Single-cell imaging reveals a key role of Bck2 in yeast cell size adaptation to nutrient challenges

The size of a cell is a critical regulator of its function, and misregulation of cell size is associated with various disease states (Chadha et al., 2024). While the underlying causal relationships are often unclear, recent studies have revealed that increased cell size promotes cellular senescence and contributes to aging (Lengefeld et al., 2021; Manohar and Neurohr, 2024; Neurohr et al., 2019). It is therefore crucial that cell size is tightly controlled and adapted according to external and internal parameters, such as dynamic environments and developmental changes. Size homeostasis, i.e., the maintenance of narrow cell size distributions, is attributed to the cell’s ability to measure its size and coordinate cell cycle progression and cell growth with cell size (Cadart et al., 2018; Ginzberg et al., 2018; Soifer et al., 2016). For example, one common size-sensing strategy that has been reported for budding yeast (Schmoller et al., 2015), plant (D’Ario et al., 2021), and mammalian cells (Zatulovskiy et al., 2020; Zhang et al., 2024) is the cell growth–based concentration decrease of a cell cycle inhibitor.

However, while such specific size control mechanisms have been identified, there is growing evidence that eukaryotic size homeostasis is a product of multiple size control strategies (Garmendia-Torres et al., 2018; Miller et al., 2023). In fission yeast, for example, diverse mechanisms integrate cell surface area, cell volume, and time information into cell size control (Miller et al., 2023). Similarly, in budding yeast, the concentration of the size-sensing protein Whi5 alone accounts for the size-dependent likelihood of commitment to the G1/S transition in a bck2Δ strain (Schmoller et al., 2015), but multiple other activators and inhibitors of the same cell cycle transition have been identified (Chen et al., 2020; Soifer and Barkai, 2014). Accordingly, disruption of the Whi5-based mechanism only leads to a partial loss of size control (Chen et al., 2020; Barber et al., 2020; Swaffer et al., 2021).

In budding yeast, size control through size-dependent cell cycle progression occurs mainly at the G1/S transition, and dilution by cell growth of the G1/S inhibitor Whi5 is one of the major underlying mechanisms (Schmoller et al., 2015; Qu et al., 2019). The G1/S transition is preceded by the commitment point Start, which is largely irreversible due to an underlying positive feedback loop controlling the G1/S transcription factors SBF and MBF (Fig. 1 A, Irvali et al., 2023; Skotheim et al., 2008). SBF is inhibited by Whi5 and activated by Cln3 and Bck2 (Bastajian et al., 2013; Costanzo et al., 2004; de Bruin et al., 2004; Kõivomägi et al., 2021). Once the positive feedback loop is triggered, Cln1 and Cln2 are expressed and, in complex with Cdk1, phosphorylate Whi5 to ensure the irreversibility of Start. All cells are born with roughly equal amounts of Whi5, and it is diluted by cell growth during G1 (Schmoller et al., 2015; Schmoller et al., 2022; Swaffer et al., 2021; Qu et al., 2019; Sommer et al., 2021; Xiao et al., 2024), whereas Cln3 and Bck2 concentrations remain mostly constant as G1 progresses (Schmoller et al., 2015; Chen et al., 2020). This widening imbalance between SBF activator and inhibitor concentrations is believed to incorporate cell size information into the cell cycle progression decision (Schmoller et al., 2015; Chen et al., 2020) and ultimately trigger the positive feedback loop.

Cln3 and Bck2 are both activators of the G1/S transition. Bck2 activates the G1/S transition in parallel to Cln3 by binding transcription factors Mcm1 and SBF at the CLN2 promoter (Bastajian et al., 2013; Ferrezuelo et al., 2009). Additionally, it promotes the expression of Cln3 and the SBF subunit Swi4 at the M/G1 transition, and of the cyclin Clb2 at the G2/M transition (Bastajian et al., 2013). Deleting either Bck2 or Cln3 leads to an increased cell volume (Costanzo et al., 2004; Wijnen and Futcher, 1999), and the double deletion causes synthetic lethality (Epstein and Cross, 1994). Despite the changing average cell volumes, size homeostasis, assessed by the coefficient of variation (CV) of cell volume of a population, is surprisingly robust to single deletions of Cln3, Bck2, and Whi5, as well as other Start regulators (Chen et al., 2020). While such robustness could be an explanation for why cells evolved multiple redundant Start regulators, an alternative explanation is that the apparently redundant regulators fulfill unique roles under specific conditions that have not yet been identified.

Most size control studies so far have been conducted under steady-state conditions, i.e., during exponential growth in constant environments. Outside laboratory conditions, however, microorganisms frequently encounter rapid changes in the nutritional quality of the environment, which can lead to immediate effects on cellular decision making at the G1/S transition (Irvali et al., 2023). Moreover, nutrient availability is known to be a major regulator of cell size, with richer nutrients leading to larger cell sizes (Qu et al., 2019; Johnston et al., 1977; Leitao and Kellogg, 2017; Talavera et al., 2024). Changing nutrient conditions therefore require dynamic adaptation of cell size, and cell size regulators that appear redundant in constant growth conditions may have specific functions during this size adaptation. Indeed, previous findings point toward specific roles of Cln3 and Bck2 during nutrient changes: the Cln3 protein is very unstable with a half-life on the order of minutes (Tyers et al., 1992), and has therefore been proposed to act as a reporter for global cellular protein synthesis (Sommer et al., 2021; Tyers et al., 1992). Consistent with such a role, both the Cln3 protein and mRNA amounts are sensitive to nutrient availability (Hall, 1998; Parviz and Heideman, 1998), and a switch from a rich to a poor carbon environment is followed by an immediate Cln3 depletion (Sommer et al., 2021). Bck2, on the other hand, is not as well studied as Whi5 or Cln3, but has been shown to interact with multiple proteins with known roles in nutrient-sensing pathways (Bastajian et al., 2013). It has been proposed to be a link between the nutrient status of the environment and passage through the M/G1 transition (Bastajian et al., 2013). However, how Bck2 affects the dynamic adaptation of cell size to changing nutrient conditions is not clear.

