In order to confirm the contribution of diffusion to the FRAP recovery curves of

Transcription

1 Fonseca et al., Supplementary Information FRAP data analysis ) Contribution of Diffusion to the recovery curves In order to confirm the contribution of diffusion to the FRAP recovery curves of PH::GFP and PC::GFP (Fig. 4) we performed curve smoothing tests for these recovery curves and compared them to GFPnls (diffusion dependent) and H2A::RFP (diffusion independent) recovery curves confirming a contribution of diffusion to recovery for all PC::GFP and PH::GFP data sets (Fig. S). 2) Parameter extraction and cross validation 2.) Extraction of kinetic parameters from FRAP data The FRAP recovery data were analysed by fitting kinetic models (Mueller et al. 28) to averaged FRAP recovery data shown in Figure 4. This fitting procedure enables the extraction of values for diffusion coefficient (Df), the pseudo first order association rate k* on and the dissociation rate k off. 2.2) Adaptation of model for optimal parameter combination An additional step was performed to optimise extracted kinetic parameters. After the calculation of the radius of the model nucleus (RM) (Mueller et al. 28) an additional set of radii was defined, composed of radii - pixels from RM to +2 pixels. These 3 radii were used as input values for the reaction-diffusion or pure-difusion model fit to the experimental data. The resulting set of individual extracted kinetic parameters and their confidence intervals as well as the goodness of fit was used to select the optimal radius for the experiment. This selection consisted of a weighted search with /3 of the

2 2 weight being given to the goodness of the confidence intervals of association and dissociation constants, /3 to the goodness of the extracted diffusion constant confidence interval, /6 to the size of the squared sum of residuals and /6 to the distance from the initial RM, with smaller distances being favoured. MATLAB files are available on request. 2.3) Contribution of binding to FRAP recovery curves To evaluate the role of binding in the recovery kinetics we compared reaction-diffusion (3 extracted parameters: Df, k* on and k off ) and pure-difusion model fits (single extracted parameter: Df) as described in (Mueller et al. 28) to our experimental data. In all cases shown in Figure 4, the best fit was given by the full reaction-diffusion model, indicating the presence of a bound fraction, and giving extracted values for Df, k* on and k off. 2.4) Cross-validation of extracted Df In addition to the extracted values for Df from fitting the reaction- diffusion model, the Df for each protein in each cell type was measured independently. This was achieved by performing FRAP on the region of the metaphase cell that is outside chromatin and fitting the pure diffusion model (Mueller et al. 28) to the recovery data, giving an independent and direct measure of Df. Interphase values were calculated by conversion via diffusion coefficients measured for GFP by fitting the pure diffusion model to FRAP recovery curves measured in both interphase and metaphase, (Table S). The values of Df thus measured showed excellent agreement with those extracted from fitting the full model (Figure S3).

3 3 2.5) Robustness of extracted k* on, k off The robustness of the extracted k* on and k off values was examined by simulations performed at the value of Df that was extracted from the reaction-diffusion model fit, and in which k* on and k off were varied, and the fit to experimental data was evaluated (Fig. S4). This analysis showed that for most data sets, a limited range of k* on and k off values gave optimal fits to the data (Fig. S4). 3) Other models 3.) Localised binding sites: metaphase The effect of localized binding sites in metaphase was examined using the local binding site model described in (Beaudouin et al. 26; Sprague et al. 26), showing that both the improved global binding (Mueller et al. 28) and the localized binding (Beaudouin et al. 26; Sprague et al. 26) models give essentially identical results in conditions of low binding, as is the case for the metaphase data shown here (data not shown). Unlike the Müller model (Mueller et al. 28) the Sprague model (Beaudouin et al. 26; Sprague et al. 26) does not include consideration of the radial bleach profile. Thus in order to achieve consistency of analysis, the Müller Model(Mueller et al. 28) was used for analysis of all data sets. 3.2) Non homogeneous distribution of proteins: interphase To test for the effect of non-homogeneity in protein distribution observed in interphase (Figure 2 and 3) on extracted kinetic parameters, we adapted the model described in (Mueller et al. 28) from its original application to redistribution of photoactivatable

