analysis of the organization and dynamics of of the ige ... · 8/9/2012 · biological dynamic...

Insights Into Cell Membrane Microdomain Organizationfrom Live Cell Single Particle Tracking of the IgE High

Affinity Receptor FcǫRI of Mast Cells

Flor A. Espinoza

Center for Spatiotemporal Modeling of Cell SignalingPathology Department

University of New Mexico

Mathematics and Statistics DepartmentKennesaw State University

SIAM Life Sciences, San Diego, CA, August 9, 2012

Flor A. Espinoza Microdomain Organization of IgE-FcǫRI

Outline

Importance

IgE high affinity receptor FcǫRI

Analysis of IgE high affinity receptor FcǫRI Temporal Data

Summary


Importance: Organization and Dynamics of Proteins inCell Membranes

Cells communicate with the outside world through membraneproteins-receptors that recognize one of many possible stimuli(hormones and antibodies) in the extracellular environmentand translate this information to intracellular responses.

Changes in the organization and dynamics of cell membraneproteins are critical to transmembrane signal transduction.Therefore, there is great interest in understanding theorganization of membrane proteins in resting cells and intracking their reorganization during signaling.

Problems in signaling networks are important in understandingmany diseases including cancer, allergy and asthma.


IgE high affinity receptor FcǫRI, IgE-FcǫRI (AllergyReactions)


Analysis of the IgE-FcǫRI Temporal Data: AnalysisBiological Dynamic Data

Explain how the biological data was generated

Our analysis approach

Summary


How the data was generated

(1)

ITAM

cytoplasm

cell membrane

βγ γ

α

FcεRI

(2)

ITAM

cytoplasm

cell membrane

βγ γ

α

FcεRI

IgE

QD

(3)

IgE

antigen

ITAM

QD

c

cell membrane

βγ γ

α

FcεRI

Experiments used RBL-2H3 Rat Mast Cells, antigen DNP25-BSAand 5-10nm quantum dots (QD) to label IgE.work done by: Nicholas Andrews, Diana Lidke and Keith Lidke.


Single frame from a movie where three QD-IgE-FcǫRIcomplexes are moving on the membrane of a mast cell

The cell was genetically altered to express green actin (that makesthe membrane visible).


Biological Dynamic Data

The experimental data were generated using RBL-2H3 ratmast cells, that expresses high levels of the IgE receptor,FcǫRI.

To prepare the cells for an experiment, they are exposed to adilute solution of anti-DNP IgE labeled with quantum dots(QD-IgE).

Next, they are exposed to a concentrated solution of dark(unlabeled) anti-DNP IgE. As a result, most of the FcǫRI inthe cell membrane are in a IgE-FcǫRI complex, but only asmall percentage of the complexes are labeled with a quantumdot (QD-IgE-FcǫRI complex).



The data are dose-response where the dose is the concentration ofstimulus added and the response is measured by tracking and thenanalyzing the motion of the QDs.

For each data set, ten seconds after an experiment is started, thecells were stimulated with six different concentrations of themultivalent antigen DNP25-BSA:

0.000; 0.001; 0.010; 0.100; 1.000, 10.00µg/ml,

which can cross link both IgE-FcǫRI or QD-IgE-FcǫRI making theminto signaling competent dimers and higher oligomers.



The QDs are tracked using a wide-field fluorescence microscopeand a digital CCD camera that makes a movie by taking an imageover 1/20th of a second for 3,000 frames, corresponding to a totaltime of 150 seconds.

Then, image processing software is used to locate the center of theQDs in each of the frames with an error of approximately 20nm.

An important difficulty in analyzing the data is that the QDs blink,that is, they emit light for some period of time, then turn off for aperiod of time and may repeat this several times.


Following Quantum Dots in Time

Track

1 1 1 1 1 1 10 0 0 0 0 0 0 00

start end

Segment

Path

x x x x x

A track is a list of the form (xn, yn, vn), where 1 ≤ n ≤ N, and N

is the total number of frames in the movie, N=3000.

If vn = 1, the QD is on, otherwise vn = 0 and the QD is off.