Here, we use the budding yeast Saccharomyces cerevisiae as a model to investigate specific functions of apparently redundant cell size regulators during dynamic cell size adaptation to environmental changes. With microfluidics-based live-cell microscopy and state-of-the-art deep learning–based image analysis, we follow the fates of single cells and their complete lineages for multiple generations before and after a nutrient switch from fermentable to nonfermentable carbon sources. By following individual cells, we gain insights into the heterogeneity of cell size adaptation and find that the cell cycle state of a cell at the time of the nutrient shift plays a crucial role for the size adaptation of its offspring. Moreover, through analysis of deletion mutants, we uncover a unique role for Bck2. We find that after the nutrient switch, size homeostasis is temporarily disrupted, and this disruption is stronger in bck2Δ mutants, which show longer cell cycle arrests. Based on our findings, we propose that Bck2 acts as an essential G1/S transition activator for the period of time following a nutrient switch when Cln3 is depleted. More generally, our work suggests that the apparent redundancy of cell size regulators observed across eukaryotes in steady-state conditions may point to specific roles during dynamic cell size adaptation.

Bck2 is mostly thought to promote the G1/S transition independently of Cln3 and Whi5 (Bastajian et al., 2013; Ferrezuelo et al., 2009). However, Manukyan et al. (2008) proposed that Bck2 stimulates the cytoplasmic deadenylase Ccr4, promoting degradation of WHI5 mRNA (Fig. 1 A). Specifically, they found that WHI5 mRNA was more stable in the absence of Ccr4 in a GALpr-WHI5 strain after switching from galactose to glucose medium. Thus, as a first step to better understand the apparent redundancies of Bck2 and Cln3 for budding yeast G1/S size control, we decided to test this proposed interaction between Bck2, Ccr4, and Whi5 under steady-state conditions and for endogenous Whi5. We used RT–quantitative PCR (qPCR) (Fig. 1 B) and single-molecule fluorescence in situ hybridization (smFISH) (Fig. 1, C and D; and Fig. S1 A) to measure the effect of deleting BCK2 or CCR4 on WHI5 transcript abundance for cells growing on glucose medium (synthetic complete medium with 2% glucose [SCD]), but did not see a significant increase. Next, to gain further insights into the genetic interaction between CCR4 and WHI5, we performed time-lapse live-cell microscopy experiments (Fig. 1, E–G) and Coulter counter measurements (Fig. S1, B and C) of cell volume for single and double deletion strains. We found that whi5Δ cells were smaller, and ccr4Δ cells were much larger than wild-type cells. However, whi5Δccr4Δ did not rescue the large-cell phenotype of ccr4Δ. Taken together, our findings are not consistent with Ccr4 impacting cell size through destabilizing Whi5 mRNA. Instead, our data show that Whi5 and Ccr4 affect cell size via independent pathways.

We also performed time-lapse microscopy experiments for WHI5 and BCK2 single and double mutants growing on glucose medium (SCD), as well as glycerol–ethanol medium (synthetic complete medium with 2% glycerol and 1% ethanol [SCGE]). Consistent with previous studies (Chen et al., 2020; Costanzo et al., 2004; de Bruin et al., 2004; Di Como et al., 1995), whi5Δ and bck2Δ led to a significant decrease and increase in cell volume, respectively, and the volume of whi5Δbck2Δ cells was strikingly similar to that of wild type in both growth media (Fig. 1 F and Fig. S1, D–G). Thus, the effect of Bck2 and Whi5 on cell size appears to be additive, indicating that Whi5 is not downstream of Bck2 and that they affect cell size via independent paths.

After analyzing mean cell volumes, we next asked how size control is affected in each of the mutants. As a measure for size homeostasis efficiency, which is comparable between differently sized strains, we chose the CV of cell volume, i.e., the mean-normalized standard deviation of the cell volume distribution. Consistent with their roles in G1/S size control, we found that deletion of either WHI5 or BCK2 leads to an increased CV of cell volume, both for cells growing on SCD or SCGE (Fig. 1 G; and Fig. S1, F and G). We expected that deletion of both genes would lead to a further reduced size homeostasis efficiency. Surprisingly, the CV of cell volume of whi5Δbck2Δ cells was not higher than that of the single deletion mutants (Fig. 1 G). For cells growing in SCD, whi5Δbck2Δ even showed a significantly decreased CV compared with both Δwhi5 and Δbck2 (Fig. 1 G), similar to wild-type cells. Thus, we found that size homeostasis as evaluated by the CV of the cell volume across a steady-state population was surprisingly robust to the double deletion of WHI5 and BCK2, in particular for cells grown in SCD. In contrast, deletion of CCR4 led to a dramatically increased CV of cell volume for cells grown on glucose, which was not rescued by an additional deletion of WHI5 (Fig. 1 G). This indicates a rare occasion of a drastically weakened size homeostasis mechanism. However, given that Δccr4 cells grow very poorly, especially in SCGE, it is unlikely that this lower size homeostasis is a result of disrupted G1/S size control alone.

Prompted by the fact that the absence of Whi5 and Bck2, two major cell size regulators acting at the G1/S transition, does not have a stronger size homeostasis phenotype, even though deletion of each protein individually leads to altered cell volume and weakened size control, we speculated that double deletion of WHI5 and BCK2 may impair cell size adaptation upon changing nutrient conditions. To investigate this, we performed a bulk nutrient switch experiment, shifting cells from SCD to SCGE (Fig. 2 A). Specifically, steady-state populations of cells growing in SCD were washed and inoculated into SCGE (Fig. 2 A) at a starting OD_600nm of 0.01. We then performed a time course of OD_600nm and Coulter counter measurements of cell volume from the time of the nutrient switch up until a new steady state in the glycerol–ethanol medium was reached (Fig. 2, B–D). The OD_600nm was maintained between 0.1 and 1 through appropriate dilutions. For the first 15 h after the nutrient switch, both mean cell volume (Fig. 2 B) and CV of cell volume (Fig. 2 D) increased. Considering the direction of the switch was from a rich medium to a poorer medium, ultimately leading to a smaller mean cell volume after switch, the initial increase in cell volume was unexpected.

This initial increase in mean cell volume and CV of cell volume was not accompanied by notable cell proliferation. Only about 15 h after the switch, OD_600nm started to increase again, and at the same time, mean cell volume and CV of cell volume started to decrease (Fig. 2, B and D). Interestingly, during the time of maximal cell volume around 10–20 h after switch, whi5Δbck2Δ cells showed significant differences compared with wild type. We found that the CV of cell volume of whi5Δbck2Δ was significantly higher than that of wild type between 10 and 20 h after switch (Fig. 2 D). After 20 h, while the CV of whi5Δbck2Δ still appeared to be slightly higher than that of wild type for the remainder of the experiment, the difference was not statistically significant. Thus, both wild-type and whi5Δbck2Δ cells showed an increase in cell volume and CV of cell volume after switch, but whi5Δbck2Δ had lower size homeostasis efficiency than wild-type cells. This suggests that the simultaneous loss of both Whi5 and Bck2 does affect size homeostasis, but this effect is more prominent under changing nutrient conditions.

