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
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
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
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
Theory Fluorescence Resonance Energy Transfer Electrodynamic phenomenon: Donor molecule gets excited by laser light and de-excites by: -photon emission (rate k rad ) -FRET (rate k FRET ) Where the following relationship exists: � 6 � R 0 k FRET = k rad r - r = distance between donor and acceptor - R 0 = Forster distance, the distance r for which 50% of de-excitations due to FRET and 50% due to donor-emission. r D A Jan-Otto Hooghoudt Some first results of PhD-project:Inference of within cell protein interactions
FRET efficiency The main parameter describing FRET is the FRET efficiency: E = rate of de-excitations due to FRET k FRET = de-excitation rate k rad + k FRET � 6 R 6 � R 0 0 k FRET = k rad → E ( r ) = 0 + r 6 . R 6 r Efficiency Highly sensitive to the 1.0 distance due to r − 6 : 6 ( R 0 6 + r 6 ) E = R 0 0.8 R 0 = 10 FRET 0.6 r < 2 R 0 E(r) D A 0.4 0.2 No-FRET r > 2 R 0 0.0 D A 0 10 20 30 40 50 distance r / [nm] Jan-Otto Hooghoudt Some first results of PhD-project:Inference of within cell protein interactions
FRET-efficiency multiple acceptors When multiple acceptors surround a donor, total rate of de-excitations due to FRET becomes: n � 6 � R 0 � k tot FRET = k rad r i i =1 And total rate of de-excitation: n � 6 � R 0 � k tot = k rad (1 + ) r i i =1 So probability of de-excitation by FRET to acceptor A i and due to emission are given by: � 6 � R 0 1 r i P A i FRET = ; P rad = � 6 � 6 � � (1 + � n R 0 (1 + � n R 0 ) ) i =1 i =1 r i r i For simulation compute transfer probability-matrix defining all probabilities of de-exitation of D j to A i or due to emission. Jan-Otto Hooghoudt Some first results of PhD-project:Inference of within cell protein interactions
Modeling the FRET efficiency Calculate dis- Assign Assign tances and trans- fluorophore positions fluorophore types fer probabilities Generate schedule of times and targets of each excitation Play next excitation Flow diagram of MC-simulation to model the FRET efficiency for: no Is target donor available? yes different types of proteins (monomer, dimer, etc) Make list of avail- Calculate rate Calculate time at able acceptors of energy release which donor de-excites absolute concentrations of the proteins Random selec- tion of relaxation Diagram by Corry et. al. (2005, FRET Fluorescence Biophys. J.) fluo=fluo+1 fret=fret+1 All exci- no tations played? Data output: E=fret/(fret+fluo) Jan-Otto Hooghoudt Some first results of PhD-project:Inference of within cell protein interactions
A FRET image 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 Figure: Wallrabe et.al 2003 Jan-Otto Hooghoudt Some first results of PhD-project:Inference of within cell protein interactions
Generating the point patterns (in R) For a Strauss hardcore point process X , the (unnormalized) density is given by: f ( x ) ∝ β n ( x ) γ s R ( x ) 0 s hc ( x ) (1) - n ( x ) number of points in pattern x - s R ( x ) number of pair-of-points within distance R in pattern x . - s hc ( x )number of pair-of-points within distance hc in pattern x . � s R ( x ) = 1 [ � u − v � ≤ R ] (2) { u , v }⊆ x 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
Generating the point patterns (in R) Further we have used the Multi-Strauss hardcore process: f ( x ) ∝ β n ( x ) γ s Raa ( x ) 0 s Raa ( x ) 0 s Rdd ( x ) 0 s Rda ( x ) γ s Rdd ( x ) γ s Rda ( x ) (3) aa dd da 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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