Some Problems in Stochastic Dynamics and Statistical Analysis of Single-Cell Biology of Cancer

Abstract

With the development of experimental apparatus and data processing softwares, one now has easy access to cancer related data on a single cell, its genome and/or molecular compositions. At this level of description, stochasticity is a significant component of the dynamics. Statistics also emerge naturally from stochastic data. In the first part, we study the cancer cell growth data with statistics, and build stochastic models to show that there exists multiple phenotypes in seemingly homogeneous cells. In the second part, we use branching processes to explain the phenomenon that the proportions of different phenotypes of cancer cells will always converge. In the third part, we consider how to quantify the causal effect from a random variable to a response variable. We prove that in special cases quantifying causal effect is impossible. In the fourth part, we consider the lifting of stochastic processes, and prove the convergence of related thermodynamic quantities, so as to explain the origin of entropy production.