Transcriptional timing and noise of yeast cell cycle regulators—a single cell and single molecule approach

Gene expression is a stochastic process and its appropriate regulation is critical for cell cycle progression. Cellular stress response necessitates expression reprogramming and cell cycle arrest. While previous studies are mostly based on bulk experiments influenced by synchronization effects or lack temporal distribution, time-resolved methods on single cells are needed to understand eukaryotic cell cycle in context of noisy gene expression and external perturbations. Using smFISH, microscopy and morphological markers, we monitored mRNA abundances over cell cycle phases and calculated transcriptional noise for SIC1, CLN2, and CLB5, the main G1/S transition regulators in budding yeast. We employed mathematical modeling for in silico synchronization and for derivation of time-courses from single cell data. This approach disclosed detailed quantitative insights into transcriptional regulation with and without stress, not available from bulk experiments before. First, besides the main peak in G1 we found an upshift of CLN2 and CLB5 expression in late mitosis. Second, all three genes showed basal expression throughout cell cycle enlightening that transcription is not divided in on and off but rather in high and low phases. Finally, exposing cells to osmotic stress revealed different periods of transcriptional inhibition for CLN2 and CLB5 and the impact of stress on cell cycle phase duration. Combining experimental and computational approaches allowed us to precisely assess cell cycle progression timing, as well as gene expression dynamics.


INTRODUCTION
Correct gene expression regulation is crucial for cell cycle progression. 1 Main regulators of the cell cycle are cyclins, cyclin dependent kinases (CDK) and CDK-inhibitors (CKI). 2 Their functions and regulatory motifs are highly conserved among eukaryotes. 3,4 Gene expression is frequently measured for cell cycle synchronized populations despite the facts that synchronization affects cell cycle progression heavily and that single cell behavior deviates from population behavior. Therefore, we aimed for a more precise analysis of transcriptional dynamics during the cell cycle.
For this work, three well-studied examples for cell cycle regulators in budding yeast were selected: Clb5, Cln2, and Sic1. The two cyclins Clb5 and Cln2 in complex with CDK1 control replication origin firing and bud formation, respectively, characterizing the exit from G1 and entrance into S phase. [5][6][7] The CDK inhibitor Sic1 prevents premature G1/S transition, also called START, by inhibiting Clb5-CDK1 during G1 phase. 8 At START Cln2 production, in turn, induces Sic1 hyperphosphorylation, ubiquitination, degradation and consequently the entrance into S phase. 9 CLN2 and CLB5 belong to the G1 gene cluster and their mRNA levels peak in late G1 phase. 10,11 SIC1 transcription is mainly induced by two transcription factors, Swi5 in late mitosis and Ace2 in newborn daughter cells in early G1. [12][13][14][15] Besides the precise timing of different processes of cell cycle progression under normal growth conditions, the selected genes are involved in stress response. Stress adaptation is critical, since its dysfunctions can lead to genomic instability. 16 Exposure to high concentrations of osmolytes activates the stress MAP kinase Hog1, responsible for downregulation of CLN2 and CLB5 transcription and stabilization of Sic1 through phosphorylation, preventing its ubiquitination and consequently delays exit from G1. 17 Furthermore, studies using synchronized cell populations showed that cells also arrest in G2 18,19 and that the S phase is delayed and elongated. 16,20 However, the immediate influence of osmotic stress on transcription in unsynchronized cells and the long-term response remain elusive.
Understanding the function of cellular regulatory networks under normal and perturbed conditions requires precise data as basis for the development of a consistent quantitative model of the dynamic behavior of these networks. 21,22 Genome-wide assays on populations synchronized with α-factor (early G1), nocodazole (G2/M) or temperature-sensitive cdc15-2 mutant (G2/M) revealed the dynamics of genes controlling cell cycle, [23][24][25][26][27] but these methods are known to perturb cell cycle regulation. [28][29][30] Besides, synchrony within a population is usually not retained over the entire cell cycle, leading to a lack of precise information for later or short events in G2 and M phases. As progression of the synchronized population is relative to the time of release from the synchronizing agent, measured time-courses are challenging to link to specific cell cycle phases.
