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1 Supplementary Information The critical size is set at a single-cell level by growth rate to attain homeostasis and adaptation Francisco Ferrezuelo 2,5, Neus Colomina 2,5, Alida Palmisano 3,4, Eloi Garí 2, Carme Gallego 1, Attila Csikász-Nagy 3 & Martí Aldea 1, * 1 Institut de Biologia Molecular de Barcelona, CSIC, 828 Barcelona, Catalonia, Spain 2 Dept Ciències Mèdiques Bàsiques, IRBLleida-UdL, 258 Lleida, Catalonia, Spain 3 The Microsoft Research-University of Trento Centre for Computational and Systems Biology, 3868 Rovereto, Italy 4 Department of Biological Sciences, Virginia Polytechnic Institute and State University, Blacksburg, VA , USA 5 These authors contributed equally to this work *Correspondence should be addressed to MA ( martialdea@ibmbcsices) Supplementary Figures S1-S7 page 2 Supplementary Tables S1-S7 page 6 Supplementary Methods: Modeling of volume growth during the yeast cell cycle page 13 Ferrezuelo et al, 212, Supplementary Information 1

2 a 4 Microscopy Coulter Counter b 4 Chamber Batch Cell number(%) Volume(µm 3 ) c Cell volume (µm 3 ) 35 3 Growth conditions Time (min) Budding time (min) Mean growth ratein G1 (α) (µm 3 /min) Confidence limits (µm 3 /min) Chamber(-FLU) Chamber (+FLU) Batch na Supplementary Figure S1 Validation of volume determination methods and growing conditions (a) Cell volume distributions obtained by microscopy from dark field images (N=28, continuous lines) or a Coulter Counter from batch cultures (N>1, broken lines) of wild type elutriated cells at 15 min (red lines) or 9 min (blue lines), and cln3 elutriated cells at 1 min (green lines) of growth in SC plus glucose (b) Volume growth kinetics in the incubation chamber (black) or a batch culture (red) for wild type elutriated cells in SC plus glucose Median volumes of cells in the incubation chamber and the batch culture were determined by microscopy (N=5) and a Coulter Counter (N>1), respectively (c) Budding times, mean volume growth rates in G1 (α) and confidence limits for the mean (significance level of 1) corresponding to wild-type elutriated cells grown in the incubation chamber and subject or not to fluorescence imaging (+/- FLU) or a batch culture and analyzed as in (b) a Growth rate in G1 (α) (µm 3 /min) BY strain asynchronous BY strain elutriated CML strain elutriated Mean CV (%) b 35 BY strain asynchronous BY strain elutriated CML strain elutriated c 7 CML strain BY strain Cellnumber(%) Growthratein G2-M (µm 3 /min) Growthratein G1 (α, µm 3 /min) Growthratein G1 (µm 3 /min) Supplementary Figure S2 Volume growth rates in asynchronous and elutriated daughter cells (a) Mean volume growth rates in G1 (α) and coefficients of variation for asynchronous and elutriated daughter cells (N=1) of either BY4741 WHI5-GFP (BY) or CML128 (CML) wild-type strain backgrounds (b) Volume growth rate in G1 (α) distributions of daughter cells analyzed in (a) (c) Growth rate in G1 versus growth rate in G2-M for elutriated daughter cells of either BY4741 (BY, open circles) or CML128 (CML, closed circles) strain backgrounds The combined coefficient of determination (r 2 ) was 141 Ferrezuelo et al, 212, Supplementary Information 2

3 a Time(min) Budding b 8 Growthrate(µm 3 /min) Growthrate(µm 3 /min) 4 3 Budding Time (min) Supplementary Figure S3 Volume growth rate changes during the cell cycle in a BY4741 strain (a) Heat map generated from volume growth rates during the cell cycle of elutriated WHI5-GFP daughter cells (N=5) derived from BY4741 Instantaneous rates were determined as described under Methods and aligned at budding time (t=) for each cell (b) Mean values and confidence limits for the mean (significance level of 5) of cells in (a) are plotted a d d r r nuclear index = 8r/15 mean(d) d = pixel distance to gravity center r = projected circle radius b 3 28 Nuclear index(relative units) Colocalization (relative units) Supplementary Figure S4 Quantification of Whi5-GFP nuclear localization (a) Whi5 localization in the nucleus was assessed as a relative index inversely proportional to the mean distance of the brightest pixels to their gravity center Brightest pixels were selected having a gray value larger than the mean plus two standard deviations, and the index was made relative to 8r/15, the theoretical mean distance to the center from random points in a sphere projected to a circle with radius r (see Methods for details) (b) Nuclear index of Whi5-GFP determined as above was plotted versus colocalization of Whi5-GFP with a nuclear marker (Htb2-mCherry) The nuclear index is expressed as a relative value (see Methods for details) for ten asynchronous daughter cells at different times of the cell cycle Ferrezuelo et al, 212, Supplementary Information 3

