How does variability in cell aging and growth rates influence the Malthus parameter?

Abstract

The aim of this study is to compare the growth speed of different cell populations measured by their Malthus parameter. We focus on both the age-structured and size-structured equations. A first population (of reference) is composed of cells all aging or growing at the same ratev. A second population (with variability) is composed of cells each aging or growing at a rate v drawn according to a non-degenerated distribution ρ with meanv. In a first part, analytical answers -based on the study of an eigenproblem -are provided for the age-structured model. In a second part, numerical answers -based on stochastic simulations -are derived for the size-structured model. It appears numerically that the population with variability proliferates more slowly than the population of reference (for experimentally plausible division rates). The decrease in the Malthus parameter we measure, around 2% for distributions ρ with realistic coefficients of variations around 15-20%, is determinant since it controls the exponential growth of the whole population.

The Effects of Stochasticity at the Single-Cell Level and Cell Size Control on the Population Growth

“…This would suggest that the growth rate may be approximated by the average of the growth rate over all leaf cells (i.e., cells growing at the time of observation), which as argued above would be biased towards favoring the smaller growth-rates. A recent study on the particular case of the sizer model led to similar conclusions ( [40]). We show here that this extends to the biologically relevant case of the adder model, and in fact, that the results are independent of the strength of size control.…”

Fluctuation relations and fitness landscapes of growing cell populations

“…This equation, together with the normalization condition of f back (y, 0) that we already noted in eq. (3.16), form an eigenproblem whose unique eigenvalue is called the Malthus parameter [7], which is indeed equal to the steady-state population growth rate. Finally, the operator acting on the left hand side of eq.…”

“…Ideally one would like be able to disentangle the various sources of stochasticity present in experimental data [5]. This would allow to understand and predict how the various sources of stochasticity affect macroscopic parameters of the cell population, such as the Malthusian population growth rate [6,7]. Beyond this specific question, research in this field attempts to elucidate the fundamental physical constraints which control growth and divisions in cell populations.…”

Bang–Bang Growth Rate Optimization in a Coupled McKendrick Model

“…In section 1, we give first results on the dynamics of (n A , n S ) solution to (4)-(5) and we show that the dynamic is time-exponential and is driven by an eigenvalue/eigenfunction. Then, in section 2, we study the optimization of this eigenvalue (to improve the growth of population) with respect to the switching probabilities (which could be a measure the ability of a population to invade (or replace) a less fitted population, i.e., with a smaller Malthusian growth rate, see [10,7,8,2,3,[11][12][13][14]. Finally, in section 4, we discuss and conclude this work.…”