Established experimental techniques like RNA sequencing or quantitative PCR provide mostly relative mRNA numbers on the population level with extremely high variation of low abundant transcripts. 31 Absolute enumeration of mRNA molecules in single cells by smFISH confirmed the low transcript numbers found in the genome-wide assays, and showed transcriptional variability among cells in a population, which is considered as transcriptional noise. [32][33][34][35][36][37][38][39][40] Such single cell microscopy methods on fixed cells usually lack timing information on cell cycle dynamics. Consequently, time-resolved monitoring of absolute changes of mRNA numbers for cell cycle regulating genes is still missing to understand and model the transcriptional network, and its robustness against external stimuli (perturbations). In order to assess critical decisions during yeast cell cycle and to characterize the impact of noise in the light of small molecule numbers, a precise quantification of the temporal behavior is essential.
Here, we combined quantitative in vivo single molecule RNA-Fluorescence in situ hybridization (smFISH) experiments, in silico synchronization and stochastic modeling to precisely assess cell cycle progression timing and gene expression dynamics and variability. The strategy is illustrated in Fig. 1. We used asynchronous cell populations to avoid adverse influences caused by cell cycle synchronization methods. Instead, we used genetic and morphological markers to assign cells to specific cell cycle phases (Fig. 1d), counted mRNA numbers per cell in each phase and used the resulting distributions of mRNAs per phase to fit a time-resolved mathematical model, which we called in silico synchronization.
In detail, we quantified absolute transcript levels of SIC1, CLN2, and CLB5 in single cells and noise levels within a population in different cell cycle phases. We found that transcription of the three genes is never turned off, instead an enduring basal level throughout the entire cell cycle was detected. The basal level for the CKI SIC1 was higher than for the two cyclins. Each gene exhibited distinct expression pattern for periods of high transcription: SIC1 had a very sharp transcription peak in M phase with an almost instant decay. Both cyclins had their main transcription peak in late G1. CLN2 exhibited a longer period of transcriptional activity with slower decay than SIC1 and CLB5 showed a longer period of moderate transcription. Additionally, we observed an increase of CLN2 and CLB5 transcription in mitosis. Using a simple stochastic model for transcription and mRNA decay, we derived respective rate constants, as well as timing of periods of high and low expression and their noise levels.
For the case of osmotic stress, our model determined two distinct periods of transcriptional repression for the two cyclins, indicating different osmoregulation mechanisms, which could be related to a loss of synchrony between the timing of DNA synthesis and budding observed in our study. Moreover, studying osmostress-induced long-term changes we elucidated a shift of gene expression to later cell cycle phases.

RESULTS
Transcript distributions for SIC1, CLN2, and CLB5 in an asynchronous population We measured absolute transcript numbers of SIC1, CLN2, and CLB5 in single budding yeast cells of an asynchronous population with smFISH. We normalized the intensity of each detected mRNA fluorescent spots by the median fluorescence intensity of the spot population (see Supplementary Information Material and Methods). 96, 92, and 88% of the spots for SIC1, CLB5, and CLN2, respectively, contained one single mRNA molecule. Nuclear spots containing at least three mRNA molecules were defined as transcription start sites (TS). 41 Microscopic images and frequency distributions of mRNA numbers per cell showed different patterns for the three genes ( Fig. 2a, b and Supplementary Table S1) with averages of 4.53, 6.46, and 1.93 and medians of 2, 1, and 1 mRNAs/cell for SIC1, CLN2, and CLB5, respectively. These values were in the same order of magnitude as other smFISH studies on budding yeast 35,41,42  ( Supplementary Fig. S1). Ninety percent of the cells contained at least one SIC1 mRNA indicating that the transcription is not turned off completely, whereas CLN2 and CLB5 mRNAs were absent from about 40% of the population (Fig. 2b). SIC1 and CLN2 had long distribution tails (Fig. 2b).
