### Abstracto

# The Kishony Mega-Plate Experiment, a Markov Process

Alan KleinmanA correct understanding of the DNA evolution of drug resistance is critical in developing strategies for suppressing and preventing this process. The Kishony Mega-Plate Experiment demonstrates this important phenomenon that occurs in the practice of medicine, that of the evolution of drug-resistance. The evolutionary process which the bacteria in this experiment are doing is called a Markov Process or Markov

Chain. Understanding this process enables clinicians and researchers to predict the evolution of drugresistance and develop strategies to prevent this process. This paper will show how to apply the Markov Chain model of DNA evolution to the Kishony Mega-Plate Experiment and why the experiment behaves the way it does by contrasting the Jukes-Cantor model of DNA evolution (a stationary model) with a

modification of the Jukes-Cantor model that makes it a non-stationary, non-equilibrium Markov Chain. The numerical behaviors of the stationary and non-stationary models are compared. What this analysis shows is that DNA evolution is a non-stationary, non-equilibrium process and that by using the correct nonstationary, non-equilibrium model that one can simulate and predict the behavior of real evolutionary examples and that these analytical tools can give the clinician guidance on how to use antimicrobial selection pressures for treating infectious diseases. This in turn can help reduce the numbers and costs of hospitalization for sepsis, pneumonia and other infectious diseases.