Temporal Analysis of Active and Passive Transport in Living Cells

The cellular cytoskeleton is a fascinating active network, in which Brownian motion is intercepted by distinct phases of active transport. We present a time-resolved statistical analysis dissecting phases of directed motion out of otherwise diffusive motion of tracer particles in living cells. The distribution of active lifetimes is found to decay exponentially with a characteristic time ${\overline{\tau }}_A=0.65\mathrm{s}$. The velocity distribution of active events exhibits several peaks, in agreement with a discrete number of motor proteins acting collectively.

Figure 1

Microfluidic test experiment: (a) bead displacement analysis during a stop-flow random sequence: $R(t)$ (top), and $p_A(t)$ for increasing window sizes (bottom), with applied steps shown in light gray; (b) scheme of the microfluidic setup; (c) PDF of active state durations, as extracted from the test sequence of equally long events ($M=40$).

Figure 2

Living DD cell experiment: (a) transmission image, with the internalized bead 2D path superimposed in white. (b) Bead motion characteristics, from the top to the bottom: displacement $R(t)$ with passive (blue) and active (red) states, standard deviation $\Delta \varphi$ of the angle correlation function, diffusion coefficient $D(t)$ retrieved during the $P$ states, instantaneous velocity (light gray) and algorithm-retrieved velocity during the $A$ states (red), and active motion probability $p_A$. The shaded part of the frame highlights an $A$ state, of duration ${\tau }_A$. (c) Examples of power-law fits on local MSD functions (thin lines, color-coded for time), with trends for $\alpha =1$ (blue dashed line) and 2 (red dash-dotted line).

Figure 3

Analysis of active and passive noise spectra in a living DD cell: PDF of (a) velocity of all events $V_{\mathrm{inst}}$ (gray) and of $A$ states $V_A$ (red), (b) $A$ state velocity (superposition of 5 Gaussians, of means $v_n=n{v}_1$, $v_1=0.225\mu \mathrm{m}·{\mathrm{s}}^{-1}$, $n=1$ to 5), (c) $P$ state diffusion coefficient $D$ (log-normal fit of median $\overline{D}=6.1\times {10}^{-3}\mu {\mathrm{m}}^2{\mathrm{s}}^{-1}$), (d) $A$ state durations ${\tau }_A$ (exponential decay fit with ${\overline{\tau }}_B=0.65\mathrm{s}$), and (e) $P$ state durations ${\tau }_P$ (log-normal fit of median ${\overline{\tau }}_P=0.45\mathrm{s}$). $N$ is the number of data points per histogram. Fits are performed on the cumulative probabilities, shown in insets.

Figure 4

Bead motion analysis: $R(t)$ (top) and $P_A(t)$ (bottom), (a) in a normal cell and (b) in a cell whose microtubule network is disrupted by Benomyl: almost no active transport event is found in this case.