Global quantitative understanding of nonequilibrium cell fate decision making in response to pheromone

Cell cycle arrest and polarized cell growth are commonly used to qualitatively characterize the fate of yeast in response to pheromone. However, the quantitative decision-making process underlying the time-dependent changes in cell fate remains unclear. Here, by observing the multi-dimensional responses at the single-cell level experimentally, we find that yeast cells have various fates. Multiple states are revealed, along with the kinetic switching rates and pathways among them, giving rise to a quantitative landscape of mating response. We developed a theoretical framework using a nonequilibrium landscape and flux theory to account for the cell morphology observed experimentally and performed a stochastic simulation of biochemical reactions to explain the signal transduction and cell growth. Our experimental results established the first global quantitative demonstration of the real-time synchronization of intracellular signaling with their physiological growth and morphological functions which reveals the underlying physical mechanism. This study provides an emerging mechanistic approach for understanding the nonequilibrium global pheromone-regulated cell fate decision-making in growth and morphology.

and pheromone-influenced signaling in the transduction process, we explored the biological 1 5 0 mechanism underlying the emergence of these two Fus3 fates. We proposed that the two fates of respectively.

4 0
To explore the molecular mechanisms underlying these four growth rates, we took both the shmoo projections (90,91,93,94,117). Thus, the indirect pathway (P be transported into or out of the nucleus, we proposed that the P ଶ pathway had a quicker response 2 4 9 speed to stimulate cell growth than did the P ଵ pathway (Fig. 5D)

5 6
To confirm that there was indeed a time lag in multi-level protein signaling, we constructed 2 5 7 a dual fluorescence system (CDC24_GFP-FUS3_RFP strain), in which CDC24 was linked to the 2 5 8 green fluorescent protein (S65T) and FUS3 was linked to the red fluorescent protein (yomCherry) 2 5 9 ( Fig. 5E and Movies S8-S9). Taking into account the order of signal transduction in yeast in 2 6 0 response to pheromone, the expression levels of Fus3 and Cdc24 would achieve the highest 2 6 1 degree of correlation or match after a certain time lag. Using a cross-correlation function, we 2 6 2 analyzed the in-and out-of-nucleus fluorescence trajectories of Fus3 and Cdc24 to compare the 2 6 3 lag times of various activation sequences (Fig. 5F). The figure shows that the lag time between 2 6 4 Fus3 in the nucleus and Cdc24 (red curve) reaching a maximum correlation was approximately 2 6 5 120 min, while the lag time between Fus3 outside the nucleus and Cdc24 (blue curve) reaching a 2 6 6 maximum correlation was approximately 300 min. The fact that the lag time of Fus3_in and 2 6 7 Cdc24_in/out (red curve) in the figure was shorter than that of Fus3_out and Cdc24_in/out (blue 2 6 8 curve) confirms the existence of a temporal delay effect in multi-level signaling and provides 2 6 9 direct evidence for the temporal distinction in the functioning of the two growth pathways.

7 0
By taking the growth rate absolute value, we divided the four states into fast growth rate 2 7 1 and slow growth rate categories ( Fig. 5G and Fig. S7). To confirm that the two forces (F and S) 2 7 2 corresponded to the high and low states of Fus3, respectively, the cell growth rate states and 2 7 3 Fus3 gene expression states were measured as the cell polar growth changed over time.

7 4
According to the proportion of statistics in the figure, the High (expression) state was primarily 2 7 5 contained within the Fast (growth) state, whereas the Low (expression) state was primarily 2 7 6 contained within the Slow (growth) state ( Fig. 5H and Table 3). Consequently, this also 2 7 7 provided quantitative experimental evidence for the cellular growth rate molecular mechanism.

7 8
Quantifying the four morphological fates and the phase transition trend 2 7 9 The morphological trajectory of the cell shape over time as described by H n fluctuated 2 8 0 continuously within a given range (Fig. 5B). Using a hidden Markov chain model to fit the time-

8 4
Due to the fact that H n is a parameter that is extremely sensitive to changes in the size and  The existence of four distinct states in the cooperative distribution of the two data, as depicted in 2 9 5 the figure, strongly suggested that the capacity to grow in different directions is a crucial factor 2 9 6 in determining cell morphology ( Fig. 6C and Fig. S9).

