Modeling and analysis of protein design under resource constraints

The potency, or fitness, of a protein-based drug can be enhanced by changing the sequence of its underlying protein. We present a novel stochastic model for the sequence-fitness relation, and estimate its four parameters from industrial data. Using this model, we formulate and analyze two variants of the protein design problem. In the single-period design problem, the designer needs to decide under capacity constraints which set of sequences to screen in order to maximize the expected fitness of the best sequence in the set. In the more general two-period design problem, the designer can afford two screening rounds and needs to allocate resources optimally across the two periods to maximize the same objective function. Analytical and simulation results allow us to assess the utility of the proposed design strategies for various parameter regimes.