Concentration differences of a few percent across a cell or a growth cone can be sufficient for their chemotactic orientation [1]. This raises the question of what mechanisms can be responsible for this extraordinary sensitivity. Time lapse studies suggest that this orientation is based on a highly dynamic process. Lamellipodia and filopodia are stretched out and retracted rapidly in a seemingly irregular way (for recent experimental observations see [5,6])
 

Many cell types show such dynamic behavior even in the absence of external signals [2,3], arguing against a simple internal amplification of the external signal. A model has been proposed that accounts for this sensitivity, for the fact that stretching out and retraction of protrusions can occur simultaneously and that this dynamic behavior is maintained even in the absence of an external signal (Meinhardt, 1999). (The essence of the model is also available in a commented PowerPoint presentation [PPT]). The primary event in directional movement is proposed to be the formation of local concentration maxima within the cell. This internal signal causes a rearrangement of the cytoskeleton and changes in the cell shape. Only the generation of these primary signals is described by the model.

Problems in the detection of an asymmetry by an activator-inhibitor system

In 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).
 

The second sequence in this simulation shows that the orientation works also with a much smaller absolute level of the external signal (smaller blue circle). This is essential for an orientation in a field that uses graded concentration profiles as guiding cues (see graded cues and growth cone navigation, see also Bonhoeffer homepage Cellular and molecular neuroembryology).
However, as shown in the third sequence, after establishment of a strong internal signal, even a much stronger and more asymmetric external signal (eccentric blue circle) is unable to reorient the once established cell-internal pattern (note that the cell copes with the higher external signal by increasing inhibitor level shown in red). Thus the problem is not the detection of the minute signal but the maintenance of the sensitivity.

Oscillating cells can maintain their sensitivity

One 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.

Remaining problems of such a mechanism: (i) there are frequently more than one protrusion formed and (ii), while some protrusions stretch out, others retract at the same time. Both observations cannot be described a single global oscillation within the cell.

The role of saturation in the formation of several hot spots
Saturation of autocatalysis leads to a larger activated region. Since the activation remains at a lower absolute level, the activated region increases in size until sufficient inhibitor is produced. Without fluctuations, the signal appears at a coherent site (left).
 

With fluctuations (right), those regions will win that have the best condition due to the combined action of the signal and the fluctuations. Several maxima can appear. The shape of the activated region depends on the strength of the signal, on the activator diffusion and on the degree of the saturation of the activator autocatalysis.

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).
 

Polarization of the cell in the absence of an external signal

The group of M. Vicker [3] observed isolated Dictyostelium cells in the absence of any external stimulation and found that the protrusions formed in the course of time were by no means random. Either stretching out occurs at opposite positions with and each further cycle appears with a 90° displacement [3].

 

Alternatively, the protrusions shift in a more continuous way such that it appears as if the cell rotated [3].
 

This behaviour is described by the model. Quenching of a maximum can either leads to a breakdown and reappearance at a least poisoned side. Alternative, if the system has less internal tendency to oscillate, the a maximum will escape to an adjacent position, leading to the apparent rotation (for more details see Meinhardt, 1999):