Markers for cell cycle phase To investigate changes of mRNA abundances over cell cycle we used an asynchronous cell culture in combination with genetic and morphological markers to assign each cell to a cell cycle phase. These are: presence and size of a bud, morphology of the . Whi5 is recruited to the nucleus between late M and early G1 and is located in the cytoplasm during the rest of the cell cycle. 43 We distinguished seven phases, i.e., early G1, late G1, S, G2, prometa-/metaphase (P/M), anaphase (Ana) and telophase/ cytokinesis (T/C) (Fig. 1d). Tagging of Whi5 and Spc42 did not alter cell cycle progression as we obtained similar growth rates and mRNA distributions of SIC1, CLN2, and CLB5 for wild type and the strain containing Whi5-TagGFP and Spc42-mTurquoise (Supplementary Fig. S2). The doubling time was 129 min in YPD at 30°C (124 min for wild type). Phase durations were determined as being proportional to the fraction of cells in each phase 41 (Fig. 1d). For determination of cell cycle phases, we used more than 2600 cells.
SIC1 mRNA is present throughout cell cycle SIC1 transcript level was minimal between G1 and early mitosis, i.e., P/M, and increased in anaphase from its basal level of about 2 mRNAs/cell to a maximum of about 25 mRNAs/cell in T/C (Fig. 2c).
It dropped to about 4 mRNAs/cell when cells entered into next early G1 and further decreased until S phase. The SIC1 mRNA transcription maximum in T/C, i.e., late mitosis, is consistent with previous studies. [12][13][14] The percentage of cells containing active transcription sites reached a maximum in Ana and T/C phases ( Fig.  2d, Supplementary Fig. S3). To conclude, basal SIC1 presence is robust over the cell cycle. Indeed, in S, G2, P/M, the phases of lowest SIC1 expression, more than 80% of the cells contained at least one SIC1 mRNA (Fig. 2e).
CLN2 and CLB5 transcription shows enduring basal levels and rises in late mitosis As expected for genes of the G1 cluster, CLN2, and CLB5 showed transcription maxima in late G1 (Fig. 2c). We observed an unexpected transcriptional activity during late mitosis with 60% and 80% of cells containing at least one mRNA of CLN2 and CLB5, respectively, in T/C (Fig. 2e). Since only about 3% of the cells were in T/C, we would need higher cell numbers to statically characterize this phenomenon. Transcript levels of CLN2 and CLB5 were low in early G1 and increased to a maximum of about 18 and 4 mRNAs/cell, respectively, in late G1. During late G1, 94% and 86% of cells contained at least one transcript of CLN2 or CLB5, respectively (Fig. 2e). After G1/S transition transcript levels dropped. From G2 until mitosis, CLN2 and CLB5 levels were minimal, however, about 30% of cells contained at least one mRNA. The dynamics of transcription sites displayed maxima in late G1 and T/C (Fig. 2d, Supplementary Fig. S3).
