During the slug stage, the cellular slime mould Dictylosielium discoideum m
oves towards light sources. We have modelled this phototactic behaviour usi
ng a hybrid cellular automata/partial differential equation model. In our m
odel, individual amoebae are not able to measure the direction from which t
he light comes, and differences in light intensity do not lead to different
iation in motion velocity among the amoebae. Nevertheless, the whole slug o
rientates itself towards the light. This behaviour is mediated by a modific
ation of the cyclic AMP (cAMP) waves. As an explanation for phototaxis we p
ropose the following mechanism, which is basically characterized by four pr
ocesses: (i) light is focused on the distal side of the slug as a result of
the so-called 'lens-effect'; (ii) differences in luminous intensity cause
differences in NH3 concentration; (iii) NH3 alters the excitability of the
cell, and thereby the shape of the cAMP wave; and (iv) chemotaxis towards c
AMP causes the slug to turn. We show that this mechanism can account for a
number of other behaviours that have been observed in experiments, such as
bidirectional phototaxis and the cancellation of bidirectionality by a decr
ease in the light intensity or the addition of charcoal to the medium.