Odell GM , Foe VE .

P50 GM066050 NIGMS NIH HHS , 1 P50 GM066050 NIGMS NIH HHS

	Figure 1. Frames from Video 1 showing cortical MKLP1 distributions caused by stable and dynamic MTs. The 80-μm spherical cell has red centrosomes. MT segment color encodes attached Clip170 concentration so recently polymerized segments are green and 25-s-old ones are orange (stable MTs become entirely orange). White dots show 33,000 MKLP1s; each moves at 0.2 μm/s along, has a binding half-life of 20 s to MTs, and stalls at MT tips. Soluble MKLP1s have a molecular diffusivity of 0.5 μm2/s. The main text explains how the gray, white, and red radial density plots surrounding the spherical cell (and their straightened out versions in F) show concentrations of MKLP1s adjacent to the cortex (gray and white) and in soluble form throughout the cell (red). (A–E) Selected time points (15, 115, 340, 390, and 480 simulated seconds from the start of anaphase) used in all figures. Simulations start at t = 0, with no MTs and all MKLP1s in soluble form distributed among randomly located, thus possibly overlapping, cytoplasmic domains. In A, at 15 s, cytoplasmic domains have moved so none intrudes into others; diffusion has equilibrated the concentration of soluble MKLP1 to spatial uniformity at the highest concentration ever reached (because there are as yet few MTs to bind to). By 115 s in B, enough MTs have formed to bind ∼50% of the MKLP1s, and the first stable MTs have reached the cortex; slight elevations of the white radial density plot at the equator occur where they touch the cortex. By 340 s in C, the asters and the cortical MKLP1 pattern have reached a dynamic equilibrium, with most MKLP1s bound to MTs (the red curve is lowest). The fall of the red profile, in A to B to C as the amount of polymerized tubulin increases, shows the effectiveness of MTs at sponging up most MKLP1s. The pronounced MKLP1 accumulation near the cortex at the equatorial spindle midplane at 340 s arises because only the stable MTs (aimed at the equator) remain in place long enough for MKLP1s to reach the cortex along them. We model nocodazole treatment by reducing the MT polymerization on-rate by a factor of 10; this commences at 345 s, and, in D at 390 s, most of the dynamically unstable MTs have depolymerized, leaving only stable MTs. The red radial density plot rises sharply as all MKLP1s previously bound to just-depolymerized MTs are cast adrift into soluble form. The amplitude of the equatorial accumulation of MKLP1s begins to rise because each stable MT now binds (and delivers to the cortex) more MKLP1s than formerly, when it had to compete with the 10-fold more numerous dynamically unstable MTs. At 480 s in E, just as simulated nocodazole washout allows MTs to start regrowing, more previously diffusing MKLP1s have bound to the remaining stable MTs and have motored to the equator, further boosting the equatorial accumulation of MKLP1s. Foe and von Dassow (2008) saw the same gradual increase in the activated myosin signal at the equator after nocodazole treatment. Painting a swarm of MKLP1s stalled at the tip of an MT in the single pixel the tip occupies would not show how many are in the swarm, so we took artistic license to draw all the MKLP1s stalled at the tip of an MT as if spread out along the terminal μm of the MT. The tiny cell above the 10 μm scale bar is the cell from the Fig. 3 simulation, drawn at the same magnification as the large cells here.
	Figure 2. MKLP1 properties (and the presence/absence of stable MTs) determine the amplitude of MKLP1 concentration in the furrow zone. Each of the eight panels, comprising frames from Video 2 (available at http://www.jcb.org/cgi/content/full/jcb.200807129/DC1), shows radial density plots of MKLP1s (in the same style, at the same time points, as in Fig. 1 F) taken from eight different simulations in 80-μm-diameter cells using different motor and/or MT properties summarized at the bottom of each panel. In all simulations except the one shown in G, stable MTs were present. In all simulations except the one shown in H, MKLP1s stall at MT tips. The main text explains the point each simulation makes and explains how the gray, white, and red radial density plots show the concentrations of MKLP1s near the cortex (gray and white) and in soluble form throughout the cell (red). See the online supplemental videos for the full simulations this figure summarizes.
	Figure 3. Frames from Video 3 showing that hypotheses H1–H3 work robustly across a wide range of cell sizes to explain furrow positioning. In this case, a small (8-μm-diameter) cell that 10 division rounds would produce from the 80-μm zygote simulated in Figs. 1 and 2 is shown. As in Fig. 1, MKLP1s stall at MT tips, move at 0.2 μm/s, and bind MTs with a 20-s half-life. The resulting 4-μm mean run length is the entire radius of this cell. In Fig. 1, an MKLP1 falls off, then rebinds an MT 10 times to move from centrosome to cortex. As explained in the text, the small cell has higher tubulin and MKLP1 concentrations. To visualize all MKLP1s stalled and clustered at MT tips, we took artistic license to draw them as if spread out along the same terminal 1 μm of the MT we used in Fig. 1. The 1-μm artwork spread is a compromise, too long in comparison to the 4-μm radius of cells here but barely long enough to show up in Fig. 1. Radial density plots show MKLP1 concentrations qualitatively, as in Fig. 1, but with different scaling because this small cell has a much higher MKLP1 concentration. Note that, at t = 340 s, the signal/noise ratio of the MKLP1 concentration peak at the equator to the levels outside the furrow zone is smaller than for the 80-μm-diameter cell in Fig. 1, but we judge that this furrow specification mechanism still works in small cells. The main text explains the meaning of the red, white, and gray lines shown in the figure.
	Figure 4. 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 (available at http://www.jcb.org/cgi/content/full/jcb.200807129/DC1) 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.

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