Activator-inhibitor coupling between Rho signalling and actin assembly makes the cell cortex an excitable medium

Abstract

Animal cell cytokinesis results from patterned activation of the small GTPase Rho, which directs assembly of actomyosin in the equatorial cortex. Cytokinesis is restricted to a portion of the cell cycle following anaphase onset in which the cortex is responsive to signals from the spindle. We show that shortly after anaphase onset oocytes and embryonic cells of frogs and echinoderms exhibit cortical waves of Rho activity and F-actin polymerization. The waves are modulated by cyclin-dependent kinase 1 (Cdk1) activity and require the Rho GEF (guanine nucleotide exchange factor), Ect2. Surprisingly, during wave propagation, although Rho activity elicits F-actin assembly, F-actin subsequently inactivates Rho. Experimental and modelling results show that waves represent excitable dynamics of a reaction-diffusion system with Rho as the activator and F-actin the inhibitor. We propose that cortical excitability explains fundamental features of cytokinesis including its cell cycle regulation.

Figure 1

Cortical waves of actin assembly and disassembly in activated frog eggs and embryos. (a) Surface view of frog blastomere expressing GFP-UtrCH to label F-actin. Top left: single frame; cortical F-actin consists of irregularly sized patches throughout cortex, which, as illustrated in the kymograph made from the outlined region (bottom left) travel continually across the surface (see Supplementary Video 1). In the kymograph, F-actin waves create slanted bands with semi-regular spacing. Right: sequential frames from the same sequence throughout cytokinesis; horizontal lines in kymograph indicate times corresponding to individual en face frames shown to the right. For this and all other figures, time in min:sec. (b) High magnification time-lapse sequence of activated frog egg expressing GFP-UtrCH (see Supplementary Video 2), color coded by rendering the current frame malachite, next frame blue, last frame copper: thus new F-actin is bluish, old F-actin reddish. On left, leading edge of F-actin wave progresses downward while trailing edge disappears. On lower right, old F-actin wave dissipates. Cables of F-actin are apparent within and between receding waves. Swatch shows colors resulting from blending RGB channels with low (bottom of swatch) to high (top of swatch) overlap. Arrowheads indicate rising (left) and falling (right) wave fronts (arrow color sampled locally). (c) Fixed frog embryo stained with fluorescent phalloidin to reveal endogenous cortical F-actin; closely resembles Fig. 1b. 2× enlarged insets (bottom) correspond to areas indicated by boxes. Inset 1 shows region between waves, inset 2 shows wave. Cables are present in both but are brighter and denser in wave. (d) Kymograph from time-series of frog embryo co-expressing GFP-Lifeact (yellow) and mCherry-UtrCH (blue) to label newer and older actin, respectively (see Supplementary Video 3, Supplementary Figure 1d); inset is a 3× blowup. Leading edges of each wave (top of bands in kymograph) have proportionately more Lifeact and trailing edges (lower part of bands) more UtrCH, even though both probes qualitatively label the same features (Sup. Fig. 1d). (d′) Cross-correlational analysis showing 15s delay between recruitment of Lifeact and UtrCH. Images are representative of at least 40 (a), at least 30 (b), and 3 (c, d) independent experiments, respectively.

Figure 2

Cortical F-actin waves in activated frog eggs are Rho-dependent and are accompanied by Rho activity waves. (a) Kymograph from control activated frog expressing GFP-UtrCH to label F-actin; (a′) Kymograph from activated frog egg expressing GFP-UtrCH and dominant negative Ect2; (a″) Kymograph from activated frog egg expressing GFP-UtrCH and C3 exotransferase to inactivate Rho. Arrowheads indicate waves. (b) Plot of wave amplitude in controls versus cells expressing dominant negative Ect2 or C3. Results are mean ± SD; n=100 waves; p=0.00012 for C3 vs. control and 0.00015 for DN Ect2 versus control; t-test. (c) Activated frog egg expressing 3xGFP-rGBD to label active Rho (see Supplementary Video 4): single frame (top) and kymograph (bottom), raw (left) and subtracted data (right, t₀–t₋₃), highlighting rising Rho activity. The kymograph demonstrates that what otherwise looks like mundane inhomogeneity in the still image actually reflects regular waves of Rho activity; these are more evident in the processed half of both the image and kymograph. (d) Activated frog egg expressing 3xGFP-rGBD to label active Rho and subjected to low-level overexpression of wild-type Xenopus Ect2 (see Supplementary Video 5); figure processed and presented as in 2c. Waves are sharper (i.e. have higher amplitude) and more continuous than normal cells (compare to 2c) and are clearly evident even without processing. 2c and 2d are derived from average projections of 4 1 micron sections at 10 sec intervals. Images are representative of at least 30 (a) 3 (a′, a″, b). 4 (c) and 6 (d)3–6 independent experiments, respectively.

