New Approaches to in silico Design of Epitope-Based Vaccines

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58 CHAPTER 5. EPITOPE SELECTION It might be desirable to obtain several optimal or nearly optimal epitope sets. As proposed in [106], suboptimal solutions can be obtained by adding the constraints given in (5.2), where Sj represents the optimal set of epitopes found in iteration j and s represents the desired number of epitope sets. xu ≤ k − q for j = 1 . . . s − 1 (5.2) u∈Sj The ILP has to be solved iteratively s times. After each iteration, the ILP for the next iteration, j + 1, is created by adding the corresponding constraint to the ILP of iteration j. Every resulting epitope set differs from all other solutions in at least q peptides, 1 ≤ q ≤ k. 5.3.2 Non-Linear Requirements In order to incorporate a requirement into the ILP framework it must be formulated as a linear constraint. There are, however, reasonable requirements for good vaccines which are non-linear. Two examples of such requirements will be discussed below. Example 1: Population coverage. A major interest in vaccine design is population coverage: For what fraction of a target population will the resulting EV be effective? In theory this corresponds to the probability of an individual in the population carrying at least one MHC allele covered by the epitopes in the EV. Given a set of MHC alleles A as before and their distribution within a population, the population coverage of a particular set of epitopes can be computed. For this computation the polygeny of the MHC has to be taken into account. It is A = A1 ∪ . . . ∪ Am with Ai being the set of alleles at locus i. Let pℓ(a) be the probability of an allele a occurring at the corresponding MHC locus. Then, disregarding linkage disequilibrium, the probability of an individual in the population carrying an allele from the set Ai at locus i corresponds to ˜pℓ(Ai) = 1 − (1 − pℓ(a)) 2 . (5.3) Let ya be as described above. It follows that the probability of an individual carrying at least one MHC allele covered by the epitopes in E, and thus the population coverage of E given A, is m κ(E, A) = 1 − (1 − yapℓ(a)) 2 . (5.4) i=1 Example 2: Average number of active epitopes per individual. Population coverage of an epitope set states what fraction of a population carries an MHC allele associated with one of the epitopes. It does not give any information on the number of active epitopes per individual. The number of epitopes within a set which are active for a specific individual depends on the individual’s MHC genotype. Given the haploidic probabilities of MHC alleles within a population the probability of an MHC genotype can be calculated. Alleles not included in the set A are accounted for by adding a representative allele x to each locus. The frequency of the representative at locus i results from pℓ(xi) = 1− a∈Ai pℓ(a). a∈Ai a∈Ai
5.4. EXPERIMENTAL RESULTS 59 Let G be the set of genotypes within the population of interest and p(g) the probability of genotype g. Furthermore, let η(E, g) be the number of epitopes in an epitope set E which are immunogenic with respect to an MHC allele in g. The average number of active epitopes per individual in the population results from ψ(E) = p(g) η(E, g). (5.5) g∈G These non-linear requirements cannot be incorporated into the ILP directly. It is, however, possible to search a sufficiently large set of optimal and suboptimal solutions for the best set of epitopes that displays the required properties. Furthermore, for some nonlinear requirements, linear substitute requirements may be found: e.g., requiring a certain degree of population coverage is equivalent to requiring a certain degree of allele coverage. It has to be noted that, while ILPs require constraints to be linear, the non-linearity of a constraint does not necessarily imply that the corresponding optimization problem cannot be solved efficiently. The solver CPLEX [53], for example, can handle integer programs with quadratic constraints. Furthermore, heuristics can be employed to determine nearoptimal solutions to such problems. For more information on optimally solving integer non-linear programs please refer to [107, 108]. 