Problems in the detection of an asymmetry by an activator-inhibitor systemIn the first simulations, it is shown that an activator-inhibitor interaction is very sensitive against imposed asymmetries. Assumed is that an external signal (blue) with an asymmetry of 2% over the cell diameter exists. It has an activating influence on the activator autocatalysis. Despite of the fact that 1% random fluctuations at each surface element blur this minute signal, the system is sensitive enough to detect this asymmetry. A local high activator maximum (green) emerges at the side pointing to the highest concentration (black arrow). The self-enhancement is antagonized by the rapidly spreading inhibitor (red).
Oscillating cells can maintain their sensitivityOne possibility to solve this problem is the use of an oscillating pattern forming systems (Meinhardt and Gierer, 1974). Then , the systems cycles through a phase in which it is sensitive to an external asymmetry, followed by a phase in which the imposed internal asymmetry is amplified, culminating in a strongly localized signal. The subsequent accumulation of the inhibitor leads to a collapse of the activation. After decay of the inhibitor, the system enters again into the sensitive phase in which a new direction can be chosen. Oscillations do occur if the inhibitor has a longer half life that the activator.
A permanent sensitivity results from a finite half life of the 'hot spots'In a situation as described above, a second antagonistic reaction that acts locally and that has a long time constant leads to a destabilization of once formed maximum. Since the total activated area is regulated, any local maximum that disappears makes place for a new one. It can emerge at a position governed by the external signal. The result is a permanent creation of hot spots and their disappearance after a certain time interval at the side exposed to the highest signal concentration (blue is again the distribution of the external signal around the cell; the asymmetry of 2% and the assumed 1% random fluctuation are hardly visible).
ConclusionA system of one autocatalytic reaction that is balanced by two antagonistic reactions with different time constants allow the generation of local activated regions on the cell cortex with a high sensitivity against external signals. The system is able to detect minute external asymmetries and can permanently adapt to changing conditions. In the absence of external asymmetries, nevertheless local are signals generated. This leads even in this situation to a dynamic regulation of protrusions - a well known feature of such cells.