Fig. 2. A time-delay model explains the relative dynamics of surface area and volume synthesis in batch cultures.
a A conceptual model for SA/V regulation. The synthesis rates of both surface area and volume scale with current cell volume (Eq. 1, 2), predicting that the time derivative of SA/V depends on α, β, and the current SA/V (Eq. 3). Steady state SA/V is therefore dictated by the ratio between β and α (Eq. 4). Using previous experimental steady-state SA/V measurements, β can be parameterized as a function of α in steady state (Eq. 5). b Given that changes in growth rate (α) are accompanied by shifts in proteome composition, our model assumes that the shift is more heavily weighted toward cytoplasmic components than surface area components, thereby causing a delayed change in β, which can be approximated by introducing a constant time delay in the function relating β to α (Eq. 6). c From the single-cell data in Fig. 1d, the experimentally measured β exhibited a delay of ~10 min compared to the steady-state β determined by Eq. 5 (i.e., f(α)). d The rate of protein abundance change from our proteome measurements (Methods) was approximated by t50, defined as the time required to reach 50% of the difference between stationary phase and log phase abundances. The t50 of proteins involved in translation was ~10 min shorter compared to proteins involved in cell wall biosynthesis. p = 10-5, one-tailed Student’s t test. Each dot is a protein (n = 61 translation genes and n = 26 cell wall genes), and bars are mean ± S.D. for each group. e Protein expression levels were measured using GFP fused to the respective promoters and normalized from 0 to 1 within their dynamic range during the time-lapse. The cytoplasmic proteins increased in expression ~10 min earlier than the cell-wall synthesis proteins. Dots represent the time points at which expression had increased by 10%. Data are mean ± standard error of mean with n > 100 cells. f Fitting our time-delay model to the experimental data in Fig. 1c with Δt = 11 min yielded an excellent fit. Data points are mean ± S.D. with n > 100 single cells. Source data are provided as a Source Data file.