4 a Asynchronous Elutriated b Glu Gal Raf Eth Time (min) Growthratein G1 (α, µm 3 /min) Time (min) Growthratein G1 (α, µm 3 /min) Supplementary Figure S5 Time from Start to budding does not correlate with the individual growth rate (a) Time to budding (T2) versus growth rate in G1 (α) for asynchronous (black, N=1) or elutriated (red, N=78) WHI5-GFP daughter cells growing in SC plus glucose (b) Time to budding (T2) versus growth rate in G1 (α) for asynchronous WHI5-GFP daughter cells growing in SC plus glucose (red, N=1), galactose (green, N=1), raffinose (orange, N=1) or ethanol (blue, N=1) a Experimental Model Volumeat Start(Vs, μm 3 ) b Time at Start(T1, min) Growthratein G1 (α, μm 3 /min) Growthratein G1 (α, μm 3 /min) c d αt α(t1-k) Vi Vi Supplementary Figure S6 Model and experimental volumes at Start, time periods and volume growth rates in G1 (a) Volume at Start (Vs) versus growth rate in G1 (α) for daughter cells growing in SC plus glucose from experimental data (red, N=1) or simulated by the germline method (black, N=1) (b) A plot of time at Start (T1) versus growth rate in G1 (α) for daughter cells in (a) is shown (c, d) Cell volume (Vs), time at Start (T1) and volume growth rate in G1 (α) determined from daughter cells as in a were made relative to the corresponding mean volume at Start, and used to generate αt1 (c) or α(t1-k) (d) versus Vi plots Ferrezuelo et al, 212, Supplementary Information 4

5 a Volumeat Start(Vs, µm 3 ) Vs=f(α) b Volumeat Start(Vs, µm 3 ) Vs=f(α) α=g(vi) β=h(vb) 5 5 Time at Start(min) Time at Start(min) Generation# Generation# c 35 d 7 Growthratein G1 (α, µm 3 /min) Growthratein S-G2-M (β, µm 3 /min) Initialvolume(Vi, µm 3 ) Buddingvolume(Vb, µm 3 ) Supplementary Figure S7 Cell size homeostasis and growth-rate dependence assumptions (a, b) Volume at Start (Vs) and time at Start (T1) fluctuations over 1 generations as predicted by the germline method assuming that volume at Start is a stochastic variable that depends on growth rate (Vs=f[α]) with no additional assumptions (a) or considering that growth rates in G1 (α) and S-G2-M (β) depend on the volumes at the beginning of the respective phases (b), assuming α=g[vi] and β=h[vb], where Vi is the initial volume for G1 phase and Vb is the budding volume as the initial volume for S-G2-M (c) Growth rate in G1 (α) versus initial volume in G1 (Vi) for daughter cells growing asynchronously in SC plus glucose (d) Growth rate in S-G2-M (β) versus budding volume (Vb) for cells growing asynchronously in SC plus glucose Ferrezuelo et al, 212, Supplementary Information 5

6 Table S1 Correlation analysis for volume at Start (Vs) versus growth rate in G1 (α) Strain Carbon source b (k) a (Vo) se(b) se(a) r 2 se(y) F df p value ssreg ssresid CL(b) rse(y) wild type Glucose E wild type Glucose* E wild type Galactose E wild type Raffinose E wild type Ethanol E wild type (all data) E whi3 Glucose E whi5n Glucose E cln3 Glucose E ydj1 Glucose E cln1,2 Glucose E sfp1 Glucose E swi6 Glucose E swi4 Glucose E mbp1 Glucose E bck2 Glucose E ocln3 Galactose E oydj1 Galactose* E cln3,whi5n,stb1 Glucose E * elutriated cells b=slope k; a=intercept V ; se(b)= standard error of the slope; se(a)= standard error of the intercept; r 2 =coefficient of determination; se(y)= standard error for the estimate; df=degrees of freedom; ssreg=regression sum of squares; ssresid=residual sum of squares; CL(b)=confidence limits for the slope (significance level of 1); rse(y)%=relative standard error for the estimate (%) Ferrezuelo et al, 212, Supplementary Information 6

