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Some first results of PhD-project: Inference of within cell protein interactions and spatial structure, using FRET Jan-Otto Hooghoudt Aalborg University Avignon SSIAB, May 10 2012 Jan-Otto Hooghoudt Some first results of PhD-project:Inference

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Some first results of PhD-project: Inference of within cell protein interactions and spatial structure, using FRET

Jan-Otto Hooghoudt

Aalborg University

Avignon SSIAB, May 10 2012

Jan-Otto Hooghoudt Some first results of PhD-project:Inference of within cell protein interactions

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Outline of the talk

  • Introduction to the general problem and research questions
  • Short review of theory of Fluorescence Resonance Energy

Transfer

  • Dependence of FRET-efficiency on point processes
  • Modeling of FRET efficiency
  • Generating the point patterns
  • Data analysis
  • Discussion of some results

Jan-Otto Hooghoudt Some first results of PhD-project:Inference of within cell protein interactions

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Introduction: Problem description

  • Distribution and interaction between proteins in cells not well

understood

  • The interactions take place at the molecular level (1-100 nm)
  • These scales can presently not be resolved directly by available

microscopic techniques.

  • However, FRET-microscopy does provide indirect information

regarding proximity of proteins at molecular level

  • By FRET, information available where in a cell proteins are

close to each other

  • But, no information available concerning the protein

distribution within a pixel

Jan-Otto Hooghoudt Some first results of PhD-project:Inference of within cell protein interactions

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SLIDE 4

Introduction: Project Objectives

The project objectives are to: develop spatial models modeling the protein distribution at the molecular level develop likelihood based inference methods using an available FRET-efficiency model as the generating stochastic

  • mechanism. Y = g(X; θ) with g(·) the stochastic mechanism

which we can simulate. infer information concerning the parameters that define the type and strength of clustering infer information concerning the absolute concentrations of proteins and their complexes throughout a cell.

Jan-Otto Hooghoudt Some first results of PhD-project:Inference of within cell protein interactions

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Theory Fluorescence Resonance Energy Transfer

Electrodynamic phenomenon: Donor molecule gets excited by laser light and de-excites by:

  • photon emission

(rate krad)

  • FRET

(rate kFRET) Where the following relationship exists: kFRET = krad R0 r 6

  • r = distance between donor and acceptor
  • R0 = Forster distance, the distance r for which 50% of de-excitations

due to FRET and 50% due to donor-emission. D A r

Jan-Otto Hooghoudt Some first results of PhD-project:Inference of within cell protein interactions

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FRET efficiency

The main parameter describing FRET is the FRET efficiency: E = rate of de-excitations due to FRET de-excitation rate = kFRET krad + kFRET kFRET = krad R0 r 6 → E(r) = R6 R6

0 + r6 .

10 20 30 40 50 0.0 0.2 0.4 0.6 0.8 1.0 Efficiency E(r) distance r / [nm] E = R0

6 (R0 6 + r6)

R0 = 10

Highly sensitive to the distance due to r−6: FRET D A r < 2R0 No-FRET D A r > 2R0

Jan-Otto Hooghoudt Some first results of PhD-project:Inference of within cell protein interactions

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FRET-efficiency multiple acceptors

When multiple acceptors surround a donor, total rate of de-excitations due to FRET becomes: ktot

FRET = krad n

  • i=1

R0 ri 6 And total rate of de-excitation: ktot = krad(1 +

n

  • i=1

R0 ri 6 ) So probability of de-excitation by FRET to acceptor Ai and due to emission are given by: PAi

FRET =

  • R0

ri

6 (1 + n

i=1

  • R0

ri

6 ) ; Prad = 1 (1 + n

i=1

  • R0

ri

6 ) For simulation compute transfer probability-matrix defining all probabilities of de-exitation of Dj to Ai or due to emission.

Jan-Otto Hooghoudt Some first results of PhD-project:Inference of within cell protein interactions

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Modeling the FRET efficiency

Assign fluorophore types Assign fluorophore positions Calculate dis- tances and trans- fer probabilities Generate schedule

  • f times and targets
  • f each excitation

Play next excitation Is target donor available? Calculate rate

  • f energy release

Make list of avail- able acceptors Calculate time at which donor de-excites Random selec- tion of relaxation Fluorescence FRET All exci- tations played? Data output: E=fret/(fret+fluo) yes no fluo=fluo+1 fret=fret+1 no

Flow diagram of MC-simulation to model the FRET efficiency for: different types of proteins (monomer, dimer, etc) absolute concentrations of the proteins Diagram by Corry et. al. (2005,

  • Biophys. J.)