Computational model for mRNA dynamics-rationalizing experimental data To understand mRNA dynamics based on static, but time-resolved, single cell smFISH data we stochastically modeled transcription and degradation for each species. In the model, signals S 1 to S 3 indicate the upregulation of transcription for SIC1 (S 1 ), CLN2 (S 2 ), and CLB5 (S 3 ) (Fig. 1c). We assumed equal degradation rate constants ( pi ) and different transcription (k ih or k il ) rate constants in periods of either high (h) or low (l) expression ( Table 1). Periods of high expression are defined by transcription start time (t Si;0 ) and transcription end time (t Si;e ). We assumed a second period of high transcription for CLN2 and CLB5, labeled as first and sec. The duration of one cell cycle is set to t = 129 min. Because the mRNA numbers were measured as distributions per cell cycle phase, a specific approach in parameter estimation was required. Since the mRNAs for each gene evolved statistically independently, we could estimate parameter values and transcription start and end times separately. We used the analytical solution of the chemical master equation for monomolecular reactions with Poisson initial conditions. We obtained the best results with a local optimizer falling into the class of "line search" algorithms (see Supplementary Information, Parameter estimation). Parameter values and transcription start and end times of our stochastic model were fitted to best reproduce the time- Fig. 2 Images and quantitative analysis of single-cell transcription for SIC1, CLN2, and CLB5 under optimal growth conditions in an asynchronous cell population. a Detection at single molecule resolution of endogenous SIC1, CLN2, and CLB5 transcriptional expressions with smFISH (red dots: mRNA molecules; blue: DAPI-stained nucleus). White arrows point towards transcription sites. Scale bar represents 5 μm. b Experimental and simulated distributions of mRNA number per cell for SIC1, CLN2, and CLB5 for the entire population (n > 900 cells). The overall averages are 4.53, 6.46, and 1.93 and medians are 2, 1, and 1 mRNAs/cell for SIC1, CLN2, and CLB5, respectively. c Measured and simulated mRNA distributions for each cell cycle phase. Lower and upper quartiles form boundaries of the boxes. Lines and white dots insight the boxes represent medians and mean values, respectively. Whiskers are given by 1.5 × IQR (interquartile range). Data points outside of the IQR define outliers. For better overview early G1 and late G1 are abbreviated to eG1 and lG1, respectively. In b and c experimental and simulated data are represented by colored and gray bars or boxes, respectively. d Fraction of cells with transcription sites (TS) in each cell cycle phase. Lines between data points are for visualization only. e mRNA distributions for each cell cycle phase grouped as follows: 0, 1-5, 6-11, 12-20, 21-30, >30 number of mRNA per cell (n > 900 cells see Supplementary Table S1 for data)  resolved frequency distributions of SIC1, CLN2, and CLB5 mRNAs (Fig. 2b,c, Supplementary Table S1 and Supplementary Fig. S4).
Transcription dynamics could only be fitted by assuming low, but non-zero, transcription outside the main transcription periods with relative promoter activities of 7.7, 0.4, and 15% for SIC1, CLN2, and CLB5, respectively. According to the Akaike criterion (AIC), the fits improved when allowing for two periods of high promoter activity for CLN2 and CLB5.
We analyzed the noise for experimental mRNA abundances and for simulated mRNAs using the coefficient of variation (CV), i.e., ratio of standard deviation to mean (Fig. 3, Supplementary Fig.  S13). Except of in late G1, SIC1 transcript population had the lowest experimental CV values and, therefore, the least degree of noise. Time-course simulations for mRNA numbers (Fig. 4a), noise over time (Fig. 4b), and noise per cell during one cell cycle period (see Supplementary Fig. S5) reproduced the experimental data (Fig. 2b,c, Fig. 3, Supplementary Fig. S4). Noise calculated in periods of either high or low expression both from the parameter values and based on the simulated time-courses (Fig. 3, Supplementary Fig. S5) revealed lower noise in high expression phases than in low expression phases.
Osmostress induces changes in the timing of cell cycle phases To test the robustness of G1/S transition with respect to perturbations, we exposed yeast cells to hyperosmolarity. Dependent on the cell cycle phase, cell cycle progression is delayed to allow stress adaptation.
To monitor stress response, we applied 0.4 M NaCl to a cell culture for 0, 15, 30, 45, 60, and 90 min and assigned each cell to a cell cycle phase (Fig. 5a and Supplementary Fig. S6). While cell cycle progression without stress is fully characterized, the cell cycle phase lengths upon stress reaction are affected to a so far unknown degree and, hence the sensitivity during different cell cycle phases to stress and the full cell cycle length remained undetermined. We found that the fraction of cells in each cell cycle phase, and hence the length of that phase, was affected differently and even after 90 min under stress conditions the distributions of cells in each phase had not totally recovered to the non-stress situation (Fig. 5a, Supplement Fig. 6). Cells accumulated in early G1 until 30 min and in G2 until 45 min of stress, respectively. The fractions of cells in both phases increased from 21.1 to 41.0% for early G1 and from 16.6 to 19.8% for G2. Simultaneously, the fractions of cells in late G1, S, and in mitosis (P/M, Ana, and T/C) decreased. Interestingly, the decrease of the mitosis fraction lasted longer than the one of late G1 and S phase fractions. Indeed, we observed that recovery of the mitosis fraction started after 60 min whereas those of late G1 and S fractions already after 30 min. The measured results are in agreement with our previous simulations obtained from modeling a cell population under osmostress. 44 Note, that since cells were not synchronized, the phase at which cells have been hit by stress could not be determined, especially after longer times of stress.
