documents:100420frapinternal
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documents:100420frapinternal [2010/04/23 08:05] – kota | documents:100420frapinternal [2020/11/26 08:05] (current) – [Fluorescence intensity and Protein Dynamics] kota | ||
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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 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 the explanation |
===== 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. |
- | < | + | $${dI(t)\over dt}=k_{on}[VSVG_{free}]- k_{off}[VSVG_{ERES}]$$ |
Here, | Here, | ||
- | * <jsm>k_{on}</ | + | * $k_{on}$ is the binding rate of VSVG protein to ER exit site |
- | * <jsm>[VSVG_{free}]</ | + | * $[VSVG_{free}]$ is the concentration of unbound VSVG protein |
- | * <jsm>k_{off}</ | + | * $k_{off}$ is the dissociation rate of VSVG protein from ER exit site |
- | * <jsm>[VSVG_{ERES}]</ | + | * $[VSVG_{ERES}]$ is the density of VSVG protein bound to the ER exit site |
- | 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: $k_{off}[VSVG_{ERES}]\simeq0$. \\Then |
- | < | + | $$ |
{dI(t)\over{dt}}=k_{on}[VSVG_{free}] | {dI(t)\over{dt}}=k_{on}[VSVG_{free}] | ||
- | </ | + | $$ |
- | Since there are enough free VSVG, we consider that <jsm>[VSVG_{free}]</ | + | Since there are enough free VSVG, we consider that $[VSVG_{free}]$ is constant, we are able to simply calculate the slope of initial increase of intensity, measure the free VSVG intensity and then calculate |
For details, see [[http:// | For details, see [[http:// | ||
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===== 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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=== pure diffusion === | === pure diffusion === | ||
Theoretical curve of the diffusion mediated fluorescence recovery was proposed by Soumpasis (1984) and has been widely used. \\ | Theoretical curve of the diffusion mediated fluorescence recovery was proposed by Soumpasis (1984) and has been widely used. \\ | ||
- | < | + | $$ |
f(t)=e^{- \frac{\tau_D}{2t}}\left(I_{0}(\frac{\tau_D}{2t})+I_{1}(\frac{\tau_D}{2t})\right) | f(t)=e^{- \frac{\tau_D}{2t}}\left(I_{0}(\frac{\tau_D}{2t})+I_{1}(\frac{\tau_D}{2t})\right) | ||
- | </ | + | $$ |
This theoretical equation assumes: | This theoretical equation assumes: | ||
* 2D | * 2D | ||
* circular (cylindrical) bleaching | * circular (cylindrical) bleaching | ||
- | when above equation could be fitted nicely (evaluated by goodness of fit, such as Pearson' | + | when above equation could be fitted nicely (evaluated by goodness of fit, such as Pearson' |
- | < | + | $$ |
D=\frac{w^{2}}{\tau_D} | D=\frac{w^{2}}{\tau_D} | ||
- | </ | + | $$ |
- | 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' | + | 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 ==== | ||
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[{{ : | [{{ : | ||
- | If molecule under study is binding/ | + | If molecule under study is binding/ |
- | - **Reaction-dominant recovery** Cases when reaction binding rate (meaning " | + | - **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 comparable. 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 (**" | + | - **Reaction-Diffusion Recovery** Other cases would be when durations of diffusion-recovery phase and reaction-recovery phase are with comparable |
- | For a simple chemical reaction with singular type of interaction, | + | For a simple chemical reaction with singular type of interaction, |
- | < | + | $$ |
\frac {df(t)} {dt} = k_{on}[free] - k_{off}[bound] | \frac {df(t)} {dt} = k_{on}[free] - k_{off}[bound] | ||
- | </ | + | $$ |
where | where | ||
- | * <jsm>k_{on}</ | + | * $k_{on}$ Binding constant |
- | * <jsm>k_{off}</ | + | * $k_{off}$ Dissociation constant |
- | * <jsm>[free]</ | + | * $[free]$ Density of free molecules |
- | * <jsm>[bound]</ | + | * $[bound]$ Density of bound-molecules |
We solve the differential equation | We solve the differential equation | ||
- | < | + | $$ |
f(t)=A(1-e^{- \tau t}) | f(t)=A(1-e^{- \tau t}) | ||
- | </ | + | $$ |
where | where | ||
- | * <jsm>\tau = k_{on} + k_{off}</ | + | * $\tau = k_{on} + k_{off}$ |
- | * <jsm>A = \frac {k_{on}}{k_{on} + k_{off}}</ | + | * $A = \frac {k_{on}}{k_{on} + k_{off}}$ |
=== Reaction Dominant Recovery with Immobile Binding Partner=== | === Reaction Dominant Recovery with Immobile Binding Partner=== | ||
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[{{ : | [{{ : | ||
[{{ : | [{{ : | ||
- | 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 | + | 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 |
- | < | + | $$ |
\frac {df(t)} {dt} = k_{on}[free][s] - k_{off}[bound] | \frac {df(t)} {dt} = k_{on}[free][s] - k_{off}[bound] | ||