To better understand why both strains underwent an increase in cell volume and CV of cell volume after the switch, and why whi5Δbck2Δ cells had a higher CV of cell volume, we performed live single-cell microscopy of cells experiencing the nutrient switch. We grew steady-state cultures of wild type, whi5Δ, bck2Δ, and whi5Δbck2Δ in SCD and transferred them to a custom microfluidics device (Kukhtevich et al., 2022) in a time-lapse microscopy setup (Fig. 3 A). We imaged the cells at 3-min intervals as they grew in SCD for 2 h and then automatically switched the medium to SCGE for the next 25 h. The videos of cell growth generated from this experiment were analyzed using the Cell-ACDC pipeline (Padovani et al., 2022; Padovani et al., 2025) and YeaZ (Dietler et al., 2020) for cell segmentation (Fig. 3 A). The cell masks and tracking were then manually corrected, and pedigrees were assigned in a semiautomated fashion in the Cell-ACDC GUI. Based on phase-contrast images, cells were classified as G1 (unbudded) or S/G2/M (budded) cells. This resulted in a fully annotated and manually corrected dataset of several thousand complete cell cycles (Fig. 3 A).

On qualitative inspection of colony growth in the live-cell microscopy videos obtained during the nutrient switch, we found that cells roughly doubled in number during the first 2 h in SCD, as is expected from steady-state cells in glucose (Fig. 3 B). After the nutrient switch to SCGE, cells arrested for a period of around 5 h (wild type) but continued to grow in volume. At 5 h after switch, the cells very slowly resumed cell cycle progression. At around 10 h after switch, the cell population appeared to have heterogeneous cell sizes, with large cells that had faced the arrest and small cells born after the arrest. It is important to note here that the limited number of cells that can be analyzed in this assay, in particular at the beginning of the experiment, leads to a large experimental error in the CV of cell volume (Fig. S2). Nevertheless, quantitative analysis confirms the general trends observed in the bulk nutrient switch experiment (Fig. 2 D), namely, that both cell volume and CV of cell volume initially increase after the nutrient switch (Fig. S2). Importantly, we found that the dynamics with which cells resume growth after the nutrient switch are very similar between wild-type and the deletion mutant cells (Fig. S3, A–D). This suggests that differences in the adaptation of cell size are dominated by differences in cell cycle progression, rather than global differences in growth rate due to differences in metabolic adaptation (Fig. S3, A–D). To better understand the postswitch adaptation and its effect on cell volume, it is necessary to consider the cell cycle history of each cell. Accordingly, cells were split into multiple categories (Fig. 3 C), which we then studied separately. All cells that were growing in SCD and faced the nutrient switch to SCGE were categorized as “switchers” (Fig. 3 C). At the time of the nutrient switch, the switchers could have been either unbudded or budded and were respectively further categorized into “G1-switchers” or “S/G2/M-switchers.” The specific cell cycle of the switchers during which the nutrient switch occurred was called the “switch-cell-cycle” (Fig. 3 C, highlighted in yellow). As these switchers overcame the postswitch arrest and finished the switch-cell-cycle, they divided to give rise to the first round of daughters. The switchers then entered the cell-cycle-after-switch-cell-cycle (Fig. 3 C, highlighted in green), at the end of which they gave rise to the second round of daughters. The following rounds of daughters were categorized analogously (Fig. 3 C, highlighted in blue). The rounds of daughters could be further categorized into daughters of G1-switchers or daughters of S/G2/M-switchers. Notably, the first round of daughters of S/G2/M-switchers was the only category apart from the switchers themselves that faced the nutrient switch—as buds of the S/G2/M-switchers. Albeit complex, this careful categorization of cells was key to identifying specific phenotypes in response to the nutrient switch in the following analysis.

As described in Fig. 4, we analyzed two specific cell cycles of switchers: the switch-cell-cycle (Fig. 4 A, highlighted in yellow) and the cell-cycle-after-switch-cell-cycle (Fig. 4 A, highlighted in green). G1-switchers arrested in G1 during the switch-cell-cycle (Fig. 4 B, left, yellow). The following S/G2/M phase of the switch cycle was not strongly affected in length and was similar to that of cells growing exponentially in SCGE. Also, the phase lengths in the next cell cycle of G1-switchers (cell-cycle-after-switch-cell-cycle, Fig. 4 B, left, green) were similar to those of cells growing exponentially in SCGE. On the other hand, S/G2/M-switchers naturally had a normal steady-state G1 length in SCD and arrested in S/G2/M after switch (Fig. 4 B, right, yellow). After completing the switch-cell-cycle, they also exhibited a strongly prolonged G1 phase in the next cycle (Fig. 4 B, right, green). However, the duration of the subsequent S/G2/M was close to that of cells exponentially growing in SCGE (Fig. 4 B, green). These results showed that all cells that faced the nutrient switch immediately arrested in the ongoing cell cycle stage. For S/G2/M-switchers, the next G1 was also prolonged.

For each strain, the immediate G1 arrest of G1-switchers led to an increased cell volume at the end of G1 (Fig. 4 C, left, yellow). The following G1, although short, slightly increased the cell volume further (Fig. 4 C, left, green). Similarly, also for S/G2/M-switchers of all strains, the G1 arrest in the cell-cycle-after-switch-cell-cycle led to cell enlargement compared with cells growing in constant SCD media (Fig. 4 C, right, green). During these G1 arrests, cells that lacked Bck2 grew more than wild-type cells with similar initial cell volume (Fig. S3, E and F) and therefore exhibited stronger enlargement and a bigger drift from their steady-state sizes as compared to wild-type and whi5Δ cells in both categories of switchers (Fig. 4 C). These G1 arrests therefore were sufficient to cause significant differences in cell volume at the end of G1 between wild-type and whi5Δbck2Δ cells. The G1 arrests also contribute to the diverging CV and mean cell volume observed after switch in the bulk nutrient switch experiment (Fig. 2).