Osmostress induces a temporary inhibition of CLN2 and CLB5 and an elongation of CLN2 transcription to later cell cycle phases Upon osmostress, SIC1 mRNA levels and transcriptional dynamics were the least affected of the three genes (Fig. 5c, d and Supplementary Figs. S7 and S12A). SIC1 mRNA maximum was detected at the end of mitosis in T/C (Fig. 5d) and its basal level stayed robust from early G1 until the beginning of mitosis in P/M. The mean SIC1 level of the asynchronous population slightly increased within the first 30 min upon stress (Fig. 5c) due to the increase of SIC1 in T/C and anaphase at 15 and 30 min stress exposure.
Contrarily, CLN2 and CLB5 mRNA levels declined within the first 15 min upon osmostress and showed distinct recovery patterns ( Fig. 5c and d, Supplement Fig. S7). Within the first 15 min, CLN2 and CLB5 levels dropped from 6.4 to 2.0 and from 1.9 to 0.5 mRNA per cell, respectively, and later increased from 15 to 45 min. From 60 until 90 min of stress, CLN2 mRNA levels recovered to unstressed transcription level, while CLB5 levels at 90 min were still lower than before stress indicating only partial recovery within the cell population (Fig. 5c). The fraction of cells with transcription sites followed the behavior of their respective cyclin mRNA levels (Fig. 5c).
CLN2 and CLB5 transcriptional timing was also perturbed regarding individual cell cycle phases (Fig. 5d, Supplementary Figs. S7 and S12A). After 15 min of stress, the transcription of both cyclins was reduced. Both cyclin maxima in late G1 reappeared after 30 min and after 90 min the CLN2 peak was higher than before stress while the CLB5 maximum was not totally recovered, yet (Fig. 5d, Supplementary Fig. S7b, c). Interestingly, we observed a broadening of the CLN2 mRNA peak in late G1 into G2 and P/M phase after 30 and 45 min of osmostress, respectively (Fig. 5d,  Supplementary Fig. S7b). CLB5 showed an extension of its transcription peak in late G1 into G2 at 45 min (Fig. 5d,  Supplementary Fig. S7c).
Partial loss of synchrony between DNA replication and bud morphogenesis under osmostress Under normal growth conditions, budding and DNA duplication occur synchronously and are hallmarks of S phase entrance. [5][6][7] Under hyperosmotic conditions, we observed a small fraction of cells (1.3% of the population under normal growth conditions, 3.1% after 30 min of osmostress, and 1.1% after 90 min) with two spindle pole bodies but without bud (Fig. 5a, green box, Fig. 5b,  Supplementary Fig. S6), indicating loss of synchrony between bud Computational modeling of mRNA levels under osmotic stress To simulate osmotic stress response of G1/S main regulators, we assumed that high-level transcription of CLN2 and CLB5 (mainly during late G1) was interrupted during the period of osmotic adaptation and resumed afterwards. Depending on the time point when osmotic stress hits the cell, the inhibitory effect on CLN2 and CLB5 transcription, as well as the delay of following cell cycle phases is different (for case-by-case analysis see Supplementary  Fig. S8). Since all other model parameters were fitted already for the non-stress scenario, the remaining parameters to fit were the periods t d of transcriptional repression. Employing the experimental single-cell mRNA distributions and means, we obtained values of t d,CLN2 = 28 min for CLN2 and t d,CLB5 = 12 min for CLB5. To determine these values, we tested 676 combinations of t d,CLN2 and t d,CLB5 ranging from 5 to 30 minutes for each gene. We run 200 simulations for 200 random stress time points for each combination and compared the simulated distributions 0, 15, 30, 45, 60 and 90 minutes after stress with our experimental data. The best combination of t d,CLN2 and t d,CLB5 minimized the total squared distance between simulated and experimental mRNA distributions during individual cell cycle phases and at different time points upon stress (Supplementary Figs. S9-S11). Figure 4c, d show resulting time-courses for mRNA numbers and noise levels over time. As expected, the time-course of SIC1 and its related noise were only slightly affected by osmotic stress (Fig. 4c, d Supplementary Fig. S13). Simulated SIC1 levels stayed low from early G1 to P/M and displayed high expression in Ana and T/C (Fig.  5d, e, Supplement Fig. S12). Both CLN2 and CLB5 showed higher noise levels compared to no stress condition in late G1 and S phases (Fig. 4c, d). Both cyclins also experienced severe downregulation at 15 min of stress, especially for cells being in late G1 phase (Fig. 5d, e, Supplement Fig. S12). During recovery, cells being in S phase had higher CLN2 and CLB5 mRNA numbers than unstressed cells (Fig. 5d, e, Supplement Fig. S12).

