Characterizing non-exponential growth and bimodal cell size distributions in fission yeast: An analytical approach

Abstract

Unlike many single-celled organisms, the growth of fission yeast cells within a cell cycle is not exponential. It is rather characterized by three distinct phases (elongation, septation, and reshaping), each with a different growth rate. Experiments also showed that the distribution of cell size in a lineage can be bimodal, unlike the unimodal distributions measured for the bacterium Escherichia coli. Here we construct a detailed stochastic model of cell size dynamics in fission yeast. The theory leads to analytic expressions for the cell size and the birth size distributions, and explains the origin of bimodality seen in experiments. In particular, our theory shows that the left peak in the bimodal distribution is associated with cells in the elongation phase, while the right peak is due to cells in the septation and reshaping phases. We show that the size control strategy, the variability in the added size during a cell cycle, and the fraction of time spent in each of the three cell growth phases have a strong bearing on the shape of the cell size distribution. Furthermore, we infer all the parameters of our model by matching the theoretical cell size and birth size distributions to those from experimental single-cell time-course data for seven different growth conditions. Our method provides a much more accurate means of determining the size control strategy (timer, adder or sizer) than the standard method based on the slope of the best linear fit between the birth and division sizes. We also show that the variability in added size and the strength of size control in fission yeast depend weakly on the temperature but strongly on the culture medium. More importantly, we find that stronger size homeostasis and larger added size variability are required for fission yeast to adapt to unfavorable environmental conditions.

Concentration fluctuations in growing and dividing cells: Insights into the emergence of concentration homeostasis

“…A similar phenomenon was also observed for fission yeast (Fig 7E and 7F). The higher-order harmonics of concentration fluctuations (second and third peaks in the spectrum) can be seen for fission yeast but not for E. this is likely due to a stronger periodicity (smaller variability) in cell cycle duration in fission yeast compared to that in E. coli [52,53]. Finally, in agreement with prediction (iii), from Fig 7D and 7H we see that for both organisms, the Hellinger distance D, which measures the distance of the concentration distribution from a gamma, is positively correlated with the non-dimensional parameter γ and the off-zero peak height H, both of which measure how strong concentration homeostasis is.…”

“…Interestingly, the condition of N � 15 holds for various cell types. Previous work estimated N to be 15 − 38 for E. coli, depending on temperature [52], 16 − 50 for fission yeast, depending on temperature and culture medium [53], 59 for the cyanobacterium S. elongatus, 21 for rat 1 fibroblasts, 27 for human B-cells, and 50 for human mammary epithelial cells [37]. In what follows, the mean-field model, rather than the full model, will be used to study the fluctuations in gene product numbers and concentrations under different rate parameters, as well as to study the conditions for accurate concentration homeostasis.…”

“…0, 1, 1, respectively. Note that in real systems, α is never much larger than 1-for fission yeast which is known to have a sizer-like mechanism, it has recently been estimated that α is 1.4 − 2.1 [53].…”

“…The first two models are simpler than the third but both of them are non-Markovian. The advantages of the third model is that (i) it can reproduce the experimentally observed Erlang distribution of cell cycle durations [37,52], (ii) it provides a convenient way to retain the Markov property which simplifies calculations, and (iii) it has a nice scaling property which naturally transforms any size control strategy into an adder [53].…”

Analytical cell size distribution: lineage-population bias and parameter inference

“…The first two questions received recent attention. For example, Jia et al proposed a method to infer single-cell parameters from size distributions, both for bacteria [2] and yeasts [3]. Also, single-lineage statistics on the number of divisions can in principle be used to estimate the population growth rate, with which the population would grow in a batch culture [4][5][6].…”