Protein, division time, and growth rate distributions in the slow fluctuations case.

<p>Parameter values for the simulation (<b>a</b>,<b>b</b>,<b>c</b>) are <i>k₁</i> = 1.6⋅10⁻⁵, <i>k₂</i> = 1.0, <i>γ₁</i> = 0.01, <i>γ₂</i> = 4⋅10⁻⁵ (all units in sec⁻¹), <i>T₀</i> = 2100 (sec), <i>κ</i> = 0.01 (nM) ⁻¹, <i>V₀</i> = 1.7 fl. The full curve in panel (<b>a</b>) corresponds to the Gamma distribution (8) with parameters <i>a</i> = 0.045 and <i>b = </i>96.78 fitted as described in the text. The full curves in panels (<b>b</b>) and (<b>c</b>) correspond respectively to the division time distribution, Eq. (12), and growth rate distribution, Eq. (13), evaluated with the same parameters. Parameter values for the simulation (<b>d</b>,<b>e</b>,<b>f</b>) are <i>k₁</i> = 1.6⋅10⁻⁴, <i>k₂</i> = 1.0, <i>γ₁</i> = 0.01, <i>γ₂</i> = 4⋅10⁻⁵ (all units in sec⁻¹), <i>T₀</i> = 2100 (sec), <i>κ</i> = 0.01 (nM) ⁻¹, <i>V₀</i> = 1.7 fl. The full curve in panel (<b>d</b>) corresponds again to the Gamma distribution (8) with parameters <i>a</i> = 0.5 and <i>b = </i>112.68 fitted as described in the text, and the full curves in panels (<b>e</b>) and (<b>f</b>) correspond to Eqs. (12) and (13), evaluated with these same parameters. The good agreement between direct simulations and the predictions (12) and (13) supports the validity of the slow fluctuations approximation, leading to Eq. (10). The peak on the right in the growth rate distribution corresponds to the majority of cells growing at the maximal growth rate.