Analyze the Jumps Between Frames

1.1 1.15 1.2 1.25 1.3 1.35

x 104

1.9

1.95

2

2.05

2.1

2.15

2.2x 10

4

Plot of big track 2023, Stimulus = 0.001 ug/mlTimeSteps = 867, t

0 = 106.65s, t

f = 150.00s, t

s = 10.00s

MaxDistX = 1638.9nm, MaxDistY = 2456.8nm

x (nm)

y (n

m)

startdot onisolateddot offmissingend


Jump Analysis

A track is a list of the form (xn, yn, vn),

the position of the QD is ~Pn = (xn, yn),

if vn = 1 and vn−1 = 1, a valid jump is defined by,

~Jn = ~Pn − ~Pn−1 , 2 ≤ n ≤ N

Let ∆Xn = xn − xn−1, and ∆Yn = yn − yn−1,

the lengths and angles of the jumps are

Ln = ‖~Jn‖ =√

∆X 2n +∆Y 2

n , Θn = arctan(∆Xn,∆Yn)


Overview of the available data from unstimulated andstimulated cells

A Bstimulus tracks jumps cells tracks jumps cells

0.000 10,894 407,669 19 9,848 353,368 160.001 1,726 85,906 4 3,113 122,761 30.010 2,151 96,179 4 2,622 106,649 50.100 1,838 89,380 4 2,809 119,306 51.000 1,178 61,928 3 2,327 123,053 5

10.000 1,802 91,142 4 3,050 139,236 5

Important: for our analysis we used the jumps between frames.


Case 1: Data from Unstimulated Cells

20 40 60 80 100 120 140−30

−20

−10

0

10

20

Stimulus = 0 ug/ml

time (s)

µ x (nm

)

20 40 60 80 100 120 140−30

−20

−10

0

10

20

Stimulus = 0 ug/ml

time (s)

µ y (nm

)

20 40 60 80 100 120 140

70

80

90

100

110

120

Stimulus = 0 ug/ml

time (s)

σ x (nm

)

20 40 60 80 100 120 140

70

80

90

100

110

120

Stimulus = 0 ug/ml

time (s)

σ y (nm

)

The mean and standard deviations of the x and y jumpcomponents are stationary.


Analysis of Data from Unstimulated Cells

Our new approach to analyze the jumps from the data istime-series analysis. But to do that, the data have to be ergodicand stationary.

We checked that the data are stationary, and we assumed theirergodicity.

Therefore, using time-series analysis, we can combine jumps fromdifferent times and locations.


Distribution of the X and Y Jump Components and theirNormal Fit

−300 −200 −100 0 100 200 3000

1

2

3

4

5

6x 10

−3 Stimulus = 0 ug/ml

x

p

datafit

−300 −200 −100 0 100 200 3000

1

2

3

4

5

6x 10

−3 Stimulus = 0 ug/ml

yp

datafit

The x and y jump components are not normally distributed!

Also verified by the Kolmogorov-Smirnov test, kstest2 in Matlab.


Distribution of the Jump Angles, Data Set A

−3 −2 −1 0 1 2 3

0.145

0.15

0.155

0.16

0.165

0.17

0.175

Stimulus = 0 ug/ml

θ

PD

F

datameanstd

−3 −2 −1 0 1 2 3

0.145

0.15

0.155

0.16

0.165

0.17

0.175

θ

PD

F

Stimulus = 0 ug/ml

randommeanstd

The angles are uniformly distributed!

Also verified by the Kolmogorov-Smirnov test, kstest2 in Matlab.


Distribution of Jump Angles and Lengths

For IID random walks, the components are normally distributed ifand only if the jump angles are uniformly distributed, and the jumplengths have a simple chi distribution, which is the same as thesimple Weibull distribution.

The components of the jumps are not normally distributed.

We also checked that the angles are uniformly distributed.

Thus, the jump lenghts cannot have a simple chi or Weibulldistribution.


Jump Lengths PDF

The general chi PDF is c(r , s, d) = c(r/s, d)/s where

c(r , d) =2

2d/2Γ(d/2)rd−1 e−

r2

2

The general Weibull PDF is w(r , s, k) = w(r/s, k)/s where

w(r , k) = k rk−1e−rk

The power law is p(r , s, α, β) = p(r/s, α, β)/s, where

p(r , α, β) =α (β − 1) rα−1

(1 + rα)β


Jump Lengths PDF

50 100 150 200 250 300

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

x 10−3

stimulus = 0.000 ug/ml

r (nm)

PD

F

datag−chig−Weibullpower−law

50 100 150 200 250 300

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

x 10−3


r (nm)

PD

F


A B

general chi general Weibull power law

d s k s α β s

A 1.35 116.79 1.49 130.39 1.54 9.78 561.02B 1.41 116.37 1.55 133.70 1.59 14.10 663.27


Behavior of the Jumps

All these distribution have the same power law near r = 0:

p ≈ C rd−1 , d ≈ 3/2 .

