First-passage-probability analysis of active transport in live cells

The first-passage-probability can be used as an unbiased method for determining the phases of motion of individual organelles within live cells. Using high speed microscopy, we observe individual lipid droplet tracks and analyze the motor protein driven motion. At short passage lengths ($<$${10}^{-2}\mu$m), a log-normal distribution in the first-passage-probability as a function of time is observed, which switches to a Gaussian distribution at longer passages due to the running motion of the motor proteins. The mean first-passage times ($\langle t_{\mathrm{FPT}}\rangle$) as a function of the passage length ($L$), averaged over a number of runs for a single lipid droplet, follow a power law distribution $\langle t_{\mathrm{FPT}}\rangle \sim L^{\alpha }$, $\alpha >2$, at short times due to a passive subdiffusive process. This changes to another power law at long times where $1<\alpha <2$, corresponding to sub-ballistic superdiffusive motion, an active process. Subdiffusive passive mean square displacements are observed as a function of time, $〈r^2〉\sim t^{\beta }$, where $0<\beta <1$ at short times again crossing over to an active sub-ballistic superdiffusive result $1<\beta <2$ at longer times. Consecutive runs of the lipid droplets add additional independent Gaussian peaks to a cumulative first-passage-probability distribution indicating that the speeds of sequential phases of motion are independent and biochemically well regulated. As a result we propose a model for motor driven lipid droplets that exhibits a sequential run behavior with occasional pauses.

Figure 1

First-passage-probability of a lipid droplet in an MRC-5 cell (darker colors are short passage lengths and lighter colors are longer passages). (a) Multiple distinct peaks, labeled A–F, are detected in the FPP plot for the complete track. (b) The position in time of a lipid droplet along a smoothed contour (the microtubule). The inset shows the first frame of the cell image with the track superimposed (arrow indicates direction). The particle undergoes several distinct epochs of movement, labeled A–F, progressing different distances at different rates. The FPP of section A alone is shown in the inset in (a). See Supplemental Material, Appendix A [23], for additional examples. Each run section has a well defined Gaussian distribution. Section D does not generate a specific peak in (a), as it is a paused section of motion.

Figure 2

(a) First-passage-probability for a passage length of 0.01 $\mu$m for section A of the track. This distribution of inverse speeds can be described by a log normal distribution. (b) First-passage-probability for a passage length of 0.1 $\mu$m for section A of the track. This distribution of inverse velocities can be described by a Gaussian curve.

Figure 3

(a) The mean square displacement of the complete track as a function of time. The motion is subdiffusive at short time scales ($<$0.01 s) and superdiffusive at longer time scales ($>$0.01 s). (b) The mean first-passage time of the track as a function of passage length. There is again a switch between two power law behaviors.