Model parameters for different species in their corresponding reference growth media.

A schematic of the osmoresponse model.

(A) The total cytoplasmic volume includes the free and bound volumes. The free volume sets the internal osmotic pressure Πin = kBTNa/Vf, where Vf is the free volume and Na is the number of osmolyte molecules. The bound volume Vb comprises the dry mass Vbd and bound water Vbw, all proportional to the total protein mass. (B) We model osmoregulation through the change of ribosome translation strategy. When the protein density increases, the fraction of ribosomes translating the osmolyte-producing protein χa is up-regulated, leading to the subsequent increase in the mass fraction of the osmolyte-producing protein ϕa. (C) The cellwall synthesis process is controlled by the turgor pressure σ, which is proportional to the cell-wall strain ϵ = (V −Vcw)/Vcw. Here, V is the cytoplasmic volume, and Vcw is the relaxed cell wall volume.

Steady-state properties under a constant external osmolarity.

(A) Normalized growth rate vs. normalized internal osmotic pressure of different species under various culture media. The experiment data (scatter markers) are fitted by our theoretical prediction Eq. (10b). The data of E. coli are from [19, 21, 22], the data of B. subtilis is from [23], and the data of S. cerevisiae is from our own experiments. (B) Growth curves of WT cells, mutant cells without osmoregulation (Ha = 0), and mutant cells without cell-wall synthesis regulation (Hcw = 0). The dotted line indicates the region where plasmolysis occurs for the mutant cells with Hcw = 0. (C) Mutant cells without cell-wall synthesis regulation cannot maintain a stable turgor pressure in a hypertonic environment, while WT cells can maintain a constant turgor pressure. The mutant cells reach plasmolysis at a threshold of external osmolarity. In (B) and (C), the parameters for WT cells are chosen as the values for S. pombe, and the mutant values are set such that they have the same growth rate as the WT cells in the reference medium (Table S2).

Transient dynamics after a constant osmotic shock.

(A) Numerical simulations of cells undergoing a constant 500 mM hyperosmotic shock. The dotted lines represent the steady-state values for the reference growth medium (green) and the medium after perturbation (yellow). (B) Numerical simulations of cells undergoing a constant 500 mM hypoosmotic shock. The purple circle in the third panel marks the growth rate peak during the supergrowth phase. (C) The dynamics of the internal state of a cell characterized by . The dotted curve represents the constraint on the steady-state solution , and the solid trajectory is from numerical simulations. The triangles indicate the steady-state solution before the perturbation and the steady-state solution after the perturbation for a long enough time. The yellow open circle represents the immediate steady-state solution after applying the hyperosmotic shock. (D) The same analysis as (C) but for a constant 500 mM hypoosmotic shock. (E) The growth rate peak in the supergrowth phase (yellow) and the immediate value of turgor pressure after the hypoosmotic shock σf (green) vs. the amplitude of the hypoosmotic shock.

Comparison between theories and experiments.

(A) Numerical simulations of WT S. pombe undergoes 24 cycles of 500 mM osmotic oscillations with a 10-minute period. We show a 30-minute window average in the third panel of growth rate. (B-D) Quantitative agreement between simulations and experiments for the growth rate peak µsg vs. different oscillation parameters, including (B) amplitude, (C) period length, and (D) number of periods. The red lines in (B, C) are predictions, and the blue line in (D) is fitting from which we infer the values of Hcw and . Green dots with error bars are experimental data from Ref. [27]. (E) In the case of osmotic oscillation with a single period, the hyperosmotic period persists for 120 min before reverting to the reference medium. The vertical dotted blue line represents the minimal amplitude to induce cytoplasm jamming during the hyperosmotic period. The excess turgor pressure σf − σc upon exiting the hyperosmotic period is approximately equal to the recovered turgor pressure δσ during the hyperosmotic period. (F) The growth rate peak µsg at different Hr vs. the amplitude of a single oscillation. Hr = 3.031 is the value of the WT S. pombe. Parameters of WT S. pombe are used in this figure unless otherwise mentioned (Table 1).