The fact that d is less than to 2 indicates that the PDF of thejump lengths are not close to normally distributed.

It is interesting that the estimates of d are so consistent for thedifferent distributions. This indicates that this behavior is veryrobust.

For intermediate jump lengths, the power-law gives the best fit.


Excess of Short Jumps: Chi Fit to the Jump Lengths(Data Set A) and the Simple Chi PDF for the same σ

0 50 100 150 200 250 3000

1

2

3

4

5

6

7x 10

−3

r (nm)

PD

F

chi fit to datasimple chi


Excess of Short Jumps

The blue curve is the general chi PDF fit to the jump lengths (setA), with second moment σ2.

The red curve is a simple chi or simple Weibull with standarddeviation σ.

The area below the red curve and above the blue curve is due toexcess of short jumps.


Case 2: Data from Stimulated Cells

Cells were stimulated at 10 seconds. Our new approach is toanalyze the time-dependent behavior of the standard deviation ofthe jump lengths.

0 20 40 60 80 100 120 14020

40

60

80

100

120

140

160

180

200Stimulus = 1 ug/ml

time (s)

σ (n

m)

dataexponentialpower−law


Time-Dependent Behavior of the Data for Stimulated Cells

To quantify the transition between the behavior of the cells beforeand after stimulation, we fit the time-dependent standard deviationof the jump lenghts with an exponential function of the form

S(t) = (Sl − Sr )e−max(0,(t−ts ))/tm + Sr

To capture any scaling behavior, we used a power law fit of theform

S(t) =Sl − Sr

(1 + max(0,t−ts )tm

)β+ Sr

ts = 10 sec, time at which the cells were stimulated.


Time-Dependent Behavior of the Standard Deviation ofthe Data for Stimulated Cells

0 20 40 60 80 100 120 14020

40

60

80

100

120

140

160

180

200Stimulus = 0.001 ug/ml

time (s)

σ (n

m)



Case 2: Time-Dependent Behavior of the StandardDeviation of the Data for Stimulated Cells

0 20 40 60 80 100 120 14020

40

60

80

100

120

140

160

180


time (s)

σ (n

m)




0 20 40 60 80 100 120 14020

40

60

80

100

120

140

160

180


time (s)

σ (n

m)




0 20 40 60 80 100 120 14020

40

60

80

100

120

140

160

180


time (s)

σ (n

m)


0 20 40 60 80 100 120 14020

40

60

80

100

120

140

160

180


time (s)

σ (n

m)


0 20 40 60 80 100 120 14020

40

60

80

100

120

140

160

180


time (s)

σ (n

m)


0 20 40 60 80 100 120 14020

40

60

80

100

120

140

160

180


time (s)

σ (n

m)


0 20 40 60 80 100 120 14020

40

60

80

100

120

140

160

180


time (s)

σ (n

m)



Exponential and power law fit parameters

exponential fit power law fitstimulus Sl Sr tm Sl Sr β

0.001 121.36 112.09 0.09 121.36 112.09 115.660.010 121.41 107.68 40.16 123.48 102.41 0.46

A 0.100 124.16 80.35 19.31 125.34 73.38 0.821.000 126.51 64.93 5.08 125.98 64.41 2.6210.000 133.15 78.15 1.14 133.18 78.14 9.47

0.001 131.04 114.90 26.43 132.81 110.65 0.650.010 134.93 107.19 32.48 136.31 83.61 0.31

B 0.100 142.22 80.68 30.09 144.48 31.50 0.331.000 138.50 62.66 4.81 139.00 61.79 2.5810.000 130.91 75.46 2.52 130.18 74.88 3.43


Visualizing the Changes in the Jump Lengths

20 40 60 80 100 120 1400

10

20

30

40

50

60

70

80

90


time (s)

perc

enta

ge

≤ 70 nm70−190 nm> 190 nm

20 40 60 80 100 120 1400

10

20

30

40

50

60

70

80

90


time (s)

perc

enta

ge

≤ 70 nm70−190 nm> 190 nm

20 40 60 80 100 120 1400

10

20

30

40

50

60

70

80

90


time (s)

perc

enta

ge

≤ 70 nm70−190 nm> 190 nm

20 40 60 80 100 120 1400

10

20

30

40

50

60

70

80

90


time (s)

perc

enta

ge

≤ 70 nm70−190 nm> 190 nm

20 40 60 80 100 120 1400

10

20

30

40

50

60

70

80

90


time (s)

perc

enta

ge

≤ 70 nm70−190 nm> 190 nm

The time dependent percentages of the jump lengths.


