1

Cell, Volume 135

Supplemental Data

Nanoclusters of GPI-Anchored Proteins Are

Formed by Cortical Actin-Driven Activity

Debanjan Goswami, Kripa Gowrishankar, Sameera Bilgrami, Subhasri Ghosh, Riya

Raghupathy, Rahul Chadda, Ram Vishwakarma, Madan Rao, and Satyajit Mayor

1. Supplemental Experimental Procedures

2. Tables S1 and S2

3. Supplemental Explanations

A1-Derivation of the dynamical equations for monomers and clusters

A2- Reduced equations, qualitative fitting and generalization to arbitrary n-

mers

A3- Simplified narrative explaining the model and solution

A4- Regarding non-Arrhenius behaviour and molecular complexation based

on activity A5-Nanoclusters are absent in fully-formed blebs generated by Lat

and Jas treatment

A5- Nanoclusters are absent in fully-formed blebs generated by Lat and Jas

treatment.

4. Supplemental figure legends

5. Figures S1-S14

2

1) Supplemental Experimental Procedures

Cell labeling, actin perturbation and observation of spontaneous blebbing:

FR-GPI was labeled with folic acid analogs, Nα-pteroyl-Nα-

(4′fluoresceinthiocarbamoyl)-L-lysine (PLF)(Sharma et al., 2004), Nα-pteroyl-Nα-

rhodaminethiocarbamoyl-L-lysine (PLR), or Nα-pteroyl-Nα-Alexa546-L-lysine (PLA)

prior to imaging. RFP-ezrin was constructed by exchanging GFP with RFP

(obtained from R. Tsien) in GFP-ezrin (where applicable cDNA constructs are

listed in Supplementary Text). Latrunculin B (25 µM), Jasplakinolide (14 µM), and

Blebbestatin (50 µM) were incubated with cells for indicated lengths of time.

Cells were incubated in 5 mM EDTA in Ca+-free HEPES-buffered salts for 15-20

min at 37°C, gently de-adhered by tapping, and re-plated on cover-slip dishes in

HEPES-buffered medium (M1) with 10% glucose prior to imaging spontaneous

bleb-activity. In all cases where the cell surface GFP-GPI was examined, cells

were treated with 50µg/ml cycloheximide for 150 min prior to imaging under

cover of the same drug.

Time resolved multi-photon excitation fluorescence emission measurements:

Steady state and time-resolved anisotropy measurements of fluorophores excited

by multi-photon excitation were made on a Zeiss LSM 510 Meta microscope

(Zeiss, Germany) with 63x, 1.4NA objective coupled to the femtosecond pulsed

Tsunami Titanium:Sapphire tunable pulsed laser (Newport, Mountain View, CA).

Parallel and perpendicular emissions were collected simultaneously into two

3

Hamamatsu R3809U multi-channel plate photomultiplier tubes (PMTs) using a

polarizing beam splitter (Melles Griot, Carlsbad, CA) at the non-de-scanned

emission side. TCSPC was accomplished using a Becker & Hickl 830 card

(Becker and Hickl, Berlin, Germany), operating in a stop-start configuration

(Becker, 2005). For multiphoton excitation of GFP or fluorescein in cells, we

used 920 nm excitation wavelength. At this wavelength, the GM of GFP

excitation is higher, enabling lower laser excitation power, and auto-fluorescence

signals are minimized. The repetition rate of the pulsed laser is 80.09 MHz (12

ns). For time-resolved anisotropy measurements, the time resolution was 12.2

ps. The beam was ‘parked’ at a single point using routines available in the Zeiss

software. The parked beam was placed at the center of the field to maintain

uniformity of G-Factor, and photons were collected for 30-50 s. Photons were

collected at a maximum rate of 0.1 MHz to ensure that TCSPC conditions were

strictly met. Because of the low laser power, <10% bleaching was observed

during a measurement. The instrument response function (IRF) was measured

using 10-16 nm gold particles dried on a coverslip as a second harmonic

generator; full width at half maximum (FWHM) of IRF is ~60 ps.

Fluorescence lifetime and anisotropy decay analyses:

Fluorescence lifetime and anisotropy decay analyses were done essentially as

described (Krishna et al., 2001; Lakshmikanth et al., 2001; Sharma et al., 2004),

with minor modifications in the analysis procedure. Briefly, the experimentally

measured fluorescence decay data is a convolution of the IRF with the intensity

4

decay function. The intensity decay data were fit to the appropriate equations by

an iterative reconvolution procedure using a Levenberg-Marquardt minimization

algorithm, taking into account the possibility that rapid repetition rate of excitation

pulses results in incomplete decay of anisotropy. It is important to note that the

measured anisotropy decay profile is the convolution of the real-time behaviour

of the fluorophore with the IRF. This distortion results in an apparent fast decay

at the start of all measurements that is an artifact and does not represent

anything physical. This artifact is apparent because our sampling rate of 12.2 ps

is smaller than the width of the instrument’s IRF (~60 ps). The G-Factor was

estimated using a fluorescein solution and setting the anisotropy at late times to

0.005. Fluorescence and anisotropy decay was considered well fit if three

criteria were met: reduced χ2 was less than 1.4, residuals were evenly distributed

across the full extent of the data, and visual inspection ensured that the fit

accurately described the decay profile.

FLIM methods:

Fluorescence lifetime imaging was performed on LSM 510 meta microscope,

63X 1.4NA objective, coupled to point-scanning multiphoton excitation and

TCSPC 830 acquisition card as described above. Due to low photon counts in

individual pixels, satisfactory fluorescence decay curves were constructed and

fitted after summing photons from 10 neighboring pixels, using an iterative

reconvolution fitting algorithm to fit the decay profile for each pixels. Pseudo

coloured, donor fluorescence lifetime images were generated and the fitting

5

routines were carried out using commercial software ‘SPC image’ by Becker &

Hickel company.

6

2) Supplemental Tables

Table S1: Time resolved HomoFRET+ measurements

Anisotropy decay rates# of GFP-GPI at the surface of GFP-GPI-expressing CHO

cells

Treatment n # r0* τ1 (ns) a1 τ2 (ns) a2 rss

Control

(Flat regions) 11

0.40

(± 0.01)

0.17

(± 0.06)

0.10

(± 0.01)

33

(± 11)

0.90

(± 0.01)

0.34

(± 0.02)

Saponin

0.2% 9

0.39

(± 0.02)

23

(± 4)

0.36

(± 0.02)

Latrunculin

(Flat regions) 7

0.40

(± 0.01)

0.2

(± 0.06)

0.08

(± 0.04)

27

(± 7)

0.92

(± 0.04)

0.34

(± 0.02)

Jasplakinolide

(Flat regions) 7

0.41

(± 0.01)

0.3

(± 0.02)

0.09

(± 0.05)

28

(± 9)

0.92

(± 0.05)

0.35

(± 0.03)

Latrunculin

(Bleb) 6

0.41

(± 0.007)

0.57

(± 0.07)

0.06

(± 0.005)

42

(± 22)

0.94

(± 0.006)

0.38

(± 0.007)

Jasplakinolide

(Bleb) 6

0.41

(± 0.01)

39

(± 13)

0.39

(± 0.01)

In all experiments CHO cells-expressing GFP-GPI were placed on the

microscope stage and the laser beam was parked on indicated regions. Time

7

correlated single photon statistics were obtained after excitation with multi-photon

excitation using a high NA objective as described in Supplemental Experimental

Procedures. Measurements on all regions were made by collecting photon

statistics using a parked beam located on the region.

Note: Cholesterol removal by saponin-treatment eliminates the fast component

due to FRET.

+Efficiency of homoFRET is obtained by estimating the amplitude of the fast

decay component of the anisotropy decay of GFP fluorescence emission(Sharma

et al., 2004). While the rate of decay of the short component is an estimate of the

distance between GFP-fluorophores, the longer decay component relates to the

rotational dynamics of the GFP-fluorophore (Gautier et al., 2001).

Note: Cholesterol removal by saponin-treatment eliminates the fast component

consistent with earlier studies(Sharma et al., 2004). Anisotropy decay rates on

blebs also have much smaller amplitude of the shorter decay rate (Lat) or no

short component (Jas), consistent with a reduction/lack of homoFRET between

GFP-GPI-APs in these regions. The presence of this small component is likely to

be due to the large volume of the confocal excitation (~ 900 nm, Z-resolution),

potentially collecting some emission from the flat-regions surrounding the blebs.

