Influence of organelle geometry on the apparent binding kinetics of peripheral membrane proteins

Information processing in living cells frequently involves an exchange of peripheral membrane proteins between the cytosol and organelle membranes. The typical time scale $\tau$ of these association-dissociation cycles is commonly quantified in vivo via fluorescence recovery after photobleaching (FRAP). Contrary to common assumptions, we show here that $\tau$ values determined by FRAP depend on the size and number of target structures. Hence, FRAP times alone are insufficient to draw conclusions about the proteins' binding kinetics. In contrast, extracting primary molecular association and dissociation rates from FRAP approaches provides a size-independent and therefore robust measure for the proteins' binding kinetics. We support our theoretical considerations with experiments on the small GTPase Arf-1 that transiently associates with Golgi membranes: While Arf-1 recovery times in untreated cells and in cells with disrupted microtubules are significantly different, the molecular kinetic rates are shown to be the same in both cases.

Figure 1

(a) Our analysis focuses on pure association-dissociation events, i.e., diffusion to, from, and within target structures (shown in light green; rest of the cell shown in dark green) is assumed to be much faster than any (un)binding reaction. Therefore, fluorescently tagged proteins can associate with target structures from any cytosolic locus (orange arrows, pointing inwards) and will dissociate to any cytosolic region with equal probability (white arrows, pointing outwards). Sketches in the lower panel highlight the three phases of a FRAP experiment on a region of interest (ROI) that encloses a single target (black dashed line): Steady state before bleaching, perturbed state right after the bleaching, and steady state after equilibration due to particle association and dissociation. Fluorescence recovery takes a typical time $\tau$ that commonly is assumed to encode the particles' binding kinetics. (b) Using standard image analysis tools, volumes and total fluorescences of cytosol and target structures can be quantified from a pre-bleach image (see also main text for details).

Figure 2

Apparent recovery time $\tau$ when fitting Eq. (6) naively with a single-exponential recovery curve [top (bottom): $\tau$ scaled with the minimal (maximal) characteristic rate in Eq. (6)]. For vanishing size of the bleached ROI ($V_{\mathrm{ROI}}\to 0$), $\tau \approx 1/k_{\mathrm{off}}$ is observed. Increasing $V_{\mathrm{ROI}}$ at the expense of nonbleached target membranes, $V_r$, while keeping the total amount of target membranes fixed (here: $V_{\mathrm{ROI}}+V_r=0.2V_{\mathrm{tot}}$) asymptotically leads to $\tau \approx 1/(k_{\mathrm{off}}+k_{\mathrm{on}}^{*})$. Yet, for a wide range in which nonbleached target membranes coexist with a bleached ROI, the apparent recovery time interpolates between these two limiting cases. Deviations from the characteristic rates in Eq. (6) are enhanced when increasing the ratio $k_{\mathrm{on}}/k_{\mathrm{off}}=1,...,10$ (shown as black to light grey lines), i.e., when more and more proteins are bound to target membranes.

Figure 3

Fluorescence images of CHO cells expressing GFP-tagged Arf-1 (a) without treatment and (b) after nocodazole treatment. In the latter case, the Golgi apparatus is fragmented into mini-Golgi stacks [19, 20]. (c) Representative recovery FRAP curves, shown as $1-F_{\mathrm{ROI}}\left(t\right)/F_{\mathrm{ROI}}^{\infty }$, show a single-exponential behavior for an unperturbed Golgi apparatus $(-\mathrm{noc})$ and for a single mini-Golgi stack (+noc). Different characteristic time scales are highlighted by full and dashed lines. (d) The probability distribution of FRAP times, $p\left(\tau \right)$, obtained for Arf-1 on Golgi membranes in untreated (dark blue, $-\mathrm{noc})$ and nocodazole-treated cells (light red, +noc) are significantly different (Student's t-test: $p<{10}^{-6}$). Arrows indicate mean recovery times of the distributions.

Figure 4

Probability distributions of (a) association rates $p\left(k_{\mathrm{on}}\right)$ and (b) dissociation rates $p\left(k_{\mathrm{off}}\right)$ found for Arf-1 in unperturbed cells (dark blue) and nocodazole-treated cells (light red) do not differ significantly. Although the associated recovery times are significantly different [Fig. 3], these primary physicochemical quantities clearly indicate that the presence or absence of intact microtubules does not modulate the binding kinetics of Arf-1 to Golgi membranes.