# Convection shapes the trade-off between antibiotic efficacy and the selection for resistance in spatial gradients

## TL;DR

This study models how convection and spatial drug gradients influence the balance between killing pathogens and promoting resistance, revealing convection's significant impact on mutation establishment and treatment efficiency.

## Contribution

It introduces a stochastic model incorporating convection in spatial drug gradients, elucidating its role in resistance evolution and treatment outcomes.

## Key findings

- Convection increases the probability of resistance mutations establishing.
- Shallow gradients combined with convection promote wild-type cell death.
- The spatial scale of gradients and dispersal influences resistance dynamics.

## Abstract

Since penicillin was discovered about 90 years ago, we have become used to using drugs to eradicate unwanted pathogenic cells. However, using drugs to kill bacteria, viruses or cancer cells has the serious side effect of selecting for mutant types that survive the drug attack. A key question therefore is how one could eradicate as many cells as possible for a given acceptable risk of drug resistance evolution. We address this general question in a model of drug resistance evolution in spatial drug gradients, which recent experiments and theories have suggested as key drivers of drug resistance. Importantly, our model takes into account the influence of convection, resulting for instance from blood flow. Using stochastic simulations, we study the fates of individual resistance mutations and quantify the trade-off between the killing of wild-type cells and the rise of resistance mutations: shallow gradients and convection into the antibiotic region promote wild-type death, at the cost of increasing the establishment probability of resistance mutations. We can explain these observed trends by modeling the adaptation process as a branching random walk. Our analysis reveals that the trade-off between death and adaptation depends on the relative length scales of the spatial drug gradient and random dispersal, and the strength of convection. Our results show that convection can have a momentous effect on the rate of establishment of new mutations, and may heavily impact the efficiency of antibiotic treatment.