7 Table S2 Correlation analysis for volume at Start (Vs) versus time at Start (T1) Strain Carbon source b a se(b) se(a) r 2 se(y) F df p value ssreg ssresid CL(b) rse(y) wild type Glucose E wild type Glucose* E wild type Galactose E wild type Raffinose E wild type Ethanol E wild type (all data) E whi3 Glucose E whi5n Glucose E cln3 Glucose E ydj1 Glucose E cln1,2 Glucose E sfp1 Glucose E swi6 Glucose E swi4 Glucose E mbp1 Glucose E bck2 Glucose E ocln3 Galactose E oydj1 Galactose* E cln3,whi5n,stb1 Glucose E * elutriated cells b=slope; a=intercept; se(b)= standard error of the slope; se(a)= standard error of the intercept; r 2 =coefficient of determination; se(y)= standard error for the estimate; df=degrees of freedom; ssreg=regression sum of squares; ssresid=residual sum of squares; CL(b)=confidence limits for the slope (significance level of 1); rse(y)%=relative standard error for the estimate (%) Ferrezuelo et al, 212, Supplementary Information 7

8 Table S3 Correlation analysis for time at Start (T1) versus growth rate in G1 (α) Strain Carbon source b a se(b) se(a) r 2 se(y) F df p value ssreg ssresid CL(b) rse(y) wild type Glucose E wild type Glucose* E wild type Galactose E wild type Raffinose E wild type Ethanol E wild type (all data) E whi3 Glucose E whi5n Glucose E cln3 Glucose E ydj1 Glucose E cln1,2 Glucose E sfp1 Glucose E swi6 Glucose E swi4 Glucose E mbp1 Glucose E bck2 Glucose E ocln3 Galactose E oydj1 Galactose* E cln3,whi5n,stb1 Glucose E * elutriated cells b=slope; a=intercept; se(b)= standard error of the slope; se(a)= standard error of the intercept; r 2 =coefficient of determination; se(y)= standard error for the estimate; df=degrees of freedom; ssreg=regression sum of squares; ssresid=residual sum of squares; CL(b)=confidence limits for the slope (significance level of 1); rse(y)%=relative standard error for the estimate (%) Ferrezuelo et al, 212, Supplementary Information 8

9 Table S4 Correlation analysis for αt1 versus Vi Strain Carbon source b a se(b) se(a) r 2 se(y) F df p value ssreg ssresid CL(b) wild type Glucose E wild type Glucose* E wild type Galactose E wild type Raffinose E wild type Ethanol E wild type (all data) E whi3 Glucose E whi5n Glucose E cln3 Glucose E ydj1 Glucose E cln1,2 Glucose E sfp1 Glucose E swi6 Glucose E swi4 Glucose E mbp1 Glucose E bck2 Glucose E ocln3 Galactose E oydj1 Galactose* E cln3,whi5n stb1 Glucose E * elutriated cells b=slope; a=intercept; se(b)= standard error of the slope; se(a)= standard error of the intercept; r 2 =coefficient of determination; se(y)= standard error for the estimate; df=degrees of freedom; ssreg=regression sum of squares; ssresid=residual sum of squares; CL(b)=confidence limits for the slope (significance level of 1) Ferrezuelo et al, 212, Supplementary Information 9

10 Table S5 Correlation analysis for αt1-k versus Vi Strain Carbon source b a se(b) se(a) r 2 se(y) F df p value ssreg ssresid CL(b) wild type Glucose E wild type Glucose* E wild type Galactose E wild type Raffinose E wild type Ethanol E wild type (all data) E whi3 Glucose E whi5n Glucose E cln3 Glucose E ydj1 Glucose E cln1,2 Glucose E sfp1 Glucose E swi6 Glucose E swi4 Glucose E mbp1 Glucose E bck2 Glucose E ocln3 Galactose E oydj1 Galactose* E cln3,whi5n,stb1 Glucose E * elutriated cells b=slope; a=intercept; se(b)= standard error of the slope; se(a)= standard error of the intercept; r 2 =coefficient of determination; se(y)= standard error for the estimate; df=degrees of freedom; ssreg=regression sum of squares; ssresid=residual sum of squares; CL(b)=confidence limits for the slope (significance level of 1) Ferrezuelo et al, 212, Supplementary Information 1

11 Table S6 Statistics of growth rates, volumes and times Growth rate in G1 (α, µm 3 /min) Initial volume (Vi, µm 3 ) Volume at Start (Vs, µm 3 ) Volume at budding (Vb, µm 3 ) Time at Start (T1, min) Time at budding (T2, min) Strain Carbon source mean cvar mean cvar mean cvar mean cvar mean cvar mean cvar wild type Glucose wild type Glucose* wild type Galactose wild type Raffinose wild type Ethanol wild type (all data) whi3 Glucose whi5n Glucose cln3 Glucose ydj1 Glucose cln1,2 Glucose sfp1 Glucose swi6 Glucose swi4 Glucose mbp1 Glucose bck2 Glucose ocln3 Galactose oydj1 Galactose* cln3 whi5n,stb1 Glucose * elutriated cells cvar=coefficient of variation (%) Ferrezuelo et al, 212, Supplementary Information 11

