*Workshop**
**in** **the**
**MIDST* of
Programming Biological Time Machines

Sabanci University - Altunizade Campus, Istanbul, Turkey

Date: November 17, 2023

Suppose we have a population of bacteria and for each bacterium of a given genotype, an antibiotic alters it to another type with some probability. We ask if it is possible to apply a set of antibiotics (K in number) with a specified precedence (in N steps) so as to maximize the fraction of bacteria (with d number of distinct genotypes) becoming again the wild type. A straightforward approach would be to explicitly enumerate all the permutations with repetitions, and then compute the probability of returning to the wild type. This procedure examines a total number of KN alternatives, in each of which we need to multiply d-by-d matrices with d-vectors N many times. It has been proved that such a plan, which may be referred to as antibiotic time machine, is NP-hard to compute. While transforming the time machine problem to an empirically tractable optimization problem, we will perform hands-on experiments including reinforced random-walks on rugged fitness landscapes to demonstrate the accessibility percolation. We will also discuss how higher order epistasis alters the adaptive evolution and will evaluate the robustness of the optimized solutions. Keywords: Antibiotic resistance, genotype, bacterial population, fitness landscape, epistasis, optimization