Figure 3

Rho activity waves in starfish oocytes and embryos. (a,b) Frames from time-lapse sequences of Rho activity during meiosis I in normal starfish oocyte (top; projection of 8 1 micron sections) and oocyte overexpressing wild-type S. purpuratus Ect2 (bottom; projection of 8 1.5 micron sections). See Supplementary Video 6. Arrow indicates animal pole. Rho activity appears at vegetal pole, spreads upward, and converges on nascent polar body, forming cytokinetic Rho zone. In Ect2-expressing oocytes the global pattern of Rho activity mirrors that of controls but waves are much brighter, travel further, and persist after polar body emission. (c) Surface view of cortical Rho activity in meiosis II oocyte overexpressing Ect2 (see Supplementary Video 7; pb = polar body; projection of 14 1 micron sections). High amplitude waves form and settle into repetitive, often spiral, patterns. Inset montages are successive 60 s time points from boxed region on left starting at 17:00 (1) or 18:36 (2), showing patterns that approximately replicate on ~ 70 sec time scale (1 is spiral, 2 is center-surround with a slash underneath). Kymograph on right generated from area indicated by outlined strip, 4th frame. Diagonal bands span half the oocyte, showing that waves travel at least this far. Horizontal lines in kymograph mark times of frames shown on left. Arrowheads point to wave front that traverses tens of microns at steady speed (d). Surface view of cortical Rho activity in normal starfish oocyte, single frames (left) and kymograph (right). Rho waves appear, brighten, and coalesce into continuous zone around nascent polar body (see Supplementary Video 8). Arrowheads indicate wavelet that appears in both kymograph and still frame. (e) Rho activity in normal starfish blastomere (1 of 4 cells), still frames and kymographs generated from strips outlined in blue: 1, furrow center; 2, furrow periphery; 3, just outside furrow; 4, across furrow. Rho waves focus at equator before ingression, appear in the furrow (arrows), and eventually merge into a coherent Rho zone. Asterisk indicates particularly bright focus that appears in 4th still frame and kymographs 1 and 4. Images are representative of 10 (a, d), 20 (b, c) and 4 (e) independent experiments, respectively.

Figure 4

F-actin assembly fronts directly follow, but overlap minimally with, Rho activity waves. Color table shown in (b) applies to all images in this figure. (a) Normal starfish blastomere co-expressing GFP-rGBD (malachite; Rho activity) and GFP-Utr (copper; F-actin), selected frames (top) from time-lapse sequence of cytokinesis (Supplementary Video 9), and raw and subtracted kymographs (bottom) made from outlined strip. In still images, cytokinetic furrow is populated by apparently random densities of active Rho and F-actin; kymographs show these correspond to wavelets in which Rho activity rises, then falls as actin assembles. (b) Still images (left) and kymographs (right) from time-lapse movie of cortical F-actin and Rho activity in frog embryo showing two cells (1, 2) undergoing cytokinesis. Rho waves in furrow are followed by F-actin assembly waves. (c) Rho activity and F-actin in a starfish oocyte modestly overexpressing wild-type Ect2; kymograph (bottom) made from strip outlined in still frame (top). See Supplementary Video 10. Except during the global burst of Rho activity accompanying each meiotic cytokinesis, Rho activity waves immediately precede F-actin assembly, and F-actin disassembly precedes each Rho activation wave. Inset magnifies 4 cycles from wave train after first meiosis, emphasizing minimal overlap (yellow) between malachite and copper, and dark zone separating copper from next malachite wave. (d) Activated frog egg subjected to Ect2 overexpression, probes and presentation as in 4c (see Supplementary Video 11). Although waves are more tightly packed in frog eggs, kymographs show strikingly similar relationship between Rho and actin waves as in normal starfish. (e) Starfish zygote overexpressing Ect2 (see Supplementary Video 12), probes and presentation as in 4c and 4d, positions of still frames (left) indicated by dashes in kymograph (right). Faint waves precede global rise in Rho activity that focuses equatorially, leaving lower-amplitude waves in non-furrow regions; throughout, F-actin assembly follows peak Rho activity, and dark phases precede each Rho wave. (f) Temporal correlation plot of Rho waves from starfish oocytes overexpressing Ect2. Wave period ~80s. (g) Spatial correlation plot of Rho waves from starfish oocytes overexpressing Ect2. Wavelength 18 μm. Images are representative of 4 (a, b) 8 (c), or 5 (d) independent experiments, respectively.