12 Table S7 Additional statistics of growth rates, volumes and times Growth rate in S-G2-M (β, µm 3 /min) Time at division (T3, min) Growth rate in S-G2-M (mother) (β, µm 3 /min) Time at Start (mother) (T1, min) Strain Carbon source mean cvar mean cvar mean cvar mean cvar wild type Glucose wild type Galactose wild type Raffinose wild type Ethanol cvar=coefficient of variation (%) Ferrezuelo et al, 212, Supplementary Information 12

13 Supplementary Methods Germline and pedigree modeling of volume growth during the yeast cell cycle We modeled volume growth for consecutive cell cycles following only the daughter cell in each generation (the germline method), or all descendants from the initial cell (the pedigree method) Independently of the method, our model complies with two generally accepted facts: (1) size control in G1 and (2) time control in S-G2-M This is the reason why we imposed a minimum number of constraints to the model, and defined the corresponding dependent variables in a deterministic manner Concerning G1, as we wanted to test the dependence of volume at Start on growth rate, we took growth rate (α) as independent variable to determine volume at Start using the observed linear correlation On the contrary, concerning S-G2-M, we took times (and also growth rate β) as independent variables to determine cell volumes at budding and division A schematic view of the piecewise linear model can be found in Fig 5a Independent variables were parameterized with experimental average data and coefficient of variations shown in Supplementary Tables S6 and S7 We assumed that independent variables followed normal distributions, which were used to generate random stochastic values and to calculate the dependent variables as follows: A new born cell is given a growth rate in G1 (α) and an initial volume (V ) volume (both determined from experimental data) Those values are used to calculate the new born cell volume at Start (Vs) as a function of volume growth rate in G1 by the following calculation Vs = kα + V [equation S1] The cell is given a time at budding (T2) value, which is used to calculate the budding volume (Vb) as Vb = Vs + αt2 [equation S2] The cell is given a growth rate in S-G2-M (β) and a time period to division (T3), which are used to calculate the division volume (Vd) by Vd = Vb + βt3 [equation S3] After division, the new daughter cell receives an initial volume (Vi) given by Vi = Vd Vb β T3 [equation S4] being β a low growth rate in S-G2-M for the mother cell (also from experimental data) In the next cycle, both daughter and mother cells are given a growth rate in G1 (α) to determine Vs=kα+V, and Vs =Vi+T1 α Then, volume at Start is set as the largest value of Vs and Vs Thus, Vs = max (kα + V, Vi + T1 α) [equation S5] Finally, T1 is obtained from T1 = (Vs Vi)/α [equation S6] Ferrezuelo et al, 212, Supplementary Information 13

14 For each cell and generation we took a random number for the independent variables, we calculated the dependent variables according to the rules above and then we let the simulation repeat the process for the desired number of generations Independent variables (determined from experimental data) were α growth rate in G1 k, V ---Vs dependence on growth rate T time at Start (mother cell) T time at budding β growth rate in S-G2-M β growth rate in S-G2-M (mother cell) T time at division Dependent variables (determined by independent variables and rules above) were Vs------volume at Start T time at Start Vb------volume at budding Vd------volume at division Vm-----volume at division (mother cell) Vi initial volume (daughter cell) In the germline study we calculated the volume of the daughter cells of 1 consecutive generations In the pedigree study the model was iteratively simulated while at each division the model of the ancestor cell generated two new instances of the model with parameters derived from the conditions at division of this ancestor cell This process was then carried on until the desired number of generations was reached The analysis of the collected ensemble of simulated traces gave a complete and detailed characterization of a colony's growth from a specific initial cell The time series generated following the steps above for a specific number of generations was collected and used to extract statistics of different quantities Single germline traces were calculated in an Excel file (see Supplementary Data) Similar but shorter germlines were collected following a single branch of the pedigree tree (ie always choosing the daughter branch) Correlation plots were extracted to link age to dependent values Pedigree trees were also analyzed at specific time points to obtain a snapshot of the entire colony and show how many cells exists at that time and what is their current volume The simulation of the pedigree tree was implemented in R programming language (see Supplementary Software 1) Ferrezuelo et al, 212, Supplementary Information 14

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