* r0 is the initial anisotropy; its value is depolarized compared to that obtained

using a low NA objective as reported earlier (Volkmer et al., 2000) (data not

shown).

8

# Anisotropy decay rates were calculated using the fitting routine outlined in

Supplemental Experimental Procedures and expressed as averages (+ S.D.)

from the indicated number of cells (n).

Table S2: HeteroFRET+ measurement

Fluorescence Lifetime§§ of PLF-labeled FR-GPI at the surface of FR-GPI-

expressing CHO cells

D A Treatment n # τavg †† (ns)

PLF Control (Flat regions) @ 10 2.28

(±0.04)

PLF PLR Control (Flat regions) @ 11 2.00

(±0.13)

PLF PLR Saponin

0.2%

5 2.30 (±0.09)

PLF PLR Latrunculin (Bleb)* 5 2.32

(±0.09)

PLF PLR Jasplakinolide (Bleb)* 5 2.16

(±0.01)

In all experiments CHO cells-expressing FR-GPI were singly labeled with donor

(D) alone (PLF, 160nM) or with donor (D) and acceptor (A) fluorophores (PLF,

160 nM; PLR, 200 nM). Time correlated single photon statistics after excitation

with multi-photon excitation were obtained as described in Supplemental

Experimental Procedures.

9

+Efficiency of heteroFRET in control cells is estimated by comparing the average

lifetimes of PLF in the presence and absence of the acceptor fluorophore (PLR);

shorter lifetime in the presence of acceptor indicates increased FRET.

Note: Cholesterol removal by saponin-treatment increases the lifetime of donor

PLF to that obtained in the absence of the acceptor. PLF/PLR-labeled blebs

exhibit a longer donor-lifetime, consistent with the lack of heteroFRET on the

blebs.

§§ Fluorescence lifetimes were calculated using the fitting routine outlined in

Supplementary Experimental Procedures and expressed as averages (+ S.D.)

from the indicated number of cells (n #).

†† τavg is the amplitude-weighted average of all lifetimes obtained from the fitting

routine; PLF in the absence of acceptor shows multiple lifetimes as reported

earlier(Sharma et al., 2004).

@Measurements on flat regions were made by scanning the laser over a small

~100x100 pixel area.

* Measurements on Blebs were made by collecting photon statistics using a

parked beam located on the bleb.

10

3) Supplemental explanations

A1. Derivation of dynamical equations for clusters and monomers.

We start with a mixture of clusters and monomers of known proportions and

model its time evolution in a confocal volume, brought about by dynamical

processes which include bleaching, diffusion and interconversion between

clusters and monomers. The confocal volume intersects at regions of the cell

surface in a plane (in some cases the confocal volume encompasses both top

and bottom surfaces of the adhered cell, in which case the intersection provides

two planes). Cluster and monomer densities follow a reaction-diffusion equation,

where we allow for the possibility that the diffusion coefficient of monomers and

clusters are different. To augment the reaction-diffusion equation by the kinetics

of bleaching, we define a quantity cnm(x, t), the concentration of n-mers of which

m are unbleached at time t. Since bleaching is a statistically independent

stochastic process, the fraction of unbleached fluorophores (belonging to any n-

mer) that get bleached in the time interval dt is simply proportional to dt. Within

mean field chemical kinetics, this Poisson process implies a first-order rate

equation for the concentrations of unbleached fluorophores. For simplicity, we

will present the derivation of the dynamical equations for a mixture of monomers

and dimers (as displayed in Analytical Methods). A schematic of the illuminated

plane of area V and perimeter p, shows the dynamical processes involving

monomers and dimers in their various states of bleaching (Fig. 3a). The

11

interconversion dynamics between monomers and dimers is independent of the

bleaching status of the fluorophores. The reaction-diffusion-bleaching dynamics

of cnm(x, t) obeys the mean field equations,

22 1122

22 22 2222

ac f

k vcc D c bc k ct

∂= ∇ − − +

∂

22121 21 22 21 11 102c f a

c D c bc bc k c k vc ct

∂= ∇ − + − +

∂

2220 10

20 21 20 2a

c fc k vcD c bc k ct

∂= ∇ + − +

∂

2 2111 11 11 11 11 10 22 212a a f f

c D c bc k vc k vc c k c k ct

∂= ∇ − − − + +

∂

2 2101 10 11 10 11 10 20 212a a f f

c D c bc k vc k vc c k c k ct

∂= ∇ + − − + +

∂ (1)

where Dc and D1 are the cluster and monomer diffusion coefficients respectively.

The other dynamical parameters are the bleaching rate, b, and the rates of

aggregation (ka) and fragmentation (kf). Note the local concentrations cnm are

defined as the number of particles of species (Volkmer et al.) in an elemental

area v; with this definition, the interconversion rates ka (kf) have units s-1.

We now perform a spatial integral of the above equation over the confocal area

V, and construct a quantity Cnm(t), the fraction of n-mers with m unbleached

fluorophores present in the confocal area at time t, i.e.,

2

( )nm

Vnm

c d xC t

N≡

∫, where N

12

is the total number of fluorophores present in the confocal area at time t = 0

(proportional to I(0)). Using a mean field decoupling, we arrive at the following set

of ordinary differential equations,

22222 22 22 22 112c f aR R

dC D p C C bC k C k NCdt + −

= − − − +

2121 21 21 22 21 11 102c f aR R

dC D p C C bC bC k C k NC Cdt + −

= − − + − +

220 10

20 20 21 20 2a

c fR R

dC k NCD p C C bC k Cdt + −

= − + − +

2111 11 11 11 11 11 10 22 212a a f fR R

dC D p C C bC k NC k NC C k C k Cdt + −

= − − − − + +

2101 10 10 11 10 11 10 20 212a a f fR R

dC D p C C bC k NC k NC C k C k Cdt + −

= − + − − + + (2)

where p is the perimeter, and R is the radius of the illuminated region. Note that

the diffusion terms in (Eqn. 1), have simply integrated to a net current of particles

in the confocal area, the first terms on the right hand side of (Eqn. 2), where

22 RC − ( )11 RC − is the fraction of clusters(monomers) just inside the confocal

volume, and 22 RC + ( )11 RC + is the fraction just outside (Main Fig. 3a). Based on

our recovery experiment following illumination within a strip (see Main text and

Fig. 2), we will take the latter to be a constant pool throughout the course of the

experiment; further, we will assume that the flux of fluorophores entering the

confocal volume from the outside pool are predominantly unbleached. These

boundary conditions on the flux of fluorophores, effectively

13

imply, 21 20 10 0R R RC C C+ + += = = , at all times. In addition,

22 22 22(0) (0)R RC C C+ −= ≡ and 11 11 11(0) (0)R RC C C+ −= ≡ i.e., the concentration of

monomers (clusters) at t = 0 is assumed to be the same in the confocal volume

as well as the thin annular strip surrounding it. The number of monomers

(clusters) in this annular strip remains constant over time, and serves to replenish

the fluorescence in the confocal volume. Defining the diffusion rates as

1 1d D p aV= and c cd D p aV= , where a is the thickness of the boundary circle

corresponding to the decay length of the intensity of the illumination in the plane

of the surrounding membrane, we arrive at the final set of equations (see

Analytical Methods),

22222 22 11 22 222 ( (0) )

2a

f ck NdC bC k C C C C d

dt= − − + + − (3)

22021 20 10 202

af c

dC k NbC k C C d cdt

= − + −

( )11

21111 11 10 22 21 11 11 12 (0)a a f f

dC bC k NC k NC C k C k C C C ddt

= − − − + + + −

10

21011 11 10 20 21 1 102a a f f

dC bC k NC k NC C k C k C d Cdt

= − − + + − (4)

Knowing the initial distribution of fluorophores, we can solve (Eqn. 4) to obtain

the fluorophore distribution at all times, using standard numerical integration

2121 21 10 11 22 212f a c

dC bC k C k NC C bC d Cdt

= − − + + −

14

routines, such as an adaptive step-size, 4th-order Runge-Kutta scheme (Press et

al., 1992). The time profiles of the intensity and anisotropy in the confocal volume

can then be easily read out using the relations,

22 21 112I C C C= + +

22 21 11

22 21 11

22

c m mA C A C A CAC C C

+ +=

+ + (5)

where Am and Ac are the anisotropy of the monomers and clusters, respectively.

