Abstract
The global regulation of cell growth rate on gene expression perturbs the performance of gene networks, which would impose complex variations on the cell-fate decision landscape. Here we use a simple synthetic circuit of mutual repression that allows a bistable landscape to examine how such global regulation would affect the stability of phenotypic landscape and the accompanying dynamics of cell-fate determination. We show that the landscape experiences a growth-rate-induced bifurcation between monostability and bistability. Theoretical and experimental analyses reveal that this bifurcating deformation of landscape arises from the unbalanced response of gene expression to growth variations. The path of growth transition across the bifurcation would reshape cell-fate decisions. These results demonstrate the importance of growth regulation on cell-fate determination processes, regardless of specific molecular signaling or regulation.
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Data availability
Major experimental data supporting the findings of this study are available within the main text and Supplementary Information. Sequencing data have been deposited to the NCBI BioProject with the accession code PRJNA835246. Flow cytometry data is available at Flow Repository (FR-FCM-Z62C, FR-FCM-Z62E, FR-FCM-Z62F, FR-FCM-Z62H, FR-FCM-Z62G). Source data are provided with this paper.
Code availability
Custom-made simulation code is available via GitHub at https://github.com/Fulab-SIAT/cell_fate_2022.Scripts for sequencing are reposited in GitHub (https://github.com/MinTTT/RNA_seq_pip).
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Acknowledgements
This work is supported by the National Key R&D Program of China (grant 2018YFA0903400 to X.F.), the National Natural Science Foundation of China (grants 32071417 and 32261160377 to X.F.), the Strategic Priority Research Program of the Chinese Academy of Sciences (grant XDB0480000 to X.F.), the Guangdong Basic and Applied Basic Research Foundation (grant 2021A1515110863 to J.Z.). We thank Prof. Chenli Liu (Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences) for sharing E. coli strain, X. Li, Y. Bai, S. Huang, C. Lou, F. Jin, C. Liu, C. He and Z. Ma for discussions, comments and technical support.
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X.F. conceived the project. J.Z., P.C. and X.F. designed the experiments. J.Z. and P.C. performed all the experiments, the numerical simulations and the mathematical analysis, with the contributions from X.F. All the authors analyzed the results and wrote and revised the paper.
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Extended data
Extended Data Fig. 1 Schematic illustration of the design of the mutual repressive circuit and demonstration of bistability.
(a) This circuit consists of reciprocal transcriptional repression by TetR and LacI. mCherry and GFP serve as reporters for TetR high state and LacI high state, respectively. The addition of cTc relieves TetR repression, allowing for high expression of LacI and GFP, whereas induction with IPTG relieves the LacI repression, allowing for high expression of TetR and mCherry. (b-c) Temporal histograms of cell states under exponential growth in RDM glucose medium following prolonged culture via successive dilution to demonstrate the irreversibility of cellular states. Owing to the fluctuations in gene expression, a small population (~ 10%) of post-inducted red state cells (that is, low GFP state) was observed to spontaneously switch to the green state (that is, high GFP state) within 20 generations (as indicated in panel d). (e, f) Hysteresis experiments were carried out by measuring the dose-response curves in varying cTc concentrations under fast and slow growth conditions (see Methods). Red and green symbols represent initial red state cells and initial green state ones, respectively. (e) A large range of hysteresis was revealed in RDM glucose medium. The bifurcation diagram calculated from the deterministic model in varying inducer concentrations with a given growth rate is shown. The red curves show the ensembles of red states, the green curves show the ensembles of green states, and the black dashed lines suggest the calculated saddle points which are unstable. The appearance of bimodal distributions in the range of 0.1 to 1.0 ng/mL cTc concentration is supposed to be the gene expression fluctuations in proximity to the bifurcation point (blue arrows in the right panel). (f) A loss of bistability was confirmed in MOPS acetate medium without inducer. The hysteresis experiment shows that the bistable range is significantly reduced in the MOPS acetate medium.
Extended Data Fig. 2 Temporal scatter density plots of cell states during nutrient depletion in SOB batch culture and re-incubation of the cells from stationary phase to fresh SOB medium.
