RESEARCH:
Spatial Organization and Trigger Waves
When I watch a movie of mitosis, I'm always struck by how abrupt and global the transition from interphase to mitosis seems to be. Is this abrupt-and-global quality surprising?
Maybe not. For a typical-sized somatic cell, all you would need would be for the Cdk1 to become activated abruptly at some given location (current evidence suggests that it is first activated at the centrosome). Then even a process as inefficient as random walk diffusion would allow the active Cdk1 to make its way to every nook and cranny of the cell in a pretty short time period.
The time it takes to diffuse a distance d in three dimensions is given by t = d2/6D. A typical value for the diffusion coefficient of a cytosolic protein is 10 µm2/sec, so for the active Cdk1 to diffuse a distance of, say, 10 µm (which is the radius of a 4 pL spherical cell), it would take 1.67 sec. As long as you do not require that the synchrony of nuclear and cortical mitotic events be better than plus-or-minus a few seconds, random walk diffusion should be sufficient.
But a Xenopus egg is 60x the radius of our typical somatic cell, and so diffusion would take 3600x longer: 1.67 h rather than 1.67 sec. This might suggest that mitosis would be a long drawn out process in a frog egg. But it is not; there is only a lag of about 10 min between when nuclear envelope breakdown happens near the center of the egg and when the Cdk1-dependent surface contraction wavse begin at the animal pole. Something quicker than random walk diffusion must be involved in the spatial coordination of mitosis.
Trafficking on microtubules, perhaps?
Probably not. It would be fast enough – typical rates of microtubule based transport are about 1 µm/sec – but Hara and Kirschner showed years ago that cortical contractions happen once every 25 min in devitellinated frog embryos, probably due to the once-per-25-min activation of Cdk1, and that the microtubule poison colchicine doesn't slow or smear-out these contractions.
How about flow?
Flow is another way of getting information through a system faster than diffusion alone would permit, but the flows in a fertilized embryo are pretty limited.
Any other good ideas?
One idea is inspired by the fact that Cdk1 promotes its own activation. Suppose then that Cdk1 gets activated somewhere – say the centrosome. The active Cdk1 can diffuse the first short distance, say a µm, very quickly since diffusion is fast over short distances, and then cause all of the inactive Cdk1 in that region of cytoplasm to get activated. Then it won't matter if half of the original active Cdk1 molecules random walk backward; there will be all this newly generated active Cdk1 to keep pushing the activity front outward.
These cycles of diffusion and autocatalytic reaction would allow the activity of Cdk1 to propagate outward from the centrosome, and without slowing down or petering out. This type of phenomenon is termed a trigger wave.
What are some other examples of trigger waves?
Action potentials propagating down an axon, for one. The positive feedback comes from the voltage-activated sodium channel. Calcium waves, for another, with the postive feedback coming from calcium-dependent IP3 generation and calcium-induced calcium release. Cyclic AMP waves in aggregating Dictyostelium for another.
Or, if you are willing to leave the realm of cellular regulation, the spread of a virus through a population, or the spread of a rumor through the internet, or the spread of a fire through a field would all be examples of trigger waves.
The three things you need for a trigger wave are (1) a bistable regulatory system (or an excitable system or a relaxation oscillator, which can be thought of as bistable systems with the addition of strong negative feedback); (2) a spatial coupling mechanism, which here we are assuming is diffusion, but in other contexts could be, say, a cell-cell interaction; and (3) some inhomogeneity to allow the bistable switch to be flipped at some region of space before it has been flipped in the surrounding regions.
Can you get a bit more quantitative about what you would expect a mitotic trigger wave to look like?
Sure. Start with a simple ordinary differential equation (ODE) model of the cell cycle oscillator as mentioned in the discussion of the embryonic cell cycle oscillator. Add Fick's law diffusion terms. Then solve the resulting partial differential equations (PDEs) numerically. If you do it for a one-dimensional system, like a long thin tube of cytoplasm, and assume that Cdk1 activation occurs early in one 5 µm section right in the middle of the tube, you get a kymograph of the system that looks like this:
The hot colors denote high levels of Cdk1 activity, and the cool colors low. The trigger waves propagate at a constant speed of about 1 µm/sec, and they eventually take control of the timing of mitosis in the whole tube.
So does mitosis spread through Xenopus cytoplasm via trigger waves?
Yes, at a constant speed of about 1 µm/sec. This is fast enough to get information from the center of an egg to the cortex in 10 min.
How was this shown?
Through video microscopy experiments with cycling Xenopus egg extracts in thin (100 µm diameter) Teflon tubes. Have a look at this time-lapse (1 sec in the video = 15 min in real time) video of mitotic trigger waves:
The green balls are interphase nuclei filled with GFP-NLS. When a nucleus goes through nuclear envelope breakdown, it gets emptied of its contents.
You can plot the times at which the nuclei disappear (red) and re-form (blue) as a function of their position in the tube, and the resulting kymograph is:
The straight lines are the propagating trigger waves. After a relatively disorganized first cycle, the extract is dominated by trigger waves originating at two foci and spreading at linear speed up and down the tube.
In an intact fertilized egg, where do the mitotic waves start?
Evidence suggess that they start at or near the congressed pronuclei, which sit in the middle of the animal hemisphere of the egg. Our guess is that the waves originate from the centrosomes, since centrosomes are where you can first detect active Cdk1 in somatic cells. The trigger waves are thought to spread outward as near-constant velocity, reaching different parts of the cortex at predictable times (animal pole first, vegetal pole last).
Positive feedback seems pretty common in cell signaling. Do you think trigger waves might be involved in coordinating other signal transduction processes over long distances?
Sure, it does seem likely, doesn't it?