Within our model of dimers and monomers, we can obtain the initial distribution

from the initial values of the intensity I(0) ∝ N and anisotropy A(0),

( )( )( )

( )22

00

2m

c m

A AC

A A−

=−

( ) ( )11

00 c

m c

A AC

A A−

=−

( ) ( ) ( )21 20 100 0 0 0C C C= = = , (6)

since at t = 0, the dimers and monomers are unbleached.

While the equations presented above are valid for a dynamical mixture of

monomer and dimers, it is simple to formally generalise these system of

equations to the case of arbitrary n-mers, Cnm. The more complex set of

aggregation-fragmentation rules, will involve many more interconversion rates.

15

Again, knowing the initial distribution, we could, in principle, solve the equations

for Cnm and obtain the time traces of I and A, which could then be compared to

the experimental intensity and anisotropy profiles. However, in practice, two

difficulties arise: (i) The initial data in I and A do not provide a detailed cluster

size distribution; we may at best obtain the relative fraction of clusters and

monomers, provided we assume (or extract) a value for Am and Ac. (ii) The bare

anisotropy and intensity time profiles shows some high frequency variation as a

result of unaccounted noise and drift, making it difficult to obtain a robust and

accurate numerical fit, especially with the increased number of fit parameters.

In the next Supplementary Explanation, we will address these issues of fitting,

both for the dynamics of dimers and monomers, and for its generalization to the

dynamics of arbitrary n-mers.

A2. Reduced equations, qualitative fitting and generalization to arbitrary n-

mers

Let us first consider the model with dimers and monomers. The number of

parameters that need to be fixed by fitting the experimental recovery profiles are

, , , , , ,1b d d k k A Ac a f c m (7)

16

WhereAm and Ac are allowed to vary between 0.23 – 0.24 (the range of values

forA ) and 0.16 – 0.18, respectively. In principle, a numerical solution of (Eqn. 4)

together with (Eqn. 5) and (Eqn. 6), can be used to compute the intensity and

anisotropy profiles, which can then be used to extract fit parameters from the

experimental profiles using a least-squares algorithm. In practice, however, such

a naive exercise does not succeed, since it often misses important qualitative

features of the data. This difficulty is augmented by noise, especially in the

anisotropy data. Our goal is to devise a fitting strategy that will faithfully

reproduce the important qualitative features, without at the same time biasing the

data.

To start with, we note that the bare anisotropy and intensity time profiles show a

lot of oscillations, as a result of unaccounted noise and drift. We therefore let the

data go through a low pass filter to cutoff the high frequency components.

We next make an additional approximation which considerably simplifies the set

of equations (Eqn. 4), allowing for an easy analytic solution. These

approximations are internally consistent and have been checked a-posteriori by

explicit numerical solution. The analytic solutions have been compared to the

numerical solutions of (Eqn. 4), and found to be accurate. The closed form

expression for the time dependence of the intensity and anisotropy that we

obtain, provides a robust and reliable fit to the data. We have checked that the

qualititative aspects of the profiles are reproduced by the analytic solution.

17

Approximations leading to reduced set of equations

Let us assume that during the course of the experiment on control cells, the

mixture of dimers and monomers is always at a steady state at that temperature.

Bleaching, only affects the fluorescing capacity of the n-mer, and thus as a

perturbation, only affects the m index inCnm . This implies that the total number

of monomers, bleached and unbleached, remains constant, thus statistically,

11 10 11( ) ( ) (0)C t C t C (8)

Fluctuations in this quantity over the time resolution of the experiment are

assumed to be negligible. This assumption has been checked to be quite

accurate, by explicit numerical solution of (Eqn. 4).

The assumption (Eqn. 8) leads to a pleasing simplification of the equations (Eqn.

4). The equations for 10C and 20C decouple from the rest, reducing the set of

equations to be solved to three. The rest of the equations are more conveniently

written in terms of 2 22 212C C C and 11C (the fractional intensities arising from

dimers and monomers, respectively),

22 2 11 11 22 2( ) ( ) (0) (2 (0) ( ))

dCbC k C t k C t C d C C ta cfdt

(9)

18

1111 11 11 2 11 11( ) ( ) (0) ( ) ( (0) ( ))1

dCbC t k C t C k C t d C C ta fdt

(10)

and 22C (Eqn. 3). Note that the equations are now linear coupled ODE's, which

can be trivially solved.

Analytic (closed form) solution of reduced equations

The reduced equations (Eqn. 10) for the dimer-monomer model are linear,

inhomogenous, coupled ODE's. Their solutions, appropriate to the first

illumination period 10 t t , take the form,

1 2

1 2

1 2 3

11 11 11 12

2 2 21 22

22 22 31 32 33

( ) ( )

( ) ( )

( ) ( )

r t r t

r t r t

r t r t r t

C t C B e B e

C t C B e B e

C t C B e B e B e

(11)

The parameters entering (Eqn. 11) are given by,

21 1

111

12

1

1 1 122

1 1

( )( )

( )( ) ( )

( )( )

( )( ) ( )

2( ) ( ) (2 2 ) ( )( )

2(2 )(( )(

c c c a c m a m

c c a mf

c c c mf f

c c a mf

c c c c a c m c mf f f f

cf f

b d d i d k i i d k iC

b d b d k b d k i

d k i d b d k iC

b d b d k b d k i

b d d b d k i d k b d k i i d k b d k iC

b d k b d b d k

) ( ) )c a mb d k i

19

1 1 2 111

1 1 2 112

1 2 1 2 221

1 2 1 2 222

1 2 1 231

( ) 2

( ) 2

( ) (2 )2

( ) (2 )2

(( ) (2 ))2 (2

c a m a m cf

c

c a m a m cf

c

c a m cf f

c

c a m cf f

c

a m c a m c f

c

d d k k i h k i h hB

d d k k i h k i h hB

d d k k i h k h h hB

d d k k i h k h h hB

k i d d k i h k h hB

b

1

1 2 1 232

1

21 1 1

331

)

(( ) (2 ))2 (2 )

((2 )( ) (2 )( ) )2(2 )( ( ) ( ) )

c a m cf

a m c a m c f

c c a m cf

a m a mf f f f

a mf f f

d d k k i

k i d d k i h k h hB

b d d k k i

b b k b d k b k b d k k i d k iB

b k b b d k k b k i

and the decay rates are given by,

1 1

2 1

3

1(2 )21(2 )

2(2 )

c a m cf

c a m cf

c f

r b d d k k i

r b d d k k i

r b d k

where the terms that enter these are given by,

11

1

2

22

21 1

221

111

1

2 2 21 1

(0)

2 (0) 1

( )(0)

( )( ) ( )

( )(0)

( )( ) ( )

( ) 2 ( )

m

c m

c c c a c m a m

c c a mf

c c c mf f

c c a mf

c c a c c a mf f

i C

i C i

b d d i d k i i d k ih C

b d b d k b d k i

d k i d b d k ih C

b d b d k b d k i

d d k k d d k i k i

(12)

20

These closed form solutions to the reduced equations reproduce the following

qualitative features of the experimental data (and the numerical solution obtained

from (Eqn. 4)):

1. The intensity profile is seen to be a sum of two exponentials while the

anisotropy profile is more complicated. This feature is confirmed by explicit

numerical solution of (Eqn. 4) and more importantly, by fitting the intensity

profiles to a sum of two exponentials.

The solutions in the second illumination period 1 21 w wt t t t t t , are simply

obtained by replacing t by 1( )wt t t in (Eqn. 11), together with different initial

conditions.

2. Thus the steady states of the intensity ( ssI ) and anisotropy ( ssA ) reached in the

two illuminations should be identical, and equal to,

11 2

22 11 21

11 2

( ) ( )

2 ( ) ( ( ) ( ))( ) ( )

ss

c mss

I C C

AC A C CA

C C

3. In addition, the decay rates towards the steady states should also be identical.

21

4. The amplitudes ijB however, depend on the initial conditions, as is evident by

the presence of 1h and 2h in them.