So far, we have shown that deletion of BCK2 leads to more enlarged switchers during their first G1 after the switch. Apart from the actual switchers, also the first round of daughters of S/G2/M-switchers faced the switch because they were present as buds (Fig. 5 A, highlighted in blue, cell number 1). The first round of daughters of G1-switchers, on the other hand, first appeared after the nutrient switch. G1 duration was three- to fourfold longer for the first round of daughters of S/G2/M-switchers, indicating that they arrested in G1 (Fig. 5 B). This phenomenon was specific for this category of cells, as daughter cells born in the following rounds and those of G1-switchers showed G1 durations more similar to steady-state growth on SCGE (Fig. 5 B). Consequently, the first round of daughters of S/G2/M-switchers was also larger at G1 end, with bck2Δ and whi5Δbck2Δ cells again growing more, even at a given starting cell volume (Fig. S3 G). Thus, they show significantly stronger enlargement compared with cells in steady state in SCD media than the other strains (Fig. 5 C). The G1 arrest was also longer for the Bck2 mutant strains as compared to the others (Fig. 5 B). It appears that the cells that faced the switch in S/G2/M, either as mother or bud, carried the memory of the switch into the next cell cycle, leading to a prolonged G1 phase in the next cycle. Moreover, the first daughters of S/G2/M-switchers showed weakened size control (Fig. S4) and lower survival (Fig. S5 A).

After showing that S/G2/M-switchers and their first daughters exhibit a prolonged first G1 following the nutrient switch, we asked at what point in G1 cells arrest, and whether this arrest depends on the exact cell cycle stage at the time of the nutrient switch. To further characterize this multigenerational arrest phenotype, we employed cell cycle reporters that allowed us to resolve the cell cycle into more specific cell cycle phases. In particular, we used a mCitrine-tagged mutant WHI5 allele, WHI5-WIQ, integrated into the URA3 locus, while the endogenous WHI5 gene remained unaltered. The Whi5-WIQ protein is a loss-of-function mutant that does not bind SBF (Travesa et al., 2013) but retains its ability to localize to the nucleus in a cell cycle–dependent manner. In addition, we tagged the histone HTB2 with the fluorescent protein mScarlet-I. The deletions of interest—Δwhi5, Δbck2, and Δwhi5Δbck2—were then introduced into this cell cycle reporter strain, and the nutrient switch experiment was repeated. Fluorescently tagged Htb2 allowed us to segment a nuclear mask for each cell. Using the nuclear mask along with cellular segmentation, we could quantify fluorescence signal in three compartments: the whole cell, the nucleus, and the cytoplasm. Whi5 has previously been reported to be nuclear from telophase until Start, while CDK activity is low (Taberner et al., 2009). For cell categories of interest, we identified Start as the G1 frame at which 50% of Whi5 had exited the nucleus (Doncic et al., 2011) (Fig. 6 A). We used the Htb2-mScarlet-I amount in the bud as a marker for the entry of the dividing nucleus into the bud, which occurs during anaphase in mitosis (Bloom, 2001) (Fig. 6 A). Anaphase was presumed to continue until Whi5-WIQ-mCitrine reentered the nucleus (Taberner et al., 2009) (Fig. 6 A). The nuclear reentry of Whi5-WIQ was annotated as the start of telophase, and subsequent frames were labeled as post-anaphase (Fig. 6 A). Fig. 6 B shows the cell cycle phases of the first round of daughters of S/G2/M-switchers. After splitting G1 into pre- and post-Start, we found that the G1 arrest observed in the first round of daughters of S/G2/M-switchers was predominantly in pre-Start G1 (dark green areas, Fig. 6 B). Upon quantification (Fig. 6 C), we found that bck2Δ and whi5Δbck2Δ cells appear to have longer pre-Start G1 durations as compared to wild type (albeit not statistically significant).

A previous study by Leitao et al. (Leitao and Kellogg, 2017) has shown that a shift from glucose to glycerol–ethanol media leads to a long arrest for cells that experience the shift in metaphase, but not for anaphase cells. We therefore asked whether the specific cell cycle phase of S/G2/M-switchers at the time of the nutrient switch also affects the severity of the G1 arrest in their first round of daughters. Thus, we categorized the first round of daughters of S/G2/M-switchers by whether the mother was in pre-anaphase, anaphase, or post-anaphase at the time of nutrient switch and analyzed the corresponding G1 lengths (Fig. 6 D; and Fig. S5, B and C). Fig. 6 D shows the durations of the G1 phases of the first round of daughters of S/G2/M-switchers that completed G1 during the course of the experiment. The fraction of the first round of daughters of S/G2/M-switchers that did not complete G1, i.e., remained arrested in G1 until the end of the experiment, is shown in Fig. 6 E, and the lower limits of their G1 durations are plotted in Fig. S5 C. For bck2Δ and whi5Δbck2Δ cells, the strongest arrest phenotype, i.e., the longest G1 lengths, was observed for the group whose mothers were in post-anaphase at the time of nutrient switch (Fig. 6 D). Especially for bck2Δ cells, we could not observe many complete G1 phases for the group of daughters whose mothers were in post-anaphase at the time of nutrient switch (Fig. 6 D) as most of these daughters stayed arrested in G1 until the end of the experiment (Fig. S5, B and C; and Fig. 6 E). In fact, for bck2Δ and whi5Δbck2Δ cells, the majority of the first round of daughters of S/G2/M-switchers did not complete G1 until the end of the experiment (Fig. 6 E). Thus, our data suggest that Bck2 has a nutrient switch–specific function after anaphase, which affects G1 exit in the next generation. Such a role for Bck2 had previously been proposed (Bastajian et al., 2013), where Bck2 was speculated to integrate environmental information into the cell cycle progression decision at multiple cell cycle phase transitions, including M/G1.

Additionally, it has previously been shown that Bck2 promotes cell cycle progression through Start by promoting the expression of Cln3, Swi4, and Cln2 (Bastajian et al., 2013). It was also shown that Cln3 is a short-lived protein and depleted after a switch from rich to poor carbon source (Sommer et al., 2021) and that cln3Δbck2Δ is inviable due to permanent G1 arrest. One explanation for the extended G1 arrests in Bck2 deletion mutants we identified here could therefore be a postswitch Cln3 depletion, which, coupled with the absence of Bck2, temporarily mimics a cln3Δbck2Δ phenotype.

