Competing evolutionary paths in growing populations with applications to multidrug resistance

TL;DR

This paper models the emergence of resistant cell types in growing populations using branching processes on graphs, providing formulas for timing and pathways of resistance development relevant to drug resistance scenarios.

Contribution

It introduces a general framework for analyzing the emergence of resistant cell types in growing populations via branching processes on graphs, with explicit formulas for timing and pathways.

Findings

Derived formulas for time to reach target cell type.

Calculated probabilities of specific evolutionary paths.

Applied models to drug resistance scenarios in bacteria and cancer.

Abstract

Investigating the emergence of a particular cell type is a recurring theme in models of growing cellular populations. The evolution of resistance to therapy is a classic example. Common questions are: when does the cell type first occur, and via which sequence of steps is it most likely to emerge? For growing populations, these questions can be formulated in a general framework of branching processes spreading through a graph from a root to a target vertex. Cells have a particular fitness value on each vertex and can transition along edges at specific rates. Vertices represents cell states, say \mic{genotypes }or physical locations, while possible transitions are acquiring a mutation or cell migration. We focus on the setting where cells at the root vertex have the highest fitness and transition rates are small. Simple formulas are derived for the time to reach the target vertex and for the probability that it is reached along a given path in the graph. We demonstrate our results on \mic{several scenarios relevant to the emergence of drug resistance}, including: the orderings of resistance-conferring mutations in bacteria and the impact of imperfect drug penetration in cancer.