Fig. 7: Changing the oscillatory frequency modulates body volume.

a dpy-9p::gfp expression of strain with blmp-1::aid, eft-3p::tir1 at indicated auxin concentrations. Averaging of individuals was conducted as described in Fig. 6a. GFP is shown as intensity per pixel. circle, square, triangle, and cross indicate M1-M4 in the respective condition. b Same as (a), but for volume. c Mathematical model of genetic oscillator based on design II of ref. ⁴⁴. Activator A activates its own production and the production of the repressor R by a factor of ρ. R degrades A at a rate σ. β and γ are the basal production rates of A and R, respectively. µ is the growth rate. R is considered stable, such that its removal rate is set by the growth rate µ. Model parameters (β = 10/h, γ = 0.3/h, σ = 10/h, ρ = 50) are close to a saddle-node on invariant circle (SNIC) bifurcation⁴⁵ as is experimentally observed²³. Modelled dynamics of A (dotted lines) and R (solid lines) for µ = 0.12/h (blue), and for µ = 0.10/h (red). d Impact of growth rate on the removal rate of a protein. In a rapidly growing individual (blue, left), a stable protein dilutes more quickly than in a slowly growing individual. The dilution rate is equivalent to the growth rate μ in the model (c). e Oscillation frequency as a function of the growth rate (red). Missing values at slow and fast growth rates are due to bifurcation to a non-oscillating state. Black dotted line: proportionality between the growth rate and the oscillation frequency, which would ensure perfect size homeostasis. Black circle: reference growth rate at which proportional scaling is precise for the given parameters (µ = 0.11/h). Insert shows the same data but mean normalized to the reference growth rate ±20%, equivalent to the display of experimental observations shown in Figs. 4 and 6. f Same as (e), but for growth rate vs. volume fold change. The invariance of the volume fold change with respect to the growth rate is qualitatively independent on parameters over a wide range (see Supplementary Fig. 10).