Competing evolutionary paths in growing populations with applications to multidrug resistance

Area of Science:

• Mathematical Biology
• Evolutionary Dynamics
• Cellular Dynamics

Background:

• Modeling the emergence of specialized cell types is crucial for understanding biological processes.
• Therapy resistance evolution is a key example, prompting questions about timing and pathways of emergence.

Purpose of the Study:

• To develop a general framework for analyzing cell type emergence in growing populations.
• To derive formulas for predicting the time and probability of reaching a target cell state.

Main Methods:

• Utilized branching processes spreading through a graph to model cell population dynamics.
• Assigned fitness values to vertices (cell states) and defined transition rates along edges (mutations/migration).
• Focused on scenarios with high root fitness and small transition rates.

Main Results:

• Derived simple formulas for the time to reach a target vertex and the probability of reaching it via a specific path.
• Demonstrated applicability to drug resistance emergence, including mutation orderings and imperfect drug penetration.

Conclusions:

• The branching process framework provides a robust method for analyzing cell type emergence.
• The derived formulas offer predictive power for understanding evolutionary trajectories in biological systems.