The development of reliable methods for restoring susceptibility after
antibiotic resistance arises has proven elusive. A greater understanding of the
relationship between antibiotic administration and the evolution of resistance
is key to overcoming this challenge. Here we present a data-driven mathematical
approach for developing antibiotic treatment plans that can reverse the
evolution of antibiotic resistance determinants. We have generated adaptive
landscapes for 16 genotypes of the TEM beta-lactamase that vary from the wild
type genotype TEM-1 through all combinations of four amino acid substitutions.
We determined the growth rate of each genotype when treated with each of 15
beta-lactam antibiotics. By using growth rates as a measure of fitness, we
computed the probability of each amino acid substitution in each beta-lactam
treatment using two different models named the Correlated Probability Model
(CPM) and the Equal Probability Model (EPM). We then performed an exhaustive
search through the 15 treatments for substitution paths leading from each of
the 16 genotypes back to the wild type TEM-1. We identified those treatment
paths that returned the highest probabilities of selecting for reversions of
amino acid substitutions and returning TEM to the wild type state. For the CPM
model, the optimized probabilities ranged between 0.6 and 1.0. For the EPM
model, the optimized probabilities ranged between 0.38 and 1.0. For cyclical
CPM treatment plans in which the starting and ending genotype was the wild
type, the probabilities were between 0.62 and 0.7. Overall this study shows
that there is promise for reversing the evolution of resistance through
antibiotic treatment plans.