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### Summer school “Economic principles in cell biology” - Paris, July 10-13, 2023

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### Exercises

** Exercise 1 (Metabolic diversity)**

In the file size_ecoli_time.dat you will find lengths of single E coli cells as a function of time measured in a Mother Machine device (original data can be freely downloaded from the SI of Tanouchi, Y., Pai, A., Park, H., Huang, S., Buchler, N. E., & You, L. (2017). Long-term growth data of Escherichia coli at a single-cell level. Scientific data, 4(1), 1-5.)

(1) Visualize the data. Parse the time traces into single cell growth curves, detecting division events and extracting division times.

(2) For each trajectory, perform an exponential fit (linearizing) and a linear fit, inferring respectively the growth rate and the elongation speed.

(3) What is a more accurate description of the growth curves: exponential or linear growth? Will one of the models model always be better than the other one? Search for literature sustaining either views.

(4) Is there a trend for these quantities (division time, growth rate, speed) in time, are they stationary?
Are they correlated? Is there a relation between the division time and the speed/growth rate?