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 documents:100420frapinternal [2010/04/23 21:49]kota read again to correct terrible writing documents:100420frapinternal [2020/11/26 08:05] (current)kota [Fluorescence intensity and Protein Dynamics] Both sides previous revision Previous revision 2020/11/26 08:05 kota [Fluorescence intensity and Protein Dynamics] 2016/05/24 15:53 kota 2016/05/24 12:46 external edit2010/05/11 13:12 kota 2010/04/26 09:49 kota 2010/04/26 09:07 christian 2010/04/23 21:49 kota read again to correct terrible writing2010/04/23 09:15 kota 2010/04/23 08:05 kota 2010/04/23 07:24 kota update on pure diffusion2010/04/22 15:38 kota 2010/04/22 15:38 kota 2010/04/22 15:21 kota 2010/04/22 15:14 kota 2010/04/22 15:10 kota 2010/04/22 15:08 kota 2010/04/22 15:01 kota 2010/04/22 14:22 kota 2010/04/22 12:05 kota 2010/04/22 12:00 kota 2010/04/22 11:59 kota 2010/04/22 11:56 kota 2010/04/22 11:46 kota 2010/04/22 11:45 kota 2010/04/22 11:39 kota 2010/04/22 11:36 kota soumpasis2010/04/22 11:24 kota 2010/04/22 11:07 kota 2010/04/22 10:47 kota 2010/04/22 10:42 kota 2010/04/22 08:23 kota 2010/04/22 08:23 kota Next revision Previous revision 2020/11/26 08:05 kota [Fluorescence intensity and Protein Dynamics] 2016/05/24 15:53 kota 2016/05/24 12:46 external edit2010/05/11 13:12 kota 2010/04/26 09:49 kota 2010/04/26 09:07 christian 2010/04/23 21:49 kota read again to correct terrible writing2010/04/23 09:15 kota 2010/04/23 08:05 kota 2010/04/23 07:24 kota update on pure diffusion2010/04/22 15:38 kota 2010/04/22 15:38 kota 2010/04/22 15:21 kota 2010/04/22 15:14 kota 2010/04/22 15:10 kota 2010/04/22 15:08 kota 2010/04/22 15:01 kota 2010/04/22 14:22 kota 2010/04/22 12:05 kota 2010/04/22 12:00 kota 2010/04/22 11:59 kota 2010/04/22 11:56 kota 2010/04/22 11:46 kota 2010/04/22 11:45 kota 2010/04/22 11:39 kota 2010/04/22 11:36 kota soumpasis2010/04/22 11:24 kota 2010/04/22 11:07 kota 2010/04/22 10:47 kota 2010/04/22 10:42 kota 2010/04/22 08:23 kota 2010/04/22 08:23 kota 2010/04/22 07:39 kota 2010/04/22 07:38 kota 2010/04/21 15:42 kota 2010/04/21 15:41 kota added slide for vsvg exit study2010/04/21 15:05 kota 2010/04/21 14:55 kota 2010/04/21 14:53 kota 2010/04/21 14:04 kota 2010/04/21 12:56 kota 2010/04/21 12:08 kota 2010/04/21 12:01 kota 2010/04/21 11:50 kota 2010/04/21 09:32 kota 2010/04/21 08:34 kota 2010/04/21 08:25 kota 2010/04/21 08:23 kota 2010/04/21 08:20 kota 2010/04/21 08:11 kota 2010/04/21 08:09 kota Line 14: Line 14: ===== Fluorescence intensity and Protein Dynamics ===== ===== Fluorescence intensity and Protein Dynamics ===== - [{{ :documents:vsvg_exit.jpg?150|Measurement of VSV-G protein exit dynamics}}] + [{{ :documents:vsvg_exit.jpg?200|Measurement of VSV-G protein exit dynamics}}] - [{{ :documents:firstorderchemicalreaction.jpg?150| First-order Chemical Reaction}}] + [{{ :documents:firstorderchemicalreaction.jpg?200| First-order Chemical Reaction}}] 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. 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}] + $${dI(t)\over dt}=k_{on}[VSVG_{free}]- k_{off}[VSVG_{ERES}]$$ Here, Here, - * k_{on} is the binding rate of VSVG protein to ER exit site + * $k_{on}$ is the binding rate of VSVG protein to ER exit site - * [VSVG_{free}] is the concentration of unbound VSVG protein + * $[VSVG_{free}]$ is the concentration of unbound VSVG protein - * k_{off} is the dissociation rate of VSVG protein from ER exit site + * $k_{off}$ is the dissociation rate of VSVG protein from ER exit site - * [VSVG_{ERES}] is the density of VSVG protein bound to the ER exit site + * $[VSVG_{ERES}]$ 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: k_{off}[VSVG_{ERES}]\simeq0. \\Then + 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 [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 k_{on}. + 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 $k_{on}$. For details, see [[http://www.ncbi.nlm.nih.gov/pubmed/16794576?dopt=Abstract |Runz et al (2006)]]. For details, see [[http://www.ncbi.nlm.nih.gov/pubmed/16794576?dopt=Abstract |Runz et al (2006)]]. Line 66: Line 66: === 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's coefficient //r// or gamma-Q value), one could calculate diffusion coeffecient by using the obtained \tau_D and radius of the circular ROI w.\\ + when above equation could be fitted nicely (evaluated by goodness of fit, such as Pearson's coefficient //r// or gamma-Q value), one could calculate diffusion coeffecient by using the obtained $\tau_D$ and radius of the circular ROI $w$.