Figure 1.
Extracting advection and diffusion parameters from single particle trajectories. (A) Schematic for decomposing trajectories into advective and diffusive components. Particle displacements are projected onto axes x and y defined as parallel and perpendicular to the local flow vector, respectively. In principle, these should take the form of a Gaussian. Drift is defined by the shift of the mean population displacement (<Δx>, <Δy>), along the relevant axis, where we expect <Δy> ∼ 0. Advection velocity (υx) is then given by mean displacement <Δx>, divided by the time lag, τ, with the cortex coupling coefficient given by ratio of advection velocity (υx) to local flow velocity cc=υx/ν.(B) Schematic for extraction of particle motion (PAR-3 clusters shown) and local flow field. Two-channel image series were captured for cortical NMY-2 and the molecule of interest using a HILO imaging regime. The resulting image series were subject to either a Python-based particle tracking scheme or particle image velocimetry (PIVLab, Matlab). Particle displacements for a given τ were then projected onto the relevant x- and y-axes defined by the local flow vector. Note, positive movement on the x-axis generally reflects motion toward the anterior. (C) Distribution of displacements in x and y for simulations of varying D for τ = 0.5 s. (D) Reliability of detection of drift as a function of D. Significance of difference between <Δx> and <Δy> calculated using 1,000 random displacements (τ = 0.5 s). Results shown for 20 independent simulations. Student’s t test, unpaired, two-tailed. (E) Mean cc ∼ 1.0 is obtained for all D, though error increases with D. Each point indicates cc measured from 1,000 random displacements from a single simulated dataset in D, with mean indicated. (F and G) Example of the distribution of displacements for NMY-2 (F) and HMR-1 (G) for single embryos (τ = 5 s, n = 1,000 randomly selected steps). In both cases, there is a characteristic drift component along the flow axis (x). Displacements parallel (red) and orthogonal (blue) to the local flow axis are shown. (H and I) Fit values for advection velocity for displacements parallel (υx, red) and orthogonal (υy, blue) to the flow axis (H) and coupling coefficients (I) shown for NMY-2 and HMR-1, as well as beads immobilized to the exterior of the eggshell. Lines in H connect paired data points from single embryos. Mean values for individual embryos shown in H and I, along with mean of all embryos in I.

Extracting advection and diffusion parameters from single particle trajectories. (A) Schematic for decomposing trajectories into advective and diffusive components. Particle displacements are projected onto axes x and y defined as parallel and perpendicular to the local flow vector, respectively. In principle, these should take the form of a Gaussian. Drift is defined by the shift of the mean population displacement (<Δx>, <Δy>), along the relevant axis, where we expect <Δy> ∼ 0. Advection velocity (υx) is then given by mean displacement <Δx>, divided by the time lag, τ, with the cortex coupling coefficient given by ratio of advection velocity (υx) to local flow velocity cc=υx/ν.(B) Schematic for extraction of particle motion (PAR-3 clusters shown) and local flow field. Two-channel image series were captured for cortical NMY-2 and the molecule of interest using a HILO imaging regime. The resulting image series were subject to either a Python-based particle tracking scheme or particle image velocimetry (PIVLab, Matlab). Particle displacements for a given τ were then projected onto the relevant x- and y-axes defined by the local flow vector. Note, positive movement on the x-axis generally reflects motion toward the anterior. (C) Distribution of displacements in x and y for simulations of varying D for τ = 0.5 s. (D) Reliability of detection of drift as a function of D. Significance of difference between <Δx> and <Δy> calculated using 1,000 random displacements (τ = 0.5 s). Results shown for 20 independent simulations. Student’s t test, unpaired, two-tailed. (E) Mean cc ∼ 1.0 is obtained for all D, though error increases with D. Each point indicates cc measured from 1,000 random displacements from a single simulated dataset in D, with mean indicated. (F and G) Example of the distribution of displacements for NMY-2 (F) and HMR-1 (G) for single embryos (τ = 5 s, n = 1,000 randomly selected steps). In both cases, there is a characteristic drift component along the flow axis (x). Displacements parallel (red) and orthogonal (blue) to the local flow axis are shown. (H and I) Fit values for advection velocity for displacements parallel (υx, red) and orthogonal (υy, blue) to the flow axis (H) and coupling coefficients (I) shown for NMY-2 and HMR-1, as well as beads immobilized to the exterior of the eggshell. Lines in H connect paired data points from single embryos. Mean values for individual embryos shown in H and I, along with mean of all embryos in I.

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