Analysis of a Stochastic Model for Bacterial Growth and the Lognormality of the Cell-Size Distribution

Abstract

This paper theoretically analyzes a phenomenological stochastic model for bacterial growth. This model comprises cell division and the linear growth of cells, where growth rates and cell cycles are drawn from lognormal distributions. We find that the cell size is expressed as a sum of independent lognormal variables. We show numerically that the quality of the lognormal approximation greatly depends on the distributions of the growth rate and cell cycle. Furthermore, we show that actual parameters of the growth rate and cell cycle take values that give a good lognormal approximation; thus, the experimental cell-size distribution is in good agreement with a lognormal distribution.

Cell-size distribution in epithelial tissue formation and homeostasis

“…Recently, it has been observed that cell-size distributions of commonly cultured epithelia and of in vivo tissues [28,33,34] are close to a lognormal with a relatively small variability in cell size. This observation has also been reported for microbial populations [35][36][37][38]. How is this distribution preserved across generations?…”

Lognormal Behavior of the Size Distributions of Animation Characters

“…In fact, many researchers have claimed that a lognormal distribution can be confused with other probability distributions such as power-law [21], stretched exponential [22], and normal [23] distributions. Stochastic processes that yield lognormallike distributions have also been proposed [24][25][26]. Therefore, we need to analyze the character size distribution of more other animation, superhero series, and so on, in order to confirm that the lognormal distribution is really appropriate.…”

Deformation of power law in the double Pareto distribution using uniformly distributed observation time

“…Thus, f uni (x) exhibits a peak at x = S 0 when (μ * , σ * ) is on the right side of this curve. By using the limit value erfc(+∞) = 0, it can be proven using equation (13) that the curve for f ′ uni (S − 0 ) = 0 asymptotically draws the parabola μ * = σ 2 * /2 for σ * ≫ 1. When μ * = 0, f ′ uni (S − 0 ) > 0 can be exactly solved to attain σ * < π/2 ≈ 1.25.…”

“…The distribution of X n for sufficiently large n can be approximated via a lognormal distribution, owing to the central limit theorem. The process (3) has been used as a simplified model for the x-ray burst [12] and the growth of organisms [13,14]; this model was originally analyzed by Kolmogorov [15]. As equation (3) has a simple form, various additional effects have been applied.…”