- | </ | + | $$ |
where | where | ||
- | * <jsm>k_{on}</ | + | * $k_{on}$ Binding constant |
- | * <jsm>k_{off}</ | + | * $k_{off}$ Dissociation constant |
- | * <jsm>[free]</ | + | * $[free]$ Density of free molecules |
- | * <jsm>[s]</ | + | * $[s]$ Density of immobile binding partner |
- | * <jsm>[bound]</ | + | * $[bound]$ Density of bound-molecules |
- | Since [s] is immobile and constant during experiment, we define | + | Since [s] is immobile and constant during experiment, we define |
- | < | + | $$ |
k*_{on}=k_{on}[s] | k*_{on}=k_{on}[s] | ||
- | </ | + | $$ |
- | in addition, density of free molecule in cytoplasm is almost constant so we assume | + | in addition, density of free molecule in cytoplasm is almost constant so we assume |
- | < | + | $$ |
\frac {df(t)} {dt} = k*_{on}F - k_{off}[bound] | \frac {df(t)} {dt} = k*_{on}F - k_{off}[bound] | ||
- | </ | + | $$ |
We get | We get | ||
- | < | + | $$ |
f(t)=1-Ce^{- \tau t} | f(t)=1-Ce^{- \tau t} | ||
- | </ | + | $$ |
where | where | ||
- | * <jsm>\tau = k_{off}</ | + | * $\tau = k_{off}$ |
- | ... note that the recovery now only depends on <jsm>k_{off}</ | + | ... note that the shape of recovery |
==== Diffusion and Reaction combined Recovery ==== | ==== Diffusion and Reaction combined Recovery ==== | ||
[{{ : | [{{ : | ||
- | < | + | $$ |
\frac{\partial [free]}{\partial t} = D_{free} \nabla ^2[free]-k_{on}[free][s]+k_{off}[bound] | \frac{\partial [free]}{\partial t} = D_{free} \nabla ^2[free]-k_{on}[free][s]+k_{off}[bound] | ||
- | </ | + | $$ |
- | < | + | $$ |
\frac{\partial [s]}{\partial t} = D_s \nabla ^2[s]-k_{on}[free][s]+k_{off}[bound] | \frac{\partial [s]}{\partial t} = D_s \nabla ^2[s]-k_{on}[free][s]+k_{off}[bound] | ||
- | </ | + | $$ |
- | < | + | $$ |
\frac{\partial [bound]}{\partial t} = D_{bound} \nabla ^2[bound]+k_{on}[free][s]-k_{off}[bound] | \frac{\partial [bound]}{\partial t} = D_{bound} \nabla ^2[bound]+k_{on}[free][s]-k_{off}[bound] | ||
- | </ | + | $$ |
Since | Since | ||
* [s] is constant and immobile | * [s] is constant and immobile | ||
- | * <jsm>k*_{on} = k_{on}[s]</ | + | * $k*_{on} = k_{on}[s]$ |
- | * <jsm>\frac{\partial [s]}{\partial t}=0 </ | + | * $\frac{\partial [s]}{\partial t}=0 $ |
- | * bound molecules do not diffuse so <jsm>D_{bound}=0</ | + | * bound molecules do not diffuse so $D_{bound}=0$ |
Then we solve only | Then we solve only | ||
- | < | + | $$ |
\frac{\partial [free]}{\partial t} = D_{free} \nabla ^2[free]-k*_{on}[free]+k_{off}[bound] | \frac{\partial [free]}{\partial t} = D_{free} \nabla ^2[free]-k*_{on}[free]+k_{off}[bound] | ||
- | </ | + | $$ |
- | < | + | $$ |
\frac{\partial [bound]}{\partial t} = k_{on}[free][s]-k_{off}[bound] | \frac{\partial [bound]}{\partial t} = k_{on}[free][s]-k_{off}[bound] | ||
- | </ | + | $$ |
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 " | 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 " | ||
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Analytical solution was made in Laplace transformed equation. | Analytical solution was made in Laplace transformed equation. | ||
- | < | + | $$ |
\overline{frap(p)} = \frac 1 p - \frac{F_{eq}}{p}\left(1-2K_1(qw)I_1(qw)\right)\times\left(1+\frac{k*_{on}}{p+k_{off}}\right)-\frac C {p+k_{off}} | \overline{frap(p)} = \frac 1 p - \frac{F_{eq}}{p}\left(1-2K_1(qw)I_1(qw)\right)\times\left(1+\frac{k*_{on}}{p+k_{off}}\right)-\frac C {p+k_{off}} | ||
- | </ | + | $$ |
=== Beaudouin Method === | === Beaudouin Method === | ||
==== Diffusion and Transport combined Recovery ==== | ==== 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 | + | 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 |
==== Diffusion and Reaction, along with Spatial Context, Geometry ==== | ==== Diffusion and Reaction, along with Spatial Context, Geometry ==== | ||
[{{ : | [{{ : | ||
- | Since molecular behavior inside cell is constrained largely by structure and geometry of intracellular architecture, | + | Since molecular behavior inside cell is constrained largely by structure and geometry of intracellular architecture, |
- | Physical parameters such as Diffusion coefficient measured | + | Physical parameters such as Diffusion coefficient measured |
- | Joel Beaudouin who did PhD study at Ellenberg lab in 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, | + | 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, |
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, | 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, | ||
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===== List of Tools for FRAP Analysis ===== | ===== 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 ==== | ||
[{{ : | [{{ : |
documents/100420frapinternal.txt · Last modified: 2020/11/26 08:05 by kota