Fine-tuning the orientation of the polarity axis by Rga1, a Cdc42 GTPase-activating protein.

In yeast and animal cells, signaling pathways involving small guanosine triphosphatases (GTPases) regulate cell polarization. In budding yeast, selection of a bud site directs polarity establishment and subsequently determines the plane of cell division. Rga1, a Cdc42 GTPase-activating protein, prevents budding within the division site by inhibiting Cdc42 repolarization. A protein complex including Nba1 and Nis1 is involved in preventing rebudding at old division sites, yet how these proteins and Rga1 might function in negative polarity signaling has been elusive. Here we show that Rga1 transiently localizes to the immediately preceding and older division sites by interacting with Nba1 and Nis1. The LIM domains of Rga1 are necessary for its interaction with Nba1, and loss of this interaction results in premature delocalization of Rga1 from the immediately preceding division site and, consequently, abnormal bud-site selection in daughter cells. However, such defects are minor in mother cells of these mutants, likely because the G1 phase is shorter and a new bud site is established prior to delocalization of Rga1. Indeed, our biphasic mathematical model of Cdc42 polarization predicts that premature delocalization of Rga1 leads to more frequent Cdc42 repolarization within the division site when the first temporal step in G1 is assumed to last longer. Spatial distribution of a Cdc42 GAP in coordination with G1 progression may thus be critical for fine-tuning the orientation of the polarity axis in yeast.

INTRODUCTION

Establishing cell polarity in a proper orientation is critical for development and cell proliferation (Drubin and Nelson, 1996; Nelson, 2003). In most fungal and animal cells, selection of a polarity axis is linked to polarity establishment via a conserved mechanism involving the Cdc42 GTPase (Johnson, 1999; Etienne-Manneville, 2004; Park and Bi, 2007). Cells of the budding yeast Saccharomyces cerevisiae grow by choosing a single bud site, which determines the axis of cell polarity and the plane of cell division. Bud-site selection occurs in a cell-type-specific manner (Freifelder, 1960; Hicks ; Chant and Pringle, 1995): a or α cells (such as wild-type haploids) bud in the axial pattern, in which a new bud site is chosen adjacent to the previous division site. In contrast, a/α cells (such as wild-type diploids) bud in the bipolar pattern, in which daughter cells typically bud at the pole distal from the division site, and mother cells choose a new bud adjacent to the division site or at the opposite pole. The axial pattern depends on a transient cortical marker that includes Bud3, Bud4, Axl1, and Axl2 (see Bi and Park, 2012). This axial landmark interacts with the Rsr1 GTPase module (Kang ; Kang ) composed of Rsr1 (also known as Bud1), its GTPase-activating protein (GAP) Bud2, and its guanine nucleotide exchange factor (GEF) Bud5 (Bender and Pringle, 1989; Chant and Herskowitz, 1991; Chant ; Park ). The Rsr1 GTPase module then interacts with Cdc42 and its GEF Cdc24 to couple the spatial cue to polarity establishment (Zheng ; Park ; Kozminski ; Kang ). Bud3 also directly activates Cdc42 in early G1, supporting a model that stepwise activation of Cdc42 is necessary for spatial cue-directed Cdc42 polarization (Kang ).

Both haploid and diploid cells select a new bud site that does not overlap with any previous bud site (Barton, 1950; Mortimer and Johnston, 1959; Hicks ; Chant and Pringle, 1995). Each cell division site on the mother cell surface is marked by a chitin-rich ring (called a “bud scar”), while the division site on the daughter cell is marked by a frail chitin-less structure (called a “birth scar”) (Bacon ; Cabib and Bowers, 1971) (Figure 1A). The interdependent transmembrane proteins Rax1 and Rax2, which mark the cell division sites through multiple generations, are known to be involved in bipolar budding as the persistent pole marker in a/α cells (Chen ; Kang ). However, their role in the axial budding pattern had not been known when this study began. Here, the bud neck during cytokinesis is referred to as the current division site and is distinguished from the immediately preceding division site (i.e., the most recently used division site), at which Rax1 and Rax2 have arrived (Figure 1A).

FIGURE 1:

Localization of Rga1 to old cell division sites. (A) Scheme depicting the cell division sites in a yeast cell budding in the axial pattern. The current division site denotes the bud neck during cytokinesis. Following cytokinesis and cell separation, the division site becomes the most recently used site (i.e., the immediately preceding division site) and is marked with a new bud scar (purple) on the mother cell and with a birth scar (green) on the daughter cell. Older cell division sites on the mother cell are marked with bud scars (blue). (B) (a) Localization pattern of GFP-Rga1 to old bud sites is summarized from time-lapse images of cells budding in different patterns (n = 26 each strain). Representative images are shown for cells with GFP-Rga1 localized to all (b) or some (c) old bud sites. Bars, 3 μm. (C) Representative SIM images of GFP-Rga1 (marked with arrowhead at old bud site) and Cdc3-mCherry. Maximum intensity projection images (left) and three-dimensional reconstruction of boxed region (right) are shown for each cell. Bars, 3 μm.

Cdc42 and its GAP Rga1 are also involved in proper bud-site selection (Johnson and Pringle, 1990; Miller and Johnson, 1997; Stevenson ; Chen ; Smith ; Lo, Lee, ; Kang ). Interestingly, among Cdc42 GAPs, Rga1 is uniquely required for preventing budding within the previous division site by inhibiting Cdc42 repolarization (Tong ). A protein complex including Nba1 and Nis1, which interact with Rax1 and Rax2, has been suggested to inhibit Cdc42 at the old division sites (referred to as “cytokinesis remnants” [CRMs]) and thus function as negative polarity cues (Meitinger ). We recently found that Rga1 localizes to old division sites in addition to the current division site (Lee ). These observations raised a number of questions, including how Rga1 might localize to the old division sites and whether its function at these sites might be related to the negative polarity cues at CRMs. To address these questions, we combined various methods including quantitative microscopy and mathematical modeling. Here we report that Rga1 localizes to the old division sites transiently via interaction with Nba1 and Nis1. We provide evidence that the Cdc42 GAP Rga1 is the core of negative polarity signaling at any previous cell division site.

RESULTS

Rga1 localizes to old division sites regardless of budding pattern

Although Cdc42 becomes enriched at the bud neck (which becomes the division site) in late M phase (Richman ), Rga1 inhibits Cdc42 activation and thus rebudding within the division site (Tong ). We thus asked whether Rga1 localizes only to old division sites that are adjacent to the bud neck (i.e., only in cells budding in the axial pattern) to inhibit Cdc42 repolarization at these sites. We examined localization of green fluorescent protein (GFP) tagged Rga1 in cells that bud in different patterns after staining with Calcofluor, which stains the bud scars and bud neck. We observed three different patterns of GFP-Rga1 localization in these cells (Figure 1B): GFP-Rga1 was present at all old bud sites (Figure 1Bb), some but not all old bud sites (Figure 1Bc), or none of the old bud sites. The percentage of these groups was not significantly different among wild-type (WT) a and a/α cells (which bud in an axial and a bipolar pattern, respectively) and rsr1∆ cells (which bud in a random pattern), indicating that Rga1 localizes to the old division sites of these cells regardless of their budding pattern. A close-up view of GFP-Rga1 by structured illumination microscopy (SIM) revealed that Rga1 localizes to the old division site as multiple dots organized as a ring (Figure 1C and Supplemental Video S1; n = 4).

