documents:100420frapinternal
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- | ====== Notes: FRAP internal course ====== | + | ====== |
- | April 20, 2010 @EMBL | + | April 20, 2010 @EMBL\\ |
Kota Miura\\ | Kota Miura\\ | ||
+ | |||
will be also further added by Sebastian Huet and Christian Tischer\\ | will be also further added by Sebastian Huet and Christian Tischer\\ | ||
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===== Introduction ===== | ===== Introduction ===== | ||
- | in vivo protein kinetics could be analyzed in two ways: measuring particular movement or averaged movement. By tracking labeled single protein molecules, | + | in vivo protein kinetics could be analyzed in two ways: measuring particular movement or averaged movement. By tracking labeled single protein molecules, |
+ | |||
+ | Here, we focus on one of such averaged movement analysis technique: Fluorescence Recovery After Photobleaching (FRAP). We first start the explanation with a simpler case of monitoring averaged movement that does not need to bleach. | ||
- | Here, we focus on one of such averaged movement analysis technique, Fluorescence Recovery After Photobleaching (FRAP). We first start with a simpler case of monitoring averaged movement that does not need to bleach. | ||
- | ~~NOCACHE~~ | ||
===== Fluorescence intensity and Protein Dynamics ===== | ===== Fluorescence intensity and Protein Dynamics ===== | ||
[{{ : | [{{ : | ||
[{{ : | [{{ : | ||
- | Increase in intensity at observed area could be measured to know the net increase in the protein at that region. To calculate biochemical kinetics, we can apply traditional biochemical kinetics. Example case: Kinetics of VSVG protein accumulation to ER exit site. | + | Increase in intensity at observed area could be measured to know the net increase in the protein at that region. To characterize this dynamics, we can apply traditional biochemical kinetics. Example case: Kinetics of VSVG protein accumulation to ER exit site. |
< | < | ||
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* < | * < | ||
- | During the initial phase of binding, when there is almost no VSVG protein bound to ER exit site, we can approximate the initial speed of the density increase at ERES site depends only on binding reaction | + | During the initial phase of binding, when there is almost no VSVG protein bound to ER exit site, we can approximate the initial speed of the density increase at ERES site depends only on binding reaction: < |
< | < | ||
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</ | </ | ||
- | We then are be able to simply calculate the slope of initial increase of intensity, measure the free VSVG intensity and then calculate < | + | Since there are enough free VSVG, we consider that < |
For details, see [[http:// | For details, see [[http:// | ||
+ | |||
===== FRAP Simple Measures ===== | ===== FRAP Simple Measures ===== | ||
[{{ : | [{{ : | ||
- | Unlike the example | + | Unlike the example |
+ | In FRAP, we bleach some population of fluorescence-labeled protein and evaluate the mobility of the protein. Typically we use confocal microscopy and bleach fluorescence of small area of the system by short pulse of strong laser beam and measure | ||
- | From measured temporal changes in the intensity at the bleached Region of Interest (this curve indeed is the Fluorescence Recovery After Photobleaching, | + | From measured temporal changes in the intensity at the bleached Region of Interest (this curve indeed is the Fluorescence Recovery After Photobleaching, |
- | Half Max and Mobile-Immobile fraction\\ | + | * Half Max |
- | Fitting | + | * Mobile-Immobile fraction |
+ | |||
+ | Fitting | ||
===== FRAP Measurements based on Modelling ===== | ===== FRAP Measurements based on Modelling ===== | ||
- | FRAP curve reflects the mobility of proteins. In dilute solution of single protein | + | FRAP curve reflects the mobility of proteins. In dilute solution of with single protein |
* reaction with other proteins | * reaction with other proteins | ||
* geometry of the system, that constrains the mobility | * geometry of the system, that constrains the mobility | ||
* active transport process | * active transport process | ||
- | By modeling how the mobility is (generate some hypothesis how the protein mobility is affected in the system), we can set up equation/s to that should describe | + | By modeling how the mobility is (generate some hypothesis how the protein mobility is affected in the system), we can set up equation/s to hypothesize what is the bases of FRAP curve. |