5.4 Experimental Results In order to show the effectiveness of the proposed approach, we compare our optimal strategy (best overall immunogenicity, BOI) with two simple approaches: • randomly select k peptides out of a pool of good epitopes (random set of epitopes, RSE) and • a simple greedy approach: pick the k best epitopes from the set (best epitope-wise immunogenicity, BEI). As performance measures the theoretical gain in overall immunogenicity as well as the number of epitopes required to achieve a similar overall immunogenicity are employed. The three epitope selection strategies were used to select different-sized sets of peptides from a set of 4,461 HCV ninemers. (The data set is described in more detail in Section 7.2.) For BOI, the basic ILP 5.1 was used to maximize overall immunogenicity. BEI selects the epitopes with the highest sum of immunogenicities irrespective of the probabilities of the corresponding MHC alleles. The overall immunogenicity of each epitope set was determined and is displayed in Figure 5.2. For RSE, mean and standard deviation of 100 random selections of differentsized epitope sets from the 100 most immunogenic peptides are shown. The BEI curve shows sudden increases in overall immunogenicity from 0 to 1, 10 to 13, and from 20 to 21 epitopes. This is caused by the selection of epitopes that are highly immunogenic with respect to HLA-A*02:01, which is the most common among the considered alleles (pℓ = 0.145). All other selected epitopes are highly immunogenic with respect to less
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New Approaches to in silico Design
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Abstract Traditional trial-and-erro
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Acknowledgments First of all, I wou
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Contents 1 Introduction 1 2 Biologi
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7.3 Design of String-of-Beads Vacci
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Chapter 1 Introduction Motivation T
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prediction of T-cell epitopes is a
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systemic property but employ peptid
Page 19 and 20: Chapter 2 Biological Background In
Page 21 and 22: 2.2. CELLULAR IMMUNE RESPONSE 9 A B
Page 23 and 24: 2.2. CELLULAR IMMUNE RESPONSE 11 [3
Page 25 and 26: 2.2. CELLULAR IMMUNE RESPONSE 13 Ho
Page 27 and 28: 2.3. VACCINES 15 the immune system
Page 29 and 30: Chapter 3 Algorithmic Background In
Page 31 and 32: 3.1. COMBINATORIAL OPTIMIZATION 19
Page 33 and 34: 3.2. MACHINE LEARNING 21 Figure 3.2
Page 41 and 42: Chapter 4 Epitope Discovery After h
Page 43 and 44: 4.1. INTRODUCTION 31 Figure 4.2: Sc
Page 45 and 46: 4.2. IMPROVED KERNELS FOR MHC BINDI
Page 51 and 52: 4.3. MHC BINDING PREDICTION FOR ALL
Page 57 and 58: 4.4. T-CELL EPITOPE PREDICTION 45 T
Page 59 and 60: 4.4. T-CELL EPITOPE PREDICTION 47 i
Page 61 and 62: 4.4. T-CELL EPITOPE PREDICTION 49 F
Page 63 and 64: 4.4. T-CELL EPITOPE PREDICTION 51 t
Page 65 and 66: Chapter 5 Epitope Selection The pre
Page 67 and 68: 5.3. MATHEMATICAL ABSTRACTION 55 im
Page 69: 5.3. MATHEMATICAL ABSTRACTION 57 fo
Page 73 and 74: 5.6. IMPLEMENTATION 61 number of no
Page 75 and 76: Chapter 6 Epitope Assembly The math
Page 77 and 78: 6.2. APPROACH 65 Figure 6.2: Graph
Page 79 and 80: 6.3. INCORPORATION OF PROTEASOMAL C
Page 81 and 82: 6.4. EXPERIMENTAL RESULTS 69 Figure
Page 83 and 84: 6.5. DISCUSSION 71 epitope sets wit
Page 85 and 86: Chapter 7 Applications In the previ
Page 87 and 88: 7.1. OPTITOPE - A WEB SERVER FOR EP
Page 89 and 90: 7.2. DESIGN OF A PEPTIDE COCKTAIL V
Page 95 and 96: 7.3. DESIGN OF STRING-OF-BEADS VACC
Page 105 and 106: Chapter 8 Discussion & Conclusion P
Page 107 and 108: selection of an optimal epitope set
Page 109 and 110: Appendix A Abbreviations AA Amino a
Page 111 and 112: Appendix B Epitope Discovery Table
Page 113 and 114: Table B.3: Regression performances
Page 115 and 116: Table B.5: Overall performance of M
Page 117 and 118: Table B.7: Gene expression omnibus
Page 119 and 120: Appendix C Applications Table C.1:
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Appendix D Contributions Chapter 4
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Appendix E Publications Published M
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Bibliography [1] M. Moutschen, P. L
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BIBLIOGRAPHY 115 [19] T. Sturniolo,
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BIBLIOGRAPHY 117 [44] F. Morein and
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BIBLIOGRAPHY 119 [72] C. Widmer, N.
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BIBLIOGRAPHY 121 [97] H. Parkinson,
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BIBLIOGRAPHY 123 [123] NCBI dbMHC d
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BIBLIOGRAPHY 125 [150] World Health
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New Approaches to in silico Design of Epitope-Based Vaccines

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