Knowing the solutions (Eqn. 11), we can use the formula (Eqn. 5) to obtain the

intensity ( )I t and anisotropy ( )A t profiles, which we can then compare with the

experimental data.

We first look at the intensity data, since it is freer from noise, and has a simpler

analytic form. From the fits to the intensity data, we can extract the values 1r , 2r ,

11 21B B and ssI by least-squares. We then look at the anisotropy data, and in

conjunction with the above fit parameters, we extract ssA by least-squares.

Knowing these values, and demanding that the parameters 1, , , , , ,c a c mfb d d k k A A

be real and positive, we can arrive at a unique set of parameter values.

Generalization to dynamics of arbitrary n-mers

Having succeeded in obtaining a simplified description for the dynamics of

dimers and monomers, we ask whether a similar approximation could be used to

simplify the more general dynamics of arbitrary n-mers. Recalling the discussion

at the end of S1, we provide arguments to reduce the number of relevant fit

parameters, without any loss of generality. First, we consider only two

independent diffusion coefficients, that of the monomer 1D and the cluster

22

cD .Our data analysis using the dimer-monomer model, shows that the cluster

diffusion is zero, and so it is reasonable to assume that cD does not depend on

the coordination number of the cluster. We will also assume that the cluster

anisotropy cA does not depend on the coordination number. The difference

between the values of the anisotropies for the monomer and dimer far exceeds

the difference between the dimer and higher n-mers (Sharma et al., 2004).

Given these reasonable assumptions, we would like to rewrite the system of

equations describing the dynamics of arbitrary n-mers, nmC , as a dynamics of

clusters (as an entity) and monomers. The fractional intensity due to clusters is

defined by (analogous to 2C in (Eqn. 10)),

1 22 21( 1) .... 2n nn nnC nC n C C C (13)

We will assume that the clusters as an entity fragment with a rate fk ; the

products of the fragmentation can be clusters of lower coordination number

and/or monomers. Similarly, the aggregation of any species occurs at a rate ak .

In addition, we make an assumption analogous to (Eqn. 8),

0(0)nm nn

n

mC C

for all n, and all times.

These assumptions, allow us to write reduced equations analogous to the

23

dimer-monomer dynamics (Eqn. 10),

11 1111 11 22 11 22 33

2 3(0) (0)(0) (0) (0) (0) (0)

2 6n

n n afC CdC bC k C k C C C C C C

dt

( (0) )c n n nd C C

1111 1111

11 11 22 11 22 33

2 3(0) (0)(0) (0) (0) (0) (0)

2 6C CdC bC kaC C C C C C

dt

1 11 11 11( (0) )f nnk C d C C

and

11 1 11 11 11 1 1(0) (0) (0)n

n n n n nn a n cfC C CdC

bC b k k C C C C d Cdt

where

1 1 11 21....n n nC C C C (15)

and the equations have been written specifically for a system where 4n . The

remainder terms 1,n and 1n are functions of the individual nmC ’s. In the

absence of the remainder terms 11 1, ,n n , these equations form a closed set.

The remainder terms are small, as explicitly checked by numerically solving the

full equations (for the case n = 4) using an adaptive step-size, 4th-order Runge-

Kutta scheme.

24

The above reduced equations are again linear, inhomogeneous ODE's and may

be solved by the same method as (Eqn. 11). The values of the interconversion

rates ( )a fk k obtained by the fitting procedure described above, lie in the same

range as that obtained from the dimer-monomer model.

A3. Simplified narrative explaining the model and solution

Here we provide a simplified guide for making the model more accessible to the

general reader. We divide this into the principal ingredients of the model building

and solution, under three headings: I. Construction of dimer model, II.

Simplification of model, and III. Generalization to the k-mer model. We hope this

will make the derivations and the solutions obtained clearer to a lay reader.

I. Construction of dimer model

We start with a mixture of dimers and monomers of known proportions (obtained

from the initial value of intensity I(0) and anisotropy A(0)) and model its time

evolution in a confocal volume, brought about by dynamical processes which

include bleaching, diffusion of monomers and clusters and interconversion

between dimers and monomers. We will describe in words, a step-by-step

account of the derivation.

25

1. We first write a Master Equation for the single-particle probability

distribution of the number of monomers and dimers of a given

bleaching state, in a small volume v surrounding a point x within the

confocal volume, taking account of the dynamics of bleaching, diffusion

of monomers and dimers and interconversion between dimers and

monomers. Note at this stage we assume that the rates of

interconversion are constant within the confocal volume. However,

since the organization and activity of cortical actin is heterogeneous on

the cell surface, we allow for the interconversion rates to vary with the

positioning of the confocal volume on the cell surface. Note further that

the interconversion transition probabilities that enter the Master

equation contain rates ak and fk which have units of 1s− .

2. We then rewrite this equation as an equation for the moments of the

probability distribution. The equation for the first moment, the local

concentrations of the dimer and monomer, gets coupled to the higher

moments, leading to an infinite hierarchy of equations, as in any kinetic

theory. The standard practice is to devise a decoupling scheme -- the

most popular one being the mean-field decoupling -- which truncates

this infinite hierarchy, resulting in a set of partial differential equations

for the moments of the distribution.

3. The mean field truncation scheme that we adopt is the following. We

first integrate the equation for the first moment (concentration) over the

spatial extent of the confocal spot. There are two non-trivial terms that

26

we need to contend with. The first is the laplacian of the concentrations

(diffusion term), which simply integrates to the boundary, giving rise to

a flux of particles flowing into and out of the confocal spot. The second

is the quadratic term in the concentrations (more correctly the average

of the square of the concentration, the second moment), which we

treat within mean-field. We first decompose the fraction of particles of

species nm, as a mean plus fluctuations,

21nmnm nm nmV

C C d x C CN

δ≡ = +∫

where the overbar are both ensemble averages (average over the

realization of configurations consistent with the given initial conditions

for the intensity and anisotropy) and spatial averages over the confocal

volume, and N is the total number of particles within the confocal

volume at 0t = . We then assume that the fraction nmC in the confocal

spot is dominated by the mean (indeed with our experimental setup,

this is all that we can measure at this stage), and that relative

fluctuations can be ignored. A similar mean-field decomposition holds

for higher moments. This is the classical mean-field decoupling

approximation. This leads to the system of ordinary differential

equations displayed in the Analytical Methods.

Notes:

27

a) The dynamics does not obey mass action. The factors of 211C in the

equation for 22C for instance, comes from purely probabilistic

considerations. The detailed balance (mass action) is paraphrased in

the rates ak and fk . While these are taken to be constants within the

confocal volume, they are allowed to vary across the cell. This is done

to reflect the heterogeneity of both the organisation and activity of the

cortical actin, which in turn is related to the net amount of clusters

found in the volume. Indeed this is corroborated by our observation of

the large spatial variation of the fitted ak and fk at a given

temperature. This spatial variation is a reflection that the processes

involved in creating transitions between the aggregated and

fragmented states is active.

b) Conservation of mass within the confocal volume is explicitly broken

(as it should be) because we are studying the dynamics within a finite

volume through which particles flow in and out. The total mass

(number of proteins) within the confocal volume is a stochastic quantity

which can also be represented by mean plus small fluctuations.

c) The parameter d that enters the final equation is a diffusion rate related

to the diffusion coefficient D by a scale parameter. This scale

parameter is proportional to the ‘thickness’ of the boundary of the

domain, set by the gaussian fall off of the focused confocal spot.

Instead of computing the value of D from the fits to d, we have simply

28

chosen to express all diffusion rates in terms of the diffusion rate

determined for FR-GPI at 37°C.

d) The diffusion coefficients (rates) of the monomers and dimers are

taken to be 1 1( )D d and ( )c cD d , respectively. Both these rates were

allowed to vary for the fits. In all cases, over the range of temperatures,

the value of cd was found to lie between 5 5[ 10 ,10 ]− −− , 4-5 orders of

magnitude smaller than the value of 1d . It was reasonable therefore to

fix it at zero, to get a better fit value for the rest of the parameters. The

relative immobilization of nanoclusters was further confirmed by

independent experiments carried out at different temperatures (Fig.2).