Data were obtained by flow cytometry at the indicated times with 50,000 events detected per experiment (Supplementary Table 5). A dashed line in the density plot is indicated to discriminate between two distinct phenotypic states (see Methods). (a) A time course is shown for cells initially induced to green state switching gradually from a green state (0 h) to a red state (15 h) throughout the nutrient depletion until the stationary phase. These cells maintained the red state when diluted into fresh SOB medium and grown on the rich-nutrient condition for another 5 h. (b) A time course for cells initially switched to the red state shows that they do not change their state during nutrient depletion. Cells can be further switched to the green state by adding cTc and maintaining this state in a no-inducer fresh medium. It shows that this circuit recaptures its bistability and suggests the phenotype changes during the nutrient depletion do not involve genetic variations.
Extended Data Fig. 3 Variations of cell growth rate and stability of mutual repressive circuit under the treatment of diverse concentrations of sublethal dose of mupirocin.
Mupirocin is a translation inhibitor that inhibits the charging of isoleucine tRNA, resulting in a reduction of the translational elongation rate of the ribosome. E coli. cells harboring the mutual repressive circuit were grown in MOPS glucose minimal medium with diverse concentrations of mupirocin varying from 0 to 60 µg/mL. A loss of bistability was observed under slow growth when varying the cell growth rate by titrating the translational elongation rate.
Extended Data Fig. 4 Growth rate dependence of constitutively expressed TetR and LacI.
(a) Two separated parts that constitutively expressed tetR and lacI with C-terminal sfgfp fusion were used for the measurement of their corresponding expression capacity. (b) Expression capacities \({{{\tilde{\mathbf \alpha }}}}_{{{\boldsymbol{R}}}}\) and \({{{\tilde{\mathbf \alpha }}}}_{{{\boldsymbol{G}}}}\) of constitutively expressed TetR and LacI, respectively, as a function of 1/λ. The dashed line indicates the steady-state expression capacity in the case of constant production of protein which is independent of growth rate (the constant value of protein production rate was the one of TetR in MOPS glucose medium). Both expression capacities increase faster than 1/λ as the growth rate decreases. (c) Relative protein expression capacity is defined as the ratio of TetR and LacI protein concentrations under different growth conditions. Results derived from data shown in Fig. 2a and Supplementary Table 7. (d) Relation between the mRNA abundance and growth rate during steady-state growth. (e) Relative mRNA level, defined as the ratio of mRNA abundance of tetR and lacI genes under different growth conditions (results derived from data shown in d). (f) Growth rate dependence of the normalized protein synthesis rates αR and αG. αR and αG are derived from experimental data of tetR and lacI expression, respectively, under different growth conditions, that is, \(\alpha _{{{{\boldsymbol{R}}}},{{{\boldsymbol{G}}}}} = \tilde \alpha _{{{{\boldsymbol{R}}}},{{{\boldsymbol{G}}}}} \cdot \lambda\). The synthesis rate obtained in different growth media was normalized to the value in MOPS glucose medium. Both synthesis rates have maxima around the moderate growth rates (~0.5 h−1 for αR and ~ 0.75 h−1 for αG). (g) Prediction of growth rate dependence of protein synthesis rate α obtained from measured mRNA abundance in panel d by considering the empirical growth rate dependence of translation activity (see details in Supplementary Note 3). Data in b, c and f are presented as mean ± SD defrom three or four independent biological replicates (n = 3-4, see Supplementary Table 7).
Extended Data Fig. 5 Dimensionless analysis of the deterministic model for the mutual repressive system.
