Theoretical values of in the original model of Ref. [4].

<p>Theoretical values of in the original model of Ref. [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0187431#pone.0187431.ref004" target="_blank">4</a>].</p

Inferred values of the transfer entropies in the directions <i>E</i> → <i>μ</i> and <i>μ</i> → <i>E</i>, and the difference for low, medium and high concentrations of IPTG based on the data of ref. [4].

<p>The TE are given in nats.</p

Transfer entropy rates and in the low IPTG experiment.

<p>(a) Original model of Ref. [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0187431#pone.0187431.ref004" target="_blank">4</a>] (b) Modified model where <i>N</i>_<i>E</i> is a white noise. The symbols are the estimates from the inference method when varying the sampling time <i>τ</i>, and the solid lines are the theoretical predictions from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0187431#pone.0187431.e050" target="_blank">Eq (13)</a> in (a) and from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0187431#pone.0187431.e215" target="_blank">Eq (60)</a> in (b). Note that diverges as <i>τ</i> goes to zero in (a) but not (b).</p

Transfer entropy <i>T</i>_{<i>Y</i>→<i>V</i>} for the feedback model governed by Eq (6) as a function of the noise intensity <i>σ</i>² for <i>k</i> = 1 (blue circles), <i>k</i> = 3 (green circles) and <i>k</i> = 5 (red circles).

<p>The parameter <i>l</i> present in the definition of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0187431#pone.0187431.e001" target="_blank">Eq (1)</a> is fixed to 1. The lower red (resp. upper blue) solid line represents the value of <i>T</i>_{<i>Y</i>→<i>V</i>} (resp. ) obtained by multiplying the theoretical rate (resp. ) given by <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0187431#pone.0187431.e119" target="_blank">Eq (21)</a> (resp. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0187431#pone.0187431.e126" target="_blank">Eq (23)</a> by the sampling time <i>τ</i> = 10⁻³. The parameters of the model are <i>T</i> = 5, <i>γ</i> = <i>m</i> = 1, <i>τ</i>_<i>r</i> = 0.1, and <i>a</i> = 8.</p

Inferred values of for the low IPTG experiment as a function of the length <i>N</i> of the time series generated by the modified model.

<p>Panels (a) and (b) correspond to sampling times <i>τ</i> = 6 min and <i>τ</i> = 1 min, respectively. is the exact asymptotic value.</p

Steady-state probability distribution of the growth rate for the three IPTG concentrations: Low (black), intermediate (red), high (blue).

<p>Steady-state probability distribution of the growth rate for the three IPTG concentrations: Low (black), intermediate (red), high (blue).</p

Pedigree tree representing the evolution of the colony of <i>E. coli</i>. studied in Ref. [4].

<p>The splitting of the branches corresponds to cell division events, each colored point is associated to a measurement of a single cell and the colors represent the growth rates as shown in the bar in the lower part of the figure.</p

Theoretical values of the transfer entropy rates and and their difference in the modified model.

<p>Theoretical values of the transfer entropy rates and and their difference in the modified model.</p

Comparison between the theoretical values of the transfer entropy rates and for the model of Ref. [4] and the values inferred from simulation data.

<p>Averages are taken over 100 times series of duration 10⁶ min, sampled every 1 min.</p

Comparison between the theoretical values of the TE rates and the information flows for the modified model and the values inferred from simulation data (all quantities are expressed in h⁻¹).

<p>The analysis was performed with a sampling <i>τ</i> = 6 min and 100 time series of 10⁶ points.</p