📃Paper

📢Workshop

Summary

Overview

• Cell division symmetry problem introduced, focusing on symmetric vs. asymmetric patterns through size-structured and age-structured (ADAM) models.
• Size-structured population model characterized by cell size S, growth rate, division rate function, and division kernel κ(θ).
• ADAM model incorporates age with partial differential equations, utilizing eigenvalue problems to test for stationary density N.
• Hypothesis testing framework established: null hypothesis (H₀) assumes symmetric division, while alternative (H₁) posits asymmetry, with a significance level of α = 5%.
• Simulation results showed size-structured model convergence power at 1 using 2,000 and 5,000 iterations, with empirical levels around 5%.
• ADAM model demonstrated variable requirements for sample sizes; some cases needing only 20-50 samples to achieve power = 1.
• Real data from E. coli (Bourgeois, 2000) tested favorably with ADAM model, indicating symmetric division and rejecting the size-structured model.
• Minimax optimality results from Laura (2005) show test performance achieved without extra regularity assumptions on stationary density.
• Discussion emphasized need to discern model deficiencies from actual biological asymmetry when testing hypotheses.
• Suggestion made to utilize duality of hypothesis testing and confidence intervals for parameter estimation in future work.

Notes

Research Problem Introduction (00:00 - 01:57)

• Cell division symmetry testing problem introduced, focusing on whether cell division is symmetric (equal size daughter cells) or asymmetric (unequal size daughter cells).
• Two population models discussed: size-structured population model and age-structured (ADAM) model for analyzing cell division patterns.
• Challenge identified that cell division cannot be directly observed, only population snapshots at discrete time points can be measured.