4 4 GFP, to render it applicable to the analysis of FRAP recovery curves, described here. Fitting this model to interphase data for individual nuclei gave similar values for the three extracted parameters whether initial distribution was assumed to be heterogenous or homogenous (Figure S2). 3.2.) Generation of images of single nuclei. In order to construct input protein distribution images for parameter extraction, all prebleach images of a single nucleus (25) were averaged and used to threshold the region of the nucleus in the total image. This region was selected to define the nucleus within the average image of 2s before photobleaching. Due to the speed of scanning, it was not feasible to image the entire nucleus. The shape of NB and SOP nuclei approximates well to a circle, thus the initial binding site distribution in the entire nucleus was reconstructed from the image of the "equatorial" region, covering approximately 2/3 of the nucleus. On the resulting image a circle of radius RM (model nucleus radius calculated as described in (Mueller et al. 28) with adaptation as described in 2. above) was defined with the bleach region centered. This image was used to give the initial distribution of binding sites in the nucleus. In order to produce the first postbleach image, a bleach pattern with parameters describing the bleach spot profile was calculated from the experimental data (Mueller et al. 28) and was superimposed on the prebleach image. Matlab files for image processing are available on request ) Extraction of kinetic parameters from FRAP data, taking non homogeneous protein distribution into account. The intensity distribution images generated as described above were used as input for

5 5 fitting the spatial model described below to the individual FRAP recovery curve for each nucleus, and extraction of parameters. The spatial model was implemented in Mathematica (Wolfram) and is available on request. The reaction-diffusion system is simulated on a 2D circular domain, with a Neumann no-flux condition imposed on the boundary. The method-of-lines is used to numerically solve the resulting partial-differential equation, where a second-order finite difference method is used to discretize the diffusion operator on a uniform mesh. The spatial discretization gives rise to a coupled system of ordinary differential equations for the free and bound concentrations at each mesh point, which is then numerically integrated using an implicit solution scheme. The unknown parameters in the model consist of: the diffusion constant Df, the off-rate of the reaction k off, and the ratio of the total amount of free molecules to bound molecules, Free. Given a value for the free fraction, Free, the initial conditions for the free and bound proteins are obtained from the smoothed, pre-bleached images. Given the values of k off and Free, the spatially varying k on [C] is computed from the intensity distribution of the averaged chromatin images, following the methodology of (Mueller et al. 28). In order to ensure the positivity of k on [C] in the model, a lower bound on the free fraction is imposed, whose value is required to be greater than the minimum chromatin intensity over its average for the circular domain. The unknown parameters (Df, k off, Free) are estimated from the measured fluorescence recovery curve for each individual nucleus by solving the inequality constrained optimization problem using the interior point method. As starting values for these three parameters, the extracted values from averaged data were used (Fig. 4, Table S).

6 6 Supplementary Legends Figure S. Diffusion influences FRAP recovery for GFPnls, PC::GFP, PH::GFP and H2A::RFP. Diffusion test was performed using an adaptation of the method of curve smoothing (Mueller et al. 28). (A-F) Radial intensity profiles of FRAP experiments at four different time points after photobleaching (time in seconds is shown at the right of each plot). The gaussian edges of intensity profiles normalized to prebleach levels (Mueller et al. 28) are plotted (symbols) and were fitted using linear regression (solid lines). The gray background indicates the bleach region. (A) H2A::RFP recovery is not affected by diffusion, indicated by similar slopes of lines at all four time points. Comparison of the extracted slopes was performed using ANCOVA (p-value given on each plot represents significance of difference between slopes at the four time points). (B-F) GFP-nls, PC::GFP and PH::GFP FRAP recovery shows an influence of diffusion, indicated by gradual flattening of radial profiles at later time points. (E) Comparative summary plot. For data in (A-F), the value /slope was calculated for each linear fit and normalized to the slope at time. These values are plotted for each data set for consecutive time points, showing a gradual increase in (/slope) at later time points for all experiments with the exception of H2A::RFP (black) for which little change was detected. Figure S2. Comparison of the effects of binding site non-homogeneity on parameters extracted from FRAP experiments. Extracted diffusion (A,D,G and J), free fraction (B,E,H and K) and dissociation rates (k off, C,F,I and L) of PH::GFP (A-C, G-I) and PC::GFP (D-F, J-L) FRAP experiments in neuroblast interphase (A-F) and sensory organ precursor cell interphase (G-L) were analysed using an adaptation of the model described in (Mueller et al. 28). (See Supplementary Information, FRAP Data