- | Currently we have more-or-less standardized protocol to analyze FRAP curve. Starting with simple model of diffusion, we test the fit of different curves and proceed to more complex models. See next section for the protocol. | + | Currently we have more-or-less standardized protocol to analyze FRAP curves. Starting with simple model of diffusion, we test the fit of different curves and proceed to more complex models. See next section for the protocol. |
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D=\frac{w^{2}}{\tau_D} | D=\frac{w^{2}}{\tau_D} | ||
</ | </ | ||
+ | |||
+ | For strip-ROI bleaching, empirical formula used by Ellenberg et al. (1997) could be used, and is also possible to use Gaussian curve fitting that **Christian Tischer** developed. For Christian' | ||
=== effective diffusion === | === effective diffusion === | ||
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(almost diffusion) | (almost diffusion) | ||
- | === special cases: | + | === anomalous diffusion === |
==== Reaction Dominant Recovery ==== | ==== Reaction Dominant Recovery ==== | ||
- | Diffusion occurs at the very beginning. Recovery curve is dominated by reaction. | ||
[{{ : | [{{ : | ||
[{{ : | [{{ : | ||
- | ==== Reaction Dominant Recovery with Immobile Binding Partner==== | + | If molecule under study is binding/ |
+ | - **Reaction-dominant recovery** Cases when reaction binding rate (meaning " | ||
+ | - **Reaction-Diffusion Recovery** Other cases would be when durations of diffusion-recovery phase and reaction-recovery phase are with comparable duration. Then recovery curve consists of a combination of fluorescence that came in with diffusion, and also by the binding of fluorescence molecule at the FRAP bleached field (**" | ||
+ | |||
+ | For a simple chemical reaction with singular type of interaction, | ||
+ | < | ||
+ | \frac {df(t)} {dt} = k_{on}[free] - k_{off}[bound] | ||
+ | </ | ||
+ | where | ||
+ | * < | ||
+ | * < | ||
+ | * < | ||
+ | * < | ||
+ | |||
+ | We solve the differential equation | ||
+ | < | ||
+ | f(t)=A(1-e^{- \tau t}) | ||
+ | </ | ||
+ | where | ||
+ | * < | ||
+ | * < | ||
+ | |||
+ | === Reaction Dominant Recovery with Immobile Binding Partner=== | ||
[{{ : | [{{ : | ||
[{{ : | [{{ : | ||
[{{ : | [{{ : | ||
+ | Next we modify above model to consider a situation a bit more frequently we see in cell biology. The protein we are analyzing is either freely diffusing in cytoplasm or bound to an immobile structure inside cell. We FRAP this structure, to know the kinetic constants of the protein interaction with the structure (e.g. microtubule binding protein, structure = microtubule) | ||
+ | < | ||
+ | \frac {df(t)} {dt} = k_{on}[free][s] - k_{off}[bound] | ||
+ | </ | ||
+ | where | ||
+ | * < | ||
+ | * < | ||
+ | * < | ||
+ | * < | ||
+ | * < | ||
+ | |||
+ | Since [s] is immobile and constant during experiment, we define < | ||
+ | < | ||
+ | k*_{on}=k_{on}[s] | ||
+ | </ | ||
+ | in addition, density of free molecule in cytoplasm is almost constant so we assume < | ||
+ | < | ||
+ | \frac {df(t)} {dt} = k*_{on}F - k_{off}[bound] | ||
+ | </ | ||
+ | We get | ||
+ | < | ||
+ | f(t)=1-Ce^{- \tau t} | ||
+ | </ | ||
+ | where | ||
+ | * < | ||
+ | |||
+ | ... note that the shape of recovery curve now only depends on < | ||
+ | |||
==== Diffusion and Reaction combined Recovery ==== | ==== Diffusion and Reaction combined Recovery ==== | ||
[{{ : | [{{ : | ||
+ | < | ||
+ | \frac{\partial [free]}{\partial t} = D_{free} \nabla ^2[free]-k_{on}[free][s]+k_{off}[bound] | ||
+ | </ | ||
+ | < | ||
+ | \frac{\partial [s]}{\partial t} = D_s \nabla ^2[s]-k_{on}[free][s]+k_{off}[bound] | ||
+ | </ | ||
+ | < | ||
+ | \frac{\partial [bound]}{\partial t} = D_{bound} \nabla ^2[bound]+k_{on}[free][s]-k_{off}[bound] | ||
+ | </ | ||
- | ==== Diffusion and Transport combined Recovery ==== | + | Since |
+ | * [s] is constant and immobile | ||
+ | * < | ||
+ | * < | ||
+ | * bound molecules do not diffuse so < | ||
+ | Then we solve only | ||
+ | < | ||
+ | \frac{\partial [free]}{\partial t} = D_{free} \nabla ^2[free]-k*_{on}[free]+k_{off}[bound] | ||
+ | </ | ||
+ | < | ||
+ | \frac{\partial [bound]}{\partial t} = k_{on}[free][s]-k_{off}[bound] | ||
+ | </ | ||
- | Hallen and Endow, 2009 | + | We could solve this either analytically (Sprague et al, 2004) or numerically (Beaudouin et al, 2006). In the latter paper, calculation involves spatial context (on-rate was spatially varied; see also " |
- | ==== Diffusion and Reaction, along with Spatial Context ==== | + | === Sprague Method === |
+ | |||
+ | Analytical solution was made in Laplace transformed equation. | ||
+ | < | ||
+ | \overline{frap(p)} = \frac 1 p - \frac{F_{eq}}{p}\left(1-2K_1(qw)I_1(qw)\right)\times\left(1+\frac{k*_{on}}{p+k_{off}}\right)-\frac C {p+k_{off}} | ||
+ | </ | ||
