[Paper Review] Correlations of single-cell division times with and without periodic forcing

Noga Mosheiff, Bruno M.C. Martins+8 more|arXiv (Cornell University)|Oct 1, 2017

Gene Regulatory Network AnalysisBiochemistry, Genetics and Molecular Biology43 references16 citations

TL;DR

This study uses high-throughput single-cell microscopy to analyze correlations in cell cycle durations across lineages in diverse organisms, with and without circadian clocks. It identifies that circadian coupling induces nonlinear correlations consistent with a 'fattened Arnold map' model, predicting increased cell-to-cell variability—confirmed experimentally by reduced variability upon circadian clock deletion.

ABSTRACT

Periodic forcing of nonlinear oscillators leads to a large number of dynamic behaviors. The coupling of the cell-cycle to the circadian clock provides a biological realization of such forcing. Using high throughput single-cell microscopy, we have studied the correlations between cell cycle duration in discrete lineages of several different organisms including those with known coupling to a circadian clock and those without known coupling to a circadian clock. Correlations between cell cycles duration in discrete lineages observed in the organisms with a circadian clock cannot be explained by a simple statistical model but are consistent with predictions of a biologically plausible two dimensional nonlinear map. Surprisingly, the nonlinear map is equivalent to a classic nonlinear map called the fattened Arnold map. The model predicts that circadian coupling may increase cell to cell variability in a clonal population of cells. In agreement with this prediction, deletion of the circadian clock reduces variability. Our results show that simple correlations can identify systems under periodic forcing and that studies of nonlinear coupling of biological oscillators provide insight into basic cellular processes of growth.

Motivation & Objective

• To determine whether correlations in single-cell division times across lineages reveal periodic forcing, such as from circadian clocks.
• To test whether observed correlations in cell cycle duration can be explained by a simple statistical model or require a nonlinear dynamical system.
• To evaluate the role of circadian coupling in increasing cell-to-cell variability in clonal populations.
• To develop and validate a two-dimensional nonlinear map model that captures the observed correlations in lineage data.
• To quantify the impact of circadian clock deletion on variability in cell cycle duration.

Proposed method

• High-throughput time-lapse microscopy was used to track cell cycle durations across multiple generations in diverse organisms, including E. coli, cyanobacteria, and Corynebacterium.
• Spearman correlation coefficients were computed for sister-sister (ρs-s), mother-daughter (ρm-d), and cousin-cousin (ρc-c) pairs across generations to quantify inter- and intra-lineage correlations.
• A two-dimensional nonlinear map model—specifically a 'fattened Arnold map'—was derived to describe the coupling of the cell cycle to a periodic oscillator (e.g., circadian clock).
• The model incorporates a periodic forcing term with period Tosc, a baseline cell cycle duration τ₀, and a feedback gain k, with noise ξ added to simulate biological variability.
• Simulations were performed over 1000 lineages and 50 generations to compute expected correlation features, which were then fitted to experimental data using ρs-s as the primary fitting criterion.
• Random simulations with normally distributed cell cycle times (CV matched to experiment) were used to assess statistical significance of deviations from expected correlations.

Experimental results

Research questions

• RQ1 Can correlations in single-cell division times across lineages distinguish systems under periodic forcing, such as circadian coupling?
• RQ2 Do observed correlations in cell cycle durations in organisms with circadian clocks deviate from predictions of simple statistical models?
• RQ3 Is the nonlinear dynamics of cell cycle duration in circadian-coupled organisms consistent with a two-dimensional nonlinear map model?
• RQ4 Does circadian coupling increase cell-to-cell variability in clonal populations, as predicted by the model?
• RQ5 What is the quantitative impact of circadian clock deletion on cell cycle duration variability?

Key findings

• Correlations in cell cycle duration among sister and cousin cells in organisms with circadian clocks cannot be explained by a simple statistical model, indicating nonlinear dynamics.
• The observed correlations are best explained by a two-dimensional nonlinear map equivalent to the 'fattened Arnold map', which captures periodic forcing effects.
• The model predicts that circadian coupling increases cell-to-cell variability in clonal populations, a prediction confirmed experimentally.
• Deletion of the circadian clock (e.g., in ΔkaiBC cyanobacteria) leads to a significant reduction in cell cycle duration variability, consistent with model predictions.
• The correlation coefficient ρs-s was found to be the most significant and stable feature, used as the primary fitting criterion for model parameters.
• Simulations showed that the model reproduces experimental features including ρs-s, ρm-d, ρc-c, mean cell cycle duration, CV, and noise level ξ with high fidelity.