DISCUSSION
Stochastic modeling simulates time-courses of mRNA and noise from static single cell mRNA microscopy data We applied smFISH to SIC1, CLN2, and CLB5, i.e., regulators of G1/S transition in yeast, and used genetic and morphological markers to assign cells to cell cycle phases and thereby obtained absolute   Supplementary Fig. S6. The cells were assigned to each phase using the markers previously described in Fig. 1 (n > 1500 cells per time point). b Fluorescence microscopy images depicting a fraction of cells that experience a loss of synchrony between DNA replication and budding under osmotic stress. Red arrows point to cells containing two separated spindle pole bodies without bud. The image is an overlay of bright field image, DAPI-stained nucleus (in blue) and mTurquoise tagged Spc42 part of the spindle pole body (in green). Scale bar represents 5 μm. (c) and (d) n > 400 cells per genes and time points. Raw data in Supplementary Table  S1 and Biological Replicates in Supplementary Information. c Changes in mRNA levels shown as mean ± SEM (dots and full lines) and transcription activity represented by percentage of cells with a transcription site (TS) (dots and dotted lines). Plot insets represent a zoom in. d Influence of osmostress on timing of mRNA abundances for SIC1, CLN2, and CLB5 during the cell cycle. Data shown are mean ± SEM. Darkest curves correspond to the shortest incubations in hyperosmotic medium. (e) Simulated changes of timing of mRNA abundances for SIC1, CLB5, and CLN2 during the cell cycle progression upon osmotic stress (n = 2000 cells). Data shown are mean ± SEM. Details of (D) and (E) depicted in Supplementary Fig. S12. In a, c, d, and e 0 min is equivalent to no stress conditions. Lines between data points in c, d, and e are for visualization only Transcriptional timing and noise of yeast cell cycle regulators A Amoussouvi et al. unperturbed situations and during stress. This is currently technically very challenging. To overcome this limitation, we used static single cell data and performed an in silico synchronization.
This approach revealed detailed quantitative insights into transcriptional regulation and profiles with and without stress that were not available from studies with synchronized cells, since all available synchronization methods have adverse side effects and only limited duration of synchrony.
We found enduring basal levels of expression of all three genes, but highest for SIC1. Therefore, we considered phases of high and low expression in the computational model. The model, revealed -as expected-lower noise during periods of high transcription than during low transcription for each mRNA species. However, we found lower noise for SIC1 than for CLN2 or CLB5 in both high and low expression periods.
A potential consequence of the basal levels of SIC1 may be to prevent strong transcriptional bursts and, thus, higher transcript noise, 45,46 as well as cell cycle timing noise. 43,47 FRET measurements revealed that Sic1 binds to Clb2, Clb3, and Clb5 suggesting a role for Sic1 in different phases and not restricted to G1/S transition. 48 Indeed, these cyclins lost their oscillation-like periodicities in cells lacking Sic1. 49 As sole CKI of B-type cyclins, Sic1 is therefore important to act as cell cycle timer under normal conditions, but as brake under stress. We suggest that the basal transcription of SIC1 might be an advantage to enable smoother and less burst-like expression peaks, as well as to provide basal Sic1 protein levels in case the cell cycle must suddenly be arrested.