\\ - + $$D=\frac{w^{2}}{\tau_D} D=\frac{w^{2}}{\tau_D} - +$$ - 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's method, maybe we should wait for him to construct another chapter or page for this... + 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's method, [[:documents:100426FRAPgaussfit]]. === effective diffusion === === effective diffusion === Line 94: Line 94: For a simple chemical reaction with singular type of interaction, we could again think of the reaction model that was already explained above, the first-order chemical reaction modeled as a compartment system (see figure right)\\ For a simple chemical reaction with singular type of interaction, we could again think of the reaction model that was already explained above, the first-order chemical reaction modeled as a compartment system (see figure right)\\ - + $$\frac {df(t)} {dt} = k_{on}[free] - k_{off}[bound] \frac {df(t)} {dt} = k_{on}[free] - k_{off}[bound] - +$$ where where - * k_{on} Binding constant + * $k_{on}$ Binding constant - * k_{off} Dissociation constant + * $k_{off}$ Dissociation constant - * [free] Density of free molecules + * $[free]$ Density of free molecules - * [bound] Density of bound-molecules + * $[bound]$ 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 - * \tau = k_{on} + k_{off} + * $\tau = k_{on} + k_{off}$ - * 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=== Line 116: Line 116: [{{ :documents:reactiondominant05_immobileentity.jpg?150| Modeling fluorescence recovery at immobile binding partner 02}}] [{{ :documents:reactiondominant05_immobileentity.jpg?150| Modeling fluorescence recovery at immobile binding partner 02}}] 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) 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) - + $$\frac {df(t)} {dt} = k_{on}[free][s] - k_{off}[bound] \frac {df(t)} {dt} = k_{on}[free][s] - k_{off}[bound] - +$$ where where - * k_{on} Binding constant + * $k_{on}$ Binding constant - * k_{off} Dissociation constant + * $k_{off}$ Dissociation constant - * [free] Density of free molecules + * $[free]$ Density of free molecules - * [s] Density of immobile binding partner + * $[s]$ Density of immobile binding partner - * [bound] Density of bound-molecules + * $[bound]$ Density of bound-molecules - Since [s] is immobile and constant during experiment, we define k*_{on} as + Since [s] is immobile and constant during experiment, we define $k*_{on}$ as - + $$k*_{on}=k_{on}[s] k*_{on}=k_{on}[s] - +$$ - in addition, density of free molecule in cytoplasm is almost constant so we assume [free] = F and does not change. We then solve + in addition, density of free molecule in cytoplasm is almost constant so we assume $[free] = F$ and does not change. We then solve - + $$\frac {df(t)} {dt} = k*_{on}F - k_{off}[bound] \frac {df(t)} {dt} = k*_{on}F - k_{off}[bound] - +$$ We get We get - + $$f(t)=1-Ce^{- \tau t} f(t)=1-Ce^{- \tau t} - +$$ where where - * \tau = k_{off} + * $\tau = k_{off}$ - ... note that the shape of recovery curve now only depends on k_{off} + ... note that the shape of recovery curve now only depends on $k_{off}$ ==== Diffusion and Reaction combined Recovery ==== ==== Diffusion and Reaction combined Recovery ==== [{{ :documents:reactiondiffusion.jpg?150| Diffusion-Reaction Combined Model}}] [{{ :documents:reactiondiffusion.jpg?150| Diffusion-Reaction Combined Model}}] - + $$\frac{\partial [free]}{\partial t} = D_{free} \nabla ^2[free]-k_{on}[free][s]+k_{off}[bound] \frac{\partial [free]}{\partial t} = D_{free} \nabla ^2[free]-k_{on}[free][s]+k_{off}[bound] - +$$ - + $$\frac{\partial [s]}{\partial t} = D_s \nabla ^2[s]-k_{on}[free][s]+k_{off}[bound] \frac{\partial [s]}{\partial t} = D_s \nabla ^2[s]-k_{on}[free][s]+k_{off}[bound] - +$$ - + $$\frac{\partial [bound]}{\partial t} = D_{bound} \nabla ^2[bound]+k_{on}[free][s]-k_{off}[bound] \frac{\partial [bound]}{\partial t} = D_{bound} \nabla ^2[bound]+k_{on}[free][s]-k_{off}[bound] - +$$ Since Since * [s] is constant and immobile * [s] is constant and immobile - * k*_{on} = k_{on}[s] + * $k*_{on} = k_{on}[s]$ - * \frac{\partial [s]}{\partial t}=0  + * $\frac{\partial [s]}{\partial t}=0$ - * bound molecules do not diffuse so 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 "geometry" section below). 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 "geometry" section below). Line 173: Line 173: 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 === Line 202: Line 202: ===== List of Tools for FRAP Analysis ===== ===== List of Tools for FRAP Analysis ===== - ==== Basic ==== ==== Basic ==== Line 211: Line 210: * [[http://cmci.embl.de/downloads/frap_analysis |FRAP analysis]] (EMBL) * [[http://cmci.embl.de/downloads/frap_analysis |FRAP analysis]] (EMBL) * 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://actinsim.uni.lu/eng/Downloads | FRAP analyzer]] (University of Luxemburg) + * Similar to above, but stand alone and also incorporated diffusion-reaction model. * [[http://mipav.cit.nih.gov/index.php | MIPAV]] * [[http://mipav.cit.nih.gov/index.php | MIPAV]] * 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. Line 217: Line 218: 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:tropical.jpg?150| Image based simulation with ODE solver}}] [{{ :documents:tropical.jpg?150| Image based simulation with ODE solver}}]