Transient localization of Rga1 to the current and old division sites

How does Rga1 localize to old cell division sites? One possibility might be that Rga1 is inherited from the division site and then stably anchored at old division sites, as in the case of Rax1 and Rax2. Alternatively, Rga1 might localize to old cell division sites transiently in every cell cycle as it does to the current division site. To distinguish between these possibilities, we performed time-lapse imaging of WT haploid cells expressing GFP-Rga1 for one round of the cell division cycle. We observed that GFP-Rga1 at the immediately preceding division site disappeared around bud emergence in the next cell cycle (98%, n = 52 mother cells; 100%, n = 32 daughter cells). GFP-Rga1 at old division sites in mother cells also disappeared around bud emergence (96%, n = 27) and then reappeared at those sites during G2/M phase (89%, n = 27) (see arrowheads, Figure 2A).

FIGURE 2:

Rga1 is dynamic at old and current cell division sites. (A) GFP-Rga1 localizes to old bud site (marked with arrowheads) transiently in WT at 30°C. Numbers indicate time (in min) from the onset of cytokinesis (t = 0). Bar, 3 μm. (B) (a) FRAP analysis of GFP-Rga1 at old bud site. Left, recovery after photobleaching is plotted (mean ± SEM), and curve fit is in red. The half-time of recovery (t1/2) (mean ± SEM) and number (n) of samples analyzed are shown. Right, representative cell before (prebleach) and after photobleaching. The red boxed region was bleached at time 0. Bar, 3 μm. (b–d) FRAP analysis of GFP-Rga1 at the bud neck prior to cytokinesis (b), during cytokinesis (c), and at the immediately preceding division site (d).

We then compared dynamics of GFP-Rga1 at different stages of the cell cycle by fluorescence recovery after photobleaching (FRAP). We found that GFP-Rga1 at old bud sites was fairly dynamic with half-time of recovery (t1/2) = 22.4 ± 1.6 s (Figure 2Ba). Similar dynamics were observed for GFP-Rga1 at the bud neck prior to cytokinesis and at the immediately preceding division site in early G1 (Figure 2B, b and d). GFP-Rga1 was most dynamic during cytokinesis (right after splitting of the Cdc3-RFP ring) (t1/2 = 4.0 ± 1.8 s; Figure 2Bc). Taken together, these results indicate that Rga1 at the old division sites is dynamic, transiently arriving at these sites in each cell division cycle.

Localization of Rga1 to old division sites depends on Rax1, Rax2, Nis1, and Nba1

While Rga1 localization to the bud neck depends on septins (Caviston ), the “old” septin ring does not remain at the division site after G1 (Oh and Bi, 2011), suggesting that Rga1 relies on another protein(s) to localize to the old division sites. We considered a number of proteins that localize to old division sites as potential binding partners of Rga1. The persistent division site markers Rax1 and Rax2 arrive at the cell division site after septa formation (Chen ; Kang ; Khmelinskii ). Nba1 and Nis1, which initially localize to the current division site via the scaffold protein Gps1, also localize to the immediately preceding division site by interacting with Rax1/2 after septation and then remain at the old division sites for multiple generations (Meitinger ). We thus asked whether Rga1 is recruited to old division sites by these proteins. First, we found that GFP-Rga1 colocalized with Rax2-RFP, Nis1-RFP, and Nba1-RFP to the old and immediately preceding division sites (marked with arrowhead and arrows, respectively; mean Pearson’s correlation coefficient, PCC > 0.5) (Figure 3A). We also tested whether localization of GFP-Rga1 to old bud sites was dependent on RAX1, RAX2, NIS1, or NBA1 by examining large-budded cells of WT or mutants deleted for each of these genes after Calcofluor staining. We found that very few of these mutant cells (all of which express GPS1) had GFP-Rga1 localization to old division sites. Similarly, GFP-Rga1 localization to old division sites was not observed in gps1Δ cells (Figure 3B), likely because Nis1 and Nba1 were not initially recruited to the division site in the absence of Gps1 and thus were not present at the old division sites, as expected from the previous report (Meitinger ). These results are consistent with the idea that Rga1 is recruited to the old division site by Nba1 and Nis1, which themselves are anchored by Rax1 and Rax2.

FIGURE 3:

Localization of Rga1 to old bud sites depends on Rax1, Rax2, Nis1, and Nba1. (A) Colocalization of GFP-Rga1 with (a) Rax2-mCherry, (b) Nis1-tdTomato, and (c) Nba1-tdTomato. Numbers indicate mean PCC values at the immediately preceding division site (within images) and at older bud sites (below images). Number of cells analyzed for colocalization (at the immediately preceding division site and at the old division site) are as follows: Rax2 (31, 31); Nis1 (31, 31); and Nba1 (32, 25). Arrowheads and arrows mark old division sites and the immediately preceding division site, respectively. Bars, 3 μm. (B) Quantification of cells with GFP-Rga1 or GFP-Rga1Δm1 present at old bud sites. Strains marked with # are congenic to ESM356-1. Only large budded cells with old bud site(s) were counted. Mean ± SEM is shown from three independent experiments with the following total number of cells analyzed: WT (301), rax1Δ (311), rax2Δ (308), nba1Δ (322), GFP-rga1Δm1 (300), WT (396), nis1Δ (338), and gps1Δ (324). (C) Yeast two-hybrid assays of full-length and the truncated forms of Rga1 (depicted on the right). Growth on the –Leu plate denotes interaction. (D) MBP pull-down assays using MBP-Nba1 (a) and MBP-Nis1 (b) with the addition of extracts containing either GST-Rga1N or GST-Rga1NΔm1 in the presence or absence of Zn++, as indicated. GST- and MBP-fusion proteins were detected with anti-GST and anti-MBP antibodies, respectively. Average recovery of GST-Rga1N pulled down with MBP-Nba1 was 4% or 0.09% in the presence or absence of Zn+2, respectively, and 0.08% GST-Rga1NΔm1 was recovered with MBP-Nba1 in the presence of Zn+2. Average recovery of GST-Rga1N or GST-Rga1NΔm1 with MBP-Nis1 was about the same (0.2%). No detectable GST-Rga1N or GST-Rga1NΔm1 was pulled down with MBP control.

The LIM domains of Rga1 are necessary for its interaction with Nba1

Since it had been suggested that Nba1 and Nis1 function as negative polarity cues independently from Rga1 (Meitinger ), it was surprising to find that Rga1 localization depends on Nba1 and Nis1. To explore this issue further, we examined whether Rga1 interacted with Nba1 and/or Nis1 by a yeast two-hybrid assay. We expressed Rga1 fused to a DNA-binding domain and Nba1 (or Nis1) fused to an activation domain in a strain carrying the LEU2 reporter. Growth on a plate lacking Leu indicated that Rga1 interacts with Nba1 and Nis1, similarly to the positive control Cdc42G12V (which is expected to be the GTP-locked state in vivo and thus to interact with its GAP). Interestingly, when we tested truncated Rga1 fusion proteins, the N-terminal half of Rga1 (amino acids 1–537; Rga1N) exhibited a similar two-hybrid interaction with Nba1 and Nis1. In contrast, the C-terminal fragment (Rga1C), which carries the GAP domain, interacted with Cdc42G12V but not with Nba1 or Nis1 (Figure 3C). These results suggest that the N-terminal region of Rga1 specifically interacts with Nba1 and Nis1.

