Patterns of interdivision time correlations reveal hidden cell cycle factors
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eLife assessment
This work makes an important contribution to the study of the cell cycle and inferring mechanisms by studying correlations in division timing between single cells. By treating the problem in a general way and computing over lineage trees, the authors can infer timescales in the underlying mechanism. This approach is able to detect a general role of circadian rhythms in cell cycle control. The method is validated on data sets from bacterial and mammalian cells and can suggest when additional measurements are needed to distinguish competing models. This paper is of broad interest to scientists in the fields of cell growth, cell division, and cellcycle control.
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 Computational and Systems Biology (eLife)
Abstract
The time taken for cells to complete a round of cell division is a stochastic process controlled, in part, by intracellular factors. These factors can be inherited across cellular generations which gives rise to, often nonintuitive, correlation patterns in cell cycle timing between cells of different family relationships on lineage trees. Here, we formulate a framework of hidden inherited factors affecting the cell cycle that unifies known cell cycle control models and reveals three distinct interdivision time correlation patterns: aperiodic, alternator, and oscillator. We use Bayesian inference with singlecell datasets of cell division in bacteria, mammalian and cancer cells, to identify the inheritance motifs that underlie these datasets. From our inference, we find that interdivision time correlation patterns do not identify a single cell cycle model but generally admit a broad posterior distribution of possible mechanisms. Despite this unidentifiability, we observe that the inferred patterns reveal interpretable inheritance dynamics and hidden rhythmicity of cell cycle factors. This reveals that cell cycle factors are commonly driven by circadian rhythms, but their period may differ in cancer. Our quantitative analysis thus reveals that correlation patterns are an emergent phenomenon that impact cell proliferation and these patterns may be altered in disease.
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Author Response
Reviewer #1 (Public Review):
This works makes an important contribution to the study of the cell cycle and the attempt to infer mechanism by studying correlations in division timing between single cells.
Given the importance of circadian rhythms to the ultimate conclusions of the study, I think it would be helpful to clarify the connection between possible oscillatory regulatory mechanisms and the formalism developed in e.g. Equation 3. The treatment appears to be a leading order expansion in stochastic fluctuations of the cell cycle regulators about the mean, but if an oscillatory process is involved, the fluctuations will be correlated in time and need not be small.
We thank the reviewer for the positive assessment of our work. We have introduced Section S7 in the Supplementary Information to address the …
Author Response
Reviewer #1 (Public Review):
This works makes an important contribution to the study of the cell cycle and the attempt to infer mechanism by studying correlations in division timing between single cells.
Given the importance of circadian rhythms to the ultimate conclusions of the study, I think it would be helpful to clarify the connection between possible oscillatory regulatory mechanisms and the formalism developed in e.g. Equation 3. The treatment appears to be a leading order expansion in stochastic fluctuations of the cell cycle regulators about the mean, but if an oscillatory process is involved, the fluctuations will be correlated in time and need not be small.
We thank the reviewer for the positive assessment of our work. We have introduced Section S7 in the Supplementary Information to address the connection between our theory and two existing models of circadian modulation of cell division. In the first model, the circadian clock drives the interdivision time, while in the second model, the clock drives cell size control. We find that, while both models satisfy the cousin inequality for comparable parameters, they differ in their interdivision time correlation patterns. The first model yields an alternatoroscillator mixed pattern, while the second gives an aperiodicoscillator pattern.
The reviewer is right that our theory presents a leadingorder expansion of cell cycle factor fluctuations. To overcome this limitation, we introduced the new Section S2 in the Supplementary Information, which shows how the correlation patterns are altered for moderately strong fluctuations. Interestingly, nonlinearity can be treated within our framework by introducing complexes of cell cycle factors. However, our model selection predicted that two cell cycle factors were enough to fit the present data without the need for complexes.
Reviewer #2 (Public Review):
This paper is of broad interest to scientists in the fields of cell growth, cell division, and cellcycle control. Its main contribution is to provide a method to restrict the space of potential cellcycle models using observed correlations in interdivision times of cells across their lineage tree. This method is validated on several data sets of bacterial and mammalian cells and is used to determine what additional measurements are required to distinguish the set of competing models consistent with a given correlation pattern.
The patterns of correlations in the division times of cells within their lineage tree contain information about the inheritable factors controlling cell cycles. In general, it is difficult to extract such information without a detailed model of cell cycle control. In this manuscript, the authors have provided a Bayesian inference framework to determine what classes of models are consistent with a given set of observations of division time correlations, and what additional observations are needed to distinguish between such models. This method is applied to data sets of division times for various types of bacterial and mammalian cells including cells known to exhibit circadian oscillations.
The manuscript is wellwritten, the analyses are thorough, and the authors have provided beautiful visualizations of how alternative models can be consistent with a finite set of observed correlations, and where and how extra measurements can distinguish between such models. Known models of growth rate correlations, cellsize regulation, and cell cycle control are analyzed within this framework in the Supplemental Information. A major advantage of the proposed method is that it provides a noninvasive framework to study the mechanism of cellcycle control.
We thank the reviewer for the positive response to our manuscript.