9 7
Notably, a phase transition trend from four states to a dominant state in the cell morphology

0 8
To explain the physical mechanism of the phase transition trend that occurs at high dose 3 0 9 (3.0 μ M), we quantified the degree of nonequilibrium in the cellular morphological system using networks (Fig. 1, Fig. 6F). This model simulated a series of biochemical reactions with the 3 2 8 Gillespie algorithm (118-120) (Table S6- context of the global response (Fig. 6G). Meanwhile, the Bni1 produced by the reactions 3 3 4 simulated the dynamic process of cell growth. Although both the growth pathways (P 1 and P 2 ) 3 3 5 were involved in the process of cellular length and width growth, the relative weights of the 3 3 6 pathways that grew in the two directions were significantly different. Therefore, we simply 3 3 7 defined Bni1_in produced by the P 1 pathway that plays a major role as the longitudinal growth 3 3 8 and Bni1_out produced by the P 2 pathway as the lateral growth.

9
In this simulation, is proportional to "PBni1_out" and inversely proportional to a .

4 3
That is, In this study, we quantitatively uncovered and interpreted the yeast cell fate decision- was considered a non-equilibrium steady state period. As our subsequent analysis centered on the 3 6 0 non-equilibrium steady-state phase, we chose five pheromone concentrations as stimuli that 3 6 1 allowed the yeast cells to maintain a stable-state phase for a sufficient amount of time.

6 2
To explore the fate of Fus3 gene expression in a non-equilibrium steady state, we chose data 3 6 3 that, after 600 min, brought all the cell fluorescence trajectories into stable-state phase (Fig. 3A).

6 4
The two fates of Fus3 that resulted from cellular decision-making were separated by the Markov 3 6 5 fitting of the trajectories (Fig. 3B). The criterion for data fitting is the probability that the

6 8
Consequently, there was a chance that the value of the fluorescence intensity in the low state was 3 6 9 greater than the value of the fluorescence intensity in the high state. We proposed that the two states did not appear in this scheme. We know from experimental evidence that the absence of and negative inhibition favored the formation of two states from a physical standpoint (Fig. 3D).

8 2
Between steady states, the cellular decision-making is primarily reflected by the transition as the barrier height decreased (Fig. 4D). In our biological system, the positive correlation 3 9 0 statement regarding barrier height and residence time was confirmed (Fig. 4C). Certainly, such 3 9 1 physical characteristics that quantify cellular decision-making have significant biological 3 9 2 implications for the study of yeast response behavior. Positive feedback regulation in the gene 3 9 3 network ("Pheromone → Fus3" and "Fus3 → Fus3"), for example, increased the potential 3 9 4 barrier height on the gene expression landscape, whereas negative feedback regulation decreased 3 9 5 it (I 1 , I 2 ) ( Fig. 1 and Fig. 3C). The residence time at various pheromone concentrations revealed 3 9 6 which gene expression fate yeast cells preferred in response to the pheromone.

9 7
Some studies believe that the establishment of polarity helps organisms to survive better in mechanism of F and S (Fig. 5H and Table 3). In addition, there must be a lag between the 4 2 8 expression of Fus3p and the observed cell growth, resulting in a low fluorescence state during 4 2 9 fast cell growth and a high fluorescence state during slow cell growth.

3 0
For statistical analysis of different cell morphologies, we distinguished four cell 4 3 1 morphological fates roughly as F 1 -F 4 to provide a more intuitive description (Fig. 6A).

3 2
Nevertheless, the division of actual cell morphological fate was determined by fitting the     The fluorescence values of the single cells were measured using an inverted fluorescence 4 9 2 microscopy (Ti-E, Nikon) with automated stage and focus, equipped with a high NA oil-4 9 3 immersion objective (1.45NA, 100×). We applied 488nm laser and set the output power at 4 9 4 30mW (only 10% of the laser beam into the microscope objective), the fluorescence signals were 4 9 5 collected by a cooled EM-CCD camera (897U, Andor). All images were acquired using both 4 9 6 bright field imaging and fluorescent field imaging. These images were acquired by Nikon 4 9 7 software. Data analysis were accomplished through a combination of manual and automated 4 9 8 analysis using custom Matlab code. Many trajectories were taken from a time-lapse microscopy.

9 9
The fluorescent images were periodically captured and recorded every 10 minutes. The   I 1 and I 2 represent different negative feedback adjustment pathways; and P 1 and P 2 represent the 8 1 5 two polar growth signaling pathways that are connected by light green arrows. landscapes U in exponential scale (defined as p ~ e -U ), which is also the population landscape; on 8 4 0 the right is the 2D underlying potential landscapes U (ܷ ൌ െ l n ܲ