Figure 5

Analysis of Rho and F-actin dynamics reveals cortical excitability and spiral turbulence. (a) Rho activation rate (mean ± SD) increases with Rho activity signal indicating that Rho activates itself in a positive feedback loop. Correlation assessed from pixels with low F-actin signal (see Supplementary Figures 4a). (b) F-actin accumulation rate is positively correlated with Rho activity (assessed from pixels with low F-actin signal). (c) Rho activation rate is inversely correlated with F-actin signal, to the point of switching to inactivation at high F-actin density (assessed from pixels with high Rho activity signal). Results are mean ± SD; n=900 cycles. (d) Each cortical locus (image pixel) can be mapped by its particular values of Rho activity and F-actin density to a single phase value, an angle between 0 and 2π, shown in rainbow colors: Cortical loci at the front of waves appear green, loci at Rho wave crests as cyan, at F-actin wave crests as dark blue-magenta, and loci at the back of the wave are red and orange. (e) Phase reconstruction for starfish oocyte overexpressing Ect2 (Supplementary Video 13). Points where all rainbow colors (phase values) merge indicate spiral cores (arrowheads). Inset: magnification of spiral wave core neighborhood outlined by dashed line. (f) Phase reconstruction for activated frog egg overexpressing Ect2. (g) Meiotic Ect2-overexpressing starfish zygotes containing GFP-rGBD (Rho activity; malachite) and mCherry-Utr (F-actin; copper), time-lapse sequence after application of high concentration of LatB (10 uM) from agarose-filled pipette (position indicated by cartoon); treatment causes rapid cortical F-actin collapse and corresponding burst of Rho activation (see Supplementary Video 14). Insets: single channel images of cells/stages indicated by numerals: 1) initial response, 2) wave regime on far side, collapse on near side, 3) total collapse, 4) wave regime on near side of distant oocyte (h) Similar to (g), but low-dose (1 uM) LatB induces shift from typical Ect2-enhanced wave regime to higher-amplitude, longer-period wave regime, in which large scale Rho waves propagate away from site of local F-actin disassembly (see Supplementary Video 15); rightmost image is kymocube rendered using ImageJ. Images are representative of 5 independent experiments.

Figure 6

Cdk1 gates excitability. (a) Kymograph from normal frog embryo showing waves of cortical F-actin (left) and cortical microtubules (right). I=Interphase; M=M-phase; Yellow lines on right indicate M-phase onset, as revealed by loss of cortical microtubules. Actin waves persist throughout M-phase but wave density varies: at M-phase onset (blue line on left), waves are spaced farther apart; this is followed by period of same length as M-phase but slightly delayed in which F-actin waves are brighter (red lines). (b) Kymograph from double-labeled starfish oocyte overexpressing Ect2 showing waves of cortical Rho activity (left) and cortical microtubules (right). Rho waves cease in each M-phase and reappear in each interphase. ms = meiotic spindle. (c) Kymograph of frog blastomere expressing Δ90 cyclin B showing cortical F-actin (left) and cortical microtubules (right). As time of high Cdk1 activity lengthens (revealed by loss of cortical microtubules) cortical F-actin waves progressively disappear. (d) Kymograph of Ect2-overexpressing starfish oocyte expressing Δ90 cyclin B as well, showing cortical Rho activity (left) and cortical microtubules (right). Rho waves fail to appear as cell remains arrested with high Cdk1 activity. (e) Top left: Rho activity in starfish oocytes overexpressing Ect2 and expressing Δ90 Cyclin B, 65 min after treatment with 40 μM roscovitine to inhibit Cdk1 (see Supplementary Video 16). Weather vane indicates direction of roscovitine flow. Roscovitine-containing seawater perfused around tight-packed oocytes from Southeast to Northwest at time 00:00; cells 1 and 2 are at cluster edge, cells 5 and 6 are in cluster center; hence, weathervane indicates presumed gradient of drug exposure. All oocytes show robust Rho waves at this time point. Top Right: kymographs of oocytes (identified by numerals) showing development of cortical Rho activity waves following Roscovitine treatment. Note that onset of waving follows expected rate of Cdk1 inhibition based on access to drug in perfused media. Bottom: successive frames showing oocyte 1 alone; inset shows chromosomes, arrowhead indicates position of meiotic spindle. Rho waves are well developed at least five minutes before anaphase begins. Images are representative of 4(a), 3(b), 5(c) and 6(d) independent experiments, respectively.

