Extended Data Fig. 10 | Optimal growth rate as a function of the expected
substrate abundance in an environment. a, Cells initially grow exponentially
by a factor N (ref lecting the expected carbon abundance) over time Tgrowth at
growth rate λ. When carbon runs out, the cells enter lag phase, chartacterized
by the lag time, Tlag. Cells then again grow exponentially; in the example here,
they use the fermentation product acetate at growth rate λace. b, The optimal
strategy for the cell minimizes the total time before postshift exponential
growth (resulting in the same cell number, but resuming growth the fastest
after the lag phase). The total time before postshift growth resumes is the sum
of the growth time, Tgrowth = log(N)/λ, and the lag time, given by equation ( 1 ),
Tlag = 1 /[α(λ 0 – λ)], both of which are inf luenced by the growth rate λ. The optimal
growth rate, λ, minimizes this total time, and is obtained from: λ=λ (^0) 1+αNlnαNln()()
c, For strain NCM3722, the optimal growth rate, λ*, given by this equation, is
plotted against the expected carbon abundance, given by N. The value of α was
determined from the fit in Fig. 1d to the majority of glycolytic carbon sources
(black line). For realistic carbon abundances, the range of optimal growth rates
spans precisely the relatively narrow range of growth rates on naturally
occurring carbon sources observed for the wild-type E. coli strain NCM3722
(ref.^2 ): for example, glucose, 0.95 h−1; mannitol, 0.90 h−1; maltose, 0.79 h−1;
glycerol, 0.70 h−1; galactose, 0.59 h−1; mannose, 0.49 h−1. The optimal growth
rate drops substantially below 0.5 h−1 only when the expected preshift carbon
abundance allows for less than a single doubling, N < 2, and surpasses 1.0 h−1 at
enormous, unrealistically high carbon abundances, N > 10^12 , explaining the
absence of naturally occurring carbon sources that result in such growth rates.