7 7 Analysis, for detailed description). Black bars represent the mean and 95% confidence intervals of the extracted parameters using the same model with an initial homogeneous distribution of binding sites and grey bars represent the mean and 95% confidence intervals of the extracted parameters using the image-based heterogeneous distribution of binding sites for each nucleus. n represents number of nuclei used in each experiment. 2-tailed paired t-tests were performed for each comparison resulting in p-values >.5 with the exception of B (p=.), C (p=.69), D (p=.282) and E (p=.63). Dashed lines represent parameters extracted using the FRAP model described in (Mueller et al. 28) and shown in Figure 4 and Table S. Figure S3. Cross validation of extracted diffusion constants by independent measurements. (A) Comparison of diffusion constants extracted from fitting 3 parameter FRAP model in all cell types (Df (), black) to diffusion constants calculated by fitting single parameter FRAP model (diffusion only) to FRAP recovery performed on the non-chromatin volume in metaphase (Df (2), grey). The interphase Df values (grey) were calculated using GFPnls for calibration as described in Supplementary Information. The Df values calculated by the two procedures show good agreement. NB and SOP indicate neuroblast and SOP interphase and NBmet and SOPmet indicate neuroblast and SOP metaphase. piia and piib indicate the interphase of the respective cells. Data show mean of at least four measurements for each cell type. Error bars represent 95% confidence intervals. (B) Estimated molecular weight of PH::GFP and PC::GFP in neuroblasts (black) and SOPs (grey). Estimations were based on the extracted Df for GFPnls, PH::GFP and PC::GFP in regions outside chromatin at metaphase in neuroblasts and SOPs and calculated using the following

8 8 equation: Mw protein = Mw GFP /(Df protein /Df GFP )^3. The Mw estimated for PC::GFP is consistent with the predicted size of the PRC complex. In contrast, the Mw estimated for PH::GFP is approximately 5MDa. The PH protein has not been reported to participate in such large complexes, thus this result suggests that the extracted diffusion constant for PH::GFP may comprise both the true diffusion and a binding component (Mueller et al. 28). Figure S4. Parameter space for best fits of FRAP model to recovery data. For each FRAP recovery data set shown in Figure 4, simulations were performed in which Df was fixed to the value extracted from the 3 parameter fit (Fig. S3a, grey bars; Table S), and k* on and k off were varied between -4 and. For each simulation, the fit to the experimental data was evaluated as squared sum of residuals (ssrs). The white, red or black lines delineate ssrs.25 times larger than the minimum ssr found. Top row: interphase and metaphase best fit regions from each data set as indicated above the plots, are superimposed for comparison. Below: ssrs for each data set are plotted individually as heat maps (colour scale for ssrs is shown at the right of the plot.) Figure S5. Dot blot analysis of α-h3k27me3s28ph antibody. Serial dilutions of synthetic peptides corresponding to N-terminal sequence of histone H3 (amino acids 9-37), with different S28 phosphorylation and K27 methylation status as indicated above the figure, were spotted on a PVDF membrane and probed with the α- H3K27me3S28ph antibody (dilution : 2). For detection a secondary anti rabbit horseradish peroxidase-conjugated antibody and the Enhanced Chemiluminescence (ECL) detection system were used. To ensure equal peptide loading, a duplicate membrane was stained with Ponceau S.

9 9 Movie S. PH::GFP in neuroblast. Green channel: PH::GFP under the worniu-gal4 driver is visualized in neuroblast and ganglion mother cells (GMCs). Red channel: Histone H2A::RFP is expressed under the ubiqutin promoter and visualized in all cells. RFP marked chromatin becomes visible in the neuroblast at mitosis. The movie starts at interphase; the largest cell is the neuroblast. One mitotic division up to the next telophase is shown. Movie S2. PC::GFP in neuroblast. Green channel: PC::GFP is expressed under the Pc promoter and is visualized in all cells. Red channel: Histone H2A::RFP is expressed under the ubiqutin promoter and visualized in all cells. RFP marked chromatin becomes visible in the neuroblast at mitosis. The movie starts at interphase; the largest cell is the neuroblast. One mitotic division up to the next telophase is shown. Movie S3. PH::GFP in SOP. Both PH::GFP (green channel) and histone H2A::RFP were expressed under the neuralized-gal4 driver and are visible in specifically in the SOP and its daughter cells piia and piib. RFP marked chromatin is visible at all stages. The movie starts at SOP interphase. One mitotic division up to the next interphase is shown. At the end of the movie, the two daughter cells piia and piib are seen. Movie S4. PC::GFP in SOP. Green channel: PC::GFP is expressed under the Pc promoter and is visualized in all cells. Red channel: histone H2A::RFP was expressed under the neuralized-gal4 driver and is visible in specifically in the SOP and its