The extracted values of 1d did not vary much with temperature. At this

stage we merely report this observation. We believe that this is

interesting, since conventional Stokes-Einstein would have predicted a

linear dependence on temperature; we revisit this issue in greater

detail in a forthcoming manuscript.

II. Simplification of model

This dimer model can of course be solved numerically. We could then use the

numerical data to fit the experiments. However our experience has been that

such multi-parameter fitting methods are fraught with difficulties and do not give

an understanding of the process. Instead, a better strategy is to derive, in a

reasonably systematic manner, a reduced set of equations whose solutions

29

compare favorably (both qualitatively and quantitatively) with the original

equation, and which has the virtue of being analytically solvable. This does not

mean that the reduced equations are exactly derivable from the original set. This

is simply a convenient and quantitatively accurate device to extract parameters

by analytically solving a good approximation to the original equations, so as to

minimize errors due to fitting.

We reiterate that the approximations we have made are internally consistent and

have been checked a-posteriori by explicit numerical solution (for the k = 2

(dimer), k = 3 (trimer) and k = 4 (tetramer) models). The analytic solutions have

been compared to the numerical solutions, and found to be accurate. The closed

form expression for the time dependence of the intensity and anisotropy that we

obtain, provides a robust and reliable fit to the experimental data.

We have used the following reasonable assumption in our subsequent reduction

of the equations: that the system of monomers and dimers (independent of their

bleaching status) is in steady state. This implies that the total concentration of

monomers (independent of their bleaching status) and dimers (independent of

their bleaching status) is constant in the mean, and bears the steady state

relationship to one another. Note that this assumption is in the mean, fluctuations

about this are small, because we are averaging over a large (1 sec) time window.

While at the higher temperatures, this assumption is fairly good, at lower

temperatures there might be some deviation from this assumption at early times.

30

Finally, we have numerically checked that the time dependence of the intensity

and anisotropy determined from the reduced model is close to the original model,

for the same set of parameters.

III. Construction of k-mer model

The construction of these systems of equations to the case of arbitrary k-mers,

follows the same step-by-step procedure outlined above, and allows for the same

mean-field decoupling. However the equations are more complex, since the set

of aggregation-fragmentation rules involve many more interconversion rates. We

reduce the number of parameters by the following arguments: we consider only

two independent diffusion coefficients, that of the monomer 1D and the

cluster cD . Our data analysis, using the dimer-monomer model, shows that the

cluster diffusion is approximately zero, and so it is reasonable to assume that cD

does not depend on the coordination number of the cluster. We will also assume

that the cluster anisotropy cA does not depend on the coordination number. The

difference between the values of the anisotropies for the monomer and dimer far

exceeds the difference between the dimer and higher order n-mers. Again,

knowing the initial distribution, we could, in principle, solve the equations for nmC

and obtain the time traces of I and A , which could then be compared to the

experimental intensity and anisotropy profiles. However, as discussed in the

Supplement, in practice, there are difficulties associated with the fitting. Since the

only experimental information that we have is on the relative fraction of

31

monomers and clusters, we rewrite the equations to obtain effective equations for

the interconversion between clusters (of any size) and monomers. We will

assume that the clusters as an entity fragment with a rate fk ; the products of the

fragmentation can be clusters of lower coordination number and/or monomers.

Similarly, the aggregation of any species occurs at a rate ak . We now use exactly

the same approximation as we did for dimers, namely, that the system of

monomers and clusters (independent of their bleaching status) is in steady state.

The resulting reduced equations have terms linear in concentrations and a

remainder which contain terms higher than quadratic. We have numerically

checked that these remainder terms are small in comparison with the terms

retained. This allows for a more accurate evaluation of the parameters of the fit;

we find that the fit values of the interconversion rates ( )a fk k lie in the same

range as that obtained from the dimer model. The philosophy is, as stated

before; instead of looking for approximate, numerical solutions of the full

equations, we look for exact, analytical solutions of an approximation to the

equations.

A4) Regarding non-Arrhenius behaviour, activity temperature, and

molecular complexation based on activity

The mere observation of non-Arrhenius behaviour in the interconversion kinetics

ofcourse does not imply the involvement of activity, since there are several

32

instances of breakdown of Arrhenius behaviour. These can typically come about

because:

i. The dynamics taking the system from one state to another, couples to

some other degree of freedom which can undergo a dramatic change (such as a

phase transition) at a particular temperature. This would lead to a change in the

potential energy landscape and therefore to a change in the energy barriers;

numerous examples in the literature exist to support this argument.

ii. The dynamics taking the system from one state to another has

significant entropic contributions (which can in addition affect the curvature at the

potential extrema), which can be temperature dependent. The competition

between entropy and enthalpy can give rise to non-Arrhenius

behaviour(Bretscher et al., 1997; Wallace et al., 2001).

The non-Arrhenius behaviour of the interconversion dynamics is a result of both

these aspects. The additional degree of freedom that it couples to is cortical

actin. The fluctuations needed to make transitions from one state to another is

provided by the activity of cortical actin which also appears to exhibit a cross-

over at 24°C as shown from a number of sources. These include the temperature

dependence of the velocity of myosin-coated bead movement on actin (Sheetz et

al., 1984), and the ATPase activity of actomyosin (Levy et al., 1959), as well as

data from a preliminary study of the dynamics, frequency and retraction of blebbs

in CHO cells at different temperatures (Supplementary Fig. S11). As established

by Charras et al (Charras et al., 2007) and confirmed by us (Main Fig. 6c, d;

33

Supplementary Fig. S13c, and Movie 6), the dynamics of blebbing and its

retraction is associated with acto-myosin contractility. We find that the blebbing

and its retraction dynamics undergoes a change at around the same temperature

as the crossover in the Arrhenius plot (Supplementary Fig. S11).

In the light of this, a more appropriate interpretation of the Arrhenius plot is to

identify an activity temperature, Tact, which is high above 28°C, and low below

24°C. Such activity temperatures have been invoked(Hatwalne et al., 2004;

Ramaswamy and Rao, 2001) to describe the amplitudes of shape fluctuations of

red blood cells (Gov and Safran, 2005), and active membranes with pumps (J.-B.

Manneville, 2001), and the microrheology of cells (Lau et al., 2003), and is a

useful parametrization of activity. The activity temperature that we define here is

distinct from these shape and rheological temperatures and is more akin to a

chemical temperature.

There are other curious features of the dynamics and spatial distribution that we

have also highlighted. The extremely small slope of the Arrhenius curve at

temperature above 28°C, the sharp change at 24°C roughly coincident with

change in actin activity, the spatial heterogeneity in the kinetic parameters at a

given temperature, the immobilization of nanoclusters, the exponential tails in the

distribution of anisotropy, the involvement of acto-myosin contractility in the

recovery dynamics of the nanoclusters on the retracting bleb ─ these results and

more, taken together and not in isolation, point to the fact that the dynamics of

34

interconversion is regulated by the active dynamics of cortical actin. Thus,

supporting the idea of actively generated membrane complexes.

The violation of mass action also may be understood from an explanation that

stems from the membrane complexes being formed by the interaction of the

membrane with CA. Here the formation of clusters in a local region of membrane

will depend only on the local CA activity, and will be independent of the

concentration of the GPI-AP. In fact the fraction of clusters is correlated by the

existence of a CA meshwork able to sustain clusters formation. We repeatedly

observe the formation of clusters in blebs in spontaneously blebbing cells where,

at the same concentration of GPI-APs in the bleb-membrane (as marked by the

fluorescence of GFP-GPI), clusters are detected only when the CA is recruited

and engaged in actively retracting blebs (Fig. 6a, b).

A5) Nanoclusters are absent in fully-formed blebs generated by Lat and Jas

treatment.

The organization of GPI-APs in fully-formed blebs has been determined by

examining steady-state anisotropy imaging (Main Fig.,5A,B) time-resolved

anisotropy decay (Main Fig. C, D), fluorescence lifetime decay (Main Fig. E, F),

and fluorescence life-time imaging (Supplementary Fig. S10). From previous

work (Sharma et al., 2004) we have shown that the anisotropy decay profile of

GFP engaged in homo-FRET may be decomposed into two components, a slow

35

component reflecting the rotational diffusion of molecules, and a fast component

that reports on the efficiency of the homoFRET process. Fluorescence lifetime

decays of the donor fluorophore on the other hand provide information on the

hetero-FRET process; reduction of donor fluorescence lifetime in presence of

acceptor compared to donor alone provides evidence for hetero-FRET.