Jan-Otto Hooghoudt Some first results of PhD-project:Inference of within cell protein interactions

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A FRET image

Figure: Wallrabe et.al 2003

To calculate the FRET efficiency, emission is measured in 3 channels:

  • Acceptor Channel: Acceptor excitation

and acceptor emission

  • Donor Channel: Donor excitation and

donor emission

  • FRET Channel: Donor excitation,

acceptor emission

Jan-Otto Hooghoudt Some first results of PhD-project:Inference of within cell protein interactions

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Generating the point patterns (in R)

For a Strauss hardcore point process X, the (unnormalized) density is given by: f (x) ∝ βn(x)γsR(x)0shc(x) (1)

  • n(x) number of points in pattern x
  • sR(x) number of pair-of-points within distance R in pattern x.
  • shc(x)number of pair-of-points within distance hc in pattern x.

sR(x) =

  • {u,v}⊆x

1[u − v ≤ R] (2) β > 0, and γ the interaction parameter defining the behavior of the process.

  • 0 < γ < 1, X is repulsive,
  • γ = 1, X ∼ Poisson hard-core
  • γ > 1, X is clustered, but repulsive at a small scale.

Jan-Otto Hooghoudt Some first results of PhD-project:Inference of within cell protein interactions

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Generating the point patterns (in R)

Further we have used the Multi-Strauss hardcore process: f (x) ∝ βn(x) γsRaa(x)

aa

γsRdd(x)

dd

γsRda(x)

da

0sRaa(x) 0sRdd(x) 0sRda(x) (3) Parameters and interaction radius depending on the type of point (Donor or Acceptor)

Jan-Otto Hooghoudt Some first results of PhD-project:Inference of within cell protein interactions

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Strauss Patterns

donor acceptor

Density in #points per pixel Pixel-size = 100x100nm

D= 50 ; Gamma = 1

  • 3162

3162

D= 50 ; Gamma = 3

  • 3162

3162

D= 50 ; Gamma = 5

  • 3162

3162

D= 50 ; Gamma = 8

  • ●
  • 3162

3162

Jan-Otto Hooghoudt Some first results of PhD-project:Inference of within cell protein interactions

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Strauss Patterns

donor acceptor

Density in #points per pixel Pixel-size = 100x100nm

D= 100 ; Gamma = 1

  • 2236

2236

D= 100 ; Gamma = 3

  • 2236

2236

D= 100 ; Gamma = 5

  • 2236

2236

D= 100 ; Gamma = 8

  • ●
  • 2236

2236

Jan-Otto Hooghoudt Some first results of PhD-project:Inference of within cell protein interactions

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Strauss process: E versus gamma

  • D = 1

1 2 3 4 5 6 8 0.00 0.01 0.02 0.03

Gamma E

  • D = 5

1 2 3 4 5 6 8 0.00 0.05 0.10 0.15

Gamma E

  • D = 10

1 2 3 4 5 6 8 0.05 0.10 0.15 0.20 0.25 0.30

Gamma E

  • D = 50

1 2 3 4 5 6 8 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Gamma E

D = 100 1 2 3 4 5 6 8 0.4 0.5 0.6 0.7 0.8 0.9

Gamma E

Jan-Otto Hooghoudt Some first results of PhD-project:Inference of within cell protein interactions

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Strauss process: Dependency E pixel on ratio #acceptors-to-#donors

  • ●

gamma = 1

(Na

Nd)pixel

Epixel

0.1 0.5 2.0 10.0 0.0 0.1 0.2 0.3 0.4

  • gamma = 3

(Na

Nd)pixel

Epixel

0.1 0.5 2.0 5.0 0.0 0.1 0.2 0.3 0.4 0.5

  • gamma = 5

(Na

Nd)pixel

Epixel

0.1 0.5 2.0 10.0 0.0 0.2 0.4

  • gamma = 8

(Na

Nd)pixel

Epixel

0.1 0.5 2.0 5.0 0.0 0.2 0.4 0.6 0.8

Jan-Otto Hooghoudt Some first results of PhD-project:Inference of within cell protein interactions

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Multi-Strauss Patterns

donor acceptor

Notation for Multi-Strauss: Gamma =

  • gDD

gDA gAD gAA

  • = (gDD, gDA, gAD, gAA)
  • D = 100 ; G = 2222

2236 2236

  • ●
  • D = 100 ; G = 5555

2236 2236

  • ●
  • ●
  • ●
  • D = 100 ; G = 10101010

2236 2236

  • D = 100 ; G = 2112

2236 2236

  • D = 100 ; G = 5115

2236 2236

  • ●
  • ●
  • ●
  • D = 100 ; G = 101110

2236 2236

  • D = 100 ; G = 1221

2236 2236

  • D = 100 ; G = 1551

2236 2236

  • D = 100 ; G = 110101

2236 2236

Jan-Otto Hooghoudt Some first results of PhD-project:Inference of within cell protein interactions

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Multi-Strauss process: E versus gamma

  • ●
  • ●
  • D = 10

1 2 4 5 6 8 10 2112 4114 5115 6116 8118 101110 1221 1441 1551 1661 1881 110101 0.1 0.2 0.3 0.4