(a) The model includes the global regulation of cell growth along with growth-dependent protein synthesis (αR and αG) and degradation (growth dilution λ under the assumption that protein turnover is negligible) as input stimuli and output of the system (Supplementary Note 1). The model for the mutual repressive system is typically written as \(\frac{{{{{\mathbf{d}}}}\left[ {{{\boldsymbol{R}}}} \right]}}{{{{{\mathbf{d}}}}{{{\boldsymbol{t}}}}}} = {{{\mathbf{\upalpha }}}}_{{{\boldsymbol{R}}}} \cdot {{{\boldsymbol{H}}}}_{{{\mathbf{R}}}}\left( {\left[ {{{\boldsymbol{G}}}} \right]} \right) - {{{\mathbf{\uplambda }}}} \cdot \left[ {{{\boldsymbol{R}}}} \right]\) and \(\frac{{{{{\mathbf{d}}}}\left[ {{{\boldsymbol{G}}}} \right]}}{{{{{\mathbf{d}}}}{{{\boldsymbol{t}}}}}} = {{{\mathbf{\upalpha }}}}_{{{\boldsymbol{G}}}} \cdot {{{\boldsymbol{H}}}}_{{{\mathbf{G}}}}\left( {\left[ {{{\boldsymbol{R}}}} \right]} \right) - {{{\mathbf{\uplambda }}}} \cdot \left[ {{{\boldsymbol{G}}}} \right]\), where \({{{\boldsymbol{H}}}}_{{{\boldsymbol{R}}}}\left( {\left[ {{{\boldsymbol{R}}}} \right]} \right)\) and \({{{\boldsymbol{H}}}}_{{{\boldsymbol{G}}}}\left( {\left[ {{{\boldsymbol{G}}}} \right]} \right)\) are the mutual repressive relations between TFs, which are described as two decreasing Hill functions of [R] (the reporter of TetR expression) and [G] (the reporter of LacI expression) with repression thresholds \({{{\boldsymbol{K}}}}_{{{{\boldsymbol{DR}}}},{{{\boldsymbol{DG}}}}}\), respectively. (b) By defining the expression capacity \({{{\tilde{\mathbf \upalpha }}}}_{{{{\boldsymbol{R}}}},{{{\boldsymbol{G}}}}}: = {{{\mathbf{\upalpha }}}}_{{{{\boldsymbol{R}}}},{{{\boldsymbol{G}}}}}/{{{\mathbf{\uplambda }}}}\), we would denote \(\left[ {{{{\tilde{\boldsymbol R}}}}} \right]: = \left[ {{{\boldsymbol{R}}}} \right]/{{{\tilde{\mathbf \upalpha }}}}_{{{\boldsymbol{R}}}}\), \(\left[ {{{{\tilde{\boldsymbol G}}}}} \right]: = \left[ {{{\boldsymbol{G}}}} \right]/{{{\tilde{\mathbf \upalpha }}}}_{{{\boldsymbol{G}}}}\) as the dimensionless concentrations, and g = λ·t as the generational time of the system, thereby obtaining: \(\frac{{d[{{{\tilde{\boldsymbol R}}}}]}}{{d{{{\boldsymbol{g}}}}}} = {{{\tilde{\boldsymbol H}}}}_{{{\boldsymbol{R}}}}([{{{\tilde{\boldsymbol G}}}}]) - [{{{\tilde{\boldsymbol R}}}}]\) and \(\frac{{{{{\mathrm{d}}}}[{{{\tilde{\boldsymbol G}}}}]}}{{d{{{\boldsymbol{g}}}}}} = {{{\tilde{\boldsymbol H}}}}_{{{\boldsymbol{G}}}}([{{{\tilde{\boldsymbol R}}}}]) - [{{{\tilde{\boldsymbol G}}}}]\). Due to the growth rate dependence, the dimensionless repressive thresholds \({{{\tilde{\boldsymbol K}}}}_{{{{\boldsymbol{DR}}}}}: = {{{\boldsymbol{K}}}}_{{{{\boldsymbol{DR}}}}}/{{{\tilde{\mathbf \upalpha }}}}_{{{\boldsymbol{R}}}}\) and \({{{\tilde{\boldsymbol K}}}}_{{{{\boldsymbol{DG}}}}}: = {{{\boldsymbol{K}}}}_{{{{\boldsymbol{DG}}}}}/{{{\tilde{\mathbf \upalpha }}}}_{{{\boldsymbol{G}}}}\) would effectively increase with the growth rates but with different magnitudes. Therefore, the dimensionless nullclines of the system where \({{{\mathbf{d}}}}\left[ {{{{\tilde{\boldsymbol R}}}}} \right]/d{{{\boldsymbol{g}}}} = 0\) and \({{{\mathbf{d}}}}\left[ {{{{\tilde{\boldsymbol G}}}}} \right]/d{{{\boldsymbol{g}}}} = 0\), such that \(\left[ {{{{\tilde{\boldsymbol R}}}}} \right] = {{{\tilde{\boldsymbol H}}}}_{{{\boldsymbol{R}}}}\left( {\left[ {{{{\tilde{\boldsymbol G}}}}} \right]} \right)\) and \(\left[ {{{{\tilde{\boldsymbol G}}}}} \right] = {{{\tilde{\boldsymbol H}}}}_{{{\boldsymbol{G}}}}\left( {\left[ {{{{\tilde{\boldsymbol R}}}}} \right]} \right)\) shifts as the growth rate changes, causing variations in the number of fixed points (Fig. 2b).