Single mRNA FISH and in silico synchronization revealed precise quantification and timing of gene expression We observed a sharper peak of SIC1 in late mitosis (Ana and T/C) dropping in early G1. In comparison, previous works using population assays reported that SIC1 mRNA and Sic1 protein levels remain high until S phase entrance. 50,51 This expanded expression of SIC1 might be due to the limitations of synchronization to resolve the short phases of mitosis. In addition previous studies differed on the initiation of SIC1 main transcription in or after anaphase. [12][13][14] We could show that the SIC1 peak in mitosis starts during anaphase.
CLN2 and CLB5 mRNA maxima in late G1 agree with previous reports for population studies using α-factor or elutriation for synchronization in G1 for CLN2 52,53 and for CLB5, 8,35,54 but timing of cell cycle phases differs between synchronized cultures and non-synchronized cultures, due to the shortened cell cycle length of chemically synchronized cells, which keep gaining size without cell cycle progression. CLB5 mRNA was found to decay after exit from S phase leading to minimal levels of CLB5 mRNA 55,56 and Clb5 protein 20 from S throughout M until G1. The CLN2 maximum was 4-fold higher than that of CLB5 as previously observed for mRNA 23,24 and protein levels. 57 This might be due to a positive feedback loop of Cln2 triggering its own expression. 52,58,59 The unexpected transcription upshift in late mitosis of both cyclins might have been overlooked in previous studies due to the loss of synchrony at later cell cycle phases in populations synchronized in G1. 35 A potential explanation for the mitotic transcription is that CLN2 and CLB5 transcription is mainly induced by the transcription factor complexes SBF (SCB-binding factor) and MBF (MCB-binding factor), respectively, in late G1. 10,11,60 In late mitosis, nuclear Whi5 inhibits CLN2 transcription by binding to SBF. 43,61 It was shown that Zinc finger protein Rme1, which has maximum expression at M/G1, induces promoter activity at CLN2 loci. 62 However, the repressor Nrm1 is inhibiting MBF outside G1 phase 63 but is degraded at the exit of mitosis. 64 As a result, there may be a short time window allowing transcription of cyclins when SBF and MBF are bound to the promoters and not yet inhibited.
Osmostress induces arrests in early G1, as well as in G2 and longterm effects We placed special emphasis on the effect of stress-here osmotic stress-on gene expression. While most previous studies focused on the initial phase of adaptation using synchronization methods, we also investigated long-term effects of hyperosmolarity on cell cycle progression. Measuring the fraction of cells per cell cycle phase at different times of stress, we observed different effects on cell cycle progression throughout the single cell cycle phases. Even after 90 min the initial subdivision of the population into cell cycle phases was not fully restored, consistent with previously reported two hours for recovery. 65 Cells accumulated in gap phases, early G1 and G2, with a preference for early G1. This may indicate that arrest in early G1 before START, which prevents DNA replication, may be more important than arrest in G2, which delays nuclear division and allows for DNA repair. Consequently, the fractions of cells decreased in late G1, S, and mitosis. Previous studies showed that S phase is delayed and elongated upon osmostress to ensure genomic integrity by preventing collisions between the replication and transcription machineries due to transcriptional bursts of stress-induced genes. 20, 66 We could not observe S phase elongation because, although some individual cells may have had longer S phases, the overall S phase group decreased as cells arrested in early G1. Since osmostress hits nonsynchronized cells at arbitrary cell cycle phase and affects all phases, measuring osmoadaptation in single living cells using e.g., microfluidic devices, cell cycle markers and MS2 tagging system 67 would provide deeper insight into the exact timing of cell cycle progression and gene expression under stress conditions. Intriguingly, after osmostress we observed cells having two spindle pole bodies but no bud, exhibiting a loss of synchrony between DNA replication and budding. This fraction of cells reached a maximum after 30 min of stress. A comparable phenomenon was observed when osmostress was applied close to or after START. 22 Adrover and colleagues suggested that after START cells lost the ability to arrest in G1 in response to stress and initiated DNA replication whereas budding was delayed by about 30 min.