10 daughter cells piia and piib. RFP marked chromatin is visible at all stages. The movie starts at SOP interphase. The SOP is the largest cell and the only one showing red signal. One mitotic division up to the next interphase is shown. At the end of the movie, the two daughter cells piia and piib are seen. Table S. Compilation of measured and extracted parameters of PH::GFP, PC::GFP and GFPnls in Neuroblast interphase (NB) and metaphase (NBmet), SOP interphase (SOP) and metaphase (SOPmet), piia interphase (piia) and piib interphase (piib). For the quantification parameters, volume measurements in cubic micrometers, determined by GFP fluorescence (Blue masks in Figure 2 and 3), are shown (A) as well as number and micromolar concentrations of GFP-fused (B, C), endogenous (D, E) and endogenous in yw flies (F,G) molecules of PH and PC. Kinetic parameters extracted using the method described in (Mueller et al. 28) are shown in the section Kinetic parameters. The radius used for the parameter extraction is shown in µm (H). (I) represents the extracted diffusion from the full model (3 parameter fit) for PH::GFP and PC::GFP and from the pure diffusion model (single parameter fit) for GFPnls. (J) represents the extracted diffusion from the pure diffusion model in regions outside chromatin in NBmet and SOPmet, and the estimated PH::GFP and PC::GFP diffusions in interphase of all other cell types through the comparison with GFPnls diffusions (Fig.S3). Residence time (M) was calculated as (/K). The fraction of bound molecules in the chromatin region (N) was calculated by the following equation: *(L)/(L+M). The total fraction of bound molecules (O) was calculated with the following equation: (N)*(T)/(B). (T) represents the number of GFP-fused proteins that are localized in the region determined by H2A::RFP fluorescence (Yellow masks in Figures 2 and 3). Number of bound GFP-fused (P), GFP-fused and endogenous (Q) and endogenous in

11 yw flies (R) molecules are shown. In the Image-based parameters section are listed the volume in cubic micrometers occupied by chromatin (S) and the number of GFP proteins that are in this volume (T). As (T), (S) was determined by H2A::RFP fluorescence. The calculated fraction of bound molecules in the chromatin region, without the assumption of equilibrium, according to equation 8 of Supplementary Information Mathematical modeling is listed as (U). The number of GFP-fused proteins bound to chromatin is listed as (W). The total fraction of bound molecules (V) was calculated with the ratio W/B. In the Modelling parameters section are listed the parameters used for the model shown in Figure 5: pseudo-first order association rate (X), the dissociation rate (Y) the number of endogenous Polycomb proteins (Z), as well as the cell (AA) and chromatin (AB) volumes. These parameters were selected from the experimentally determined values listed in (L), (K), (F), (A) and (S). Also shown are the assumed number of binding sites (AC), representing the maximum possible number of H3K27 methylated tails in the diploid genome based on H3K27me3 distributions in polytene chromosomes and genome-wide ChIP profiles, assuming methylation of all H3 tails within a region of H3K27me3 signal. Based on this number of binding sites, the calculated micromolar dissociation constant (AD) is shown.

12 84648, FigureS, Fonseca A H2A::RFP - SOP E Diffusion test Normalised Intensity.2. P= Radius ( m) normalised /slope time points H2A::RFP (SOP) GFPnls (SOP) PC::GFP (SOP) PH::GFP (SOP) PC::GFP (NB) PH::GFP (NB) B GFPnls - SOP F GFPnls - NB Normalised Intensity..4 P=.3..5 Radius ( m) Normalised Intensity. P= Radius (um).4.2 C PC::GFP - SOP G PC::GFP - NB Normalised Intensity..4 P< Radius (um).6.3 Normalised Intensity. P= Radius (um)..8 D PH::GFP - SOP H PH::GFP - NB Normalised Intensity. P< Radius (um) 8 5 Normalised Intensity.2. P=.2..5 Radius (um).2