Extended Data Fig. 6 Growth-rate-dependent gene expression and promoter leakage enable phase transition in the bistable mutual repression circuit.
We demonstrate that the growth-rate-dependent protein synthesis rate origins the bifurcation of the mutual repression circuit by mathematic modeling. (a) As the experimental data (Extended Data Fig. 4f) indicated, the protein synthesis rates, αR,G, are nonlinear to growth rate and shown in a context-dependent manner. (b) \({{{\tilde{\boldsymbol K}}}}\) is the dimensionless repressive threshold which is linear to λ/α (Supplementary Note 1), and the bistability of the circuit is determined. We plot the phase diagram of the circuit with the promoters without expression leakage (that is, both τ are equal to 0). When both \({{{\tilde{\boldsymbol K}}}}\) stay at the gray region, the circuit exhibits bistability. Titrate the growth rate λ from 1.6 h−1 to 0.2 h−1, both \({{{\tilde{\boldsymbol K}}}}\) of the two mutual repression sides are varying and the trajectory of the circuit state indicates the bifurcation process (orange dashed line). Both protein synthesis rates are two orthogonal forces driving the system to traverse the phase diagram and lead to a long and curved trajectory than if α is constant (c), resulting in bifurcation. (c) The trajectory of the strain (blue dashed line) with protein synthesis rates α is constant and is plotted as a reference, which doesn’t enable the bifurcation. (d) The bistable region can be eroded by the leakage expression (blue dashed line encircled). We fix τR and τG are 0.035 and 0.002, respectively. The green dashed line is the trajectory that is fitted from experimental data (Fig. 2a).
Extended Data Fig. 7 Measurement of response curves of the regulatory systems and parameter fitting.
(a) The expression level of this transcriptional repressor LacI is indicated via the intensity of fluorescent protein, mVenus, which is independently driven by the identical input promoter, that is, Psali. The output of this regulatory system is indicated by the same reporter. By this means, the input-output response function could quantitatively describe the properties of the interaction between the lac repressor and its binding site. The plasmids used are given in Supplementary Table 2. (b) Experimental measurements, and parameter fitting of the response curves for different circuits. For each of the measurements, various concentrations of sodium salicylate were used to induce the Psali promoter activity. Input and output were both identified as fluorescent intensity per mass using flow cytometry (see Methods). Only a moderate range of data (within the dotted box in the left panel) was taken for parameter fitting. The Hill coefficient n was fixed at 1.15 and other parameters were obtained using best-fit.
Extended Data Fig. 8 Cell fate determination trajectories during growth shift.