eLife assessment
This work makes an important contribution to the study of the cell cycle and inferring mechanisms by studying correlations in division timing between single cells. By treating the problem in a general way and computing over lineage trees, the authors can infer timescales in the underlying mechanism. This approach is able to detect a general role of circadian rhythms in cell cycle control. The method is validated on data sets from bacterial and mammalian cells and can suggest when additional measurements are needed to distinguish competing models. This paper is of broad interest to scientists in the fields of cell growth, cell division, and cellcycle control.

Reviewer #1 (Public Review):
This works makes an important contribution to the study of the cell cycle and the attempt to infer mechanism by studying correlations in division timing between single cells.
Given the importance of circadian rhythms to the ultimate conclusions of the study, I think it would be helpful to clarify the connection between possible oscillatory regulatory mechanisms and the formalism developed in e.g. Equation 3. The treatment appears to be a leading order expansion in stochastic fluctuations of the cell cycle regulators about the mean, but if an oscillatory process is involved, the fluctuations will be correlated in time and need not be small.

Reviewer #2 (Public Review):
This paper is of broad interest to scientists in the fields of cell growth, cell division, and cellcycle control. Its main contribution is to provide a method to restrict the space of potential cellcycle models using observed correlations in interdivision times of cells across their lineage tree. This method is validated on several data sets of bacterial and mammalian cells and is used to determine what additional measurements are required to distinguish the set of competing models consistent with a given correlation pattern.
The patterns of correlations in the division times of cells within their lineage tree contain information about the inheritable factors controlling cell cycles. In general, it is difficult to extract such information without a detailed model of cell cycle control. In this manuscript, …
Reviewer #2 (Public Review):
This paper is of broad interest to scientists in the fields of cell growth, cell division, and cellcycle control. Its main contribution is to provide a method to restrict the space of potential cellcycle models using observed correlations in interdivision times of cells across their lineage tree. This method is validated on several data sets of bacterial and mammalian cells and is used to determine what additional measurements are required to distinguish the set of competing models consistent with a given correlation pattern.
The patterns of correlations in the division times of cells within their lineage tree contain information about the inheritable factors controlling cell cycles. In general, it is difficult to extract such information without a detailed model of cell cycle control. In this manuscript, the authors have provided a Bayesian inference framework to determine what classes of models are consistent with a given set of observations of division time correlations, and what additional observations are needed to distinguish between such models. This method is applied to data sets of division times for various types of bacterial and mammalian cells including cells known to exhibit circadian oscillations.
The manuscript is wellwritten, the analyses are thorough, and the authors have provided beautiful visualizations of how alternative models can be consistent with a finite set of observed correlations, and where and how extra measurements can distinguish between such models. Known models of growth rate correlations, cellsize regulation, and cell cycle control are analyzed within this framework in the Supplemental Information. A major advantage of the proposed method is that it provides a noninvasive framework to study the mechanism of cellcycle control.
