Reproduction rate, feeding process, and leibich limitations in cell populations—Part 1. Feeding stochasticity and reproduction rate

Abstract

A population of cells suspended in a liquid nutrient medium is considered. The process of growth, division and death of a cell is interpreted mathematically as the Bellman-Harris stochastic process governed by random meetings between the cell and nutrient particles. Growth of a cell is considered to be a result of two processes: mass inflow into and mass outflow from the cell. It is found that, in the absence of food limitations and inhibitors, population growth is not exponential. However, the exponential increase is approached asymptotically over time. Population net growth rate is a variable rather than a constant, but tends over time to a constant value which is the rate of exponential growth. The rate of exponential growth, the probabilities of cell division and death, and the life expectancy of a cell are expressed analytically via average rate of meetings between a cell and nutrient particles. The paper presents an independent phase in calculating mathematical relations between the rate of exponential growth and the concentration of food in a substrate.