A model for the regulation of the timing of cell division by the circadian clock in the cyanobacterium Synechococcus elongatus

Abstract

Cells of the cyanobacterium Synechococcus elongatus possess a circadian clock in the form of three core 9 clock proteins (the Kai proteins) whose concentrations and phosphorylation states oscillate with daily pe-10 riodicity under constant conditions [1]. The circadian clock regulates the cell cycle such that the timing of 11 cell divisions is biased towards certain times during the circadian period [2, 3, 4, 5], but the mechanism un-12 derlying how the clock regulates division timing remains unclear. Here, we propose a mechanism in which 13 a protein limiting for division accumulates at a rate proportional to cell volume growth and modulated by 14 the clock. This "modulated rates" model, in which the clock signal is integrated over time to affect division 15 timing, differs fundamentally from the previously proposed "gating" concept, in which the clock is assumed 16 to suppress divisions during a specific time window [2, 3]. We found that while both models can capture 17 the single-cell statistics of division timing in S. elongatus, only the modulated rates model robustly places 18 divisions away from darkness during changes in the environment. Moreover, within the framework of the 19 modulated rates model, existing experiments on S. elongatus are consistent with the simple mechanism that 20 division timing is regulated by the accumulation of a division limiting protein in phase with genes whose 21 activity peak at dusk. 22 2 Results 23Modeling the growth and division of S. elongatus cells 24 To construct a model to describe how the clock affects division timing, we analyzed data from Ref. [5], 25 which observed the growth and division of single cells for a wild type strain of S. elongatus and a strain 26 without the Kai B and Kai C proteins, referred to here as the clock-deletion strain. Since S. elongatus cells 27 require light to grow, they were grown and imaged under constant light (LL) or periodic cycles of light and 28 darkness (12:12 LD, i.e. 12 hours of light with a graded intensity profile, followed by 12 hours of darkness, 29 and 16:8 LD) to probe the effects of the clock on division timing under different environments. For each 30 cell, its length at birth l b and division l d and its generation time (the time between birth and division) t d 31 were measured. Before imaging, the cells were grown under 12:12 LD to entrain and synchronize the 32 activity of the clock to the environmental light conditions. The circadian phase θ corresponding to the 33 internal, subjective time of day encoded by the clock can then be assumed to be set to the environmental 34 light-dark cycle. We defined θ = 0 h to be dawn, or the beginning of the period under light. Each cell 35 can then be assigned a circadian phase at birth θ b . We analyzed the distributions of (denoted p (·)) and 36 correlations among the four stochastic variables (l b , l d , t d , θ b ), and compared these statistics of division 37 timing to those generated by our models (Fig. 1). Similar approaches have led to insights on other aspects 38 ...