Transmembrane protein CD93 diffuses by a continuous time random walk.

Molecular motion within the cell membrane is a poorly-defined process. In this study, we characterized the diffusion of the transmembrane protein CD93. By careful analysis of the dependence of the ensemble-averaged mean squared displacement (EA-MSD, $r^2$) on time $t$ and the ensemble-averaged, time-averaged MSD (EA-TAMSD, $\delta^2$) on lag time $\tau$ and total measurement time $T$, we showed that the motion of CD93 is well-described by a continuous-time random walk (CTRW). CD93 tracks were acquired using single particle tracking. The tracks were classified as confined or free, and the behavior of the MSD analyzed. EA-MSDs of both populations grew non-linearly with $t$, indicative of anomalous diffusion. Their EA-TAMSDs were found to depend on both $\tau$ and $T$, indicating non-ergodicity. Free molecules had $r^2\propto t^\alpha$ and $\delta^2\propto(\tau/T^{1-\alpha})$, with $\alpha\approx0.5$, consistent with a CTRW. Mean maximal excursion analysis supported this result. Confined CD93 had $r^2\propto t^0$ and $\delta^2\propto(\tau/T)^\alpha$, with $\alpha\approx0.3$, consistent with a confined CTRW. CTRWs are described by a series of random jumps interspersed with power-law distributed waiting times, and may arise due to the interactions of CD93 with the endocytic machinery.