This led us to ask whether similar to bck2Δ, cln3Δ also has a strong arrest phenotype after a nutrient switch, or whether, as would be expected if Cln3 is depleted, Cln3 is dispensable for cell size adaptation after the switch. During steady-state growth on SCD, cln3Δ cells are larger than wild-type cells, similar to bck2Δ (Fig. 7 A). The large size of bck2Δ and cln3Δ can be partially rescued by an additional deletion of Whi5 (Fig. 7 A). The whi5Δbck2Δcln3Δ triple deletion is similar in size to the bck2Δ and cln3Δ single deletions (Fig. 7 A), which further highlights that the effects of the Whi5, Bck2, and Cln3 deletions are additive.

In contrast, during adaptation to the nutrient switch, cln3Δ cells do not have as strong a phenotype as bck2Δ cells, in terms of both the G1 length of the first daughters of S/G2/M-switchers (Fig. 7 B) and their volume at G1 end (Fig. 7 C). While in steady state, the whi5Δbck2Δcln3Δ triple deletion resembles the bck2Δ and cln3Δ single deletions in size (Fig. 7 A), in the first daughters of S/G2/M-switchers born after the nutrient switch, its size is closer to the whi5Δbck2Δ double deletion, not the bck2Δ single deletion (Fig. 7 C). This observation is consistent with a nutrient switch–associated depletion of Cln3, rendering Bck2 critical during the nutrient switch.

To further test this hypothesis, we then asked whether the strong bck2Δ phenotype during the nutrient switch could be mitigated by induced expression of CLN3. Specifically, we expressed either CLN3 or the stabilized but less active variant CLN3-11A from a MET25 promoter (Schmoller et al., 2015), and investigated how this affects the phenotype of bck2Δ and whi5Δbck2Δ deletions during the nutrient shift. Consistent with the MET25 promoter leading to CLN3 overexpression, all strains showed reduced cell volumes during steady-state growth on SCD (Fig. 7, A and D). Moreover, as predicted by our hypothesis, the constitutive expression of CLN3 in the bck2Δ and whi5Δbck2Δ strains largely prevents the enlargement of the first round of daughters of S/G2/M-switchers compared with steady-state growth (Fig. 7, E and F).

Taken together, our results are consistent with the model that a depletion of Cln3 during the nutrient shift makes Bck2 temporarily essential (Fig. 7 G), leading to longer G1 arrests and cellular enlargement in bck2Δ cells. Importantly, this highlights that unique functions for seemingly redundant proteins can be uncovered by studying single cells in dynamically changing environments.

In nature, yeast cells regularly face changing environments. Cell size control therefore comprises two tasks: size homeostasis, which is the maintenance of narrow size distributions in largely constant environments, and size adaptation, which is the adjustment of cell size to the optimum for a changed environment. So far, most studies on cell size regulation have focused on steady-state conditions. While these studies have been useful for identifying size homeostasis mechanisms and size regulators, they cannot, by design, provide insights into mechanisms of size adaptation. This suggests that studying cell size adaptation in response to nutrient switches may reveal aspects of cell size regulation that were not accessible through steady-state experiments. In particular, we asked whether nutrient switches could give insights into specific functions of cell size regulators that appear redundant in steady-state size control.

The analysis of nutrient switch experiments at the single-cell level is even more complex than that of steady-state experiments. In steady state, key insights can be gained by analyzing individual cell cycles, without tracking cells over multiple generations. In nutrient switch experiments, the history of a cell, specifically the cell cycle stage at the time of the nutrient shift, affects how the cell and its offspring adapt to the new environment (this study and [Irvali et al., 2023]). To understand cell size adaptation, it is therefore crucial to categorize cells based on their cell cycle stage at the time of the nutrient switch before following their progeny over multiple generations. Several studies have investigated nutrient switches with live-cell microscopy in different contexts (Irvali et al., 2023; Bheda et al., 2020; Schuh et al., 2022; Shabestary et al., 2024; Stockwell and Rifkin, 2017). However, none of them performed multigenerational lineage tracking in addition to cell categorization based on the cell cycle stage at the time of the nutrient switch. Here, we built on recent progress in machine-learning approaches and performed the required analysis using the image analysis tools YeaZ and Cell-ACDC (Padovani et al., 2022; Dietler et al., 2020). This enabled us to track complete cell lineages over multiple generations throughout the adaptation to a nutrient switch and create a framework for dealing with the complexity of single-cell categorization.

From bulk experiments, we found that while the simultaneous deletion of two important size regulators, Whi5 and Bck2, hardly affects cell size or cell size homeostasis during steady-state growth in glucose media, it disrupts both after a nutrient switch from glucose to glycerol/ethanol media. Around 10–25 h following a nutrient switch, both wild-type and whi5Δbck2Δ cells show a strong increase in the CV of cell volume, indicating weaker size homeostasis. This disruption of size homeostasis is stronger in the whi5Δbck2Δ strain. Consistent with our findings, a similar postswitch increase in the CV of cell volume has also been observed in a recent study that analyzes budding yeast adaptation to a nitrogen downshift (Shabestary et al., 2024). Using the cell history–based categorization explained above, we followed single cells through the nutrient switch and found that bck2Δ mutants show longer cell cycle arrests after the nutrient switch. Cells that were already budding at the time of the nutrient switch, as well as their first daughters born after the nutrient switch, exhibit the longest cell cycle arrests, the strongest cellular enlargement, and the lowest survival after switch. Interestingly, this implies that cells that experience the nutrient shift in their S/G2/M phase carry some sort of “memory” into their next G1 phase, leading to a delay in cell cycle progression. While the molecular origin of this memory remains to be identified, one possibility is that the nutrient shift and the associated changes in growth rate and cell cycle progression alter the concentration of regulatory proteins up to the next cell cycle. This type of mechanism has been proposed to integrate environmental inputs in yeast (Qu et al., 2019) and mammalian cells (Min et al., 2020) to control following cell cycle phase transitions. In our case, the memory seems to be limited to a single cell cycle, since the following rounds of daughters closely resemble those in exponential growth in terms of cell cycle phase durations and cell size.

