Fonseca, Steffen, Müller, Lu, Sawicka, Seiser and Ringrose 1 Fonseca et al., Supplementary Information FRAP data analysis 1) 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. S1). 2) Parameter extraction and cross validation 2.1) Extraction of kinetic parameters from FRAP data The FRAP recovery data were analysed by fitting kinetic models (Mueller et al. 2008) 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. 2008) an additional set of radii was defined, composed of radii -10 pixels from RM to +20 pixels. These 30 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 1/3 of the
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Fonseca, Steffen, Müller, Lu, Sawicka, Seiser and Ringrose
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Fonseca et al., Supplementary Information
FRAP data analysis 1) 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. S1).
2) Parameter extraction and cross validation
2.1) Extraction of kinetic parameters from FRAP data
The FRAP recovery data were analysed by fitting kinetic models (Mueller et al. 2008)
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 koff.
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. 2008) an additional
set of radii was defined, composed of radii -10 pixels from RM to +20 pixels. These 30
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 1/3 of the
Fonseca, Steffen, Müller, Lu, Sawicka, Seiser and Ringrose
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weight being given to the goodness of the confidence intervals of association and
dissociation constants, 1/3 to the goodness of the extracted diffusion constant
confidence interval, 1/6 to the size of the squared sum of residuals and 1/6 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 koff) and pure-difusion model fits (single extracted
parameter: Df) as described in (Mueller et al. 2008) 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
koff.
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. 2008) 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
S1). The values of Df thus measured showed excellent agreement with those
extracted from fitting the full model (Figure S3).
Fonseca, Steffen, Müller, Lu, Sawicka, Seiser and Ringrose
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2.5) Robustness of extracted k*on, koff
The robustness of the extracted k*on and koff 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 koff 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 koff
values gave optimal fits to the data (Fig. S4).
3) Other models
3.1) 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. 2006; Sprague et al. 2006), showing
that both the improved global binding (Mueller et al. 2008) and the localized binding
(Beaudouin et al. 2006; Sprague et al. 2006) 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. 2008) the Sprague model
(Beaudouin et al. 2006; Sprague et al. 2006) does not include consideration of the
radial bleach profile. Thus in order to achieve consistency of analysis, the Müller
Model(Mueller et al. 2008) 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. 2008) from its original application to redistribution of photoactivatable
Fonseca, Steffen, Müller, Lu, Sawicka, Seiser and Ringrose
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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).
3.2.1) Generation of images of single nuclei.
In order to construct input protein distribution images for parameter extraction, all
prebleach images of a single nucleus (250) 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. 2008) with adaptation as
described in 2.1 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. 2008) and was
superimposed on the prebleach image. Matlab files for image processing are available
on request.
3.2.2) 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
Fonseca, Steffen, Müller, Lu, Sawicka, Seiser and Ringrose
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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 koff, 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 koff and Free, the spatially
varying kon [C] is computed from the intensity distribution of the averaged chromatin
images, following the methodology of (Mueller et al. 2008). In order to ensure the
positivity of kon [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, koff, 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 S1).
Fonseca, Steffen, Müller, Lu, Sawicka, Seiser and Ringrose
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Supplementary Legends
Figure S1. 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. 2008). (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. 2008) 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 1/slope was calculated for each linear fit
and normalized to the slope at time 0. These values are plotted for each data set for
consecutive time points, showing a gradual increase in (1/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 (koff, 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. 2008). (See Supplementary Information, FRAP Data
Fonseca, Steffen, Müller, Lu, Sawicka, Seiser and Ringrose
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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 > 0.05 with the exception of B (p=0.0001), C
(p=0.0069), D (p=0.0282) and E (p=0.0163). Dashed lines represent parameters
extracted using the FRAP model described in (Mueller et al. 2008) and shown in
Figure 4 and Table S1.
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 (1), 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.