11/15/2023
A stochastic first-order reaction gene translation and nuclear-to-cell ratio homeostasis model
Xuesong Bai
Department of Mathematics
Brandeis Universtiy
Cell size varies between different cell types, and between different growth and osmotic conditions. However, the nuclear-to-cell volume ratio (N/C ratio) is largely maintained. In this talk, I will first introduce an osmotic pressure balance model of N/C ratio determination, which relates the N/C ratio to protein number in the nucleus and cytoplasm. Then I will present a simplified stochastic gene translation model and its corresponding chemical master equation (CME). Next, I will show how the CME can be solved analytically to obtain a joint probability distribution of the protein numbers, and how this distribution is used to calculate the mean and variance of the N/C ratio. Finally, I will present a Taylor expansion approximation of the N/C ratio, and use this approximation to show how the system size will affect the mean and variance of the N/C ratio, and how an N/C ratio homeostasis is achieved.