In contrast to steady-state conditions, where deletion of the G1/S activators BCK2 and CLN3 leads to comparable size phenotypes, cln3Δ cells show a much weaker phenotype in response to the nutrient shift. Moreover, an additional deletion of CLN3 in the whi5Δbck2Δ strain does not affect the postswitch arrest or enlargement phenotype. Taken together, our findings suggest that while Cln3 and Bck2 have an apparently redundant role in steady-state size control, Bck2 fulfills a specific function during nutrient adaptation. One intriguing explanation for this is that Cln3 may be depleted after the nutrient switch, as observed by Sommer et al. (2021). Following this lead, we found that expressing CLN3 from a constitutive MET25 promoter rescues the cellular enlargement of bck2Δ cells during the nutrient shift. We therefore propose that the shared role for Bck2 and Cln3 in activating the G1/S transition serves as a potential “backup plan” for G1 exit when Cln3 is depleted due to changing nutrient environments (Fig. 7 G).

It is also known that Bck2 interacts with multiple proteins involved in nutrient sensing and promotes expression of cell cycle regulators (Bastajian et al., 2013). One of the proteins it interacts with is Tpd3, which is the scaffolding subunit of the protein phosphatase PP2A (Bastajian et al., 2013). PP2A is part of the cascade by which two nutrient-sensing pathways, TOR and PKA, regulate Start (Ewald, 2018; García-Blanco et al., 2019; Pedruzzi et al., 2003). This interaction places Bck2 directly at the link between nutrient-dependent growth signaling and cell cycle progression. Thus, a role of Bck2 in nutrient signaling could also contribute to the longer cell cycle arrests and stronger cellular enlargement observed in bck2Δ cells after a nutrient switch event. Additionally, Bck2 has been shown to contribute to cell wall maintenance during growth and to the cell wall stress response (Ferrezuelo et al., 2009; Kuravi et al., 2011). It has been shown to induce the expression of nearly 20 proteins involved in cell wall structure and biosynthesis (Ferrezuelo et al., 2009) and is associated with the activation of the MAP kinase Mpk1 in the Pkc1-dependent cell wall integrity pathway (Kuravi et al., 2011). Therefore, it cannot be ruled out that the increased importance of Bck2 after the nutrient switch stems from its role in the maintenance of cell wall integrity.

In conclusion, our work here provides new insights into size adaptation to nutrient challenges. We show that the apparent redundancy between the roles of Bck2 and Cln3 at the G1/S transition is specific to steady-state growth and Bck2 becomes the more crucial G1/S transition activator following a nutrient switch (Fig. 7 G). More generally, our work suggests that studying cell size regulation in conditions other than steady state is key to revealing unique roles for apparently redundant size regulators. We therefore expect that using similar approaches for a broader range of mutants and perturbations in yeast and other organisms will give new mechanistic insights into the processes underlying size homeostasis and adaptation.

All S. cerevisiae strains used in this study are haploid derivatives of W303. They were constructed using standard methods and sequence information obtained from SGD (Engel et al., 2025). They were verified by sequencing. A full genotypic description of the strains is available in Table S1. Yeast strains are available upon reasonable request.

This process was repeated for five different RNA extractions (experimental replicates). These were plotted as a boxplot in Fig. 1 B. For WHI5, the forward primer used had the 5′-3′ sequence 5′-ACA​AGA​CAC​TTC​CCG​AGC​TG-3′ and the reverse primer used had the 5′-3′ sequence 5′-CGC​GTC​TGC​ACT​ATC​TGG​AA-3′. For ACT1, the forward primer used had the 5′-3′ sequence 5′-AGT​TGC​CCC​AGA​AGA​ACA​CC-3′ and the reverse primer used had the 5′-3′ sequence 5′-GGA​CAA​AAC​GGC​TTG​GAT​GG-3′ (Claude et al., 2021).

smFISH was performed using WHI5-mRNA-specific Stellaris FISH probes from Biosearch Technologies. The targeted probes consisted of thirty-seven 18-nucleotide-long oligonucleotides, each labeled with the Quasar-570 dye. The smFISH protocol for S. cerevisiae described on www.biosearchtech.com/stellarisprotocols was used for sample preparation. Cells were grown for a minimum of 17 h in 50 ml SCD and maintained at OD_600nm <1. At an OD_600nm between 0.3 and 0.5, 45 ml of these cultures was fixed by application of 4% formaldehyde (final concentration) for a period of 45 min. The cells were centrifuged at 1,600 g for 4 min and washed twice, each time with 1 ml of ice-cold fixation buffer comprising 1.2  M sorbitol (Sigma-Aldrich) and 0.1 M K₂HPO₄ (Sigma-Aldrich) at pH 7.5. Cells were then incubated in 1 ml of fixation buffer containing 6.25 µg Zymolyase (Biomol) for 55 min at 30°C. After two more washes with ice-cold fixation buffer, the fixed and digested cells were stored overnight in 70% ethanol at 4°C. On the next day, 300 μl of cells in 70% ethanol was centrifuged (400 g, 5 min) and resuspended in 100 μl of Stellaris RNA FISH hybridization buffer (Biosearch Technologies) containing 10% vol/vol formamide and 125 mM smFISH probes. These cells were incubated overnight in the dark at 30°C to allow for hybridization of smFISH probes to mRNA. After overnight hybridization, cells were washed with Stellaris RNA FISH wash buffer A (Biosearch Technologies) containing 10% vol/vol formamide and resuspended in 1 ml Stellaris RNA FISH wash buffer A (Biosearch Technologies) containing 10% vol/vol formamide and 5 ng/ml DAPI stain. Cells were incubated in the DAPI staining solution for 30 min at 30°C, before being washed with Stellaris RNA FISH wash buffer B (Biosearch Technologies). Washed cells were mounted onto glass slides in Vectashield mounting medium (Vector Laboratories) for the first replicate and in ProLong Gold mounting medium (Thermo Fisher Scientific) for the second replicate due to unavailability of Vectashield. The prepped smFISH samples were imaged on a Zeiss LSM 800 microscope using a 63×/1.4 NA oil immersion objective and an Axiocam 506 camera. The Zen 2.3 software was used to acquire multicolor z-stacks containing 20–25 z-slices at 240-nm intervals. Bright-field images were acquired with the TL LED using an exposure time of 140 ms at 6% of maximum intensity. For imaging Quasar-570, an exposure time of 5 s to illumination by a 530-nm LED at 50% intensity was used. DAPI was imaged with an exposure time of 130 ms and illumination at 385 nm and 30% intensity.