+ | === Beaudouin Method === | ||
+ | |||
+ | |||
+ | ==== Diffusion and Transport combined Recovery ==== | ||
+ | We did not talk about this issue in the course, but there is another factor that could interfere with recovery curve in vivo: active transport. There is some trial on including this factor by Hallen and Endow (2009). | ||
+ | |||
+ | ==== Diffusion and Reaction, along with Spatial Context, Geometry | ||
[{{ : | [{{ : | ||
- | ===== Tools for FRAP Analysis ===== | + | Since molecular behavior inside cell is constrained largely by structure and geometry of intracellular architecture, |
+ | |||
+ | Physical parameters such as Diffusion coefficient measured by FRAP is affected largely by geometrical constraint. Even if the geometry is rather simple, there are many obstacles in intracellular space which will cause longer time for molecules to reach from one point to the other. In such cases (which probably is frequently the case), estimated diffusion coefficient would calculated to be smaller than that of the "true diffusion coefficient" | ||
+ | |||
+ | Joel Beaudouin who did PhD study in the Ellenberg lab in the EMBL actually encountered such question in his project on nuclear protein study and solved the problem by using initial image frames of the FRAP experiment and let the molecule to diffuse by simulation, then fit the simulation with the experimental FRAP image sequence. Diffusion-reaction model was used and simulation was done (see above) using ODE solver to scan through the parameter space. Excellent idea. For more details, see Beaudouin et al. (2006). We will later add some protocol to this lecture notes on how to fit FRAP image sequence data using ODE solver (with help of Sebastian Huet). Joel's method was actually made into application called " | ||
+ | |||
+ | Other papers we could refer to are Sbalzarini et. al. (2005, 2006). In these papers, authors did two things in parallel: 3D reconstruction of ER membrane structure and FRAP of certain molecule moving around along ER membrane. Using the 3D structure they reconstructed, | ||
+ | |||
+ | ===== Pitfalls in FRAP Analysis ===== | ||
+ | |||
+ | Refer to Mueller et. al.(2008). In their paper, they pointed out | ||
+ | * Shape of the FRAP ROI largely affect estimated value of biochemical rate constants(diffusion is important) | ||
+ | * Problems of fitting double exponential curve | ||
+ | * Initial condition (laser intensity profile) is important | ||
+ | * “blinding” of photomultiplier after the FRAP bleaching | ||
+ | ===== List of Tools for FRAP Analysis ===== | ||
==== Basic ==== | ==== Basic ==== | ||
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* [[http:// | * [[http:// | ||
* Import data output from Zeiss, Leica, Olympus measurements and do FRAP fitting. | * Import data output from Zeiss, Leica, Olympus measurements and do FRAP fitting. | ||
+ | * [[http:// | ||
+ | * Similar to above, but stand alone and also incorporated diffusion-reaction model. | ||
* [[http:// | * [[http:// | ||
* Does measurement and fitting. Sprague et al. (2004) Reaction-Diffusion Full model is implemented. | * Does measurement and fitting. Sprague et al. (2004) Reaction-Diffusion Full model is implemented. | ||
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Requires your own coding, customization\\ | Requires your own coding, customization\\ | ||
- | === Analytical Approach === | + | ==== Analytical Approach |
Sprague et. al. (explained above) is an example case of analytically solving the model for the fitting. | Sprague et. al. (explained above) is an example case of analytically solving the model for the fitting. | ||
+ | |||
==== ODE Simulation ==== | ==== ODE Simulation ==== | ||
[{{ : | [{{ : | ||
Tropical | Tropical | ||
- | | + | |
**General Solvers** | **General Solvers** | ||
- | * Berkley Madonna | + | * [[http:// |
* Joel and Sebastian uses this software for fitting ODE. | * Joel and Sebastian uses this software for fitting ODE. | ||
- | * MATLAB | + | * [[http:// |
==== Particle Simulation ==== | ==== Particle Simulation ==== | ||
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* GridCell | * GridCell | ||
* MCell | * MCell | ||
+ | |||
===== References recommended ===== | ===== References recommended ===== | ||
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* full reaction-diffusion fitting by numerical approach, with spatial context | * full reaction-diffusion fitting by numerical approach, with spatial context | ||
* [[http:// | * [[http:// | ||
+ | * [[http:// | ||
+ | * Pitfalls on FRAP analysis. You will be shocked by how problematic it could be... |
documents/100420frapinternal.txt · Last modified: 2020/11/26 08:05 by kota