PMC

Single-cell responses of WT, NLS 4A, NLS 4E, and NES 2A to glucose limitation (A), osmotic stress (B), and oxidative stress (C) (n: ~50 cells, each stress condition). Representative single-cell time traces of Msn2 nuclear translocation are shown. Asterisks emphasize the conditions under which the mutants fail to distinguish two different stresses. Quantification of the time traces is presented in . (D) Time traces of WT Msn2-mCherry and mutant Msn2-YFP, monitored in the same cells, in response to glucose limitation (black – WT, blue – NLS 4A, green – NLS 4E, red – NES 2A). More single-cell traces are shown in .

(A) Averaged single-cell time traces of Msn2 nuclear translocation in response to sustained inputs with low (0.2 μM 1-NM-PP1, solid triangles) or high (3 μM 1-NM-PP1, solid circles) amplitudes. Inputs were applied at time point zero. (B) Averaged single-cell time traces of Msn2 nuclear translocation in response to removal of high-amplitude input (3 μM 1-NM-PP1). (C) Averaged single-cell time traces of Msn2 nuclear translocation in response to oscillatory high-amplitude (3 μM 1-NM-PP1) inputs. Pulse duration – 3 min; pulse interval – 4 min. (D) Time traces of Msn2 nuclear translocation in response to oscillatory inputs with a mixture of low (0.2 μM 1-NM-PP1) and high (3 μM 1-NM-PP1) amplitude pulses. (E) Time traces of Msn2 nuclear translocation in response to input fluctuating between high (3 μM 1-NM-PP1) and low (0.2 μM 1-NM-PP1) amplitudes. For (A)–(E), data points are average single-cell time traces (n: ~50 cells; error bar: single-cell variances). The simple model in has been fit to the time trace data in this figure and the solid lines in (A)–(E) are model fitting results (see - “Model parameters are constrained by experimental data” for details). The dependence of the responses on the timescales of input and transport rates is presented in - “The relationship between timescales of input and timescales of transport rates”.

(A) Illustration of the distinct single cell dynamic responses of Msn2 to various stresses. (B) Steady state abundance of Msn2 in the nucleus in response to various concentrations of 1-NM-PP1. In response to each concentration of 1-NM-PP1, Msn2 exhibited uniform and stable nuclear localization in single cells and did not exhibit stochastic fluctuations as observed in natural stress responses. Open circles: responses to different concentrations of 1-NM-PP1; closed circles: responses to 3 μM and 0.2 μM 1-NM-PP1, which are used as high and low amplitude inputs, respectively, for the following analysis. AU – arbitrary unit. (C) Averaged single-cell time traces of Msn2 nuclear translocation (Lower panels: n: ~50 cells; error bar: single-cell variances) in response to oscillatory inputs with high and low amplitudes (Upper panels). Left: high-amplitude input produced by 3 μM 1-NM-PP1; right: low amplitude input produced by 0.2 μM 1-NM-PP1. Pulse duration - 3 min; pulse interval - 2 min. To emphasize the fact that 3 μM 1-NM-PP1 elicits a steady state response that is approximately twice the response elicited by 0.2 μM 1-NM-PP1, the y-axes of the upper panels are not presented on a linear scale.

(A) Nomenclature used to define the status of phosphorylation and localization of the TF: the 1^st “P/U” - the NES is phosphorylated (P) or unphosphorylated (U); the 2^nd “P/U” - the NLS is phosphorylated (P) or unphosphorylated (U); “c/n” - in the cytoplasm (c) or nucleus (n). (B) Phosphorylation states determine the rate constants of nucleocytoplasmic transport. Unphosphorylated (U) or phosphorylated (P) NES has slow (dashed line) or fast (solid line) nuclear export rates (k_out, k_out′), respectively; unphosphorylated (U) or phosphorylated (P) NLS has fast (solid line) or slow (dashed line) nuclear import rates (k_in′, k_in), respectively. Thus, each phosphoform has a specific combination of nuclear import and export rates. (C) Schematic of the translocation model. Left: schematic of WT and phosphosite mutants; right: model structures and reaction flows (grey arrows) in response to strong or weak inputs and input removal. 1^st row: WT; 2^nd row: NLS 4A - S582A, S620A, S625A, S633A; 3^rd row: NLS 4E – S582E, S620E, S625E, S633E; 4^th row: NES 2A – S288A, S304A. We did not specifically study the case in which the NES sites are constitutively phosphorylated because Ser-to-Glu mutants of the NES sites behaved similarly to Ser-to-Ala mutants, suggesting that Glu cannot mimic phosphorylation on NES sites (). (D) Predicted responses to various dynamic inputs: 1^st column: oscillatory high-amplitude input; 2^nd column: oscillatory input with varied amplitudes; 3^rd column: input fluctuating between high and low amplitudes. Black: responses of WT; blue: NLS 4A; green: NLS 4E; red: NES 2A. The ranges of input timescales necessary to generate the predicted responses are determined by the fast and slow timescales of transport rates and are listed above each column. Model output was generated by a steady-state analysis of the translocation system ().