13. The best are control regions which are located in as close
z position to the bleached region as possible and have a relatively similar intensity, as the side-effects of image acquisition
such as z-drift and photobleaching will be comparable,
enabling more accurate normalization. Therefore, while one
control region might be possible to use for all bleached ROIs,
it might be advisable to select a different appropriate control
region for each bleached ROI in a time series.
14. Although more accurate equations exist for the various hypothetical methods of how protein exchanges and the signal
recovers, e.g., diffusion only, diffusion-coupled, diffusionuncoupled [23], we find that a general fit by using a sum of
exponential components provides a valid linearization of a set
of nonlinear first-order differential equations according to Lyapunov’s first method [42, 43].
15. If the recovery is fit by a single exponential model, and appropriate tests are performed to determine whether the recovery
occurs via diffusion or reaction-dominant mechanisms, it is
possible to obtain additional information about protein
dynamics. In the case of a pure-diffusion dominant recovery,
the exact solution exists for a circular bleach area in form:
f t
ð Þ ¼ e
À T D= 2t I 0 T D= 2t
ð
ÞþI 1 T D= 2t
ð
Þ
ð
Þ , where I 0 and I 1 are modified Bessel functions of the first kind. In this case, T D ¼ w
2
= D f ,
where w is the radius of the circular beam, and D f is the
diffusion coefficient [20, 21]. If the recovery is reaction dominant, the following solution describes the recovery: f t
ð Þ ¼
1 À C eq e
Àk off t , where C eq is a constant which depends only on
the dissociation (off-rate, k off ) and association (pseudo-onrate, k on ) of the reaction [20, 44]. We would like to highlight
that in this case the rate of the reaction depends only on the
off-rate and does not reflect the on-rate, which can be a common misapprehension when interpreting the results of FRAP
experiments [4].
References
1. Erami Z, Timpson P, Yao W, Zaidel-Bar R,
Anderson KI (2015) There are four dynamically and functionally distinct populations of
E-cadherin in cell junctions. Biol Open
4:1481–1489
2. Foote HP, Sumigray KD, Lechler T (2013)
FRAP analysis reveals stabilization of adhesion
structures in the epidermis compared to
cultured keratinocytes. PLoS One 8:e71491
3. Indra I, Choi J, Chen C-S, Troyanovsky RB,
Shapiro L, Honig B, Troyanovsky SM (2018)
Spatial and temporal organization of cadherin
in punctate adherens junctions. Proc Natl Acad
Sci U S A 115:E4406–E4415
4. Wehrle-Haller B (2007) Analysis of integrin
dynamics by fluorescence recovery after photobleaching. In: Coutts AS (ed) Adhesion protein
protocols. Humana Press, Totowa, NJ, pp
173–201
5. Cluzel C, Saltel F, Lussi J, Paulhe F, Imhof BA,
Wehrle-Haller B (2005) The mechanisms and
dynamics of αvβ3 integrin clustering in living
cells. J Cell Biol 171:383–392
6. Changede R, Sheetz M (2017) Integrin and
cadherin clusters: a robust way to organize
adhesions for cell mechanics. Bioessays 39:
e201600123
FRAP to Study the Dynamics of Proteins in vivo
157
z position to the bleached region as possible and have a relatively similar intensity, as the side-effects of image acquisition
such as z-drift and photobleaching will be comparable,
enabling more accurate normalization. Therefore, while one
control region might be possible to use for all bleached ROIs,
it might be advisable to select a different appropriate control
region for each bleached ROI in a time series.
14. Although more accurate equations exist for the various hypothetical methods of how protein exchanges and the signal
recovers, e.g., diffusion only, diffusion-coupled, diffusionuncoupled [23], we find that a general fit by using a sum of
exponential components provides a valid linearization of a set
of nonlinear first-order differential equations according to Lyapunov’s first method [42, 43].
15. If the recovery is fit by a single exponential model, and appropriate tests are performed to determine whether the recovery
occurs via diffusion or reaction-dominant mechanisms, it is
possible to obtain additional information about protein
dynamics. In the case of a pure-diffusion dominant recovery,
the exact solution exists for a circular bleach area in form:
f t
ð Þ ¼ e
À T D= 2t I 0 T D= 2t
ð
ÞþI 1 T D= 2t
ð
Þ
ð
Þ , where I 0 and I 1 are modified Bessel functions of the first kind. In this case, T D ¼ w
2
= D f ,
where w is the radius of the circular beam, and D f is the
diffusion coefficient [20, 21]. If the recovery is reaction dominant, the following solution describes the recovery: f t
ð Þ ¼
1 À C eq e
Àk off t , where C eq is a constant which depends only on
the dissociation (off-rate, k off ) and association (pseudo-onrate, k on ) of the reaction [20, 44]. We would like to highlight
that in this case the rate of the reaction depends only on the
off-rate and does not reflect the on-rate, which can be a common misapprehension when interpreting the results of FRAP
experiments [4].
References
1. Erami Z, Timpson P, Yao W, Zaidel-Bar R,
Anderson KI (2015) There are four dynamically and functionally distinct populations of
E-cadherin in cell junctions. Biol Open
4:1481–1489
2. Foote HP, Sumigray KD, Lechler T (2013)
FRAP analysis reveals stabilization of adhesion
structures in the epidermis compared to
cultured keratinocytes. PLoS One 8:e71491
3. Indra I, Choi J, Chen C-S, Troyanovsky RB,
Shapiro L, Honig B, Troyanovsky SM (2018)
Spatial and temporal organization of cadherin
in punctate adherens junctions. Proc Natl Acad
Sci U S A 115:E4406–E4415
4. Wehrle-Haller B (2007) Analysis of integrin
dynamics by fluorescence recovery after photobleaching. In: Coutts AS (ed) Adhesion protein
protocols. Humana Press, Totowa, NJ, pp
173–201
5. Cluzel C, Saltel F, Lussi J, Paulhe F, Imhof BA,
Wehrle-Haller B (2005) The mechanisms and
dynamics of αvβ3 integrin clustering in living
cells. J Cell Biol 171:383–392
6. Changede R, Sheetz M (2017) Integrin and
cadherin clusters: a robust way to organize
adhesions for cell mechanics. Bioessays 39:
e201600123
FRAP to Study the Dynamics of Proteins in vivo
157