(a) Time course of the instantaneous growth rate of cell cultures measured throughout nutrient downshift and upshift in batch culture. Nutrient shift experiments were performed between RDM glucose medium containing high-quality nitrogen sources (mixture of amino acids and ammonia) and MOPS (-NH4Cl) glucose minimal medium supplemented with glutamate as the sole nitrogen source. The instantaneous growth rate is derived by calculating the derivative of OD600 concerning time \(\lambda \left( {t_i} \right) = \left[ {{{{\mathrm{lnOD}}}}\left( {{{{\mathrm{t}}}}_{{{{\mathrm{i}}}} + 1}} \right) - {{{\mathrm{lnOD}}}}\left( {{{{\mathrm{t}}}}_{{{\mathrm{i}}}}} \right)} \right]/\left( {{{{\mathrm{t}}}}_{{{{\mathrm{i}}}} + 1} - {{{\mathrm{t}}}}_{{{\mathrm{i}}}}} \right)\). The instantaneous growth rate dropped abruptly after the nutrient downshift. This can be explained by the growth adaptation right after the depletion of amino acids and ammonia when the metabolic bottleneck for amino acid synthesis is significant. Rapid recovery and overshot its post-shift steady-state value until 0.9 h−1 was observed, presumably because of the relatively high level of glucose uptake. The subsequent slowing down was observed until the final exponential growth rate at approximately 0.18 h−1. Growth rate data from three different designs of circuits (LO1, LO2, and LO3) triggered to two distinct initial states (G and R) are plotted. (b) Growth downshift and upshift experiments were carried out with cells initially triggered to the red state (pre-cultured in RDM glucose medium supplied with 0.2 mM IPTG, see Methods). Noise-induced spontaneous state transitions from red state to green state under fast growth conditions were identified after removing the inducer. For strains LO1 and LO2, only a small proportion of cells flip (red dashed lines). This observation is consistent with the result shown in Extended Data Fig. 10d. In the case of LO3, all red state cells were destabilized, leading to the green state under fast growth (red solid line). The high RFP state is maintained throughout the growth downshift as well as the subsequent upshift for LO1 and LO2 strains.
Extended Data Fig. 9 Cell fate determination trajectories of initial green state cells predicted by simulation.
(a) Curve fitting of instantaneous growth rate across nutrient upshift and downshift conditions. The gray scatters are the instantaneous growth rate, and the colored solid line denotes the growth rate which is fitted using a series of Hill functions. The slate blue part indicates the nutrient downshift, and the orange one shows the nutrient-upshift condition. (b) We applied the deterministic model (Supplementary Notes 1 and 3) to capture the growth-mediated dynamics of cell fate decision trajectories for each of the systems (Fig. 4b). The dynamics of model prediction closely follow the main features of the population-averaged dynamics of cell fate determination for each case. Three panels plot the predicted cell-fate decision trajectories of strains LO1, LO2, and LO3, respectively.
Extended Data Fig. 10 Probability potential landscape is reshaped during growth-rate fluctuation.
Computed potential landscapes of the mutual repression switch illustrate the robustness of the states of cells with different growth rates and genetic backgrounds (Supplementary Note 5). The contour lines indicate the potential at the specific protein concentration ([G] and [R] axes). (a–c) Strains growing at varied growth rates show distinct potential landscapes. (a) As the decreasing of the growth rate, the bistability of the strain LO1 remained when the growth rate is greater than the critical growth rate, however, the bistability catastrophe happens at the critical growth rate, and the system remains the red stable state only when the growth rate is lower than the critical growth rate. (b) The strain LO2 remaining two stable states in our experimental conditions, the computed potential landscapes indicate the intrinsic parameters of promoter make the system behave more robustly to the fluctuation in growth rate. (c) The strain LO3 shows bistability only at slow growth rates. (d) the relation between growth rate and barrier height of the strains LO1, LO2, and LO3. The green squares denote the barrier heights between the G state and saddle point (G→R), and the red circles indicate the barrier heights between the R state and saddle point (R→G). The black triangles denote the relative changes of the two barrier heights (R→G/G→R).
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Zhu, J., Chu, P. & Fu, X. Unbalanced response to growth variations reshapes the cell fate decision landscape. Nat Chem Biol 19, 1097–1104 (2023). https://doi.org/10.1038/s41589-023-01302-9
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DOI: https://doi.org/10.1038/s41589-023-01302-9
