Global quantitative understanding of non-equilibrium cell fate decision-making in response to pheromone

Abstract

Cell-cycle arrest and polarized growth are commonly used to characterize the response of yeast to pheromone. However, the quantitative decision-making processes underlying time-dependent changes in cell fate remain unclear. In this study, we conducted single-cell level experiments to observe multidimensional responses, uncovering diverse fates of yeast cells. Multiple states are revealed, along with the kinetic switching rates and pathways among them, giving rise to a quantitative landscape of mating response. To quantify the experimentally observed cell fates, we developed a theoretical framework based on non-equilibrium landscape and flux theory. Additionally, we performed stochastic simulations of biochemical reactions to elucidate signal transduction and cell growth. Notably, our experimental findings have provided the first global quantitative evidence of the real-time synchronization between intracellular signaling, physiological growth, and morphological functions. These results validate the proposed underlying mechanism governing the emergence of multiple cell fate states. This study introduces an emerging mechanistic approach to understand non-equilibrium cell fate decision-making in response to pheromone.

Keywords: Biological sciences; Cell biology; Cellular physiology.

Graphical abstract

Figure 1

Schematic diagram of the mating signal pathway of the yeast cell pheromone pathway The red horizontal line represents the inhibition of negative feedback; the green arrow represents the activation of positive feedback; the dashed arrow represents a shift in localization; I₁ and I₂ represent different negative feedback adjustment pathways; and P₁ and P₂ represent the two polar growth signaling pathways that are connected by light green arrows. The outline of the pathway is as follows: The binding of α-factor to its transmembrane receptor Ste2 leads to activation of the heterotrimeric G protein complex consisting of Gpa1 (Gα), Ste4 (Gβ), and Ste18 (Gγ). This causes dissociation of the Gβγ dimer (Ste4/Ste18) from Gα (Gpa1). The released Gβγ then recruits the PAK kinase Ste20 to the membrane and activates it. Ste20 initiates the MAPK cascade by phosphorylating the MAPKKK Ste11. Activated Ste11 phosphorylates the MAPKK Ste7, which then phosphorylates the MAPK Fus3. The activated Fus3 has two downstream effects: First, Fus3 directly phosphorylates and activates the formin Bni1, which nucleates actin cables for polarization. Second, Fus3 enters the nucleus and phosphorylates Ste12, a transcription factor that induces mating-specific genes. Fus3 also phosphorylates Far1, which inhibits the G1–S transition by binding to Cdc28-Cln2 complex. The Fus3-Far1 complex exits the nucleus and binds to Cdc24, promoting the activation of the Rho-GTPase Cdc42. Activated Cdc42 in turn stimulates Bni1.

Figure 2

A non-equilibrium biological model for cellular responses (A) The fluorescence intensity of FUS3-GFP was measured using flow cytometry. The yeast cells were cultured in YPD medium containing different concentrations of pheromone for 24 h. The x axis represents the logarithmic scale (base 10) of fluorescence intensity, specifically the FL1-A parameter in flow cytometry; FL1-A is a measurement channel in flow cytometry that captures the fluorescence emission of a specific fluorochrome or fluorescent protein; it reflects the intensity of FUS3-GFP fluorescence. The y axis represents the normalized probability density, indicating the relative frequency of intensity values within each histogram bin. Normalized method: $\int P\left(x\right)dx=1$. The black curve represents the overall fluorescence intensity statistics, and the green and red curves represent the two fitted statistical peaks. The sample size for each pheromone concentration test was 105,000 yeast cells. (B) Fus3 gene expression was observed microscopically in response to 0.2 μM and 0.7 μM pheromone. The x axis represents the duration of exposure to the pheromone-containing medium. The y axis represents the fluorescence intensity of FUS3-GFP; and images a₁–a₃ and b₁–b₃ depict the living states of yeast cells as observed through a microscope at their corresponding times. For the 0.2 μM fluorescence trajectory, the specific yeast cell it belongs to has been indicated with a red arrow. (C) A 3D top view of the probability density distribution for dual-angle scattering data. The x axis represents the logarithmically transformed values of FSC-A, while the y axis represents the logarithmically transformed values of SSC-A. FSC-A (Forward Scatter-Angle) refers to the intensity of light scattered at a forward angle in flow cytometry; it reflects the size and complexity of cells or particles. SSC-A (Side Scatter-Angle) represents the intensity of light scattered at a side angle in flow cytometry; it provides information about the internal structure and complexity of cells. The z axis represents the probability density distribution, indicating the density of probability at each data point. (D) The microscopically captured living state of yeast at various pheromone concentrations. The green fluorescence in cells represents the expression of FUS3-GFP; 60 min on the x axis represents the time when yeast cells were switched to a culture medium containing pheromone.