In the anisotropy measurements, together with the high value of steady-state

anisotropy (Fig.5A-B) and single exponent anisotropy decay (Fig.5C-D;

Supplementary Table ST1) obtained from fully-formed blebs, confirms the lack of

GFP-GPI nanoclusters in the bleb. This is further corroborated by an increase in

donor fluorescence lifetime in presence of acceptor on blebs (Fig.E-F;

Supplementary Table ST2) compared to that obtained on the flat parts of cell as

also observed in the fluorescence lifetime image (Supplementary Fig. S10A-C).

36

4) Supplementary Figure Legends for Goswami et al:

Figure S1: Experimental setups to measure fluorescence

intensity and anisotropy in real time.

A) Spatially resolved, intensity and anisotropy measurements were carried out on

Nikon TE2000 epifluorescence microscope equipped with a 100 x, variable NA

(0.7 -1.2) objective with the tube lens below the objective removed for obtaining a

parallel beam of emitted light. A sheet polarizer placed just after the mercury arc

lamp polarizes excitation illumination, and a polarizing beamsplitter (Melles Griot

Optical Systems, NY, USA) placed in the emission path after the microscope,

transmitting emitted fluorescence in parallel orientation while reflecting the

perpendicular orientation to the two cameras placed after focusing optics. Images

were collected at 1.0 NA using two identical 16-bit EM-CCD cameras

(Photometrics Inc.USA) aligned to each other and set up for simultaneous

imaging using the MetamorphTM software drivers. Emission side depolarization

was determined by placing a polarizer in the path of the bright field lamp into the

collection side optical path and measuring the extinction of polarization in the

parallel and perpendicular light paths. The dual camera-imaging set up was

aligned for maximum possible extinction ratio [ /( 2 )pa pa peI I I+ where

paI represents the intensity of illumination detected at the parallel side when the

illumination was polarized in the orientation parallel to the microscope axis, and

peI when the illumination was polarized perpendicular to the microscope axis] of

0.98 in the parallel beam path.. The G-factor, calculated as the ratio of parallel to

37

perpendicular intensities at identical camera settings was 1.1, as measured for a

solution of fluorescein in water. Images were aligned using Matlab programming

software, by customized routines (see Methods).

B) Confocal measurements of anisotropy at high-temporal and spatial resolution

were made on a custom-designed line-scanning LSM 5 Live microscope (Zeiss,

Jena, Germany) adapted for fluorescence polarization measurements. This set-

up is also equipped with a separately steered laser beam for patterned photo-

bleaching. For the purpose of anisotropy measurements, main dichroic in the

emission path was replaced with a nanowire-based polarization beam splitter

(ProFlux™ polarizing beamsplitter, Moxtek Inc., USA), and matched emission

filters were mounted in the emission filter wheels in front of the linear array CCD

detectors. The spatial resolution achievable here is 230nm in x-y and 660nm in z

(using 1.4NA, 63X objective for 495-530nm fluorescence emission), and high

numerical aperture anisotropy imaging is feasible due to the confocal

arrangement. Emission side depolarization was determined by a polarizer in the

path of the bright field lamp into the collection side optical path, measuring the

extinction of polarization in the parallel and perpendicular light paths. An

extinction ratio of 95% in the parallel beam path was characteristic of the system.

The G-factor, calculated as the ratio of parallel to perpendicular intensities at

identical gain settings for the CCD-array detector was 1.3, as measured for a

solution of fluorescein in water.

38

C) The microphotolysis experimental set up to monitor intensity and anisotropy

traces from a fluorescent sample was constructed from a multi-photon excitation

volume focused on the sample plane. This was achieved with a 20x - objective

lens (0.7NA), using Zeiss LSM 510 Meta microscope (Zeiss, Germany) to steer a

femtosecond 80.09 MHz (12 ns) pulsed Tsunami Titanium:Sapphire (Ti:S)

tunable laser (Newport, Mountain View, CA). The Ti:S laser was parked at a

single point for continuous illumination at or near the cell periphery at the center

of the field of observation, or scanned across the field for collecting images.

Time correlated single photon counting (TCSPC) is used to image cells (inset)

over an acquisition time 204 µs/pixel in the imaging mode. TCSPC was

accomplished using a Becker & Hickl 830 card (Becker and Hickl, Berlin,

Germany) as described (Becker, 2005). Parallel ( IP ) and perpendicular ( I⊥ )

emissions were collected simultaneously into two Hamamatsu R3809U multi-

channel plate photomultiplier tubes (PMTs) using a polarizing beam splitter

(Melles Griot, Carlsbad, CA) to separate the parallel and perpendicular

components of the fluorescence emission, at the non de-scanned side. Emission

side depolarization was measured by directing polarized illumination as above.

An extinction ratio of 96% in the parallel beam path was characteristic of the

system. The G-factor, calculated as the ratio of parallel to perpendicular

intensities as detected at the MCP-PMT detectors was 0.67, as measured for a

solution of fluorescein in water.

39

Note: In all the three set ups above there was no significant spatial variation in

anisotropy as measured for a GFP-solution. In the confocal measurements the

variation in anisotropy was less than the detectable limit over a 15 µm range.

Figure S2: Anisotropy imaging upon photobleaching in live

cells at high spatial resolution reveals regions enriched and depleted of

nanoclusters.

CHO cells expressing FR-GPI were labeled with PLF, and imaged on real-time

wide-field anisotropy set-ups at room temperature. Grey scale denotes

fluorescence intensity images; anisotropy values in the images are pseudo-

coloured according to the indicated LUT. A∞ range is indicated by a vertical line

(magenta) at the right of the LUT bar. Note the presence of high intensity and

anisotropy structures corresponding to microvilli [A, box(i)], and low anisotropy

regions in relatively flat regions of the cell [A, box(ii-iv)]. Panel B shows magnified

intensity and anisotropy images corresponding to panel A, boxes(i, ii). Graph (C)

shows local changes in anisotropy ( A ) corresponding to changes in intensity I ,

(normalized to 0I , the initial intensity of the region) upon photobleaching the

whole cell shown in panel A. Photobleaching does not significantly affect the

anisotropy value which starts out close to A∞ in high anisotropy regions marked

in box(i) (pink spots correspond to circles in B(i)]. At the same time low

anisotropy areas [box(ii-iv) in a] exhibit a steep change in anisotropy. Scale bar,

8 µm.

40

Note: In an earlier paper we had ascertained that enrichment of clusters would

be characterized by differences in the photobleaching profile of PLF-labeled FR-

GPI (Sharma et al., 2004). Our analysis showed that the photobleaching profile

was typical of a distribution of molecules in nanoclusters and monomers. Low-

anisotropy regions in the cell membrane have a higher rate of photo-bleaching

and exhibit a bleaching profile typical of a mixture of nanoclusters and

monomers, consistent with a high concentration of nanoclusters. High-anisotropy

regions show a value of anisotropy which does not change appreciably upon

photobleaching and is close to that expected for isolated fluorophores, A∞ . This

is consistent with a lack (or depletion) of clusters in these regions.

Figure S3: NBD-SM and BODIPY-SM anisotropy distribution.

NBD-SM (A; 6-((N-(7-nitrobenz-2-oxa-1,3-diazol-4-yl)amino) hexanoyl)

sphingosyl phosphocholine) or BODIPY-SM (B; N-(4,4-difluoro-5,7-dimethyl-4-

bora-3a,4a-diaza-s-indacene-3-pentanoyl sphingosyl phosphocholine;, Invitrogen

Corporation, USA) complexes with BSA (ratio 1:1) in a 10 µM solution was

incorporated onto the surface of CHO cells by incubating for 30 min on ice. Cells

were subsequently maintained at 20°C and imaged on a wide field microscope

as described in Fig.1A. Intensity (grey scale) and anisotropy (pseudo-coloured)

images from regions outlined by the square box are shown at the right of each

panel. Main Fig. 1D shows analysis of many 50 x 50 pixel regions taken from

within the areas outlined by a square box above, from multiple cells labeled with

the same concentration of probes. Scale, 8µm.

