Sequential mutations in exponentially growing populations

Area of Science:

• Evolutionary biology
• Mathematical biology
• Genetics

Background:

• Stochastic models are crucial for understanding cancer and bacterial evolution, particularly for tracking sequential mutation acquisition.
• Key questions involve determining the number of cells with specific mutations and their appearance time, especially in exponentially growing populations.
• Previous models have addressed these questions only in limited scenarios.

Purpose of the Study:

• To develop a general framework for modeling sequential mutation acquisition in evolving populations.
• To derive probability distributions for the number and arrival time of cells with n mutations under broad conditions.
• To provide a method for assessing the impact of demographic and mutational rates on mutant cell emergence.

Main Methods:

• Utilizing a multitype branching process framework to model population growth and mutation.
• Analyzing biologically relevant limiting regimes characterized by large times and small mutation rates.
• Deriving analytical probability distributions for cell counts and their appearance times.

Main Results:

• The number of cells with n mutations follows a Mittag-Leffler distribution.
• The arrival time of cells with n mutations follows a logistic distribution.
• These distributions hold true irrespective of the number of mutations (n) or their selective effects (advantageous, neutral, or deleterious).

Conclusions:

• The derived distributions offer a generalized solution for predicting mutant cell dynamics in evolving populations.
• The findings enable rapid assessment of how changes in division, death, and mutation rates influence the emergence of mutant cells.
• Results have implications for improving mutation rate inference methods, such as those used in fluctuation assays.