Cells were segmented in bright field using the YeaZ neural network (Dietler et al., 2020) in the Cell-ACDC interface (Padovani et al., 2022). After manual correction of segmentation masks and annotation of bud–mother relationships in Cell-ACDC, the smFISH fluorescence spots were counted using an early version of SpotMAX (Padovani et al., 2026), described in detail in Chatzitheodoridou et al. (2024); Kukhtevich et al. (2022). For each strain and experimental replicate, the following settings of the custom routine were adjusted to optimize spot detection. The 3D Gaussian filter was applied with a Sigma in the range of 0.3–2 voxels. The “threshold_triangle” automatic thresholding algorithm was used for instance segmentation of the spot signal. The “effsize_glass_s” filter was used to filter for valid peaks using an effect size threshold in the range of 1–2.1. Spots were also filtered for size with the lower limit ranging from 1.6 to 2 pixels and the upper limit ranging from 4 to 20 pixels.

Spot detection was followed by categorization of cells into one of three different cell cycle stages: G1, S, and G2/M. Unbudded cells with a single nucleus were categorized into G1 stage. Budded cells with a bud volume-to-mother volume ratio of <0.3 were categorized as S stage. The remaining budded cells were categorized as G2/M cells. Since Whi5 transcription peaks in the S phase, Fig. 1 C shows the average number of WHI5 mRNA in S-phase cells.

For statistically comparing the two strains, we divided the time course into three 10-h intervals and grouped the remaining time points together (Fig. 2, B and D). We used the Shapiro–Wilk normality tests to confirm that the measurements are normally distributed within each time interval. For each time interval, we performed a mixed ANOVA test, with time as the within-subjects factor and strain as the between-subjects factor for classification. The interaction between the two factors was not significant, and therefore, we could interpret the effects of each factor individually. The P values obtained for each time interval based on the between-subjects factor, i.e., strain, were represented in statistical annotations in the figure (Fig. 2, B and D).

Yeast cells were inoculated into 3 ml YPD and incubated at 30°C in a shaking incubator at 250 rpm (Infors, Ecotron) for at least 5 h. After 5 h, cells were washed and inoculated into 50 ml SCD or 2% glycerol and 1% ethanol (SCGE). The cells were allowed to grow for at least 16 h and maintained at OD_600nm <1. They were then diluted to OD_600nm = 0.1 for microscopy. An analogous strategy was used for the experiments with constitutive Met-inducible expression of Cln3 (Fig. 7, D–F), only that cells were instead immediately inoculated into SCD-Met media.

Live-cell time-lapse microscopy was performed using a Nikon Eclipse Ti-E microscope in combination with a custom microfluidics device, described in detail in Kukhtevich et al. (2022). The microfluidics device consisted of a polydimethylsiloxane replica with functional structures bonded to a glass coverslip. This created a cavity that could trap cells and limit colony growth to the XY-plane. Growth medium was pumped through the microfluidics device at a constant rate of 20 μl/min to sustain the growth of cells in the device during the imaging process. For steady-state experiments, filtered SCD or SCGE was used for the entire duration of the experiment. For nutrient switch experiments, cells were grown in SCD (or SCD-Met for experiments with inducible Cln3, Fig. 7, D–F) for the first 2 h of the experiment, and then, the medium was switched to SCGE (SCGE-Met) for the rest of the experiment. The time taken for the medium to be completely switched within the device was calculated to be 30 min, and medium switch was therefore annotated at 2.5 h in the downstream analysis of the live-cell microscopy data. To maximize the rounds of daughters observed per video before crowding of the field of view prevented further analysis, the microscopy experiments were started with only one or 2 cells per position. This limited the number of cells that could be analyzed at the time of the nutrient switch, which was further reduced by repeated categorization.

The epifluorescence microscopy setup included the Nikon Eclipse Ti-E microscope with NIS-Elements software, SPECTRA X light engine illumination, and the Andor iXon Ultra 888 camera. Phase-contrast and fluorescence images were acquired at 3-min intervals via a Plan-Apo λ 100×/1.45 Na Ph3 oil immersion objective. An additional magnification of 1.5× was applied at the time of imaging. The phase-contrast images were acquired using an exposure time of 100 ms. For mCitrine fluorescence imaging, an exposure time of 300 ms was used and the SPECTRA X light engine was used for illumination at 508 nm and 40% power (24.8 mW). mScarlet-I fluorescence was imaged with an exposure time of 200 ms and illumination at 555 nm and 10% power (26 mW). The image acquisition settings were the same across all live-cell microscopy experiments. The incubation temperature of the cells during live-cell microscopy was maintained at 30°C using the objective heater and a custom heatable insertion.

Live-cell microscopy data were analyzed with the open-source Cell-ACDC software (Padovani et al., 2022; Padovani et al., 2025). In the data preparation step, the images were aligned and cropped to the region of interest. Automated segmentation and tracking were performed on the phase-contrast channel using the YeaZ neural network (Dietler et al., 2020) in the Cell-ACDC interface. The resulting segmentation masks were manually corrected, and pedigrees were assigned in the Cell-ACDC GUI. The annotated and manually corrected dataset could then be exported for downstream analysis.

For the mean cell volume and CV of cell volume plots (Fig. 1, F and G, respectively), live cells were pooled from the last frames of all imaging positions per strain, to maximize the number of cells in the analysis. The mean cell volume and its CV were calculated from this pooled population. In Fig. 1 G, the bar plot heights are the CV values obtained from the pooled data and the •, ■, and x symbols show CV values obtained if the pooled data are split into the underlying experimental replicates. To statistically compare the CV values between strains, bootstrapping was used to randomly sample positions from each strain in 10,000 iterations with replacement. For each combination of positions, live cells in the last frame were pooled and the CV of cell volume was calculated. To compare the bootstrapped CV distributions between strains, the vector of the CV distribution of one strain was subtracted from the vector of the CV distribution of the other. To estimate P values, the 95, 99, and 99.9% confidence intervals were calculated for the thereby obtained difference vector. If the confidence interval of the difference vector contained 0, it was concluded that the CV distributions overlapped considerably for the two strains at the given confidence level and their difference was not significant.