41

Figure S4: Endocytosis does not contribute significantly to

fluorescence intensity measurements made at the cell surface.

A) FR-GPI expressing CHO cells were labeled with PLBTMR on ice for 1 h,

washed and transferred to a 37 °C bath for two minutes before being imaged on

a temperature controlled stage at 37 °C on the LSM 5 Live confocal set up

described in Supplementary Fig. S1B. Cells were images within two minutes of

placing on the stage before and after treatment with PI-PLC (40µg/ml; 2 min). B)

Histogram shows average intensity of fluorescence (+S.D) measured from 6 cells

before and after PIPLC-treatment of the same cells. Scale bar= 5 µm

Note: The data show that there is an insignificant amount of fluorescence

detected post PI-PLC treatment, indicating that endocytosed probes do not

contribute significantly to the total or local signal detected in such a

measurement.

Figure S5: BODIPY-SM diffusion.

BODIPY-SM (N-(4,4-difluoro-5,7-dimethyl-4-bora-3a,4a-diaza-s-indacene-3-

pentanoyl) sphingosyl phosphocholine, Invitrogen Corporation, USA) complex

with BSA (ratio 1:1) in a 5 µM solution was incorporated onto the surface of CHO

cells by incubating for 30 min on ice. Cells were subsequently maintained at

20°C on a Laser scanning confocal microscope equipped with MP-excitation (790

nm) and optics as described in Supplementary Figure 1C. Cells were imaged

using MP excitation (A) and intensity (blue line) and anisotropy traces (red line)

42

were obtained simultaneously from a confocal volume (red crosshair) during an

illumination sequence outlined at the top of the trace (B). The concentration of

BODIPY-SM incorporated on the cell surface, is sufficient to record significant

homoFRET at time, t=0. During the initial illumination period (t1), the anisotropy of

BODIPY-SM, increases and approaches A∞, similar to that observed for PLF-

labeled FR-GPI (Main Figure 2A). A∞ (pink band) was measured after

photobleaching the BODIPY-SM so that there was no further change in

anisotropy. However, during the waiting time (tw), unlike PLF-FR-GPI, the

anisotropy of BODIPY-SM recovers to its original value. On the other hand, the

intensity of the two probes recovers substantially during this time. This result

suggests that a cell surface molecule (largely on the outer leaflet of the plasma

membrane) such as BODIPY-SM, capable of unhindered diffusion (Klein et al.,

2003), recovers its intensity and anisotropy (and hence its original steady state

distribution) following localized photobleaching. Scale bar 6.6µm.

Note: This is in direct contrast to the observation that GPI-AP nanoclusters do

not reassemble from the monomers, nor do they move in from the adjoining

regions of the membrane at the same temperature (see Main Fig. 2).

Figure S6:

A) Recovery of fluorescence intensity after first illumination period, t1, is not due

to the contribution of an internal (recycling) pool of fluorophores.

43

Fluorescence intensity trace from PLF-labeled cells at 37°C was recorded during

t1. At the beginning of the waiting time tw, PI-specific phospholipase (PIPLC;

arrow; 40µg/ml) was added to cleave surface GPI-APs . One minute later, the

enzyme was washed off with medium 1 buffer (M1) containing 30 mM NH4Cl to

dequench the fluorescence of PIPLC-protected fluorophores, likely to be located

in highly acidic early endosomes that form during the internalization of GPI-APs

via the cdc42-regulated GEEC pathway (Kalia et al., 2006); a fraction of these

endosomes are capable of recycling (Chadda et al., 2007). During t2, the

fluorescence intensity trace clearly shows that there is no significant contribution

from an internalized pool of PLF-labeled receptors to the intensity recorded trace

recorded during t2. The measured photon counts during t2 can accounted for by

autofluorescence (shown in B).

B) Auto-fluorescence generated during MP-excitation is insignificant. Photon

counts obtained from unlabeled cell over a typical illumination sequence as

indicated confirm that there is no significant contribution (< 1-3% of PLF-labeled

cell fluorescence intensity) of auto-fluorescence to the total intensity recorded.

Figure S7: Range of fitted parameter values.

Variation of the measured parameters obtained upon fitting, across different cells

at temperatures ranging from 15°C - 37°C

A) Diffusion of monomers of FR-GPI 1d measured across different cells as a

function of temperature. The range of values for 1d is shown normalized to a

typical value of FR-GPI diffusion (0.1078s-1) extracted at 37oC. This is consistent

44

with those obtained from measurements on FR-GPI on similar blebs and

BODIPY-SM on the cell surface. In addition, independently measured variation of

diffusion coefficients from FCS measurements of FR-GPI and GFP-GPI across

the temperature range are 0.516 ± 0.135 µm2/s (20°C) and 1.276 ± 0.469 µm2/s

(37°C). B) The rates of fragmentation ( fk ) versus aggregation ( ak ) measured

across different cells as a function of temperature. The ranges of data that

correspond to the classes elaborated in the main text are indicated by FR, PR

and NR. The relative population of cells at different temperatures in a given class

is highlighted with a darker shade.

Figure S8: Extraction of typical values for ln ka/kf versus

roomT T .

The cumulative distribution of the ln ka/kf values obtained from the fit are further

fit to an error function (cumulative normal distribution) indicated by the red curve,

whose parameters are the mean and standard deviation. The green crosses

which mark the typical values obtained at (A) 37°C , (B) 33°C and (C) 28°C are

joined with the black line and used to generate the Arrhenius plot shown in Main

Fig. 3.

Figure S9: Nanoclusters are absent in membrane regions

devoid of actin

A) GFP-GPI expressing cells were treated with Jas (14µM) for 30min at 37 °C,

fixed and stained with rhodamine phalloidin, before imaging on confocal. Images

45

from the bottom, medial and top planes of a confocal stack of images show that

membrane blebs (green) are devoid of polymerized actin (red) as observed by

the lack of Rhodamine-phalloidin staining.

B, C) Multi-photon laser-excited intensity (blue) and anisotropy (red) traces of

PLF-labeled FR-GPI expressing cells from membrane blebs generated by 30 min

incubation at 37 °C with Lat (12 µM; B) or Jas (15 µM; C) show high anisotropy

values close to A∞ (pink band) indicating membranes devoid of pre-existing GPI-

AP nanoclusters. Scale bar, 6 µm.

Figure S10: Hetero-FRET measurements confirm spatial

heterogeneity of nanocluster distribution. Actin-perturbation generates

blebs devoid of FRET signals.

A-C) Donor (PLF) alone (A) or donor and acceptor (PLF/PLR)-labeled FR-GPI

expressing CHO (B, C) cells were imaged using a multi-photon excitation FLIM

set up either before (A, B) or after treatment with Jas (C). Donor fluorescence

intensity (grey scale) and lifetime (pseudo-colour) images were generated at 1 x

1 µm2 resolution as described (Supplementary Methods). The pseudo-coloured

life-time images were obtained from specific regions of the cells, demarcated by

boxes and displayed at the right of each intensity image. They are coloured with

respect to the LUT scale corresponding to the indicated life-time ranges. The

spatial resolution of PLF-fluorescence at the signal levels obtained is not

sufficient to resolve the micron-scale features, such as distinct punctuate

microvilli. However, the spatial variation of heteroFRET signal estimated from the

46

measured distribution of average fluorophore lifetimes compared to that

observed for donor-alone labeled cells [A, boxes (1-6)], reveals regions with high

FRET [B, flat regions in boxes (i-iii, v)] and low FRET [B, membrane ruffles in (iv,

vi); C, blebs in boxes (1-6)]. In general, lower donor lifetimes (corresponding to

high levels of heteroFRET) are observed in the flat regions of cells while higher

donor lifetimes are recorded from the edges of cells at regions identifiable as

membrane ruffles or extending lamellipodium or blebs in Jas-treated cells. The

higher lifetimes obtained are comparable to cells labeled only with donor

fluorophores (A), and PLF-PLR labeled cells treated with saponin to eliminate

clustering (see Supplementary Table ST2), confirming a reduction in heteroFRET

in these regions. Scale bar,5 µm.

