Using the here presented model, we will examine how to infer the signal detection time from the amount of methylated plasmids. The cellular division rate determines how long a signal is stored in the Cellular Logbook. All units are dimensionless in this model, as its sole purpose is clarification of usage of the 'Cellular Logbook'.

Inferring the time of signal onset

Methylated bits over time

Numerous copies of identical plasmids are often present in single cells and plasmids replicate independently of the bacterial chromosome (Scott 1984). A plasmid copy number (PCN) has been determined for all plasmids in the Parts Registry, which indicates a likely amount of copies of the plasmid to be present in each cell. Unlike eukaryotes, prokaryotes do not copy DNA methylation patterns to the newly synthesized strand during DNA replication. This will lead to a dilution of the amount of ‘written’-plasmids over time, mostly due to cell replication and the ensuing binomial division of the plasmids in the parent cell among the two daughter cells.

Due to cell division, the amount of methylated plasmids will be approximately halved during each divison cycle. In this picture a lower opacity indicates a lower amount of methylated plasmids

The volatilty of this memory design seemed a downside at first, but quickly opened our eyes to a very exciting feature of this system. By analyzing the fraction:

at the time of memory read-out, the time at which the signal was registered by can be inferred.

Model definition

First, let’s model the input signal/compound which is to be reported on. Imagine the to be stationary and positioned along a fluidic stream so that the signal to be registered can pass the. Modelling the signal using the piecewise function <math>S(t)</math> now seems appropriate. Here, <math>s_{\text{on}}</math> is defined as the time at which the signal is first encountered and <math>s_{\text{off}}</math> as the time at which the signal is turned off.