Quantitative examination of five stochastic cell-cycle and cell-size control models forEscherichia coliandBacillus subtilis

Abstract

We examine five quantitative models of the cell-cycle and cell-size control in Escherichia coli and Bacillus subtilis that have been proposed over the last decade to explain single-cell experimental data generated with high-throughput methods. After presenting the statistical properties of these models, we test their predictions against experimental data. Based on simple calculations of the defining correlations in each model, we first dismiss the stochastic Helmstetter-Cooper model and the Initiation Adder model, and show that both the Replication Double Adder and the Independent Double Adder model are more consistent with the data than the other models. We then apply a recently proposed statistical analysis method and obtain that the Independent Double Adder model is the most likely model of the cell cycle. By showing that the Replication Double Adder model is fundamentally inconsistent with size convergence by the adder principle, we conclude that the Independent Double Adder model is most consistent with the data and the biology of bacterial cell-cycle and cell-size control. Mechanistically, the Independent Adder Model is equivalent to two biological principles: (i) balanced biosynthesis of the cell-cycle proteins, and (ii) their accumulation to a respective threshold number to trigger initiation and division.

Robust replication initiation from coupled homeostatic mechanisms

“…It has been proposed that cell division control is tightly coupled to the control over replication initiation 3,16,17 , via a sizer on replication initiation and a timer for cell division. Yet, recent experiments revealed the existence of two adders, one on cell division and the other on replication initiation, and that these two processes are more loosely coupled than hitherto believed 8,[18][19][20][21][22][23] . While these phenomenological observations are vital because they constrain any model on the molecular mechanism for initiation and cell division control, no such molecular model has yet been presented that is consistent with the experimental data.…”

Robust replication initiation from coupled homeostatic mechanisms

“…While in our model cell division is tightly coupled to replication initiation, with a constant τ cc between these two events, in the other two models the coupling is more loose. The first of these two models is based on that of Si et al [8, 19], which, following [20], we call the Independent Double Adder (IDA) model. In this model, the cell division cycle is completely independent of the replication cycle.…”

Cellular resource allocation strategies for cell size and shape control in bacteria

“…Recently, a replication double adder model has been proposed [72], where cells grow by a fixed volume per replication origin between two consecutive initiation cycles, and cell divides after elongation by a constant volume per origin of replication. The replication double adder model, however, is inconsistent with the adder principle of cell size homeostasis and predicts a more sizer-like behavior [73]. With the aid of experimental data in varying growth conditions, the chromosome replication initiation and cellular division have been shown to be controlled independently in both E. coli and B. subtilis [20], pointing toward an independent double adder model [73].…”

“…The replication double adder model, however, is inconsistent with the adder principle of cell size homeostasis and predicts a more sizer-like behavior [73]. With the aid of experimental data in varying growth conditions, the chromosome replication initiation and cellular division have been shown to be controlled independently in both E. coli and B. subtilis [20], pointing toward an independent double adder model [73].…”