13 84648, Figure S2, Fonseca NB PH Diffusion Free Fraction k off A B C D f (µm 2.s - ) n = 5 Homogeneous Heterogeneous Free Fraction..4.2 n = 5. Homogeneous Heterogeneous k off (s - ).. Homogeneous Heterogeneous n = 5 D E F. NB PC D f (µm 2.s - ) Homogeneous Heterogeneous n = 4 Free Fraction.4.2. Homogeneous Heterogeneous n = 4 k off (s - ). Homogeneous Heterogeneous n = 4 G H I.5 SOP PH D f (µm 2.s - )..5. Homogeneous Heterogeneous n = 6 Free Fraction.4.2. Homogeneous Heterogeneous n = 6 k off (s - ).. Homogeneous Heterogeneous n = 6 SOP PC D f (µm 2.s - ) J K L n = 6 Homogeneous Heterogeneous Free Fraction..4.2 n = 6. Homogeneous Heterogeneous k off (s - )... Homogeneous Heterogeneous n = 6

14 84648, Figure S3, Fonseca A D f (µm 2.s - ) B Estimated MW (kda) PH NB PH NBmet PH SOP PH SOPmet PH piia PH piib PC NB PC NBmet PC SOP PC SOPmet PC piia Df () Df (2) PC piib NB SOP Polycomb Polyhomeotic

15 84648, Figure S4, Fonseca

16 84648, Figure S5, Fonseca H3 unmodified H3 S28ph H3K27me3 H3K27meS28ph H3K27me2S28ph H3K27me3S28ph H3K9me3Sph 5 pmol pmol 2 pmol Ponceau S (5 pmol)

17 PH::GFP PC::GFP GFPnls Section Variable ID Variable NB NBmet SOP SOPmet piia piib NB Nbmet SOP SOPmet piia piib NB Nbmet SOP SOPmet piia piib A Volume (µm 3 ) ± ± ± ± ± ± ± ± ± ± ± ± 9.76 B # GFP 3949 ± ± ± ± ± ± ± ± ± ± ± ± 484 Image-based parameters Kinetic parameters Quantification C µm GFP.98 ±.6.9 ±.3.36 ± ±.4 6 ±.2 ±..7 ±.8.27 ±.2.36 ±.2. ±..36 ±.3.36 ±.3 D # end ± ± ± ± ± ± 87 E µm end.23 ±.3.9 ±..2 ±..6 ±.2.2 ±..2 ±.2 F # end yw 465 ± ± ± ± ± ± 5355 G µm end yw.38 ±.9.5 ±.3.48 ±.3.4 ±.4.48 ±.3.48 ±.3 H Radius (µm) I Df (µm 2.s - ).5 ±.7.26 ±.5.76 ± ±.56.2 ±.3. ± ± ± ± ± ± ± ±.96.5 ± ± ± ± ± J Df 2 (µm 2.s - ).4 ±.7.5 ±.6 8 ±.5.77 ±.6.57 ±.4.48 ± ± ± ± ± ±.4.97 ±.2 K k off (s - ).23 ±.5.2 ±.7. ±..24 ±.6.5 ±..3 ±. 2.9 ±.75.3 ±.8.72 ±.4.2 ±.7.24 ±..27 ±.4 L k* on (s - ). ±.4. ±.5.3 ±.4.5 ±.8.29 ±.5.27 ±.6.5 ±.38.6 ±.6.8 ±.8.3 ±.3.7 ±.4.4 ±.3 M Rtime (s) N Fbound chr (%) O Fbound total (%) P # GFP bound 436 ± ± ± ± ± ± ± ± ± ± ± ±97 Q #GFP + end bound 8498 ± ± ± ± ± ± 34 R # end bound yw 7688 ± ± ± ± ± ± 255 S Volume chr (µm 3 ) T # GFP chr 3,977 6,365 3,562 3,75 U Fbound chr (%) V Fbound total (%) W # GFP chr bound ,82 X k* (s - ) Y k - (s - ) Modeling parameters Z # PC AA Volume Cell (µm3) AB Volume Chr (µm3) AC # chromatin sites AD Kd (µm)