The N-terminal region of Rga1 contains tandem LIM domains (amino acids 1–122) (Chen ), which are named after their initial discovery in the proteins Lin11, Isl-1, and Mec-3. LIM domains are characterized by a unique cysteine-rich motif with a zinc-finger structure that often functions as a protein-binding interface (Kadrmas and Beckerle, 2004). Interestingly, it has been reported that Rga1 LIM domain mutants exhibit an abnormal budding pattern (Chen ). We thus postulated that the LIM domains of Rga1 might be involved in interaction with Nba1 and/or Nis1. To test this idea, we performed in vitro binding assays using recombinant proteins. Rga1N or Rga1NΔm1 (which lacks LIM domains; denoted Δm1) was expressed as a glutathione S-transferase (GST) fusion protein, and Nba1 or Nis1 was expressed as an maltose binding protein (MBP) fusion protein from Escherichia coli. We found that MBP-Nba1 associated efficiently with GST-Rga1N but not GST-Rga1NΔm1 in the MBP pull-down assay. Moreover, this Rga1N-Nba1 association was dependent on the presence of Zn+2 (Figure 3Da), indicating that the LIM domains of Rga1 are indeed necessary for its interaction with Nba1. MBP-Nis1 associated similarly with both Rga1N and Rga1NΔm1 in vitro (Figure 3Db), suggesting that another region in Rga1N is involved in interaction with Nis1.

We then examined how LIM domains might be involved in localization of GFP-Rga1 to old cell division sites by introducing the same LIM domain deletion mutation (Δm1). GFP-Rga1Δm1 poorly localized to old division sites in large budded cells, despite its localization to the bud neck (Figure 3B; see Figure 8 later in this article). Together, these results suggest that Rga1 localizes to old division sites via interaction with Nba1 and that the LIM domains of Rga1 are necessary for its interaction with Nba1.

FIGURE 8:

Localization of GFP-Rga1∆m1 carrying a deletion of the LIM domains. (A) Localiza­tion of GFP-Rga1∆m1 and Whi5-mCherry at 30°C. Numbers indicate time (in min) from the onset of cytokinesis (t = 0). An arrowhead marks when GFP-Rga1 delocalizes. Bar, 3 μm. (B) (a) Normalized global intensity (mean ± SEM) of GFP-Rga1 or GFP-Rga1∆m1 in cells with large buds before cytokinesis. (b) Local intensity of GFP-Rga1 or GFP-Rga1∆m1 at the bud neck is shown for individual cells as in Figure 7B. The number of time-lapse images analyzed are as follows: WT, n = 26 and GFP-rga1Δm1, n = 10 before cytokinesis, and WT, n = 17 and GFP-rga1Δm1, n = 10 at other cell-cycle stages. **p < 0.0001; ns, not significant; p > 0.05. (c) Length of T1 and T2 (min) in each daughter cell (WT, n = 17; and GFP-rga1Δm1, n = 10). Mean (horizontal lines) ± SEM (error bars).

Rga1 at the immediately preceding division site and older division sites may affect the orientation of the polarity axis

If Rga1 functions to prevent Cdc42 repolarization at old division sites, as it does at the current division site (Tong ), then we would predict that rax1∆, rax2∆, nba1∆, and nis1∆ mutants exhibit improper bud-site selection. To test this idea, we examined the division sites of these mutants by staining cells with Calcofluor and wheat germ agglutinin conjugated to fluorescein isothiocyanate (WGA-FITC). WGA-FITC stains the division site in daughter cells (i.e., “birth scar”) as well as bud scars in mother cells (see Figure 1A). Almost all daughter cells of rax1∆, rax2∆, nba1∆, and nis1∆ mutants budded within the birth scar (marked with an arrow; Figure 4A). The majority of mother cells of these mutants had bud scars that often appeared adjacent to one another, although these bud scars (or a bud) were present within the birth scar (Figure 4B, ii). A smaller percentage of mutant mother cells had bud scars (or a bud) within a bud scar (Figure 4B, iii) or at the opposite poles (Figure 4B, iv), and these bud scars were also present within the birth scar. These analyses indicate that rax1∆, rax2∆, nba1∆, and nis1∆ mutants are severely defective in selecting the first bud site, whereas subsequent budding events are partially defective.

FIGURE 4:

Bud-site selection of daughter and mother cells. Left, a representative image of each pattern is shown. Arrows mark birth scars. Bar, 3 μm. Right: Budding patterns (mean ± SEM) are plotted from three independent countings. Strains marked with # are congenic to ESM356-1. (A) The first bud position (purple) relative to birth scar (green) in daughter cells: (i) bud neck adjacent to the birth scar, (ii) bud neck within the birth scar, and (iii) bud neck at the opposite pole of birth scar. Total number of daughter cells counted: WT (257), rax1Δ (261), rax2Δ (274), rga1Δ (263), nba1Δ (260), rga1Δm1 (165), rga1 (264), rax1Δ nba1Δ (238), rga1Δ nba1Δ (283), rax1Δ whi5Δ (351), WT (243), and nis1Δ (305). *p = 0.01 for t test comparing the axial pattern in rax1Δ vs. rax1Δwhi5Δ, and p > 0.2 for rga1Δ nba1Δ vs. rga1Δ and rga1Δ nba1Δ vs. nba1Δ; ns, not significant; p > 0.05. (B) Budding pattern of mother cells: (i) bud scars and bud neck adjacent to the birth scar (i.e., axial pattern), (ii) bud scar(s) and bud neck within the birth scar, (iii) bud scars (or a bud) within a bud scar (that is also within the birth scar), and (iv) bud scars or bud neck within the birth scar and at the opposite pole of the cell (i.e., a variation of the bipolar pattern). Total number of mother cells counted: WT (265), rax1Δ (269), rax2Δ (310), rga1Δ (323), nba1Δ (349), rga1Δm1 (239), rga1 (256), rax1Δ nba1Δ (268), rga1Δ nba1Δ (407), WT (254), and nis1Δ (323).

Because there was some difficulty visualizing bud scars within a bud scar from the static images, we took a complementary approach to determine the role of Rga1 at the old division sites. We monitored Cdc42 polarization in rax1∆ cells by time-lapse imaging using the p21-binding domain of Gic2 fused to tdTomato (PBD-RFP), a biosensor for active Cdc42, which specifically interacts with Cdc42-GTP (Ozbudak ; Tong ; Okada ). The transcriptional repressor Whi5 fused to GFP was used as a cell-cycle marker, since its nuclear exit divides the G1 phase into two temporal steps, T1 and T2 (Di Talia ). In addition, Cdc3-GFP was used as both a cell-cycle and positional marker, since the septin hourglass splits into a double ring at the division site around the onset of cytokinesis (Kim ; Lippincott ). The PBD-RFP signal peaks at the presumptive bud site prior to disassembly of the septin ring at the division site, approximately concurrent with the appearance of new septin clouds (Okada ; Kang ; Lee ). Cdc42 always polarized at a site adjacent to the septin ring in mother and daughter cells of WT haploids (Figure 5B and Supplemental Figure S1), as expected. In contrast, Cdc42 polarized within the septin ring in a subset of rax1Δ mother cells (9.7%, n = 31; Figure 5B and Supplemental Figure S2B) and in the majority of rax1Δ daughter cells (Figure 5). This relatively minor defect of Cdc42 polarization in rax1Δ mother cells is thus consistent with the budding pattern (see Figure 4B).