Figure 3

The two steady states of expression levels of Fus3 (A) Trajectories of fluorescence intensity of Fus3 at 0.7 μM inside and outside the nucleus (only a portion shown). The red vertical line at 600 min was used to approximate the time node at which all cell fluorescence trajectories had entered a non-equilibrium steady state. (B) Three-dimensional distribution graph of Fus3 fluorescence intensity inside and outside the nucleus of yeast cells in the stationary phase under different pheromone concentrations. On the left is the 3D distribution of fluorescence or the 3D population landscape, in the middle is the 2D histograms or the 2D underlying potential landscapes U in exponential scale (defined as p ∼ e^−U), which is also the population landscape; on the right is the 2D underlying potential landscapes U ($U=-\ln P$). The sample sizes at steady state for each pheromone concentration are as follows: 0.7 μM was equivalent to 21,335 cells, 0.8 μM to 18,408 cells, 1.0 μM to 23,041 cells, 2.0 μM to 36,886 cells, and 3.0 μM to 18,276 cells. (C) Diagram illustrating the molecular mechanism by which yeast cells respond to pheromone. The $\text{Outer}\_{\mathrm{P}}_1$ represents the indirect pathway taken by Fus3 from the cytoplasm to the nucleus in order to inhibit the cell cycle; $\text{Inner}\_{\mathrm{P}}_1$ represents the indirect pathway by which Fus3 in the nucleus promoted polar growth; $\text{Outer}\_{\mathrm{P}}_2$ represents the direct pathway of Fus3 in the cytoplasm for polar growth; $\text{Inner}\_{\mathrm{P}}_2$ represents the direct pathway for the transfer of Fus3 from the nucleus to the cytoplasm for polar growth; I₁ and I₂ represent the inhibitory effects of the negative feedback regulation; and the two gray dashed lines represent the cell membrane and the nuclear membrane. “α” stands for α-factor pheromone. The signaling cascade follows the following logic: Upon receiving sufficient external signals (α-factor), yeast cells activate Fus3, leading to a significant increase in phosphorylated Fus3 levels. Subsequently, activated Fus3 translocates into the cell nucleus (Outer_P₁), initially engaging the branch involved in cell cycle inhibition, namely, Fus3 → Far1. Once the cell cycle is inhibited, activation of mating-specific proteins like Ste12 ensues. Within the nucleus, the activated Far1 not only contributes to cell-cycle arrest but also facilitates the activation of the first polarity growth pathway (Inner_P₁) upon exiting the nucleus. As the nuclear Fus3 reaches a threshold level, excess Fus3 exits the nucleus and triggers Bni1 activation to facilitate polarized growth (Inner_P₂). Concurrently, cytoplasmic Fus3 initiates the second polarity growth pathway (Outer_P₂). (D) Schematic representation of two negative feedback models for regulating Fus3 gene expression. A and B represent, respectively, two different types of proteins that interact with Fus3 in the signaling pathway; “α” stands for α-factor pheromone. (E) Fluorescence intensity trajectories of Fus3 inside and outside the nucleus over time under non-equilibrium steady state. The red line represents the fitting by the hidden Markov model to distinguish high- and low-expression states. Arrows indicate spontaneous state switching events between the high state (H_I/H_O) and low state (L_I/L_O). The x axis is shared between the two panels to optimize figure clarity. The high and low states were distinguished by hidden Markov modeling of the fluorescence trajectories, with iterative optimization of model parameters to ensure global convergence. The expression fate at each time point was determined by the relative probability and transition dynamics between the two expression states.

Figure 4

The physical characteristics of cellular decision-making landscapes (A) Trends in the statistical distribution of barrier heights for high and low states at varying pheromone concentrations. (B) Trends in the statistical distribution of residence time for high and low states at varying pheromone concentrations. The residence time represents the average duration the system stays in a particular state among all trajectories simulated using Markov chain modeling. The residence time is measured in minutes. (C) Correlation analysis between residence time and barrier height. The red circles are the data points; the blue line is the fitted line of the data. (D) The ratio of the physical characteristics of high and low states at various concentrations. The k_LH is the transition rate from a low state to a high state; k_HL is the transition rate from a high state to a low state. (E) Simple schematic diagram of the potential landscape topography under different pheromone dosages. L stands for the low state, H stands for the high state; k_LH and k_HL are the transition rates between the low state and the high state, respectively; h_L and h_H represent the respective barrier heights of the low and high states, respectively.

