# Growth rate oscillation in the a population of non-interacting bacteria

I have come across this theoretical paper claiming that if you start a batch culture from a single E. coli cell, the exponential growth rate of the population defined as $$k = \frac1N \frac{dN}{dt}$$ could oscillate for as long as 30 to 40 generations. In this equation, $$N$$ is the number of cells, and $$\frac{dN}{dt}$$ is the rate of change of the number of cells with time.

My question is:

Have these oscillations been ever observed? This seems like a very simple experiment. Looking for references.

Edit: As mentioned in the paper, the "oscillations are hidden to the optical density measurements which provide a proxy for the total mass of the population" and not the number of cells.

• The quoted paper on arxiv.org (The link given by the OP is behind a paywall, at least for me) – user1136 Aug 6 at 20:17

The theoretical article concerns growth rates of single cells. There are many studies that model cell cycle as a non-linear oscillator (see Tyson and Novák, 2015).

However, growth rate measurements in microbiology are usually done on cell populations consisting several cells. You generally do not observe any oscillation because:

1. Cells are not synchronized
2. There can be variations in growth rate of different cells because of noise
3. The measurement time points are much larger than the period of oscillation

Some of these reasons are already mentioned in the paper you linked (Jafarpour, 2019).

I do see some ups and downs in the growth rate in my own data; E. coli growing in LB in a 96 well plate. X-axis is the time in seconds; measurement was made every 15minutes. Y-axis denotes difference in OD between two consecutive measurements. The different colors are biological replicates. However, I cannot say that this is the kind of oscillation that Jafarpour talks about. It appears more like stochastic fluctuations in growth rate or measurement errors (they are also not damping by the end of growth).