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Peptide Vaccine Design by Evolutionary Multi-Objective Optimization

Dan-Xuan Liu, Yi-Heng Xu, Chao Qian

TL;DR

This work tackles the challenge of designing peptide vaccines that remain effective across diverse human MHC genotypes by selecting a compact, diverse peptide subset. It introduces PVD-EMO, an evolutionary multi-objective optimization framework that reframes the task as a bi-objective problem and solves it with MOEAs like GSEMO and NSGA-II, enhanced by warm-start and repair strategies and accelerated objective evaluation. Theoretical analysis shows the method retains the same worst-case approximation guarantees as the state-of-the-art greedy approach, while empirical results on a COVID-19 design demonstrate superior performance and robustness to local optima. The contribution provides a flexible, scalable approach to population-wide peptide vaccine design with practical implications for rapid vaccine development against emerging pathogens.

Abstract

Peptide vaccines are growing in significance for fighting diverse diseases. Machine learning has improved the identification of peptides that can trigger immune responses, and the main challenge of peptide vaccine design now lies in selecting an effective subset of peptides due to the allelic diversity among individuals. Previous works mainly formulated this task as a constrained optimization problem, aiming to maximize the expected number of peptide-Major Histocompatibility Complex (peptide-MHC) bindings across a broad range of populations by selecting a subset of diverse peptides with limited size; and employed a greedy algorithm, whose performance, however, may be limited due to the greedy nature. In this paper, we propose a new framework PVD-EMO based on Evolutionary Multi-objective Optimization, which reformulates Peptide Vaccine Design as a bi-objective optimization problem that maximizes the expected number of peptide-MHC bindings and minimizes the number of selected peptides simultaneously, and employs a Multi-Objective Evolutionary Algorithm (MOEA) to solve it. We also incorporate warm-start and repair strategies into MOEAs to improve efficiency and performance. We prove that the warm-start strategy ensures that PVD-EMO maintains the same worst-case approximation guarantee as the previous greedy algorithm, and meanwhile, the EMO framework can help avoid local optima. Experiments on a peptide vaccine design for COVID-19, caused by the SARS-CoV-2 virus, demonstrate the superiority of PVD-EMO.

Peptide Vaccine Design by Evolutionary Multi-Objective Optimization

TL;DR

This work tackles the challenge of designing peptide vaccines that remain effective across diverse human MHC genotypes by selecting a compact, diverse peptide subset. It introduces PVD-EMO, an evolutionary multi-objective optimization framework that reframes the task as a bi-objective problem and solves it with MOEAs like GSEMO and NSGA-II, enhanced by warm-start and repair strategies and accelerated objective evaluation. Theoretical analysis shows the method retains the same worst-case approximation guarantees as the state-of-the-art greedy approach, while empirical results on a COVID-19 design demonstrate superior performance and robustness to local optima. The contribution provides a flexible, scalable approach to population-wide peptide vaccine design with practical implications for rapid vaccine development against emerging pathogens.

Abstract

Peptide vaccines are growing in significance for fighting diverse diseases. Machine learning has improved the identification of peptides that can trigger immune responses, and the main challenge of peptide vaccine design now lies in selecting an effective subset of peptides due to the allelic diversity among individuals. Previous works mainly formulated this task as a constrained optimization problem, aiming to maximize the expected number of peptide-Major Histocompatibility Complex (peptide-MHC) bindings across a broad range of populations by selecting a subset of diverse peptides with limited size; and employed a greedy algorithm, whose performance, however, may be limited due to the greedy nature. In this paper, we propose a new framework PVD-EMO based on Evolutionary Multi-objective Optimization, which reformulates Peptide Vaccine Design as a bi-objective optimization problem that maximizes the expected number of peptide-MHC bindings and minimizes the number of selected peptides simultaneously, and employs a Multi-Objective Evolutionary Algorithm (MOEA) to solve it. We also incorporate warm-start and repair strategies into MOEAs to improve efficiency and performance. We prove that the warm-start strategy ensures that PVD-EMO maintains the same worst-case approximation guarantee as the previous greedy algorithm, and meanwhile, the EMO framework can help avoid local optima. Experiments on a peptide vaccine design for COVID-19, caused by the SARS-CoV-2 virus, demonstrate the superiority of PVD-EMO.
Paper Structure (12 sections, 2 theorems, 9 equations, 3 figures, 4 algorithms)

This paper contains 12 sections, 2 theorems, 9 equations, 3 figures, 4 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Our Contribution
  4. Peptide Vaccine Design
  5. Previous Algorithm
  6. PVD-EMO Framework
  7. PVD-GSEMO-WR Algorithm
  8. PVD-NSGA-II-WR Algorithm
  9. Acceleration of Objective Evaluation
  10. Theoretical Analysis
  11. Empirical Study
  12. Conclusion

Key Result

Theorem 1

For peptide vaccine design in Definition def-problem, PVD-GSEMO-WR, or PVD-NSGA-II-WR with a population size of at least $4(k+1)$, can achieve the same approximation guarantee as the previous greedy algorithm Optivax-P.

Figures (3)

  • Figure 1: The similarity graph $G=(V,E)$ of an example of peptide vaccine design, where the vertices correspond to the peptides, and edges exist between the peptides that are deemed similar.
  • Figure 2: The average objective value of each algorithm minus the objective value of Optivax-P (the larger, the better).
  • Figure 3: The average objective value $\pm$ the standard deviation vs. runtime (i.e., number of objective evaluations) with $k=40$.

Theorems & Definitions (6)

  • Definition 1: Peptide Vaccine Design
  • Definition 2: Domination
  • Theorem 1
  • Definition 3: An Example of Peptide Vaccine Design
  • Theorem 2
  • proof