as an optimization problem Given: A set of antigens (and their sequences) A set of alleles and their frequencies (a target population) Goal: Identify a minimal set of epitopes yielding the best immune response 14 Optimization Problem Toussaint, Dönnes, Kohlbacher, PLoS Comput. Biol., 2008, 4(12): e A Good Vaccine Definition of a good vaccine is highly controversial. Interesting properties: Overall immunogenicity Capability to induce potent immunity Mutation tolerance Mutations can lead to immune escape HIV, herpes C virus, influenza display high h genetic variability Population coverage MHC distribution differs between populations Epitope set that works for one population might not work for another Antigen coverage At different developmental stages different proteins are expressed Probability of passing antigen processing pathway 16 5

6 Immunogenicity Prediction Computational prediction of immunogenicity is a hard problem Immunogenicity depends on host immune system, in particular on HLA types present in T cell repertoire Immunogenicity ygoverned by negative T cell selection (central tolerance) Previous work mainly focused on antigen processing as crude assumption Often MHC binding affinity is taken as value for immunogenicity 17 Evolutionary Algorithm Vider Shalit et al. suggested a genetic algorithm to produce an optimal polypeptide Scoring function aims at high antigen coverage, MHC allele coverage, allele wise antigen coverage Consider only peptides that are highly conserved, likely to result from antigen processing Use MHC binding affinity instead of immunogenicity Vider-Shalit, Raffaeli, Louzoun. Mol. Immunol., 2007, 44: Evolutionary Algorithm Results 19 6

7 Evolutionary Algorithm Results 20 Linear Programming Many optimization problems can be formulated as linear programming (LP) problems Linear programming problems are optimization problems with linear objective function and linear inequalities as constraints They can thus be written in the form maximize c T x subject to Ax b Another common notation for this is z = max{ c T x : Ax b, x i 0} Lee et al., Brief. Bioinformatics (2006), 7: Linear Programming The inequalities define the polytope of feasible solutions to the problem (if there exists a solution!) Assume a simple example: max Z = 15 x x 2 subject to 0 x x 2 3 x 1 + x

8 Linear Programming Two different values of the objective function correspond to parallel lines (linear objective function!) 23 Linear Programming Finding the maximum corresponds to finding the maximum value of this objective function that still lies within the feasible region 24 Algorithms The best known algorithm for solving LP problems is the simplex algorithm introduced by George Dantzig in 1947 The simplex algorithm is quite involved in detail, so we will only discuss the basic ideas: Start at some vertex of the polytope defined by the LP constraints Move along these facets to an adjacent vertex Move only to vertices with better or equal value of the objective function Terminate if no such vertex can be found G.B. Dantzig. Linear Programming and Extensions. Princeton, NJ: Princeton University Press,

9 Simplex Algorithm Example Start at the origin, which is always a feasible vertex 26 Simplex Algorithm Example Move to the next vertex (2, 0), Z has increased to Simplex Algorithm Example The next vertex improves Z again to

10 Simplex Algorithm Example The next vertex would be (1,3), but here Z would be 45 only, so we do not accept that and abort the search. 29 Simplex Algorithm Example If we had moved along x 2 constraints as a first step, we would have taken a different route. 30 Simplex Algorithm Example gotten to (1,3) with a Z of

11 Simplex Algorithm Example and ended up in the same maximum as through the other way. 32 Integer Linear Programs A special type of optimization problem: LPs with unknowns that are integers Assume a simple example: max Z = 15 x x 2 with x 1 : racing bikes, x 2 : mountain bikes Maximize the profit Z given the profits per bike (15, 10) and constraints on the number of bikes one can produce in a given time Since fractional bikes cannot be produced, feasible solutions of x 1 and x 2 are integers 33 Complexity While the simplex algorithm usually performs well in practice, it has worst case exponential run time It could be shown, however, that LP problems can be solved in polynomial time Unfortunately, this is not true for integer linear programs, which have been shown to be NP hard in the general case For real life problems one usually employs libraries of (I)LP solvers, that are freely or commercially available, as the correct and efficient implementation of these algorithms is very difficult CPLEX (by ILOG Inc.) GNU Linear Programming Kit (GLPK) SCIP (by Zuse Institute Berlin) Mathematica (Wolfram Research) 34 11