Mean Percentage of jump length sizes

A Bstimulus ≤ 70 70 − 190 > 190 ≤ 70 70− 190 > 190

0.000 32.89 49.68 17.44 30.80 51.37 17.830.001 46.56 43.27 10.17 44.97 44.55 10.480.010 48.94 41.34 9.72 50.94 39.83 9.230.100 68.97 26.44 4.59 72.55 23.31 4.141.000 77.48 20.40 2.12 81.11 17.02 1.8710.000 69.30 27.21 3.49 72.17 24.78 3.06


Time in Seconds to Reach Stationary Behavior,S(tst)− Sr ≤ 1 nm, data set A

20 40 60 80 100 120 14020

40

60

80

100

120

140

160

180

200

Stimulus = 0.001 ug/ml, tst

= 10.20 s

time (s)

σ (n

m)

datatst

tail

20 40 60 80 100 120 14020

40

60

80

100

120

140

160

180

200


= 101.10 s

time (s)

σ (n

m)

datatst

tail

20 40 60 80 100 120 14020

40

60

80

100

120

140

160

180

200


= 82.40 s

time (s)

σ (n

m)

datatst

tail

20 40 60 80 100 120 14020

40

60

80

100

120

140

160

180

200

Stimulus = 1 ug/ml, tst

= 30.85 s

time (s)

σ (n

m)

datatst

tail

20 40 60 80 100 120 14020

40

60

80

100

120

140

160

180

200

Stimulus = 10 ug/ml, tst

= 14.60 s

time (s)

σ (n

m)

datatst

tail


Time in Seconds to Reach Stationary Behavior

A Bstimulus tst tst

0.001 10.20 81.500.010 101.10 107.650.100 82.40 120.051.000 30.85 30.8510.000 14.60 20.15


Analyzing the Tails

The analysis of the tails is done in the same way as the analysis ofthe unstimulated data.

50 100 150 200 250 300

1

2

3

4

5

6

7

8

x 10−3


r (nm)

PD

F


50 100 150 200 250 3000

0.002

0.004

0.006

0.008

0.01

0.012

0.014


r (nm)

PD

F


Examples of jump lengths PDFs with the general Weibull, chi andpower-law fits.


Dynamic Data Summary

The stimulated data has three parts: before stimulus, it isstationary, then decays for a period of time, and finally goes backto being stationary.

We classify the stimuli into weak (0.001, 0.010) and strong (0.100,1.000, 10.000). The effects of the weak stimuli are small anddifficult to quantify because of the noise in the data.

For the strong stimuli, the time it takes for the data to reachstationarity decreases rapidly with increasing stimulus.

For the data from stimulated cells, especially for the strongerstimuli, the power-law fits to the jump lengths is significantlybetter than the general chi or general Weibull.


Summary Continue

Our discovery of an excess of short (< 70 nm) jumps inunstimulated data shows that membranes contain submicrometerbarriers to unrestricted receptor movement.After stimulation, receptor mobility decays rapidly and reaches anew plateau where the jumps are even shorter, indicating a furtherlevel of receptor confinement.


Summary

Insights Into Cell Membrane Microdomain Organization from

Live Cell Single Particle Tracking of the IgE High Affinity

Receptor FcǫRI of Mast Cells

Flor A. Espinoza, Michael J. Wester, Janet M. Oliver, Bridget S.Wilson, Nicholas Andrews, Diane S. Lidke and Stanly L. Steinberg.Bulletin of Mathematical Biology, Volume 74, Issue 8 (2012), Page1857-1911.


Acknowledgments

Stanly Steinberg

Janet Oliver

Michael Wester

Bridget Wilson

Nicholas Andrews

Diana Lidke

Keith Lidke

Becky Lee

Lily Chylek

STMC


analysis of the organization and dynamics of of the ige ... · 8/9/2012 · biological dynamic...

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