Figure 7

Excitability does not require spindles but is locally modulated by microtubules (a) Still frame (top) and kymograph (bottom) from time-lapse movie showing cortical Rho activity in two nucleate fragments derived from bisection of Ect2-overexpressing starfish oocyte. Waves of Rho activity appear and disappear in synchrony in each half. Pseudocolor table shown applies to a,b,b′, and e; in a and b′, outlined strips indicate kymograph region, dashes in kymographs are times of still frames. (b) Frames from time-lapse movie showing cortical Rho activity in nucleate half (top) and anucleate cytoplast (bottom) after bisection of Ect2-overexpressing starfish oocyte just before meiosis I. Waves appear and disappear on time in anucleate cytoplast in spite of the fact that it lacks spindle, chromosomes, or even centrosomes (see Supplementary Video 17) (b′) Similar bisection but after meiosis; two frames (top), during and after first cleavage, and kymographs (bottom, 1: nucleated, 2: anucleate). Cortical Rho waves appear and disappear in both halves, although first mitosis is delayed in the anucleate cytoplast. (c) Frames from time lapse movie showing microtubules (cyan) and active Rho (gold) in normal starfish oocyte during meiosis I. Rho activity is suppressed in the region occupied by spindle aster. (d) Frames from time lapse movie showing microtubules (cyan) and active Rho (gold) in starfish zygote with two spindles. Rho activity waves are excluded from regions occupied by spindle asters leading to focusing of Rho waves into cruciform Rho zone. (e) Meiotic Rho activity in normal starfish oocyte after treatment with 5 uM nocodazole to depolymerize microtubules (see Supplementary Video 18). The overall pattern of Rho activation is similar to controls – initiation at vegetal end, rapid progression to animal pole, inactivation in M-phase – except that animal pole is a Rho hotspot instead of a suppressed area; sep=sperm entry point, ms=meiotic spindle. Images are representative of 3(a, b), 12(c),17 (d) and 3(e) independent experiments, respectively.

Figure 8

Model of excitable dynamics predicts that Ect2 spatio-temporal distribution determines the pattern of Rho-actin cortical activity. (a) Schematic diagram of the molecular processes described by the model (see Methods). Numbers on the arrows correspond to numbers of rate constants in b. (b) Model equations (see Supplementary Figure 6a and Methods). (c) Top: Simulation of wave turbulence with Ect2 level representing interphase wave pattern in starfish oocytes with extra Ect2 (see Supplementary Video 19), active Rho (malachite) and F-actin (copper). Bottom: image of cortical Rho (malachite) and F-actin (copper) from Ect2-overexpressing starfish oocyte for comparison. (d) Top: Model dynamics at the peak of global Ect2 activity – representing polar body emission phase – demonstrates a characteristic wave pattern with broad crests, substantial overlap of Rho and F-actin maxima and narrow refractory zones between wave crests (see also Supplementary Figures. 6b,c and Methods). Bottom: image of cortical Rho (malachite) and F-actin (copper) from Ect2-overexpressing oocyte at time of polar body emission for comparison. (e) Top: Model kymograph of Rho activity and F-actin prior to, during, and after polar body emission (see Supplementary Video 19). Bottom: experimental kymograph for comparison. (f) Emergence of furrow through condensation of waves in a simulation representing mitotic starfish cells with progressive focusing of Ect2 at the cell equator (see Supplementary Video 20). (f′) Kymograph along a line perpendicular to the furrow for model behavior in f. (g) Simulation of rapid microtubule depolymerization after furrow zone formation: furrow signal dissipates and spatially-homogeneous waves return. (g′) Kymograph of simulation shown in f. (h) Behavior of cortical Rho waves following experimental microtubule depolymerization by nocodazole in binucleate starfish zygote at the onset of cytokinesis. Cytokinetic Rho zones dissipate quickly and waves repopulate the entire cortex. Asterisks indicate spindle pole positions; solid arrowheads indicate Rho zones in nascent furrows; hollow arrowheads point out instances of cortical Rho waves in once-bare territory (see Supplementary Video 21). Images in h are representative of 3 independent experiments.