FIGURE 5:

Cdc42 polarization in rax1∆ cells. (A) (a) Time-lapse images of PBD-RFP, Cdc3-GFP, and Whi5-GFP in rax1∆ cells at 30°C. Numbers indicate time (in min) from the onset of cytokinesis (t = 0). Yellow arrow indicates the time when the Cdc42 polarization axis becomes stabilized within the old septin ring. Bar, 3 μm. (b) Kymograph shows distribution of PBD-RFP and Cdc3-GFP (or Cdc3-GFP alone) in the region marked by a rectangle (size 1.73 × 3.89 μm) in the daughter cell. A heat map represents the Cdc42-GTP level of the kymograph shown on the left. The black and white bars on the sides of kymograph mark the position of the old and new septin rings, respectively. Note: New septin ring appears at the same position as the old septin ring in rax1∆ daughter cell. Arrows mark the T1/T2 boundary. (B) Localization pattern of Gic2-PBD-RFP (red) relative to the old septin ring (green) at the division site is quantified from a number (n) of time-lapse images. Mother cells of WT and rax1∆ are analyzed from time-lapse images taken at 22°C (see Supplemental Figures S1 and S2B).

We then employed mathematical modeling to simulate how Rga1 localization to the old bud site affects Cdc42 polarization. We extended our previous generic model of Cdc42 polarization on a two-dimensional computational domain with the axial landmark ring in the center (Figure 6A). This model incorporated two temporal steps in G1—the first step included positive feedback and delayed negative feedback, whereas the second step included stronger positive feedback with diminished negative feedback (Lee ). When Rga1 distribution at the current division site and at the previous division site (adjacent to the current division site) was implemented, our simulations showed that Cdc42 always polarized to a site that was outside of the old division site (Figure 6B, a and c). In contrast, if Rga1 was absent at the old division site, one of 10 simulations resulted in Cdc42 polarization within the old division site (Figure 6B, b and d), consistent with a minor defect in Cdc42 polarization in vivo (see Figure 5B). Collectively, both experimental data and computational modeling suggest that Rga1 localization to the immediately preceding division site and older division sites is important for inhibiting Cdc42 repolarization at these sites. However, having Rga1 activity at older division sites in mother cells may be less critical than at the current division site (see below for more discussion).

FIGURE 6:

Modeling Cdc42 polarization during G1 in WT and rax1∆ cells. (A) Scheme of an axially budding cell with the current (red ring) and an old cell division site (green ring). The spatial cue distribution (red circle) at the current division site is shown in a two-dimensional computational domain (below). (B) Simulation of Cdc42 polarization with Rga1 distribution at the current and old division site (a and c) or in the absence of Rga1 at an adjacent old bud site (b and d). The first phase with delayed negative feedback is assumed to last for 6 min (toff = 6 min), and Rga1 delocalizes at 18 min, as in mother cells. The white dashed circles with a radius of 0.5 μm are reference positions for the immediately preceding division site. (c, d) White dots mark the positions of the Cdc42-GTP clusters after 21 min from 10 different simulations. (C) Simulation of Cdc42 polarization with transient Rga1 distribution at the current division site and the following assumptions: (a and c) the first phase lasts for 25 min (toff = 25 min), and the Rga1 delocalizes at 39 min; (b, d) the first phase lasts for 25 min (toff = 25 min), and Rga1 delocalizes at 29 min. (c, d) White dots mark the positions of the Cdc42-GTP clusters after 45 min from 10 different simulations.

Mutational analyses suggest Rga1 functions in the same pathway with Nba1 and Nis1

Our data described so far support the idea that Rga1 functions together with Nba1 and Nis1. To explore further the functional interaction between Rga1 and these negative polarity cues, we asked whether improper bud-site selection of rax1∆, rax2∆, nba1∆, and nis1∆ mutants was caused by their inability to recruit Rga1 to the previous division sites. To this end, we examined the rga1Δm1 mutant, because this LIM domain deletion disrupted the interaction between Rga1N and Nba1 in vitro, and GFP-Rga1Δm1 poorly localized to the old bud sites in large-budded cells (see Figure 3, B and Da). It is noteworthy that the LIM domain mutant rga1 (=dbm1-5,7) has been shown to exhibit an abnormal budding pattern (Chen ). Indeed, we found that the budding phenotypes of rga1Δm1 and rga1 were very similar to those observed in mother and daughter cells of rax1∆, rax2∆, nis1∆, and, in particular, an nba1Δ mutant (Figure 4). These observations suggest that the Rga1 LIM domain mutant protein, which poorly interacts with Nba1, is unable to promote proper bud-site selection. With the same logic, rax1∆, rax2∆, nis1∆, and nba1Δ mutants exhibit improper bud-site selection, likely because Rga1 is not recruited to the previous division sites in these mutants.

If Rga1 and Nba1 function independently of each other to inhibit Cdc42 repolarization, as previously suggested (Meitinger ), then we would expect that a rga1Δ nba1Δ double mutant might have an additive budding defect compared with each single mutant. Remarkably, the pattern of bud positions of rga1Δ nba1Δ daughter cells was almost identical to that of rga1Δ or nba1Δ daughters. Indeed, no statistically significant difference was observed between daughter cells of these mutants with respect to the percentage of budding within the birth scar (Figure 4A). The budding patterns of the rga1Δ nba1Δ mother cells were also similar to those of rga1Δ mother cells, while the defect was slightly less severe in nba1Δ mother cells (Figure 4B). Therefore, these data strongly support the idea that Rga1 functions in the same pathway with Nba1 and Nis1 at the previous division sites, rather than in a parallel pathway, to inhibit Cdc42 polarization.

Rga1 localizes to the immediately preceding division site via interaction with Nba1

As described above, almost all daughter cells of rax1∆, rax2∆, nba1∆, and nis1∆ bud within the birth scar, while subsequent budding events in mother cells of these mutants are only partially defective. What could account for this difference between mother and daughter cells of these mutants? To address this question, we performed a series of time-lapse imaging and compared localization of GFP-Rga1, together with Whi5-RFP, in mother and daughter cells. We found that GFP-Rga1 remained at the immediately preceding division site almost until bud emergence in mother cells of WT, nba1∆, and rax1∆ (100%, n = 21, WT and rax1∆; 96%, n = 28, nba1∆; Figure 7A and Supplemental Figure S2A). In contrast, localization of GFP-Rga1 in daughter cells of these mutants was clearly different compared with WT daughter cells. While GFP-Rga1 delocalized at the immediately preceding division site during T2 in WT daughter cells (100%, n = 21; Figure 7Aa), GFP-Rga1 delocalized before transition to T2 in rax1Δ daughter cells (83%, n = 18; Supplemental Figure S2A). GFP-Rga1 delocalized even earlier in nba1Δ daughter cells: 71% during T1 and 29% at T1/T2 transition (n = 17; Figure 7, Ab and Bb). Local intensity of GFP-Rga1 at the immediately preceding division site was indeed significantly lower at the T2 boundary in nba1Δ and rax1Δ daughter cells compared with WT daughter cells (Figure 7Bb). However, the global intensity and local intensity of GFP-Rga1 (at the bud neck) before cytokinesis were similar in all these strains (Figure 7B, a and b). The duration of T1 and T2 was also about the same among daughter cells of these strains (Figure 7Bc). Since Rga1 delocalizes earlier in nba1∆ daughter cells even during T1, Rga1 may interact with Nba1 prior to interacting with other proteins at the immediately preceding division site.

FIGURE 7:

Localization of GFP-Rga1 in WT and nba1Δ cells. (A) Time-lapse images of GFP-Rga1 and Whi5-mCherry in (a) WT and (b) nba1Δ cells at 30°C. Numbers indicate time (in minutes) from the onset of cytokinesis (t = 0). Arrowheads mark when GFP-Rga1 delocalizes (see Materials and Methods). Bars, 3 μm. (B) (a) Normalized global intensity (mean ± SEM) of GFP-Rga1 in cells with large buds before cytokinesis. (b) Local intensity of GFP-Rga1 at the bud neck is plotted for individual cells at different cell cycle stages: before cytokinesis (WT, n = 26; and nba1Δ, n = 24); peak intensity during T1; and at the T1/T2 transition from time-lapse imaging (WT, n = 17; nba1Δ, n = 17; and rax1Δ, n = 18). Values were normalized to the average GFP-Rga1 intensity prior to cytokinesis in WT cells. *p = 0.0003, **p < 0.0001; ns, not significant; p > 0.05. (c) Length of T1 and T2 (min) in each daughter cell (WT, n = 17; nba1Δ, n = 17; and rax1Δ, n = 18). Mean (horizontal lines) ± SEM (error bars).

To confirm that premature delocalization of Rga1 from the immediately preceding division site in these mutants is indeed due to lack of interaction between Rga1 and Nba1, we imaged GFP-Rga1Δm1, which lacks the LIM domains. Indeed, GFP-Rga1Δm1 delocalized during T1 (Figure 8A), similarly to premature delocalization of GFP-Rga1 in nba1Δ cells with minor differences. Local intensity of GFP-Rga1Δm1 at the bud neck and the division site was lower than WT GFP-Rga1 prior to cytokinesis, during T1, and at the T1/T2 transition (Figure 8Bb), although the global intensity of both proteins was about the same in large budded cells before cytokinesis (Figure 8Ba). The average duration of T1 and T2 in daughter cells was also similar between the strains expressing GFP-Rga1Δm1 and GFP-Rga1 (Figure 8Bc). Since localization of GFP-Rga1Δm1 to the bud neck was reduced prior to cytokinesis (unlike in the case of GFP-Rga1 in nba1Δ cells; see Figure 7Bb), the LIM domains may thus affect Rga1’s localization even before its interaction with Nba1. Collectively, these observations suggest that Rga1 localizes to the immediately preceding division site via interaction with Nba1 (and likely also with Nis1), similarly to its localization to older division sites (see above).

Premature delocalization of Rga1 in mid G1 may lead to budding within the division site in daughter cells

To explain how the timing of Rga1 delocalization in G1 can affect the orientation of the Cdc42 polarization axis, we extended our computational modeling. When localization of Cdc42 GAP resembled that of Rga1 in WT daughter cells (see Figure 6C), our biphasic model for Cdc42 polarization predicted that the Cdc42-GTP cluster level fluctuated around the division site during the first phase and then became stabilized at a single site that is adjacent to the axial landmark (Lee ; Figure 6C, a and c). In contrast, when the Cdc42 GAP was assumed to delocalize from the division site prior to the second phase, as in rax1Δ or nba1Δ daughter cells, Cdc42 always polarized within the division site (Figure 6C, b and d). Therefore, our model recapitulates time-evolved Cdc42 polarization in vivo, consistent with the same site rebudding phenotype of the daughter cells of rax1Δ, rax2Δ, nis1Δ, and nba1Δ mutants (see Figure 4A).

Why does this premature delocalization of Rga1 have a more pronounced effect in daughter cells of these mutants? One critical difference between mother and daughter cells is cell size. Since mother cells are larger than newly born daughter cells, the duration of T1 is shorter (Di Talia ). We postulated that this cell-cycle difference could account for the different bud-site selection defect in mother versus daughter cells. To explore this idea, we modeled how different lengths of the first phase (equivalent to T1) of G1 would affect Cdc42 polarization when premature delocalization of Rga1 was implemented (see Figure 9A). Interestingly, when the first phase was assumed to last for 10 or 15 min (which is a little longer than T1 in typical mother cells at 30°C), Cdc42 cluster became stabilized at a site adjacent to the preceding division site (Figure 9, B and C). In contrast, when the first phase was modeled longer than 20 min (T1 = 25–27 min in daughter cells), Cdc42 repolarized within the division site more frequently in our simulations (Figure 9C). By implementing the similar premature delocalization of Rga1, we ran additional independent simulations with different lengths of the first phase and randomly generated parameters within certain ranges (see Materials and Methods). These simulations confirmed that Cdc42 repolarizes within the division site at a higher frequency as the first phase is assumed to last longer (Supplemental Figure S3). Our model thus supports the idea that premature delocalization of Rga1 in the mutants causes a more severe defect in orienting the polarity axis in daughter cells because of their longer T1 compared with mother cells. An interesting prediction from this model is that even with premature delocalization of Rga1, if a cell traverses G1 rapidly, the cell might be able to establish a proper bud site prior to delocalization of Rga1. To test this prediction by manipulating the G1 length in vivo, we introduced whi5 deletion into a rax1Δ mutant, since cells are smaller and progress through T1 more quickly in the absence of START inhibitor Whi5 (Jorgensen ; Di Talia ). We then examined the bud site and birth scar positions of rax1Δ whi5Δ daughter cells. We found a statistically significant increase of the axial budding events in the rax1Δwhi5Δ daughter cells compared with rax1Δ daughter cells (*p = 0.01; Figure 4A). Although whi5Δ did not completely rescue the “budding-within-the-birth-scar phenotype” of rax1Δ daughters, these observations are consistent with our model’s prediction.

FIGURE 9:

Modeling Cdc42 polarization with different lengths of the first phase in mutant haploid daughter cells. (A) Scheme of Rga1 localization (in green) relative to Whi5 (yellow in the nucleus and light yellow in the cytoplasm). Rga1 localizes to the current division site and old bud sites (gray rings) in WT (a) but only to the current division site in rax1Δ cells (b). Blue bars mark the time window when Rga1 delocalizes in daughter cells. Relative time from the onset of cytokinesis (t = 0) at 30°C is marked. (B) Simulation of Cdc42 polarization with time-dependent Rga1 localization and delayed negative feedback in the first phase. The first phase is assumed to last for 15 min (toff = 15 min). The Rga1 delocalizes from the division site at 29 min, as in rax1∆ daughter cells (t = 0 at the onset of cytokinesis). (C) The positions of the Cdc42-GTP clusters at 45 min are shown from 10 independent simulations with the same Rga1 delocalization time (at 29 min) but with different length of the first phase as indicated below. The axial landmark is depicted as a red circle.

DISCUSSION

Despite significant progress made in recent years, how a single axis of cell polarity is established is not fully understood. The axis of Cdc42 polarization in budding yeast is critical for mitotic spindle orientation as well as determination of the plane of cell division. Rga1, a Cdc42 GAP in budding yeast, is required for proper bud-site selection (Stevenson ; Chen ; Smith ; Lo, Lee, ) and for preventing rebudding at the previous division site by inhibiting Cdc42 repolarization (Tong ). Whether Rga1 functions independently or interacts with other negative polarity cues to prevent Cdc42 repolarization at all previously used divisions sites had been elusive. It was also not clear how Rga1 is recruited to the old division sites. Our studies reported here answer some of these outstanding questions and also raise new ones.

We provide several lines of evidence that Rga1 is recruited to the immediately preceding division site and older division sites by Nba1 and Nis1, which localize to these sites via interaction with Rax1 and Rax2 (Meitinger ). However, unlike Nba1, Nis1, Rax1, and Rax2, which are stably anchored to these sites, Rga1 arrives transiently at the old division sites in each cell division cycle. Our FRAP analyses indicate that Rga1 is very dynamic at old division sites as well as at the current division site, unlike Nba1 and Nis1 (Meitinger ). It is, however, not known whether and why such transient delivery, as opposed to stable anchoring, of Rga1 to old division sites is necessary. We speculate that a regulatory mechanism might exist to conserve the critical enzyme Rga1 during repeated cell divisions. As expected from their role in recruitment of Rga1 to previous division sites, we find that cells lacking NBA1, NIS1, RAX1, or RAX2 as well as cells expressing an Rga1 LIM domain mutant protein, which is defective in interaction with Nba1, exhibit improper bud-site selection. While RAX1 and RAX2 are known to be involved in bipolar budding of diploid a/α cells (Chen ; Kang ), our analyses of bud scars and birth scar show that haploid rax1Δ and rax2Δ mutants are also defective in bud-site selection. Because of the relatively minor defect in mother cells of these mutants (see below), the role of Rax1 and Rax2 in axial budding might have been overlooked in previous studies.

We show that Rga1 interacts with Nba1 efficiently in the presence of Zn++ ion, consistent with the requirement of Rga1 LIM domains for the interaction. Known functions of LIM domains, which have a characteristic cysteine-rich motif with a zinc-finger structure, include mediating intramolecular and intermolecular protein interactions (Feuerstein ; Schmeichel and Beckerle, 1994). The LIM domains might also regulate Rga1 activity, since a Rga1 protein lacking functional LIM domains could suppress defects caused by a mutation of Rho-GAP Bem2 (Chen ). In addition, a recent study reported that overexpression of a C-terminal Rga1 fragment (i.e., lacking the LIM domains) leads to a loss-of-polarity phenotype, while the overexpression of full-length Rga1 results in no defects, suggesting a possible inhibitory function of the N-terminal domain (He ). Whether Nba1 is involved only in recruiting Rga1 to previous division sites or also in regulating its GAP activity remains an open question.

We suggest that Rga1 functions in the same pathway with Nba1 and Nis1 to inhibit Cdc42 based on the following data presented in this study: First, localization of Rga1 to the immediately preceding division site as well as older division sites is dependent on Nba1, Nis1, Rax1, and Rax2 (Figures 3 and 7 and Supplemental Figure S2). Second, Rga1 interacts directly with Nba1 and likely with Nis1 (Figure 3). Third, a rga1Δ nba1Δ double mutant exhibits an almost identical defect of Cdc42 repolarization as rga1Δ or nba1Δ single mutant (rather than having an additive defect) (Figure 4). Furthermore, an rga1 mutant lacking LIM domains fails to interact with Nba1 and exhibits a similar defect as nba1Δ (Figures 3D, 4, and 8). We note that Meitinger reached a different conclusion from analyses of these mutants. Although we are unsure about the cause of this discrepancy, it is not due to difference of strain backgrounds, since we have examined mutants in two different strain backgrounds including one used in their report (see Materials and Methods). Our analyses distinguished the cell division sites in mother and daughter cells by staining with two fluorescent dyes, while their analyses did not separate mother and daughter cells but used transmission electron microscopy images to visualize a bud-neck “collar” (excess cell wall material indicative of rebudding at a previously used site). We speculate that the previous study might have reached a similar conclusion about the functional interaction between Rga1 and Nba1-Nis1, if it had included separate analyses of daughter cells in addition to the cytokinesis remnants remained at the old division sites in mother cells. To clarify this issue will require further investigation.

It has been suggested that Nba1 and Nis1 prevent Cdc42 reactivation at previous division sites by inhibiting the interaction between the Cdc24 polarity complex and Rsr1 (Meitinger ). While we cannot rule out the possibility that another mechanism may also be involved in the process, we favor the idea that the inhibitory function of Nba1 in Cdc42 repolarization at the old division sites relies on the recruitment of Rga1. We thus propose inhibitory pathways for Cdc42 polarization as follows (Figure 10): During cytokinesis, Rga1 and Gps1-Nba1-Nis1 inhibit Cdc42 polarization at the current division site (Tong ; Meitinger ). Once cytokinesis and septation have been completed, that is, when Rax1-Rax2 have arrived at the immediately preceding division site (Kang ), Nba1 and Nis1 are anchored to the site via interaction with Rax1-Rax2 (Meitinger ). This complex at the immediately preceding division site then recruits Rga1, which inhibits Cdc42 (this study). Rga1 is also recruited to older division sites and inhibits Cdc42 repolarization, although Rga1’s role at the old division site(s) seems to be relatively less critical (this study). Similarly, Meitinger noted that disruption of Nba1 at the immediately preceding division site (referred to as “emergent CRMs”) caused a greater defect in Cdc42 inhibition than removal of Nba1 from older cell division sites. How these protein–protein interactions are altered during cytokinesis and subsequent G1 also remains an open question.

FIGURE 10:

Model for inhibition of Cdc42 repolarization at the current and old cell division sites. During cytokinesis, Rga1 (green circle) and the Nba1-Nis1-Gps1 inhibit Cdc42 repolarization to the division site. After cytokinesis and septum formation, Nba1-Nis1 (solid and dotted red boxes) are inherited to the immediately preceding site and remain at the older division sites via interaction with Rax1/Rax2 (blue lines). Rga1 is recruited to the immediately preceding site as well as at the older division sites via interaction with Nba1-Nis1. Rga1 then inhibits Cdc42 repolarizaiton at these previous cell division sites. The complex at the old division site is omitted in the cell shown on the left.

An unexpected, interesting finding from this study is the distinct effect of Rga1 distribution on polarization of mother versus daughter cells. While Rga1 localization to the immediately preceding division site is critical for positioning a proper bud site in daughter cells, this localization has a relatively minor role in mother cells. This is likely due to the intrinsic difference in the cell-cycle progression (Di Talia ). Selection of a bud site and thus establishing the axis of Cdc42 polarization occur long after cytokinesis in daughter cells, unlike in mother cells (Lee ). Consequently, Rga1 localization to the current division site is most critical in mother cells (Tong ), whereas transient localization of Rga1 to both current division site and immediately preceding division site until T1/T2 transition are equally important in daughter cells (this study). Indeed, our mathematical modeling can recapitulate distinct dynamics of Cdc42 polarization in mother and daughter cells by implementing transient distribution of Cdc42 GAP (Lee ; this study). According to our model, Cdc42 is more likely to repolarize within the previous division site when the first temporal phase of G1 is longer and premature delocalization of Cdc42 GAP is implemented (as observed in rax1∆ or nba1∆ mutants). This model thus provides a possible explanation for the different phenotypes of the mutant mother and daughter cells. A logical extension of this model is that even with premature delocalization of Rga1 from the division site, if a cell is forced to pass through T1 rapidly, then the cell might be able to establish a proper bud site. Our experimental test of this prediction by introducing a whi5 deletion to shorten G1 resulted in only partial rescue of the rax1∆ daughter cells. A caveat to such a test is that deleting the key START regulator Whi5 might affect not only T1 length but also potentially the activity or assembly of the polarity complex. Because cell-to-cell variations of the G1 length is observed even in WT cells (Di Talia ), it would also be imperative to access the G1 length of individual cells and examine its correlation with the budding pattern. Other factors at the division sites might also contribute to differential Cdc42 polarization in mother versus daughter cells of these mutants. For example, distinct components in bud scar versus birth scar might affect these cortical polarity components differently. While a crucial test waits for a deeper understanding of regulation of these polarity factors, our modeling introduces an intriguing concept that delicate coordination of the spatial distribution of a Cdc42 GAP with cell-cycle progression is critical for establishing a proper axis of cell polarization and thus selection of a new nonoverlapping plane of cell division in budding yeast.

MATERIALS AND METHODS

Strains, plasmids, and general methods

Standard methods of yeast genetics, DNA manipulation, and growth conditions were used (Guthrie and Fink, 1991). All yeast strains used for imaging express tagged and truncated genes under their native promoters from the chromosomes. Yeast strains and plasmids used in this study are listed in Supplemental Tables S1 and S2, respectively, with a brief description of construction methods.

Microscopy and image analysis

Cells were grown in appropriate synthetic medium overnight and then freshly subcultured for 3–4 h in the same medium. Time-lapse imaging was performed at 30°C (except those indicated, at 22°C) essentially as previously described (Kang ) using a spinning disk confocal microscope (Ultra-VIEW VoX CSU-X1 system; Perkin Elmer-Cetus) equipped with a 100×; 1.4 NA Plan Apochromat objective lens (Nikon); 440-, 488-, 515- and 561-nm solid-state lasers (Modular Laser System 2.0; Perkin Elmer-Cetus); and a backthinned electron-multiplying charge-coupled device (CCD) camera (ImagEM C9100-13; Hamamatsu Photonics) on an inverted microscope (Ti-E; Nikon). For most time-lapse imaging, images were captured (9 z-stacks; 0.3 μm step) every 2 or 4 min using cells either mounted on an agarose slab or in a glass-bottomed dish (MatTek) containing medium with 5 μM propyl gallate (Sigma), an anti-fade reagent. Cells were adhered onto the microwell of the dish, which was pretreated with 0.2% concanavalin A (Sigma) and then covered with proper medium containing 0.6% agarose and propyl gallate. For long-term time-lapse microscopy (in Figure 2A), images were captured every 6 min at 30°C. For Figure 1B, time-lapse images were captured (11 z-stacks; 0.4 μm step, 4-min interval) after staining cells with Calcofluor White (see below).

SIM was performed using a GE DeltaVision OMX SR equipped with an Olympus 60× (1.42 NA) objective lens. Static images were captured (19 z-stacks; 0.125 μm step) at 25°C. Cells were mounted onto a glass-bottomed dish as described above. SoftwoRx v6.5.2 was used to capture images and create three-dimensional projections.

Image processing and analyses were performed using ImageJ (National Institutes of Health). Maximum intensity projections of z-stacks were generated to make figures and videos, except where noted. To estimate colocalization, z-stack images were used after background subtraction to calculate Pearson’s correlation coeffcient (PCC) using the Coloc 2 plug-in, and PCC >0.5 was considered as colocalization.

To quantify the local fluorescence intensity of GFP-Rga1, first a rectangular region of interest (ROI) that included the GFP-Rga1 signal was used to measure the intensity from z-stacks. A second ROI that included the first ROI and the surrounding cytoplasmic region (approximately twice as big as the first ROI) was used for background subtraction (Coffman ). The intensity of GFP-Rga1 at the bud neck before cytokinesis (i.e., 3 min before the Cdc3-mCherry ring split), peak intensity of GFP-Rga1 localized at the division site during T1, and GFP-Rga1 localized to the division site at the T1/T2 transition were measured for each individual cell. For global intensity quantification, average intensity projections were created from all 9 z-sections at 0.3 μm spacing, and an ROI was drawn around the outline of cells. The intensity of WT cells without any fluorescently tagged proteins were used to subtract background. To determine the time when GFP-Rga1 delocalized from the immediately preceding division site in daughter cells (marked with a yellow arrowhead in Figures 7 and 8 and Supplemental S2A), the same threshold was applied to quantify the GFP-Rga1 intensity at each time point using ImageJ.

To quantify the Whi5-mCherry signal in the nucleus at each time point, a circular ROI that included the Whi5-mCherry signal in the nucleus was used to measure the intensity from z-stack images. Background subtraction was done as described above for GFP-Rga1. The duration time of T1 and T2 was determined by monitoring the intensity of the nuclear Whi5-mCherry signal as well as the onset of cytokinesis (identified by a split Cdc3-mCherry ring) and bud emergence in individual mother and daughter cells. The T1/T2 transition was marked when the Whi5-mCherry intensity in the nucleus was ∼50% of its peak level. The duration time of T1 and T2 was found to be similar for all the strains examined in this study (ns: p > 0.6; Figures 7Bc and 8Bc).

Kymographs and heatmaps were generated from maximum intensity projection images of z-stacks, except noted, using the multiple kymograph plug-in and heat map histogram plug-in for ImageJ. Kymograph of Cdc3-GFP, in Supplemental Figure S2Bb, was generated from a single z-stack to show the hollow septin ring more clearly.

FRAP analysis

Images were captured at a single z-section on a gelatin slab at 22°C using the photokinesis unit on the Ultra-VIEW VoX confocal system (see above), similarly to the assays described previously (Coffman ). Prior to beginning each FRAP experiment, a z-stack image was taken with the 561-nm laser to examine Cdc3-mCherry signal and select cells in specific stages of the cell cycle. In the FRAP assay, the middle focal plane of cells was bleached to <50% of the original fluorescence intensity after collecting five prebleach images. Postbleach images were acquired for a duration long enough such that the recovery curve reached a plateau. Background and photobleaching during image acquisition were corrected using empty space among cells and unbleached cells in the same image. The prebleach intensity of the ROI was normalized to 100%, and the first postbleach intensity was normalized to 0%. The intensities of every three consecutive postbleach time points were averaged to reduce noise. Then the intensity data were plotted and fitted using the exponential decay equation y = m exp(-m where m is the off-rate, using Prism 6 (GraphPad Software). The half-time of recovery was calculated using the equation t ln2/m.

Analysis of cell division sites

Bud scars and birth scars were stained with Calcofluor White (0.5 μg/ml) and WGA-FITC (100 μg/ml), as previously described (Lee ). Maximum intensity projections were generated from 17 z-stacks (0.3 μm step size) of images captured with a fluorescence microscope (E800; Nikon) fitted with a 100× 1.3NA oil Plan Fluor objective lens (Nikon), a CCD camera (ORCA-ER; Hamamatsu Photonics), and FITC-GFP and DAPI (4’,6-diamidino-2-phenylindole) filters (Intelligent Imaging Innovations). Cell division sites were analyzed in three independent experiments. The budding pattern of ESM356-1 nba1∆ cells was determined from time-lapse images by analyzing the position of the new septin ring in relation to the old septin ring (marked with Cdc3-mCherry). We found that the majority of mother cells appeared to bud in an axial pattern (84%, n = 32), similarly to nba1∆ mutants in the YEF473A (Bi and Pringle, 1996) strain background. Staining of both bud scars and birth scar indicated that the bud scars were adjacent to one another but within the birth scar in the majority of mother cells of this mutant (see the text and Figure 4).

Yeast two-hybrid assay

Two-hybrid assays were performed using EGY48 carrying the LEU2 reporter (and the lacZ reporter plasmid pSH18-34, URA3), as previously described (Gyuris ). The full-length, N-terminal half (amino acids 1–537) and the C-terminal half (amino acids 538–1007) of Rga1 were expressed as DNA-binding domain fusions using pEG202 clones (Supplemental Table S2). The full-length Nba1 and Nis1 were expressed as activation domain fusions using pJG4-5 clones (Supplemental Table S2). pJG4-5-cdc42G12V (a gift from M. Peter, ETH Zurich, Switzerland) carries the C188S mutation (in addition to G12V) to avoid membrane targeting (Butty ). About 1.5 × 105 cells of each transformant of a DBD and an AD fusion or a vector control were spotted on SGal-His-Trp-Ura and SGal-His-Trp-Ura-Leu plates and incubated at 30°C for 4–5 d. At least three independent transformants of a DBD and an AD fusion were tested and spot assays were repeated in triplicate.

In vitro binding assay and immunoblotting

GST or MBP fusion proteins were expressed in protease-deficient E. coli cells (BL21-CodonPlus), and in vitro binding assays were performed using the S10 fraction as previously described (Kozminski ; Kang ) except some modifications described below. Cell lysates carrying MBP fusion proteins were prepared using a lysis buffer (10 mM sodium phosphate buffer, pH 8.0, 500 mM NaCl, 10 mM β-mercaptoethanol, 1 mM EGTA (ethylene glycol-bis(β-aminoethyl ether)-N,N,N’,N’-tetraacetic acid), 0.2% Triton X-100). To pull down MBP fusion proteins, the S10 fraction was incubated with 40 μl amylose resin (New England BioLabs) for 1 h at 4°C by rocking. The beads were then washed four times using the same lysis buffer and once using a binding buffer (10 mM sodium phosphate buffer [pH 8.0], 100 mM NaCl, 10 mM β-mercaptoethanol, 0.2% Triton X-100, 50 μM Zn(OAc)2) or the same buffer without Zn(OAc)2. The S10 fractions containing GST-Rga1N or GST-Rga1NΔm1 were prepared using the same binding buffer with or without 50 μM Zn(OAc)2. To perform binding assays, the S10 fractions containing GST-Rga1N and GST-Rga1NΔm1 were incubated with an equal amount of MBP-Nba1 (or MBP-Nis1 or MBP control) on amylose resin either in the presence or absence of Zn++ for 2.5 h at 4°C by rocking. After washing the amylose resin using the binding buffer with or without Zn++ (see above), proteins were eluted from the resin with Laemmli sample buffer and subjected to SDS–PAGE and immunoblotting. GST- and MBP-fusion proteins were detected using monoclonal antibodies against GST (Novus Biologicals) and polyclonal rabbit anti-MBP antibodies (New England Biolabs), respectively. Protein bands were then visualized using Alexa Fluor 680 goat anti-rabbit immunoglobulin G (IgG; Molecular Probes) or IRDye 800CW-conjugated goat anti-mouse IgG (LI-COR Biosciences) secondary antibodies and the Odyssey CLx system (LI-COR Biosciences). Proteins were quantified using the software of the Odyssey CLx system, and relative recovery of GST-Rga1N or GST- Rga1NΔm1 was estimated by the ratio of each pulled-down protein over the input and then normalized against pulled-down MBP fusion proteins. Binding assays were repeated two to four times with or without Zn2+ for each combination of proteins, and the average recovery was calculated (see legend to Figure 3D).

Statistical analysis

Data analysis was performed using Prism 6 (GraphPad Software). A two-tailed Student’s t test was performed to determine statistical differences between two sets of data.

MODELING

A two-dimensional model of Cdc42

A two-dimensional model applied in the study is based on our previous model, and the details are previously described (Lee ). Briefly, the model consists of the particle density of membrane-bound Cdc42, denoted by a. The computational domain, denoted by M in the model, is a two-dimensional region of cell membrane, in which the landmark cue is located at the center. For simplicity, we assume that membrane-bound Cdc42 appears only in this domain and the domain is taken as planar without considering the effect of the surface curvature. Another key assumption is mass conservation: that is, the total number of molecules in the whole cell remains constant in time (Altschuler ; Howell ; Lo, Lee, ).

The dynamics of a is governed by the following reaction-diffusion equation: with the function φ(a) defined as the average value of a over the membrane, namely, (Lo, Lee, ; Lo ), where equals the total area of domain M. Three key components of Cdc42 dynamics included in the model are lateral membrane diffusion of Cdc42, recruitment (activation) of Cdc42 from the cytoplasm to the membrane, and the reverse reaction (Altschuler ).

The activation term is based on the following form of feedback:

In the formula, the first term of the right-hand side represents the axial landmark [denoted by u(x)] and the Rsr1 module feedback (Goryachev and Pokhilko, 2008; Howell ; Lo, Lee, ; Lo ; Goryachev and Leda, 2017), with K1 a normalizing factor; the second term of the right-hand side represents the feedback in Cdc42-signaling network. We consider two temporal phases: 1) in the first phase, the axial landmark and the Rsr1 module are involved in positive feedback; 2) in the second phase, the spatial cue is excluded and the Cdc42-signaling feedback is active with stronger positive feedback strength. Since we assume that the feedback is stronger than the Rsr1 module feedback, we apply smaller normalizing factor K2 (

The function is defined as where δ(x) is a spatial uncorrelated random function with uniform distribution between 0 and 1 for each x; Ri(x) is defined as

The on–off function θ1(t) controls a switch from time phase 1 and time phase 2 at time toff, and θ1(t) is defined as where ε is a very small value .

Similarly to the activation term, we define the deactivation term as where H is defined as

The function g(x,t) will be specified later in “parameter settings.” Note that the negative feedback functions when a(x, t−t1) is larger than Koff. δ(x,t) is a spatiotemporal uncorrelated random function with uniform distribution between 0 and 1 for each x and t.

Parameter settings

Based on previous studies (Goryachev and Pokhilko, 2008; Lo, Lee, ), the diffusion rate of Cdc42 on the membrane was around 0.1–0.15 μm2 min–1; the recruitment rate and the activation rate of Cdc42 were 10 and 0.1 min–1, respectively; the normalizing parameter K1 was taken to be less than 0.3 to achieve spontaneous budding without spatial cues. In this paper, we take D = 0.1 μm2 min–1; and since the activation/recruitment process considered here combines both activation and recruitment processes, we take kon1 = kon2 = 1 min–1, K1 = 0.3, and K2 = 0.2. We take K2 less than K1, because we assume that the second feedback is stronger than the first one. Based on our previous work (Lee ), we take the parameters for modeling delayed negative feedback as Koff = 2, the threshold of Cdc42 for functioning negative feedback; and t1 = 1 min, the time delay for negative feedback. For modeling the change of Rga1 distribution, we define the function g(x,t) according to the changes of the nonzero regions (higher value = 3, lower value = 1, r is the distance from a point to the center of the domain, r′ is the distance from a point to the point 1 μm right to the center of the domain):

For wild-type daughter cells, we take {0.35(1 − t/10) + 0.35 < r < 0.35(1 − t/10) + 0.65} for 0 < t < 10; {r < 0.35} for 10 < t < 15; {0.35(t − 15)/8 < r < 0.35(t − 15)/8 + 0.3} for 15 < t < 23; {0.35 < r < 0.65} for 23 < t < 32.2. The Rga1 ring level is decreasing at 32.2 min and totally delocalizes at 39 min in WT daughter cells.

For wild-type mother cells, we take {0.3 < r < 0.65} for 0 < t < 3; {0.3 < r < 0.65}; {0.5 < r′ < 0.65} for 3 < t < 6. The Rga1 ring level is decreasing at 6 min and totally delocalizes at 18 min in WT mother cells.

The parameter toff depends on the time the first phase ends in different types of cells and mutations, and the values are mentioned in each figure legend.

For each simulation in Supplemental Figure S3, we generate three independent random variables (δ1, δ2, and δ3) from a uniform distribution between 0.5 and 1.5 and then set kon1 = kon2 = δ1, the highest value of the function g(x,t) = 3δ2, K1 = 0.3δ3, and K2 = 0.2δ3.