Based on phase-contrast images, cell cycle annotations in Cell-ACDC categorized unbudded cells into the “G1” phase and all budded cells into an umbrella category: the “S/G2/M” phase. The following functions from the Cell-ACDC downstream analysis Jupyter Notebook were used for calculating cell cycle properties such as phase lengths, and volume changes per phase and for retrieving relatives’ data for each cell: cca_functions.calculate_downstream_data, cca_functions.calculate_per_phase_quantities and cca_functions.calculate_relatives_data. From the resulting dataset, multigenerational mother–bud relationships, or pedigrees, could be acquired for cell populations of interest. Each cell cycle and cell cycle phase was labeled as complete or incomplete, based on whether the cell died during that cycle or phase and whether the cycle or phase was interrupted by the start or the end of the experiment. Unless specified otherwise, only complete cycles or complete phases were used for further analysis.

For the cell cycle reporter strain, fluorescently labeled Htb2 allowed us to segment a nuclear mask for each cell. Using this along with cellular segmentation, we could quantify fluorescence signal in three compartments: the whole cell, the nucleus, and the cytoplasm. Comparing Whi5-WIQ-mCitrine signal and Htb2-mScarlet-I signal between these compartments allowed us to further resolve the cell cycle into more specific phases than just G1 and S/G2/M, as described in the Results section. For budded cells, mean pixel intensity was calculated by calculating the sum of the total pixel intensities of mother and bud, and the combined cell area in pixels for mother and bud, and then dividing the total sum pixel intensity by the total area in pixels. The cytoplasm-adjusted nuclear mean pixel intensity of Whi5-WIQ-mCitrine (Fig. 6 A) was calculated by subtracting cytoplasmic mean pixel intensity of Whi5-WIQ-mCitrine from nuclear mean pixel intensity of Whi5-WIQ-mCitrine. Htb2-mScarlet-I amount was background-adjusted using a background ROI created during the data preparation step of the Cell-ACDC analysis pipeline (Fig. 6 A).

For assigning the time point at which Start occurs, nuclear mean pixel intensity of Whi5-WIQ-mCitrine was plotted against time for each cell of interest. The frame at which nuclear mean pixel intensity of Whi5-WIQ-mCitrine started to decrease during G1 was manually identified (Whi5_export_start_frame). Similarly, the frame at which nuclear mean pixel intensity of Whi5-WIQ-mCitrine stopped decreasing was manually identified (Whi5_export_end_frame). The nuclear mean pixel intensities of Whi5-WIQ-mCitrine at these two frames were retrieved (Whi5_intensity_export_start, Whi5_intensity_export_end), and the difference between the two intensities was calculated. The difference was divided by 2 and added to Whi5_intensity_export_end to get nuclear mean pixel intensity of Whi5-WIQ-mCitrine when half of Whi5 has been exported from the nucleus (Whi5_intensity_50%_export). Starting from Whi5_export_start_frame and proceeding frame by frame, the nuclear mean pixel intensity of Whi5-WIQ-mCitrine was compared with Whi5_intensity_50%_export. The first frame where frame-specific nuclear mean pixel intensity of Whi5-WIQ-mCitrine was less than Whi5_intensity_50%_export was assigned as the first post-Start frame. All following G1 frames were categorized as post-Start G1, and all previous G1 frames were categorized as pre-Start G1.

Nuclear mean pixel intensity of Whi5-WIQ-mCitrine was also used for assigning the time point at which cells enter telophase. The first frame of nuclear reimport of Whi5-WIQ-mCitrine in S/G2/M cells was manually identified for individual cells in cell categories of interest. All frames including and after this frame were categorized as post-anaphase.

Background-adjusted Htb2-mScarlet-I amount in the bud was used to assign the beginning of anaphase. The first frame showing increasing Htb2-mScarlet-I amount in the bud was manually identified for cells of interest. All frames after and including this frame and before the first telophase frame were categorized as anaphase.

Finally, all S/G2/M frames starting from and including bud emergence and going until the first anaphase frame were assigned to the bud emergence to anaphase category, spanning S, G2, prophase, and metaphase.

Statistical analysis, except for bootstrapping, was performed using the SciPy package (Virtanen et al., 2020) written in Python. The code is available online in our GitHub repository.

Normality tests were performed using the Shapiro–Wilk test. In most cases, the tests showed that the microscopy data are not normally distributed. For consistency, except for data shown in Fig. 2, we therefore do not assume normality throughout the paper and chose statistical tests accordingly.

Fig. S1 shows extended analyses of the steady-state experiments. Fig. S2 shows an analysis of population-level behavior of cell volume and its variability during the nutrient shift based on single-cell measurements. Fig. S3 shows that the enlargement phenotype of bck2Δ cells is not explained by different durations of metabolic reprogramming or different starting cell volumes. Fig. S4 shows an analysis of cell size homeostasis at the G1/S transition during the nutrient shift. Fig. S5 shows an analysis of cells dying during the nutrient shift and of how the arrest phenotypes depend on mother cell cycle stage. Table S1 shows a list of the budding yeast strains used in this study.

Data are available in a permanent BioImage Archive (Hartley et al., 2022) repository: https://doi.org/10.6019/S-BIAD4064. The code used for the analysis is available on the GitHub page https://github.com/SchmollerLab/Nutrient-switch-analysis.

We thank Benedikt Mairhörmann, Mardo Kõivomägi, Jennifer Ewald, Pascal Falter-Braun, Andreas Klingl, and members of the Institute of Functional Epigenetics for helpful discussions.

Work in the K.M. Schmoller lab was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through project 431480687, by the Human Frontier Science Program (career development award to K.M. Schmoller, CDA-00018/2019-C), by the Helmholtz Gemeinschaft, and by the European Union (ERC, MITOSIZE, 101169998). Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them. Work in the R. Schneider lab was funded by the DFG through SFB 1064 (Project-ID 213249687) and SFB 1309 (Project-ID 325871075) and the Helmholtz Gemeinschaft. Open Access funding provided by Helmholtz Zentrum München.

Author contributions: Yagya Chadha: conceptualization, data curation, formal analysis, investigation, methodology, software, validation, visualization, and writing—original draft, review, and editing. Igor V. Kukhtevich: conceptualization, formal analysis, investigation, methodology, resources, validation, and writing—original draft, review, and editing. Timon Stegmaier: data curation, formal analysis, investigation, methodology, software, validation, visualization, and writing—review and editing. Francesco Padovani: data curation, formal analysis, investigation, methodology, resources, software, and writing—review and editing. Robert Schneider: funding acquisition, supervision, and writing—review and editing. Kurt M. Schmoller: conceptualization, formal analysis, funding acquisition, investigation, methodology, project administration, resources, supervision, validation, and writing—original draft, review, and editing.