12 ILP based Vaccine Optimization Rewrite epitope selection problem as ILP Maximize overall immunogenicity for the target population Key assumptions: Immunogenicities are additive, across alleles & across epitopes Probability directly affects allele s contribution to overall immunogenicity Constraints Maximum number of peptides/epitopes Cover a large number of alleles Cover a large number of antigens Advantage: finds an optimal solution no heuristic! 35 Overall Immunogenicity Key assumptions: Immunogenicities are additive, across alleles & across epitopes Probability directly affects allele s contribution to overall immunogenicity with epitopes e from the set of epitopes E alleles a from the set of alleles A allele probabilities p a immunogenicity i e,a of epitope e for allele a 36 ILP Formulation Objective function with E: candidate epitopes, A: MHC alleles, p a : MHC allele probabilities, i e,a : immunogenicities, x e : binary decision variables Binary decision variables, if epitope e belongs to optimal solution, otherwise Toussaint, Dönnes, Kohlbacher, PLoS Comput. Biol., 2008, 4(12): e

13 ILP Formulation Constraint: allow a maximum number of epitopes only Max. number of epitopes k to select Toussaint, Dönnes, Kohlbacher, PLoS Comput. Biol., 2008, 4(12): e ILP Formulation Constraint: cover a minimum number of alleles y a = 1 if allele is covered by the optimal set; I a : set of epitopes which, when bound to MHC allele a, display immunogenicity threshold MHC allele coverage; MHC : Minimum number of alleles to be covered Toussaint, Dönnes, Kohlbacher, PLoS Comput. Biol., 2008, 4(12): e ILP Formulation Constraint: cover a minimum number of alleles Toussaint, Dönnes, Kohlbacher, PLoS Comput. Biol., 2008, 4(12): e

14 ILP Formulation Constraint: cover a minimum number of antigens E i : Set of epitopes from the i-th antigen Toussaint, Dönnes, Kohlbacher, PLoS Comput. Biol., 2008, 4(12): e Results Overall immunogenicity of a set of 10 epitopes Optimal solution yields significantly better overall immunogenicity for the same number of epitopes Number of epitopes required to achieve a given overall immunogenicity (of 2,700) Optimal solution requires a significantly smaller number of epitopes to reach the same level of immunogenicity Toussaint, Dönnes, Kohlbacher, PLoS Comput. Biol., 2008, 4(12): e Results Comparison with evolutionary algorithm of Vider Shalit et al. Toussaint, Dönnes, Kohlbacher, PLoS Comput. Biol., 2008, 4(12): e Vider-Shalit, Raffaeli, Louzoun. Mol. Immunol., 2007, 44:

15 OptiTope Web Server 44 OptiTope Web Server 45 OptiTope Web Server 46 15

16 OptiTope Web Server 47 OptiTope Web Server 48 OptiTope Web Server 49 16

17 Summary Epitope selection is a key step in the design of epitope based vaccines Key goals are Broad population coverage Antigen coverage Good overall immunogenicity A minimal number of epitopes The problem can be addressed with evolutionary algorithms or (optimally) using combinatorial optimization (ILP) 50 References Original Papers Vider Shalit T, Raffaeli S, Louzoun Y. Virus epitope vaccine design: informatic matching the HLA I polymorphism to the virus genome. Mol Immunol 44: Toussaint NC, Dönnes P, Kohlbacher O. A Mathematical Framework for the Selection of an Optimal Set of Peptides for Epitope Based Vaccines. PLoS Comput Biol, 2008, 4(12): e doi: /journal.pcbi Toussaint, NC, and Kohlbacher, O (2009). OptiTope A Web Server for the Selection of an Optimal Set of Peptides for Epitope based Vaccines. Nucl Acids Res (in print). doi: /nar/gkp293 Links Optitope: