SUPPLEMENTARY INFORMATION

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1 doi: /nature06072 SUPPLEMENTARY INFORMATION Molecular noise and size control: origins of variability in the budding yeast cell cycle. Stefano Di Talia 1,2, Jan M. Skotheim 2, James M. Bean 1,*, Eric D. Siggia 2 and Frederick R. Cross 1 1 The Rockefeller University New York, NY Center for Studies in Physics and Biology, The Rockefeller University New York, NY * Present Address: Human Oncology and Pathogenesis Program, Memorial Sloan-Kettering Cancer Center, New York, NY Contents S1. Materials and Methods 2 S1.A Plasmids and strains construction 2 S1.B Time-lapse microscopy 3 S1.C Image analysis 4 S1.D Data analysis 4 S1.E Fluorescence-based measurements of single-cell growth 8 S2. Statistical analysis of the correlation between αt and ln(m birth ) 9 S3. Analysis of the independence of the two regulatory steps of Start 15 S4. Analysis of movies in glycerol/ethanol 16 S5. Additional supplementary tables 18 S6. Additional supplementary figures 21 References

2 S1. Material and Methods S1.A Plasmids and strains construction Name MMY116-2C SD06-A-4A SD06-B-5D SD08-C-12A SD08-D-5D SD09 SD-tet SD15-6C SD15-8A SD20-1A SD21-1-5C SD24-1-5A SD24-3-6A SD27-1-1A SD27-1-2B SD28-3C SD28-5A SD29-1-2A JS19 Genotype MATα MATa ACT1pr-DSRED::TRP1 MYO1-GFP::KanMX MATα ACT1pr-DSRED::TRP1 MYO1-GFP::KanMX MATα cln3::ura3act1pr-dsred::trp1 MYO1-GFP::KanMX MATa cln3::ura3 ACT1pr-DSRED::TRP1 MYO1-GFP::KanMX Diploid MATa/MATα ACT1pr-DSRED::TRP1 MYO1-GFP::KanMX Tetraploid MATa/MATa/MATα/MATα ACT1pr-DSRED::TRP1 MYO1-GFP::KanMX MATa ACT1pr-DSRED::TRP1 WHI5-GFP::KanMX MATα ACT1pr-DSRED::TRP1 WHI5-GFP::KanMX MATα 2xACT1pr-DSRED::URA3 MYO1-GFP::KanMX 5xCLN3::TRP1 MATα 2xACT1pr-DSRED::URA3 WHI5-GFP::KanMX 5xCLN3::TRP1 MATα 2xACT1pr-DSRED::URA3MYO1-GFP::KanMX MATa 2xACT1pr-DSRED::URA3 MYO1-GFP::KanMX MATα 2xACT1pr-DSRED::URA3 MYO1-GFP::KanMX 5xCLN2::HIS3 MATα 2xACT1pr-DSRED::URA3 MYO1-GFP::KanMX 5xCLN3::TRP1 5xCLN2::HIS3 MATa ACT1pr-DSRED::TRP1WHI5-GFP::KanMX cln3::ura3 MATα ACT1pr-DSRED::TRP1 WHI5-GFP::KanMX cln3::ura3 MATα 2xACT1pr-DSRED::URA3 WHI5-GFP::KanMX 5xCLN2::HIS3 MATα 2xACT1pr-DSRED::URA3 MYO1-GFP::KanMX MET3-CLN2::TRP1CLN2pr-GFP PEST ::HIS3 Table S1 Strain list. All strains are congenic W303 (leu2-3,112 his3-11,15 ura3-1 trp1-1 can1-1), but converted to ADE2 by transformation with ADE2 PCR product in MMY116-2C (from M. Miller), and were constructed from lab stocks by standard methods. The ADE2 conversion was used to reduce vacuolar autofluorescence that can occur in ade2 strains. Tetraploid SD-tet was constructed as follows. SD06-A-4A and SD06-B-5D were mated by cell-to-cell mating using a micromanipulator, followed by isolation of the resulting diploid SD09. Mating type switching was induced in SD09 cells, transformed with a 2µ plasmid carrying GAL-HO (pjh132, kind gift from Jim Haber), by plating cells on galactose for 4 hours. Purified single colonies were tested for mating type. Diploids 2

3 homozygous at the mating locus (a/a and α/α) and that lost the GAL-HO plasmid were subsequently mated by micromanipulation to obtain the tetraploid SD-tet. This strain was confirmed to be a true 4N strain by sporulation and dissection of tetrads. Most tetrads gave 4 viable spores; from a few tetrads in which all 4 spores were non-maters, all the progeny were sporulated, yielding on subsequent tetrad analysis haploid MATa or MATα segregants with high viability. Name Description Construction pjb06t prs404-act1pr-dsred see Methods pty24 DsRed source plasmid NCRR Yeast Resource Center, University of Washington psd02 prs406-act1pr-dsred see Methods psd03 prs403-cln2 see Methods pjh132 YCp50-GAL-HO kind gift from Jim Haber Table S2 Plasmid list S1.B Time-lapse microscopy Preparation of cells and time-lapse microscopy were performed as previously described [S1]. Detection of GFP and DsRed fluorescence was by illumination with a 100 W short arc mercury lamp type 103 W/2. Illumination was passed through a Chroma neutral density filter ND 2.0 allowing 1% transmission and either a Chroma EGFP filter set #41001 (peak excitation wavelength at 480 nm, peak emission at 535 nm) or a Chroma TRITC filter set #41002c (peak excitation wavelength at 545 nm, peak emission at 620 nm). The frame rate was 1frame/3min for cells grown in glucose and 1frame/6min for cells grown in glycerol/ethanol. The exposure time was 1 second for GFP and 0.35 seconds for DsRed for cells grown in glucose and 0.4 seconds for GFP and 0.1 seconds for DsRed for cells grown in glycerol/ethanol (cells grown in glycerol/ethanol were more sensitive to light damage). Fluorescent images of strains grown in glycerol/ethanol were acquired by 2x2 binning of camera pixels, which allows detection of Myo1-GFP and Whi5-GFP using reduced exposure times. With these exposures the two chromophores were well separated and we did not observe any significant photo-toxicity or 3

4 perturbations of cell cycle timing except for a few sporadic cells having a long budded period, perhaps due to damage from illumination. These events did not affect our quantitative or qualitative results. S1.C Image analysis Automated image segmentation and fluorescence quantitation of yeast grown under time-lapse conditions and semi-automated assignment of microcolony pedigrees were performed as previously described [S1]. Budding and division were scored by visual inspection for the appearance and disappearance of the Myo1-GFP signal at the bud neck. The detection of the Myo1-GFP signal was facilitated by setting pixels whose value was smaller than a suitably chosen threshold (median+1.5 standard deviations of cell fluorescence values) to zero (black color). The remaining pixels were plotted in gray scale with white color assigned to the highest pixel value. The ring disappearance was easy to score. Myo1-GFP appearance at the bud neck was usually detected for the first time 6-9 minutes before budding could be scored by visual inspection. Uncertainty in the ring appearance was confined to 1-2 frames for most cells. Occasional cells that budded upwards in the middle of the colony were hard to score. We consistently decided not to score cells for which the uncertainty on the ring appearance was bigger than 2-3 frames. The nuclear residence of Whi5-GFP was scored by visual inspection of composite phase contrast-fluorescent movies [S1] and confirmed by the method described for Myo1-GFP detection. S1.D Data analysis We measure cell size as the total cell fluorescence from DsRed protein expressed from the constitutively active ACT1 promoter. Background autofluorescence was measured as the average fluorescence of unlabelled cells for each movie and subtracted from the measured pixel intensities of labeled cells. We observed almost no detectable red autofluorescence from unlabelled cells, so that the background could be well approximated by the zero of the camera. The objective depth of focus allowed us to reliably collect almost all the fluorescence coming from every cell body. The total cell fluorescence was only slightly affected (<7%) by displacement of the objective position from the plane of focus 4

5 up to a distance of 3-4 microns (data not shown), larger than the typical error in the autofocusing routine. The growth of single cells as a function of time was well approximated by an exponential. Given the limited range of changes in cell size it is hard to distinguish exactly between different growth laws. Fit to linear growth was slightly but consistently worse than an exponential fit (χ 2 lin ~1.2 χ 2 exp) and a fit with two different lines (one from cell birth to bud and the other from bud to cell division, assuming a model in which DNA content is limiting for cell growth) was as good as an exponential fit (χ 2 2lines ~χ 2 exp). However the two slope fit has two more free parameters than an exponential fit (no continuity condition was imposed on the fit). The measurement of cell size using total red fluorescence at each time point displayed an appreciable variability (average deviation from exponential fit 6% of the average size at budding, Fig. S1), probably due to noise in the imaging process and errors in cell body segmentation. The effect of this noise on size measurements was reduced by extracting cell size at a given time point from the fit of exponential cell growth, instead of using the value obtained for cell size at that frame (see Figure S1). To do this, a line was fit to the log of cell size as function of time by the least-squares method (there is no statistically significant deviation from linearity in these plots, as indicated by the fact that fits to higher order polynomials do not perform any better than a linear fit). The points (red points in Figures S1a, b, c) whose distance to the line was bigger than 2 standard deviations (from the distribution of distances from the fitted line) were excluded and the fit was repeated. The residuals of the fit are symmetric around zero and there is no tendency for errors to vary between early and late points. Hence we can conclude that there is no evidence for systematic errors and the error in size at birth or bud can be estimated by the error on the determination of the fit parameters and time frame. This procedure increases the accuracy of cell size determination by 3 fold on average (average error on single points 2% of the average size at budding). Occasional bad fits (residual error R 0.10) were omitted from the data (Fig. S1d). Bad fits included about 5% of the data and were mostly restricted to cells at the end of the movie for which the segmentation software had trouble identifying the bud. 5

6 Figure S1 Examples of the linear fit of the logarithm of cell size, M, as a function of time and distribution of residual errors R. a), b) Examples of two fits considered good, c) example of a bad fit that was excluded from final tabulation in the data set. Time of budding is indicated with arrow. d) Distribution of the average distance, R, of points from the fit. The excluded fits with R 0.10 account for about 5% of the total number of cells. To compare our fluorescence based method of cell size determination with the geometrical determination of cell size based on area (pixel number) within segmented cell boundaries, we computed the R 2, i.e. the average square residual error, of an exponential fit using the two different measures (see Figures S2a, S2b). We found that the average R 2 of a fit using cell area or volume (estimated as area 3/2 ) is about 2.2 times bigger than the R 2 obtained by using total cell fluorescence (Figures S2c, S2d). Furthermore, individual growth rates extrapolated by using an exponential growth model for area or volume are not in perfect agreement with the population doubling time estimated by counting cell bodies (data not shown). These observations indicate that neither area nor estimated volume is as good a measure of cell size as cell fluorescence 6

7 using ACT1pr-DsRed. We also observe that the fluorescence measurement is more robust to changes in the position of the focal plane, does not necessitate a cell shape model and corrects for variation in vacuole size. We conclude that in our setup it is easier and more accurate to measure cell size with a fluorescent marker. On the other hand, our methods are not geared to the most accurate determination of cell volume from microscopic geometry, and while fluorescence, as we determine it, is a better measure than cell volume extracted directly from the automated segmenter, it is possible that another method measuring cell volume would be equivalent. We have not explored this because of the ease and simplicity of our method, and its independence of the vacuole issue. Figure S2 Fluorescence based measurements of cell size are more accurate than geometrical measurements. a) Example of a fit of the logarithm of cell size, M, measured by total cell fluorescence, as a function of time, b) fit of the logarithm of cell area, A, for the same cell as a function of time. c), d) Distribution of the ratio between the average square distance, R 2, of points from the fit of area (c) or volume (d) as a function of time and the average square distance, R 2, of points from the fit using total cell fluorescence, demonstrating almost uniformly better fits using fluorescence. 7

8 S1.E Fluorescence-based measurements of single-cell growth Here we discuss how to measure single-cell growth using a stable fluorescent reporter expressed from a constitutively active promoter. We take R to be the amount of immature fluorescent protein, R * to be the amount of fluorescing protein and define k(r+ R * ), where k is a constant, as cell size. The kinetics of maturation of R into R * will be assumed to be first order with time constant τ, not negligible compared to cell doubling time. We concentrate on two simple mathematical models of cell growth, i.e. an exponential and a linear model. The exponential model is then the following: dr * 1 = α( R + R ) R dt τ * dr 1 = R dt τ The linear model is the following: dr 1 = α R dt τ * dr 1 = R dt τ The solution of these models requires the knowledge of the initial conditions R(0), R * (0). The only quantity accessible to experiments is R *. This implies that a further condition is necessary to solve the models. We impose the condition that the ratio of fluorescent and non-fluorescent proteins is constant at cell division, i.e. R * (0)/R(0)=R * (T)/R(T), where 0 and T indicate the two successive division times. It is easy to show that the solution of the exponential model is given by: R(t)=α τ R * (0) e αt, R * (t)=r * (0) e αt. This implies that for an exponential model the amount of fluorescent protein is proportional to cell size, defined as k(r+r * ). If growth is exponential, then measures of R * can be directly used to measure cell size. This is not true for the linear growth model, in which the ratio of R * to R is not constant during the cell cycle. Given the quality of our fits to exponential growth we can use R * to measure cell size and ignore the correction necessary for linear growth. 8

9 S2. Statistical analysis of the correlation between αt and ln(m birth ) We showed that the slope of a fit of αt vs. ln(m birth ) is a good indicator of the efficiency of size control. This analysis was used to infer differences in size control between mothers and daughters and between daughters of different sizes. In this Section, we present a detailed analysis of the statistical significance of the estimated values of the various slopes. Correlating αt G1 or αt 1 and ln(m birth ) shows that G1 duration or the duration of the period from cytokinesis to Whi5 nuclear exit in mother cells is basically independent of cell size (Table S3). The estimated slopes and their 95% confidence bounds are for αt G1 : (-0.20:-0.08), and for αt 1 : (-0.09:-0.02). The estimated slopes for the entire daughter dataset and their 95% confidence bounds are (-0.49:-0.24) (αt G1 ) and (-0.56:-0.31) (αt 1 ), significantly different from the value observed for mothers (Table S3). This shows that mothers and daughters differ in their size control properties. Binning of the data suggests that the fit for daughter cells can be decomposed in two linear fits, one for daughters smaller than about 67% of the average size at budding and one for bigger daughters. The breakpoint can be empirically determined by looking at the binned data, and essentially the same breakpoint is determined for the two independently measured data sets: αt G1 and αt 1 vs. ln(m birth ) (see Figures 2e, 3e and Methods for a description of the binning procedure). Pearson s χ 2 test is a rigorous statistical tool to establish the statistical significance of the two slope model. This analysis takes into account the fact that a two slope model has more fitting parameters than a linear model. Pearson s χ 2 test (on the binned data, see Figure S3d and Table S4) for linear vs. two slope linear model shows that a two slope model is a better model for the correlation of αt 1 vs. ln(m birth ) (P=0.65 for two slope linear model and P=0.05 for the linear model). The difference between the two models when the same analysis is repeated on the αt G1 vs. ln(m birth ) dataset is suggestive but cannot be strongly supported statistically. This is likely due to the fact that we have added to a two slope model an extra, noisy variable uncorrelated to cell size (i.e., the interval from Whi5 nuclear exit to budding) and also to under-representation of small new-born daughter cells, which lowered confidence in the apparent steep slope for small cells. Therefore, we used two complementary methods to produce small daughter cells. 9

10 First, we employed essentially the method of Dirick et al. [S2] to produce unusually small wild-type (wt) daughter cells. We used a strain containing a MET3-CLN2 gene in addition to ACT1pr-DsRed and MYO1-GFP, and pregrew the strain in the absence of methionine (MET3-CLN2 on). The ectopic CLN2 over-expression resulted in small cell size [S2]. We then plated these cells on medium containing methionine, and scored the first complete daughter cell cycle under conditions of MET3-CLN2 repression. As described [S2], this resulted in a population of unusually small wild-type daughter cells. Pooling the data for these daughter cells with the previous data set (Figure 2f) showed that the two data sets were congruent (very similar in the region of overlap). Pearson s χ 2 test on the binned data of this extended dataset (see Figure S3a and Table S4) clearly documents the 2-slope behavior, with high statistical confidence (a linear fit was rejected with P=0.02, while the 2-slope fit was accepted with P>0.7). As an alternative method we grew cells in glycerol/ethanol (see Section S4). Growth in glycerol/ethanol instead of glucose is known to result in slow growth and the production of very small daughter cells. When we combine the data for glycerol-ethanol-grown daughter cells with the glucose-grown data set (Figure S3b), we observe that the data sets are essentially continuous; therefore it may be appropriate for statistical purposes to pool the data sets. For the combined data sets, Pearson s χ 2 test on the binned data (see Figure S3c and Table S4) clearly documents the 2-slope behavior, with very high statistical confidence (a linear fit was rejected with P=10-5, while the 2-slope fit was accepted with P=0.22). Similar results can be obtained by combining the glucose-grown data set with the glycerol/ethanol-grown data set for the analysis of αt 1 vs. ln(m birth ). The data sets are essentially continuous (Figure S3e), so we can again for statistical purposes pool them. For the combined data sets, Pearson s χ 2 test on the binned data (see Figure S3f and Table S4) clearly rejects 1-slope behavior, with very high statistical confidence (a linear fit was rejected with P=2 10-5, while the 2-slope fit was accepted with P=0.07). We can also combine the glucose-grown data set with data from glycerol/ethanolgrown cells for the analysis of αt G1 vs. ln(m birth ) for cells of higher ploidy, to investigate if these strains also exhibit the two slope behavior. This analysis cannot be performed only on the glucose-grown data set due to the under-population of the region of small 10

11 daughters. The data set are essentially continuous (Figure S4a) and we can again pool them. For the combined data sets, Pearson s χ 2 test on the binned data (see Figure S4b and Table S4) clearly rejects the 1-slope behavior, with very high statistical confidence (a linear fit was rejected with P=2 10-7, while the 2-slope fit was accepted with P=0.06). We observe that higher order polynomial fits (second and third order) behave worse than the two slope model, indicating that there is no need for more complicated size control models. Another strong reason to prefer linear fits is that we can easily associate the values of the slope with the efficiency of size control. We can interpret a slope of -1 as a perfect sizer and a slope of 0 as a timer; hence linear slopes have an immediate physiological and biological interpretation. Having established the statistical significance of the two slope model, we can analyze the values of the two slopes in the wt data set (see Table S3). The estimated values of the slopes of the two linear fits of αt G1 vs. ln(m birth ) are: ((-1.10:-0.27) 95% confidence bound, (-0.95:-0.45) 80% confidence bound) and ((-0.52:-0.12) 95% confidence bound, (-0.44:-0.19) 80% confidence bound). The values of the slopes of the two linear fits of αt 1 vs. ln(m birth ) are: ((-1.00:-0.30) 95% confidence bound, (-0.97:-0.35) 90% confidence bound) and ((-0.37:0.00) 95% confidence bound, (-0.34:-0.03) 90% confidence bound). The two slopes for αt G1 vs. ln(m birth ) are thus likely to differ with P<0.2 (since the two 80% confidence bound intervals do not overlap), while the two slopes for αt 1 vs. ln(m birth ) are likely to differ with P<0.1 (since the two 90% confidence bound intervals do not overlap). The statistical significance of the two linear fits is made stronger by noticing that we observe essentially the same behavior with P<0.2 and P<0.1 in two independent data sets (αt G1 vs. ln(m birth ) and αt 1 vs. ln(m birth )). Therefore, we can combine the data sets to say that the two slopes are different with P<0.02, and the estimates for the two slopes in the two data sets are quite similar (-0.69 and for the first steep slope; and for the second slope). 11

12 αt G1 vs. ln(m birth ) αt 1 vs. ln(m birth ) wt mothers (Figs 2d, S9) (-0.20:-0.08) (-0.09:-0.02) wt daughters (Figs 2e, S10) (-0.49:-0.24) (-0.56:-0.31) small wt daughters (Figs 2e, S10) (-1.10:-0.27) (-1.00:-0.30) big wt daughters (Figs 2e, S10) (-0.52:-0.12) (-0.37:0.00) small wt+met3-cln2daughters (Figs 2f, S3) (-1.10:-0.58) N/A big wt+met3-cln2daughters (Figs 2f, S3) (-0.56:-0.17) N/A small wt in D+g/e daughters (Fig. S3) (-1.01:-0.67) (-1.02:-0.46) big wt in D+g/e daughters (Fig. S3) (-0.48:-0.13) (-0.38:-0.13) small tetraploid daughters in D+g/e (Fig. S4) (-1.12:-0.47) N/A big tetraploid daughters in D+g/e (Fig. S4) (-0.37:-0.14) N/A 6xCLN3 daughters (Figs 3g, S10) (-0.34:-0.16) (-0.31:-0.06) 6xCLN3 small daughters (Figs 3g, S10) (-0.52:-0.12) (-0.51:-0.11) 6xCLN3 big daughters (Figs 3g, S10) (-0.54:-0.13) (-0.56:-0.06) whi5 daughters (Fig. 3h) (-0.30:-0.15) N/A whi5 small daughters (Fig. 3h) (-0.43:-0.02) N/A whi5 big daughters (Fig. 3h) (-0.39:-0.05) N/A Table S3. Values of the estimated slopes for the correlation of αt G1 and αt 1 with the ln(m birth ). The table shows the values of the slopes and their 95% confidence bounds. The figures with the raw and binned data are referenced in parenthesis. All the strains are haploid except when indicated. (D = glucose, g/e = glycerol/ethanol). Linear model Two slopes model αt 1 vs. ln(m birth ) haploid wt dataset P=0.05 P=0.65 αt 1 vs. ln(m birth ) haploid wt glucose + glycerol/ethanol datasets αt G1 vs. ln(m birth ) haploid wt+small MET3-CLN2 daughters datasets αt G1 vs. ln(m birth ) haploid wt glucose + glycerol/ethanol datasets αt G1 vs. ln(m birth ) tetraploid wt glucose + glycerol/ethanol datasets P= P=0.02 P= P= P=0.07 P=0.72 P=0.22 P=0.06 Table S4. A two slopes model fits the correlation between αt G1 and αt 1 with the ln(m birth ) of daughter cells better than a linear model. The table shows the p values of a Pearson s χ 2 test using a linear or two slopes model. 12

13 Figure S3 A two slope model describes the correlation of αt 1 or αt G1 with the ln(m birth ) better than a linear model. a) Two slope model fit or one slope model fit of binned data of αt G1 vs. ln(m birth ) combining the data obtained with the MET3-CLN2 strain and with the wt strain, b) combination of data sets of wt cells grown in glucose (blue closed circles) and in glycerol/ethanol (black open circles) for αt G1 vs. ln(m birth ), c) two slope model fit or one slope model fit of binned data of αt G1 vs. ln(m birth ) combining the wt data obtained for cells grown in glucose and in glycerol/ethanol (data from b)), d) two slope model fit or one slope model fit of binned data of αt 1 vs. ln(m birth ) for glucose grown cells, e) combination of data sets of wt cells grown in glucose (green closed circles) and in glycerol/ethanol (black open circles) for αt 1 vs. ln(m birth ), f) two slope model fit or one slope model fit of binned data of αt 1 vs. ln(m birth ) combining the wt data obtained for cells grown in glucose and in glycerol/ethanol (data from e)). 13

14 Figure S4 A two slope model describes the correlation of αt G1 with the ln(m birth ) for tetraploid cells better than a linear model. a) Combination of data sets of wt tetraploid cells grown in glucose (blue circles) and in glycerol/ethanol (green circles) for αt G1 vs. ln(m birth ), b) two slope model fit or one slope model fit of binned data of αt G1 vs. ln(m birth ) combining the data obtained for cells grown in glucose and in glycerol/ethanol (data from a)). In addition, we also provide evidence that the two slope behavior is under genetic control (Table S3). The -0.7 slope in the small daughter cell population is eliminated either by increasing the copy number of CLN3 or by deleting WHI5 (see Figures 3g, 3h). Correlations of αt G1 and αt 1 with ln(m birth ) for 6xCLN3 cells do not show a two slope behavior. The slopes for the entire 6xCLN3 daughter data set estimated with a 95% confidence bound are respectively: (-0.34:-0.16) (αt G1 ) and (-0.31:-0.06) (αt 1 ). The slopes of αt G1 and αt 1 vs. ln(m birth ) for small daughters (i.e. smaller than 67% of the average size at budding of wt cells) are respectively: ((-0.52:-0.12) 95% confidence bound, (-0.46:-0.23) 80% confidence bound) and ((-0.51:-0.11) 95% confidence bound, (-0.43:-0.18) 80% confidence bound). The slopes for big daughters are respectively: ((-0.54:-0.13) 95% confidence bound, (-0.46:-0.21) 80% confidence bound) and ((-0.56:-0.06) 95% confidence bound, (-0.49:-0.17) 80% confidence bound). 14

15 Similar results hold for whi5 cells: the slope of αt G1 and vs. ln(m birth ) for the entire data set estimated with a 95% confidence is (-0.30:-0.15). The slope for small daughters (i.e. smaller than 67% of the average size at budding of wt cells) is ((- 0.43:-0.02) 95% confidence bound, (-0.36:-0.10) 80% confidence bound). The slope for big daughters is ((-0.39:-0.05) 95% confidence bound, (-0.32:-0.11) 80% confidence bound). Thus, no difference in the behavior of big and small daughter cells can be detected in these genetic backgrounds. These findings indicate that the observation of the steep slope for small daughters is not an artifact of measurement or data analysis, since equivalently small cells in altered genetic backgrounds do not exhibit this slope. These genetic backgrounds are not arbitrarily selected; they are exactly the backgrounds that our 2-step model predicts should eliminate the sizer component of Start control (see Figure 3i). This proves that the size control properties of small daughters are under genetic control. S3. Analysis of the independence of the two regulatory steps of Start Analysis of the localization of Myo1-GFP and Whi5-GFP (bud neck, nucleus) allows us to partition Start in two independent and functionally distinct steps. Measurements of the correlation between the period from cytokinesis to Whi5 nuclear exit and the period from Whi5 exit to bud emergence are complicated by the fact that Whi5 nuclear exit is not easy to score in strains labeled with both Myo1-GFP and Whi5-GFP. However, analysis of movies (frame rate 1frame/3minutes) of doubly labeled strains shows that the time of Whi5 entry into the nucleus and the time of cytokinesis are strongly correlated, at least in cells where these two events can be clearly independently scored (scorable cells constitute a majority of the total). Whi5 enters the nucleus 1-3 frames before cytokinesis, with a strong peak at 2 frames (6 min) (Figure S5, average 6.4±0.2 min). Entry of Whi5- GFP into the nucleus can then be used to infer that cytokinesis happens 6 min later. Analysis of the correlation between the period from cytokinesis to Whi5 nuclear exit and the period from Whi5 nuclear exit to bud emergence was performed in strains expressing only Whi5-GFP by scoring bud emergence by visual detection of the bud. Using these conditions, we avoid additional problems in the detection of Whi5-GFP without introducing additional variability, given the tight correlation between Myo1 ring 15

16 appearance and bud emergence. We found that the durations of the period from division to Whi5 exit and the period from Whi5 exit to bud emergence are almost independent in all the analyzed strains (correlation coefficients: -0.1 wt, -0.1 cln3, X CLN3, X CLN2). Figure S5 Histogram of the duration of the interval from Whi5 nuclear entry to Myo1 disappearence. S4. Analysis of movies in glycerol/ethanol To expand the analysis of Start regulation to daughter cells of small size and to poor nutrient conditions, we studied the correlation between both the period from cytokinesis to Whi5 nuclear exit and G1 with cell size at birth for cells grown in glycerol/ethanol as carbon source, rather than glucose. Glycerol/ethanol supports a much slower growth rate than glucose (170 min compared to 100 min doubling time), and glycerol/ethanol-grown daughter cells are much smaller at birth than glucose-grown daughters. Analysis of the growth of individual cells in glycerol/ethanol media shows that single cell growth in these conditions may not be exponential. We fit cell size as function of time using a smoothing spline routine (Curve Fitting Toolbox, MATLAB7.0) and extract cell size at birth and bud as the values of the fit at the time of cell birth and bud emergence. In order to extend the analysis presented in the text to non-exponential growth we redefine: αt G1,1 = ln(m bud,wo ) - ln(m birth ) (M WO indicates cell size at the time of Whi5 nuclear exit). This 16

17 definition allows us to get equivalent plots to those for cells grown in glucose for the analysis of size control. We observe that the correlation between the period from cytokinesis to Whi5 nuclear exit and the size of cells at birth is identical to the correlation of G1 duration and the size of cells at birth indicating that also in poor nutrient conditions size control is operative only during the period from cytokinesis to Whi5 nuclear exit (Figure 3f). Daughter size at Whi5 exit for cells grown in glycerol/ethanol is about 90% of the size at Whi5 exit for cells grown in glucose despite a big difference in size at birth (the average size at birth for cells grown in glycerol/ethanol is 65% of the average size at birth of cells grown in glucose). This is due to the fact that for daughter cells grown in glycerol/ethanol the period from cytokinesis to Whi5 nuclear exit (94 min) is much longer than for cells grown in glucose (20 min). This period accounts for most of the difference in total cell cycle timing of daughter cells (Table S5 and Table S6). Even in glycerol-ethanol, mother cells exhibit no evidence of size control (Figure S6). Figure S6 Absence of size control in mother cells grown in glycerol/ethanol. Correlation between the duration of G1, T G1, scaled to the growth rate, α, and the logarithm of cell size at birth for mothers shows the lack of size control in mother G1 (slope = - 0.1). 17

18 T 1 in daughters 94±3 (108) T 2 in daughters 32±4 (108) T 1 in mothers 8±1 (178) T 2 in mothers 25±4 (178) Table S5. Average duration of the period from cytokinesis to Whi5 nuclear exit (T 1 ) and the period from Whi5 exit to bud emergence (T 2 ) for wt haploid cells grown in glycerol/ethanol. The table shows the mean +/- standard error of the mean in minutes with the number of observations reported in parenthesis. G1 daughter 126±4 (90) Budded period daughter 106±2 (54) G1 mother 33±1 (118) Budded period mother 101±2 (83) Total cycle daughter 219±3 (54) Total cycle mother 133±2 (84) Table S6. Average duration of cell cycle periods for wt haploid cells grown in glycerol/ethanol. The table shows the mean +/- standard error of the mean in minutes with the number of observations reported in parenthesis. S5. Additional supplementary tables Haploids Diploids Tetraploids G1 daughter 37±2 (158) 25.7±0.8 (164) 30.5±0.8 (100) Budded period daughter 76±2 (97) 81±1 (95) 82±2 (52) G1 mother 15.6±0.5 (202) 14.1±0.4 (184) 16.2±0.4 (104) Budded period mother 72±1 (116) 71±1 (105) 74±2 (54) Total cycle daughter 112±3(97) 106±2 (95) 113±2 (52) Total cycle mother 87±1 (116) 85±1 (105) 90±2 (54) Table S7. Average cell cycle periods for cells of different ploidy. The table shows the mean +/- standard error of the mean in minutes with the number of observations reported in parenthesis. 18

19 Coefficient of variation Haploids Diploids Tetraploids G1 daughter 0.50±0.05 (158) 0.41±0.04 (164) 0.26±0.03 (100) Budded period daughter 0.20±0.06 (97) 0.17±0.05 (95) 0.15±0.04 (52) G1 mother 0.50±0.05 (202) 0.42±0.4 (184) 0.28±0.03 (104) Budded period mother 0.17±0.02 (116) 0.16±0.02 (105) 0.15±0.02 (54) Total cycle daughter 0.22±0.02(97) 0.16±0.01 (95) 0.14±0.02 (52) Total cycle mother 0.14±0.01 (116) 0.13±0.02 (105) 0.14±0.02 (54) Table S8. Coefficient of variation of cell cycle periods for cells of different ploidy. The number of observations is reported in parenthesis. wt 6xCLN3 6xCLN2 6xCLN3 6xCLN2 Daughter G1 37±2 (158) 26.1±0.9 (98) 27±1 (87) 23.6±0.9 (76) Budded period 76±2 (97) 89±2 (55) 90±3 (43) 94±3 (36) daughter Mother G1 15.6±0.5 (202) 14.3±0.6 (119) 13.1±0.4 (92) 12.0±0.4 (83) Budded period 72±1 (116) 81±1 (68) 81±2 (55) 88±2 (43) mother Total cycle 112±3(97) 113±2 (55) 117±4(43) 116±3(36) daughter Total cycle 87±1 (116) 95±1(68) 93±2(55) 98±2(43) mother Table S9. Average cell cycle periods for different haploid strains. The table shows the mean +/- standard error of the mean in minutes with the number of observations reported in parenthesis. Coefficient of wt 6xCLN3 6xCLN2 6xCLN3 6xCLN2 variation G1 daughter 0.50±0.05 (158) 0.32±0.03 (98) 0.44±0.06 (87) 0.35±0.04 (76) Budded period 0.20±0.06 (97) 0.18±0.04 (55) 0.19±0.06 (43) 0.19±0.06 (36) daughter G1 mother 0.50±0.05 (202) 0.43±0.04 (119) 0.27±0.03 (92) 0.29±0.03 (83) Budded period 0.17±0.02 (116) 0.13±0.02 (68) 0.15±0.03 (55) 0.16±0.02 (45) mother Total cycle 0.22±0.02(97) 0.16±0.02(55) 0.21±0.03(43) 0.17±0.03 (36) daughter Total cycle 0.14±0.01 (116) 0.13±0.02 (68) 0.12±0.03(55) 0.14±0.02 (45) mother Table S10. Coefficient of variation of cell cycle periods for different haploid strains. The number of observations is reported in parenthesis. 19

20 Average size at bud wt haploids 1.00±0.06 wt diploids 2.0±0.1 wt tetraploids 3.9±0.1 6xCLN2 0.94±0.06 6xCLN3 0.77±0.05 6xCLN3 6xCLN2 0.81±0.05 Table S11 Average size at budding for various strains. The data were normalized to the average size at budding of wt haploid cells. The comparison was done only for cells imaged the same day to reduce variation due to the illumination source. The table shows the mean +/- standard error of the mean. Measured doubling time Doubling time predicted from individual cells growth rate Coefficient of variation of growth rates wt haploids 99±1 100±1 0.18±0.02 wt diploids 95±1 93±1 0.14±0.01 wt tetraploids 101±2 97±2 0.13±0.01 6xCLN2 104±3 103±3 0.17±0.02 6xCLN3 103±1 105±2 0.21±0.03 6xCLN3 6xCLN2 106±3 107±3 0.17±0.03 Table S12 Comparison between colony doubling time and doubling time predicted from measurements of growth rate of individual cells. The table shows the mean +/- standard error of the mean in minutes. 20

21 S6. Additional supplementary figures Figure S7 Molecular noise is responsible for most of the fluctuations of the duration of G1 period. Plot of the noise (coefficient of variation: CV) as a function of ploidy for the duration of G1 (CV G1 ), for the duration of G1 scaled to the growth rate, CV αt and for the portion of this noise that is size and growth rate-independent and can be attributed to molecular noise (see Table 1) (i.e., this is variation about the αt vs ln(m birth ) line for cells of varying ploidy). The black lines are curves ~1/ ploidy. 21

22 Figure S8 Noise in G1 duration is reduced by increasing the number of copies of G1 cyclins. a), A map of the core molecular network driving Start. Histograms of the G1 duration for daughters wt (b), 6xCLN3 (c), 6xCLN2 (d), 6xCLN3 6xCLN2 (e). Histograms of the G1 duration for mothers wt (f), 6xCLN3 (g), 6xCLN2 (h), 6xCLN3 6xCLN2 (i). For every histogram we report the number of measurements, the average G1 duration and the coefficient of variation, i.e. standard deviation divided by the mean. 22

23 Figure S9 Size independent noise is reduced by ploidy and by increasing the number of copies of G1 cyclins in mother cells. Correlation between the duration of G1, T G1, scaled to the growth rate, α, and the logarithm of cell size at birth shows the lack of size control in mother G1 and that cell size independent noise (Table 1) is reduced by ploidy and by increasing the number of copies of G1 cyclins. The size of all haploid strains was normalized to the average size at budding of wt cells. The size of diploid and tetraploid cells was normalized to the average size at budding of diploid and tetraploid cells respectively. 23

24 Figure S10 Size independent noise is reduced by ploidy and by increasing the number of copies of G1 cyclins in mother cells. Correlation between the duration of G1, T G1, scaled to the growth rate, α, and the logarithm of cell size at birth shows that cell size independent noise (Table 1) is reduced by ploidy and by increasing the number of copies of G1 cyclins. An inverse correlation (significantly different from both 0 and -1) is observed for all the strains and is indicative of a sloppy size control. The size of all haploid strains was normalized to the average size at budding of wt cells. Small wt daughter cells exhibit an efficient size control (slope= - 0.7). Cells with more copies of CLN3 no longer show efficient size control (slope= - 0.3), indicating that CLN3 gene dosage alters the properties of size control. In contrast, increasing CLN2 gene dosage does not alter size control (see also Fig. S11). The size of diploid and tetraploid cells was normalized to the average size at budding of diploid and tetraploid cells respectively. The lack of a clear component of high negative slope for smaller daughter cells in diploids and tetraploids is not fully understood, but may be largely due to the lack of unusually small daughter cells generated by these higher-ploidy cells, due to a slightly longer 24

25 budded period during which the bud grows, combined with a reduction in variability of growth rate of individual cells (Fig. S12 and Table S10). These explanations do not account for the lack of this slope in 6X CLN3 and 6X CLN3 6X CLN2 cells. We have tested this explanation by growth of tetraploids in glycerol/ethanol (Fig. S4) where we find that combining the small daughters obtained from glycerol/ethanol growth with the larger daughters obtained from glucose growth gives a continuous data set well fit with two slopes. Figure S11 CLN2 gene dosage does not affect the duration of the period from cytokinesis to Whi5 nuclear exit. Correlation between the duration of the period from cytokinesis to Whi5 nuclear exit, T 1, scaled with growth rate, α, and the logarithm of cell size at birth for wt (blue points and lines) and 6xCLN2 strains (red points and lines). 25

26 Figure S12 Distribution of growth rates for various strains. The average growth rate <α> agrees well with the colony growth rate (see Table S10). References [S1] Bean, J. M., Siggia, E. D. & Cross, F. R. Coherence and timing of cell cycle start examined at single-cell resolution. Mol. Cell 21, 3-14 (2006). [S2] Dirick, L., Bohm, T. & Nasmyth, K. Roles and regulation of Cln-Cdc28 kinases at the start of the cell cycle of Saccharomyces cerevisiae. Embo J. 14, (1995). 26