Figure S11: Latrunculin inhibits actin dynamics at the cell

cortex

Maximum intensity projections of 15 s movies made from cells before (Pre Lat A)

and after (Post Lat A) Lat A treatment at 37°C showing all the actin-GFP

molecules recruited in a 15 second period. Notice that the number of molecules

being recruited to cell cortex decreases upon Lat A treatment; boxed number

indicates of molecules detected in each cell pre- and post- treatment. Cells were

treated with Lat A (400 nM) for 4-5 minutes and imaged immediately before and

after treatment. Histogram shows the average extent of reduction in the number

of recruitment events from 5 cells post-latrunculin treatment, where the number

47

of recruitment events varied from 60 to 250 in the cells that were being imaged.

Scale bar, 5 µm.

Figure S12: Graphs of variation of bleb-area, anisotropy of

GFP-GPI, CA and CA-associated molecules during spontaneous bleb-

formation and retraction in freshly plated fibroblasts.

Freshly-plated CHO cells, stably expressing GFP-GPI (A, B) or FR-GPI (C) were

co-transfected with C-terminal Ezrin-RFP alone (B), or with MRLC-GFP (C).

These cells develop spontaneous blebs before they spread out and acquire a flat

morphology at 37°C. GFP-GPI intensity, anisotropy, RFP-ezrin and MRLC-GFP

in the blebs were imaged on wide-field dual-camera set-up (Supplementary Fig.

S1A). Images were collected for GFP-fluorescence every 5 sec (A) or 11s (B, C).

Ezrin-RFP images were collected in between the GFP-GPI (B) or MRLC-GFP (C)

images. Blebs appeared spontaneously from the cell edge, grow to their

maximum size in ~10-20 s, and retract in ~ 1-2min. Blebs are derived from

regions where anisotropy is low to begin with, but as the bleb grows, anisotropy

rapidly rises to the value of isolated monomers. After maximal extent, anisotropy

slowly reduces during the retraction of bleb area. Graph shows the change in

bleb area (blue line; normalized to the maximum area), GFP-GPI anisotropy

(magenta line in A, B; normalized to the highest anisotropy during this dynamics),

MRLC-GFP fluorescence (magenta line in C; normalized to the maximum

intensity during this dynamics; see Supplementary Fig. S13 for a typical

48

montage) and C-terminal Ezrin-RFP (green line in C; normalized to the initial

value at the site of the bleb).

Figure S13: Recruitment of myosin regulatory light chain

during bleb retraction dynamics.

FR-GPI expressing CHO cells stably were transiently co-transfected with MRLC-

GFP (A) and Ezrin-RFP (B), de-adhered, plated onto coverslip dishes in M1 with

glucose and imaged at 37°C after labeling the cell surface with PLB. The images

of GFP (A) and RFP (B) were sequentially collected within 5 s of each other, by

toggling appropriate excitation and emission filters for GFP-anisotropy (ex

480df30/em 520df20) and PLB-intensity images (ex 550df30/ em 600LP). Each

set of images is separated from the next by 11s, with the PLB image collected 5

s after the GFP image. Note during the retraction phase punctuate spots of

MRLC are recruited to the bleb membrane outlined by PLB fluorescence. Scale

bar, 3.2 µm.

Figure S14: Temperature sensitive bleb retraction dynamics.

CHO cells were de-adhered and replated on to cover-slip dishes as described in

Fig. 7 and Supplementary Methods, and the dynamics of the spontaneously

formed blebs were monitored by wide-field microscopy, at the indicated

temperatures. Bleb retraction and expansion dynamics were monitored by

recording the number of frames (collected every 5 sec) required for the bleb to

retract into the main body of the cell after complete extension; expansion was

monitored by measuring the number of frames required to achieve maximum

expansion of the bleb. For each temperature we show a representative example

49

of the change in normalized bleb area (inset) versus time, where the maximum

expansion time of the bleb has been set t=0. This allows a direct comparison of

the mean rate of retraction of the bleb. Graph shows mean rate of retraction

(standard deviation) plotted against corresponding temperatures as Troom/T

where Troom = 25°C obtained from 32 blebs at 25 °C, at from 34 blebs at 30 °C,

and from 42 blebs at 37 °C, from 6-8 cells at each temperature. The data show

that the rate of retraction is sensitive to temperature and exhibits a sharp

crossover at ~ 30 °C. The experiment was repeated twice with similar results.

50

Supplemental References

Becker, W. (2005). Advanced Time-Correlated Single Photon Counting Techniques: Springer.).

Bretscher, A., Reczek, D., and Berryman, M. (1997). Ezrin: a protein requiring conformational activation to link microfilaments to the plasma membrane in the assembly of cell surface structures. J Cell Sci 110 ( Pt 24), 3011-3018.

Chadda, R., Howes, M. T., Plowman, S. J., Hancock, J. F., Parton, R. G., and Mayor, S. (2007). Cholesterol-sensitive Cdc42 activation regulates actin polymerization for endocytosis via the GEEC pathway. Traffic 8, 702-717.

Charras, G. T., Coughlin, M., Mitchison, T. J., and Mahadevan, L. (2007). Life and Times of a Cellular Bleb. Biophys J, biophysj.107.113605.

Gautier, I., Tramier, M., Durieux, C., Coppey, J., Pansu, R. B., Nicolas, J. C., Kemnitz, K., and Coppey-Moisan, M. (2001). Homo-FRET microscopy in living cells to measure monomer-dimer transition of GFT-tagged proteins. Biophys J 80, 3000-3008.

Gov, N. S., and Safran, S. A. (2005). Red blood cell membrane fluctuations and shape controlled by ATP-induced cytoskeletal defects. Biophys J 88, 1859-1874.

Hatwalne, Y., Ramaswamy, S., Rao, M., and Simha, R. A. (2004). Rheology of active-particle suspensions. Phys Rev Lett 92, 118101.

J.-B. Manneville, P. B., S. Ramaswamy, and J. Prost (2001). Active membrane fluctuations studied by micropipet aspiration. Phys Rev E , 64, 1908.

Kalia, M., Kumari, S., Chadda, R., Hill, M. M., Parton, R. G., and Mayor, S. (2006). Arf6-independent GEECs fuse with sorting endosomes via a Rab5/PI-3' kinase-dependent machinery. Mol Biol Cell.

Klein, C., Pillot, T., Chambaz, J., and Drouet, B. (2003). Determination of plasma membrane fluidity with a fluorescent analogue of sphingomyelin by FRAP measurement using a standard confocal microscope. Brain Res Brain Res Protoc 11, 46-51.

Krishna, M. M., Srivastava, A., and Periasamy, N. (2001). Rotational dynamics of surface probes in lipid vesicles. Biophys Chem 90, 123-133.

51

Lakshmikanth, G. S., Sridevi, K., Krishnamoorthy, G., and Udgaonkar, J. B. (2001). Structure is lost incrementally during the unfolding of barstar. Nat Struct Biol 8, 799-804.

Lau, A. W., Hoffman, B. D., Davies, A., Crocker, J. C., and Lubensky, T. C. (2003). Microrheology, stress fluctuations, and active behavior of living cells. Phys Rev Lett 91, 198101.

Levy, H. M., Sharon, N., and Koshland, D. E. (1959). Purified Muscle Proteins and the Walking Rate of Ants. Proc Natl Acad Sci U S A 45, 785-791.

Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (1992). Numerical Recipes (London Cambridge University Press).

Ramaswamy, S., and Rao, M. (2001). The Physics of Active Membranes. C R Acad Sci Paris 2 IV, 817.

Sharma, P., Varma, R., Sarasij, R. C., Ira, Gousset, K., Krishnamoorthy, G., Rao, M., and Mayor, S. (2004). Nanoscale organization of multiple GPI-anchored proteins in living cell membranes. Cell 116, 577-589.

Sheetz, M. P., Chasan, R., and Spudich, J. A. (1984). ATP-dependent movement of myosin in vitro: characterization of a quantitative assay. J Cell Biol 99, 1867-1871.

Volkmer, A., Subramaniam, V., Birch, D. J., and Jovin, T. M. (2000). One- and two-photon excited fluorescence lifetimes and anisotropy decays of green fluorescent proteins. Biophys J 78, 1589-1598.

Wallace, M. I., Ying, L., Balasubramanian, S., and Klenerman, D. (2001). Non-Arrhenius kinetics for the loop closure of a DNA hairpin. Proc Natl Acad Sci U S A 98, 5584-5589.