A mechanistic stochastic framework for regulating bacterial cell division

Abstract

How exponentially growing cells maintain size homeostasis is an important fundamental problem. Recent single-cell studies in prokaryotes have uncovered the adder principle, where cells add a fixed size (volume) from birth to division, irrespective of their size at birth. To mechanistically explain the adder principle, we consider a timekeeper protein that begins to get stochastically expressed after cell birth at a rate proportional to the volume. Cell-division time is formulated as the first-passage time for protein copy numbers to hit a fixed threshold. Consistent with data, the model predicts that the noise in division timing increases with size at birth. Intriguingly, our results show that the distribution of the volume added between successive cell-division events is independent of the newborn cell size. This was dramatically seen in experimental studies, where histograms of the added volume corresponding to different newborn sizes collapsed on top of each other. The model provides further insights consistent with experimental observations: the distribution of the added volume when scaled by its mean becomes invariant of the growth rate. In summary, our simple yet elegant model explains key experimental findings and suggests a mechanism for regulating both the mean and fluctuations in cell-division timing for controlling size.

Mycobacteria Modify Their Cell Size Control under Sub-Optimal Carbon Sources

“…The molecular mechanism underlying cell size control remains an open question, but several authors have proposed a model by which a protein accumulates proportionally to cell size, and triggers division after reaching a threshold (Fantes et al, 1975; Ghusinga et al, 2016). Such a model can explain both adder and sizer principles, where degradation of the protein at cell birth leads to adder, and equal sharing leads to sizer (Deforet et al, 2015; Bertaux et al, 2016).…”

Evidence that the human cell cycle is a series of uncoupled, memoryless phases

“…Conceptually, the steps simply refer to some sequence of events in a cell cycle phase that need to be completed in order to proceed to the next phase. These events could be, for example, the sequential degradation of proteins (Coleman et al, 2015) or the stepwise accumulation of a molecular factor (Ghusinga et al, 2016;Garmendia-Torres et al, 2018) that must reach a threshold in order to complete the phase. The total amount of time needed to complete all steps in the phase has an Erlang distribution (Soltani et al, 2016).…”

Cell size control – a mechanism for maintaining fitness and function

“…On the other hand, the apparent uniformity of cell sizes (including non-dividing cells in most animal tissues), suggests that cell size homeostasis is important and should thus be actively maintained [16]. The main limitation of the adder model is that it cannot easily explain why larger cells would add less (in relative terms) and smaller cells add more volume (again in relative terms) during the cell cycle [17]. To achieve constant volume addition, abnormally small and large cells would require a cell size or growth rate sensing mechanism that is somehow linked to cell cycle machinery to maintain size uniformity [16].…”

“…The adder model favours a passive mechanism for the maintenance of cell size and size distribution within the cell population. The main limitation of the adder model is that it cannot easily explain why larger cells would add less (in relative terms) and smaller cells add more volume (again in relative terms) during the cell cycle [17]. The main limitation of the adder model is that it cannot easily explain why larger cells would add less (in relative terms) and smaller cells add more volume (again in relative terms) during the cell cycle [17].…”