Fluctuation analysis on mutation models with birth-date dependence

Area of Science:

• Mathematical Biology
• Population Genetics
• Computational Biology

Background:

• The Luria-Delbrück model provides a foundational framework for understanding spontaneous mutations in cell populations.
• Classic models often assume simplified conditions, such as independent cell division times and exponential clone growth.

Purpose of the Study:

• To generalize the Luria-Delbrück model by incorporating time-inhomogeneous cell division rates and cell deaths.
• To develop and analyze robust estimation methods for this more complex mutation model.

Main Methods:

• Mathematical modeling extending Poisson compound distributions with non-i.i.d. cell lifetimes.
• Adaptation and analysis of robust estimation techniques for consistency and asymptotic normality.
• Simulation experiments to evaluate estimation biases.

Main Results:

• The generalized model recovers previous results on mutant count distributions and classic models (Luria-Delbrück, Haldane) under specific conditions.
• Adapted estimation methods retain desirable statistical properties (consistency, asymptotic normality).
• Simulation studies quantify estimation biases when using simplified models.

Conclusions:

• The developed inhomogeneous cell division model offers a more realistic framework for studying mutation dynamics.
• Robust estimation methods are effective for the generalized model, providing reliable parameter estimates.
• Understanding model-induced biases is crucial for accurate interpretation of experimental mutation data.