Figure 5

Quantification of the deformation of yeast cells during polar growth (A) A simple diagram of cell shapes with circle filling patterns. The image on the left depicts a yeast cell cultured for 1,020 min in a medium containing 0.7 μM pheromone; the red line indicates the contour of the cell; the image on the right is the filling model for the image on the left; ${\mathrm{R}}_1-{\mathrm{R}}_4$ are the radii of the circle. (B) Real-time trajectory of the cell morphology (H_n) at 0.7 μM under non-equilibrium steady state. F₁–F₄ indicate the four distinct cell morphological fates. The horizontal dashed lines mark the approximate centers of the fates. Arrows highlight spontaneous state switching events between fates F₃ to F₂ (green) and F₂ to F₄ (red). The inset shows a magnified view of the trajectory over time points t₁–t₅. Cell morphologies during the initial non-equilibrium non-steady-state period before 600 min are omitted. (C) The distribution statistics of the cell growth rate at 0.7 μM. The red dashed line serves as the dividing line between positive and negative data. WF and LS represent the lateral-fast and lateral-slow rates, respectively; LF and WS represent the longitudinal-fast and longitudinal-slow rates, respectively. (D) Schematic illustration of the molecular mechanism underlying the formation of the four growth rates. Model W indicates that the polar growth pathway P₁ is not yet connected, so only the P₂ pathway operates; Model L depicts the cooperative operation of polar growth pathways P₁ and P₂. Models F and S describe the polar growth patterns of the two growth forces, which correspond to the high and low states of Fus3, respectively. (E) Dual fluorescent protein system in yeast. The three images on the left, from top to bottom, depict bright field cells, cells excited at 488 nm, and cells excited at 561 nm. The white circle within the cell represents the nucleus boundary; S65T and yomCherry are the fluorescent proteins that were linked to CDC24 and FUS3, respectively. (F) Cross-correlation of two levels of gene expression at distinct positions. Gene_in and gene_out represent the gene expression levels inside and outside the nucleus, respectively. The red curve represents the cross-correlation between Fus3_in and Cdc24_in/out, while the blue curve corresponds to the cross-correlation between Fus3_out and Cdc24_in/out. (G) Statistical graph of the distribution statistics of the absolute value of the cell growth rate at 0.7 μM. (H) The proportion of high-state and low-state data present in high and low states at various pheromone concentrations.

Figure 6

The interpretation of the different cell morphological fates (A) Statistical distribution of the cell morphology at 0.7 and 3.0 μM. The red dashed lines roughly correspond to the boundary between distinct cell morphological fates; F₁–F₄ represent the four cell morphological fates. (B) Photographs taken with a fluorescence microscope of cells exhibiting four distinct morphological fates in response to varying pheromone concentrations. (C) The synergistic effect of both lateral and longitudinal cell growth capabilities at a pheromone concentration of 0.7 μM. The x axis represents the ability of the cells to grow longitudinally, as indicated by the rate of change in the sum of the radii of the filled circles within the cells, i.e., ${({\mathrm{R}}_1+{\mathrm{R}}_2+\dots +{\mathrm{R}}_{\mathrm{n}})}^{\prime }$; the y axis represents the ability of cells to grow laterally, as indicated by the rate of change in the average radius of the filled circles within the cells, i.e., ${\left(\frac{{\mathrm{R}}_1+{\mathrm{R}}_2+\dots +{\mathrm{R}}_{\mathrm{n}}}{\mathrm{n}}\right)}^{\prime }$. (D) Changes in the average cell length as a function of pheromone concentration. (E) The sum of the net fluxes among the four cell morphologies at various pheromone concentrations. (F) The scheme for the simulated cell growth; a represents the length of the cell; $\Delta \mathrm{a}$ is the increased length of the cell; b represents the width of the cell; and $\Delta \mathrm{b}$ is the increased width of the cell; the scheme of the H_n calculation; c is the remainder of the cell length divided by b; N represents the number of b. (G) Distribution graph of the negative log of the value of the Fus3 fluorescence intensity inside and outside the nucleus of yeast cells in the stationary phase using simulation. (H) The distribution of the cell morphology (H_n) using simulation.