Using conditional independence tests to elucidate causal links in cell cycle regulation in Escherichia coli

Abstract

How cells regulate their cell cycles is a central question for cell biology. Models of cell size homeostasis have been proposed for bacteria, archaea, yeast, plant, and mammalian cells. New experiments bring forth high volumes of data suitable for testing existing models of cell size regulation and proposing new mechanisms. In this paper, we use conditional independence tests in conjunction with data of cell size at key cell cycle events (birth, initiation of DNA replication, and constriction) in the model bacterium Escherichia coli to select between the competing cell cycle models. We find that in all growth conditions that we study, the division event is controlled by the onset of constriction at midcell. In slow growth, we corroborate a model where replication-related processes control the onset of constriction at midcell. In faster growth, we find that the onset of constriction is affected by additional cues beyond DNA replication. Finally, we also find evidence for the presence of additional cues triggering initiations of DNA replication apart from the conventional notion where the mother cells solely determine the initiation event in the daughter cells via an adder per origin model. The use of conditional independence tests is a different approach in the context of understanding cell cycle regulation and it can be used in future studies to further explore the causal links between cell events.

Mid-cell migration of the chromosomal terminus is coupled to origin segregation inEscherichia coli

“…S3D). These results complement recent studies on the relative timing of replication termination and the onset of cell constriction (Kar et al, 2023; Tiruvadi-Krishnan et al, 2022) and contribute to our understanding of cell cycle progression. The large size of our dataset (tens of thousands of cell cycles) also allows us to quantify the substantial variation between cells.…”

Mechanisms of Cell Size Regulation in Slow-GrowingEscherichia coliCells: Discriminating Models Beyond the Adder

“…As explained in Figure 2b, a comparison between experiment and theory requires the calibration of the model parameters. This is done by estimating the moments of s d using the estimated ρ sd (s) in (7). If ⟨.⟩ defines the averaging operator, the α-moment of the distribution of s d , written as ⟨s α d ⟩, is defined as follows, The size distribution at division sd is obtained from the division times distribution and considering the exponential growth using (7).…”

“…This is done by estimating the moments of s d using the estimated ρ sd (s) in (7). If ⟨.⟩ defines the averaging operator, the α-moment of the distribution of s d , written as ⟨s α d ⟩, is defined as follows, The size distribution at division sd is obtained from the division times distribution and considering the exponential growth using (7). (c) The comparison with the data is made using methods based on likelihood.…”

“…The adder model has one parameter (M), the degradation and power-law models have two (γ, M and λ, M respectively), and the commitment size model has three (s 0 , β and M). Taking into account all experiments, for each pair of data (s b , ∆) normalized by ⟨s b ⟩ we numerically compute the size-at-division distribution ρ sd (s|s b ) given s b using (7).…”

“…Recent measurements indicate that bacteria, such as Escherichia coli and Bacillus subtilis, regularly divide using the adder division strategy [3,4], where the size (∆) added during a division cycle (birth to division) is not correlated with the size at birth (s b ) [5,6]. The molecular mechanisms behind adder division in bacteria are complex including the coordination of several processes, such as septal ring formation, DNA replication, and cell wall synthesis [4,[7][8][9][10][11]. A recent hypothesis suggests that a single factor, the accumulation of the FtsZ protein, is the main contributor to determining the timing of division under optimal growth conditions [4].…”