We measured different inhibition duration and recovery patterns for CLN2 and CLB5 indicating distinct osmoregulation mechanisms of these cyclins. In unstressed cells, their transcription is triggered synchronously 11,68 ensuring simultaneous budding and DNA replication. However, upon osmostress Hog1 appears to downregulate CLN2 and CLB5 transcription independently and for different periods. Whereas Hog1 is specifically recruited to the CLB5 promoter inhibiting transcription, 22 Hog1 targets Whi5 to downregulate CLN2. 69 In contrast to the transient inhibition of CLN2 and CLB5 transcription, SIC1 expression was less affected upon hyperosmolarity. The differential behavior of SIC1 and the cyclins is reflected by their different roles in cell cycle progression and stress response. Sic1 as inhibitor of B-type cyclins and, hence, inhibitor of cell cycle progression may be crucial to control the delay of cell cycle events required under stress. In contrast, Cln2 and Clb5 are activators of the G1/S transition.

CONCLUSION
Combination of single molecule FISH and microscopy with a mathematical model revealed detailed and quantitative regulatory patterns in gene expression of three well-known G1/S regulators. Detection of a ubiquitous basal expression level, an unexpected mitotic expression, the determination of molecular noise, as well as dynamics of transcription recovery upon hyperosmolarity required a quantitative single cell resolution method. Furthermore, the use of morphological cell cycle markers can avoid adverse side effects and the averaging effect of synchronized population Transcriptional timing and noise of yeast cell cycle regulators A Amoussouvi et al.
assays. Our mathematical model enabled computational cell cycle synchronization and to rationalize the experimental data. Future investigations could address the question whether these patterns are specific to SIC1, CLN2, and CLB5 or general to other cell cycle regulators in yeast or to homologous genes in other organisms.

Strain and plasmid construction
For allocation of the cell cycle state of individual cells we cloned a marker strain, with mTurquoise labeled spindle pole bodies and TagGFP labeled Whi5. 41 We used BY4741 (MATa his3Δ1 leu2Δ0 met15Δ0 ura3Δ0) haploid yeast strain as parental strain (EUROSCARF n. Y00000). For detailed protocol, see Supplementary  Single molecule RNA-Fluorescent in situ Hybridization (smFISH) procedure For each transcript, SIC1, CLN2, and CLB5, a set of approximately 35 fluorescently labeled probes was used as described in ref. 70

Stochastic model of transcription regulation
The model as described in Table 1 has been stochastically simulated using the Gillespie algorithm. For simulation of mRNA time-courses, 2000 cells have been simulated. In order to have comparable values at comparable time points, snapshots of the system have been taken every minute, i.e., the current molecule numbers at every full minute have been recorded. The resulting lists of 129 values for one cell cycle have then been used to calculate means, standard deviations and coefficients of variation for each mRNA. However, the simulation started 15 min before cell cycle start (starting from anaphase of one cell cycle to the T/C phase of the next cell cycle). In case of osmotic stress, 250 min were simulated to cover 129 min of cell cycle, 15 min for anaphase and T/C phase, the delay due to osmostress and the up to 90 min of stress duration. The respective number of time points was analyzed, depending on the time point of stress. Code availability: The code can be sent upon request.

Data availability statement
Experimental frequency distributions of mRNA numbers per cell of SIC1, CLN2, and CLB5 under normal (Fig. 2b, c) and hyperosmotic (Fig. 5c, d) conditions are available as excel table in Supplementary Table S1. Numerical values of Fig. 5a are given in Fig. S6. Additional data that support the findings of this study are available from the corresponding author upon reasonable request.