Cutaway views showing spherical cytoplasmic domains with the concentrations (proportional to yellow brightness) of soluble-form MKLP1 they contain. This is an alternative to the red profiles for visualizing MTs sponging up MKLP1s. It highlights graphically our model's infrastructure for tracking gradients of soluble proteins, gradients that play a crucial part in the outcomes of confining Rho activation to the future furrow zone only when convection of MKLP1s along MTs overpower diffusive scattering of those MKLP1s. Cytoplasmic domains (plus two centrosomes) nearly fill the cell, and are closely packed, obscuring most MTs. The four panels are from the Fig. 1 simulation, taken at the same times. At t = 15 s (not depicted), before MTs polymerize, all cytoplasmic domains have equal numbers of MKLP1s: all domains are bright yellow. At 115 s in B, the concentration of soluble MKLP1 has fallen near the centrosomes because enough MTs have polymerized near the center of the cell for MKLP1s to bind to. At 340 s in C, most domains contain few MKLP1s because most MKLP1s are bound to MTs. At 390 s in D, just after nocodazole caused depolymerization of dynamic MTs, casting previously bound MKLP1s adrift, the peripheral cytoplasmic domains are transiently bright. At 480 s in E, when nocodazole has been acting for 135 s, the stable MTs have rebound most MKLP1s (note that MKLP1s falling off the tips of the stable MTs transiently elevate soluble MKLP1s near the furrow zone). Always, there is a gradient of soluble MKLP1s, with the lowest concentration (dimmest cytoplasmic domains) nearest the centrosomes. This gradient, strongest in B and D, but always present, drives a diffusive flux of soluble-form MKLP1 from the periphery of the cell toward the centrosomes. When the MKLP1 distribution reaches a dynamic equilibrium, as it has by 340 s, this inward diffusive flux of soluble-form MKLP1s just balances the outward convective MKLP1 flux due to motoring along MTs. Video 4 makes the diffusive inward flux of MKLP1s more apparent as cytoplasmic domains near the cortex brighten transiently (due to MKLP1s falling off MTs into soluble form), then dim as the soluble-form MKLP1 concentration equilibrates via diffusion among adjacent domains. Video 4, from which these panels are taken, shows cytoplasmic domains moving very little. Why? The resultant of forces exchanged between centrosomes and their MTs would act to move (and rotate) centrosomes, and movement of centrosomes would displace cytoplasmic domains. No such movement of centrosomes occurs in these simulations because we fixed centrosome positions to prevent their movements from tilting the furrow zone differently in different simulations. The only other forces acting on cytoplasmic domains (other than collision forces between domains preventing their intruding into each other) are simulated thermal agitation forces, which buffet cytoplasmic domains around slightly, but cause no coherent flow of them. In other applications of this model when, e.g., dynein motors attached to the cell cortex or nuclei pull on MTs, dramatic translation of centrosomes and nuclei does occur; or when the flow of the cell cortex entrains the outermost cytoplasmic domains, the domains make long-range movements and transport with them the soluble factors they contain. The main text explains the meaning of the red, white, and gray lines shown in the figure.