Gamma E

  • ●
  • D = 50

1 2 4 5 6 8 10 2112 4114 5115 6116 8118 101110 1221 1441 1551 1661 1881 110101 0.0 0.2 0.4 0.6 0.8

Gamma E

  • D = 100

1 2 4 5 6 8 10 2112 4114 5115 6116 8118 101110 1221 1441 1551 1661 1881 110101 0.0 0.2 0.4 0.6 0.8

Gamma E Jan-Otto Hooghoudt Some first results of PhD-project:Inference of within cell protein interactions

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Variogram: correlation E values between pixels

  • hc=30 ri=50 ga=10 D=50

4472 4472

  • ●
  • ●
  • 2

4 6 8 10 12 0.11 0.12 0.13 0.14 0.15 0.16 0.17

Variogram pattern 1

  • 2

4 6 8 10 0.11 0.12 0.13 0.14 0.15 0.16

Averaged

  • hc=30 ri=50 ga=10 D=50

4472 4472

  • ●
  • 2

4 6 8 10 12 0.12 0.13 0.14 0.15 0.16 0.17 0.18

Variogram pattern 2

  • 2

4 6 8 10 0.12 0.13 0.14 0.15 0.16

Averaged

  • ●
  • hc=30 ri=50 ga=10 D=50

4472 4472

  • ●
  • ●
  • 2

4 6 8 10 12 0.10 0.11 0.12 0.13 0.14 0.15

Variogram pattern 3

  • 2

4 6 8 10 0.10 0.11 0.12 0.13 0.14

Averaged

pixel-resolution used = 25 x 25 nm empirical pixel sizes = 100x100 nm

Jan-Otto Hooghoudt Some first results of PhD-project:Inference of within cell protein interactions

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Variogram: correlation E values between pixels

  • hc=30 ri=50 ga=10 D=50

4472 4472

  • ●
  • 1

2 3 4 5 6 0.16 0.17 0.18 0.19 0.20 0.21

Variogram pattern 1

  • 1.0

1.5 2.0 2.5 3.0 3.5 4.0 0.170 0.175 0.180 0.185 0.190 0.195 0.200

Averaged

  • hc=30 ri=50 ga=10 D=50

4472 4472

  • 1

2 3 4 5 6 0.16 0.18 0.20 0.22

Variogram pattern 2

  • 1.0

1.5 2.0 2.5 3.0 3.5 4.0 0.16 0.17 0.18 0.19 0.20 0.21

Averaged

  • ●
  • hc=30 ri=50 ga=10 D=50

4472 4472

  • ●
  • 1

2 3 4 5 6 0.14 0.16 0.18 0.20 0.22

Variogram pattern 3

  • 1.0

1.5 2.0 2.5 3.0 3.5 4.0 0.165 0.170 0.175 0.180 0.185 0.190 0.195 0.200

Averaged

pixel-resolution used = 50 x 50 nm empirical pixel sizes = 100x100 nm

Jan-Otto Hooghoudt Some first results of PhD-project:Inference of within cell protein interactions

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Inference

Possibilities: method of moments: match empirical summary statistics (pixel means, variances, variograms...) with theoretical counterparts (approximated using simulation) implicit likelihood: approximate likelihood function for FRET pixel intensities using simulation Bayesian inference (MCMC): X viewed as missing data.

Jan-Otto Hooghoudt Some first results of PhD-project:Inference of within cell protein interactions

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Implicit likelihood

Defining θ as a multi-dimensional parameter containing; type of model, clustering strenght, absolute concentrations of proteins. we obtain a probability distribution function P(X; θ) from P(X; θ) we generate Y = g(X; θ), with g(·) the MC-simulation, and Y the FRET efficiency In this way we obtain the likelihood function: L(θ) = P(Y ; θ) which can not be obtained explicitly.

Jan-Otto Hooghoudt Some first results of PhD-project:Inference of within cell protein interactions

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1st trial with estimating implicit likelihood Density function estimation: E image-to-image

E Frequency 0.48 0.52 0.56 5 10 15

Hist E for r66hc40ga5

0.40 0.50 0.60 2 4 6 8 10 12 E Density

  • Densfun. Estimate

hc = 30 ri = 40, 50, 60, 70 hc = 35 ri = 46, 58, 70, 81 hc = 40 ri = 53, 66, 80, 93 hc = 45 ri = 60, 75, 90, 105 hc = 50 ri = 66, 82, 100, 116 γ = 5

Jan-Otto Hooghoudt Some first results of PhD-project:Inference of within cell protein interactions

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Likelihood function...

  • θ

L(θ)

2 6 10 14 18 −20 −15 −10 −5 5

Jan-Otto Hooghoudt Some first results of PhD-project:Inference of within cell protein interactions

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...

Questions ... ?

Jan-Otto Hooghoudt Some first results of PhD-project:Inference of within cell protein interactions