Efficient computation of stochastic cell-size transient dynamics

Abstract

BackgroundHow small, fast-growing bacteria ensure tight cell-size distributions remains elusive. High-throughput measurement techniques have propelled efforts to build modeling tools that help to shed light on the relationships between cell size, growth and cycle progression. Most proposed models describe cell division as a discrete map between size at birth and size at division with stochastic fluctuations assumed. However, such models underestimate the role of cell size transient dynamics by excluding them.ResultsWe propose an efficient approach for estimation of cell size transient dynamics. Our technique approximates the transient size distribution and statistical moment dynamics of exponential growing cells following an adder strategy with arbitrary precision.ConclusionsWe approximate, up to arbitrary precision, the distribution of division times and size across time for the adder strategy in rod-shaped bacteria cells. Our approach is able to compute statistical moments like mean size and its variance from such distributions efficiently, showing close match with numerical simulations. Additionally, we observed that these distributions have periodic properties. Our approach further might shed light on the mechanisms behind gene product homeostasis.

Cell size statistics in cell lineages and population snapshots with different growth regimes and division strategies

“…gas a−1n (t, s)ds = 0 (7) We see that the first and last term in (7) cancel out. We notice that the second term is the integrand function of the a th raw moment.…”

“…Either they (i) track single lineages as observed in the mother machine [4], either (ii) they take population snapshots of descendant cells of a common ancestor, like in flow cytometry [5] experiments. Understanding the differences between these experimental viewpoints [6] has become an expanding area of research [7], [8], [9], [10].…”

Continuous Rate Modelling of bacterial stochastic size dynamics

“…Some studies have explored the particular case where h(s) = ks with k being a constant and discarding the dependence upon s [17,22]. This, resulting on:…”

“…To overcome these instabilities, other studies reparametrize the size distribution adding an additional variable: the number of divi- [22]. In this case, the probability distribution is now p(s, n; t) with transition rates satisfying:…”

“…Hence, P m,n (t) can be obtained knowing P m−1,n (t) with m ∈ 1, ..., M and P 0,n (t), can be estimated from P M,n−1 (t). Both, using, using the closed recurrence expression: As we explained before [22], this infinite set can be projected into a finite set using the known Finite State Projection (FSP) algorithm [23]. Using this approach, the number of equations in (24) are truncated up to a maximum divisions N and the number of possible division states is now finite.…”