Cytoplasmic Flow and Mixing Due to Deformation of Motile Cells

Abstract

The cytoplasm of a living cell is a dynamic environment through which intracellular components must move and mix. In motile, rapidly deforming cells such as human neutrophils, bulk cytoplasmic flow couples cell deformation to the transport and dispersion of cytoplasmic particles. Using particle-tracking measurements in live neutrophil-like cells, we demonstrate that fluid flow associated with the cell deformation contributes to the motion of small acidic organelles, dominating over diffusion on timescales above a few seconds. We then use a general physical model of particle dispersion in a deforming fluid domain to show that transport of organelle-sized particles between the cell periphery and the bulk can be enhanced by dynamic deformation comparable to that observed in neutrophils. Our results implicate an important mechanism contributing to organelle transport in these motile cells: cytoplasmic flow driven by cell shape deformation.

Figure 1

Lysosome motion in motile HL60 cells is correlated in space and time. (a) Lysosomal particle trajectories for an example cell, tracked over 90 s, shown in the laboratory frame of reference (top) and the cell frame of reference (bottom). (b) Velocity autocorrelation function (relative to cell frame), averaged over time and cell ensemble, indicating persistently correlated particle velocities. (c) Time- and ensemble-averaged MSD of interparticle distances, showing superdiffusive scaling. (d) Time- and ensemble-averaged cross correlation of particle velocities (relative to cell frame), as a function of separation between particles. Dashed line shows $1/r$ scaling expected for a quiescent continuous medium (50). Error bars in (b)–(d) correspond to standard error of the mean, assuming measurements from individual cells to be independent. To see this figure in color, go online.

Figure 2

Simulation of fluid flow driven by deforming boundary of HL60 cells. (a) Phase-contrast image together with lysotracker fluorescence in an example cell, overlayed by cell contour outline (blue). (b) Colored contours show outline of the cell tracked over 96 s, in the laboratory frame of reference (top) and the cell frame of reference (bottom). (c) Snapshots of two-dimensional fluid flow solution using cell contour motion as a boundary condition. Blue arrows show the calculated velocity field. Red arrows indicate time- and space-smoothed velocities of tracked lysosomal particles. (d) Example trajectories for simulated particles undergoing diffusion on top of the calculated fluid flow. To see this figure in color, go online.

Figure 3

Interparticle MSD for particles in a deforming cell. Time and ensemble averages for lysosomes tracked in individual cells are shown as thin curves, with the average for all cells shown in the top thick curve. Central and bottom thick curves show interparticle MSD for simulated particles with and without diffusion, respectively. The thick black line gives expected MSD for diffusive motion alone. The circled point indicates the values used for calculating effective Péclet number $\left({\text{Pe}}_{\text{eff}}\right)$. The starred point indicates the time where motion due to fluid flow begins to dominate over purely diffusive motion for simulated particles. To see this figure in color, go online.

Figure 4

Simplified in silico model for particle motion in a deforming fluid domain. (a) Deformation of a two-dimensional domain, and example trajectory of an embedded particle driven by diffusion and deformation-associated fluid flow. Times are shown in multiples of the deformation period. (b) Snapshots of deforming domain in three dimensions, demonstrating mixing of particles. Particles are colored by initial position. Dimensionless parameters are set to $\hat{D}=0.004,\hat{\gamma }=1.5$. (c) Particle mixing by diffusion only, with no domain deformation, is shown for comparison. To see this figure in color, go online.

Figure 5

Effect of deformation-driven flow on rate of encounter to cell periphery. (a) For two-dimensional simulations with particle diffusivity $\hat{D}=0.004$, the cumulative fraction of particles that arrive at the outer boundary is plotted versus nondimensionalized time. Dashed lines indicate fits to analytical solution for diffusion in a spherical domain (Supporting Materials and Methods, Fitting D_efffor boundary encounter rates), with effective diffusivity ${\hat{D}}_{\text{eff}}$ allowed to vary. The black dashed line gives exact solution with no domain deformation $\left({\hat{D}}_{\text{eff}}=\hat{D}\right)$. The inset shows initial and final particle distributions. (b) Fitted effective diffusivity is plotted as a function of axis rotation rate $\hat{\gamma }$, for different values of particle diffusivity. The ratio $D_{\text{eff}}/D$ indicates the relative extent to which particle encounter is accelerated by domain deformation. Results for each set of parameters are averaged over 10 simulation replicates. (c and d) Equivalent plots for three-dimensional simulations. To see this figure in color, go online.

Figure 6

Effect of deformation-driven flow on rate of encounter to central frozen region. (a) Effective diffusivity obtained by fitting cumulative encounter time distributions to analytical solution for undeformed domain (Supporting Materials and Methods, Fitting D_efffor boundary encounter rates), plotted for two-dimensional simulations, averaged over 10 replicates each. Inset shows start and end particle distributions for an example simulation, with central frozen region shown in purple. (b) Effective diffusivity for three-dimensional deforming domain, fitted to corresponding analytical solution. To see this figure in color, go online.