The microorganism Dictyostelium discoideum is extensively studied in biology, as the life cycle of this organism provides a unique opportunity to study the relation between signal transduction at the cellular level and morphogenesis and behaviour at the multicellular level. Upon starvation, solitary amoebae start to aggregate and form migrating multicellular slugs, which show a pronounced thermo- and phototaxis.
We model the motion of a D. discoideum slug in absence of attractants and in presence of a thermal gradient or light source. Our model is a hybrid cellular automata/partial differential equation model. Although we are interested in the global behaviour of the slug, the model itself is defined on the level of individual amoebae, which are represented as a group of connected automata instead of a point-like object. Therefore amoebae can slide past one another, and deform themselves and adjoining amoebae by means of small changes in their boundaries. This method of cell modelling lends itself excellently for describing the morphogenesis of D. discoideum, since the behaviours observed during the developmental processes are entirely driven by the local movements and responses of individual amoebae. Besides, the formalism handles pressure, deformation and motion in a very elegant way, because with these processes only local decision rules are involved.
Using our model we were able to reproduce some main features and processes which occur in the slug, such as cell sorting, shape conservation, and the dependence of slug velocity on its mass.
We were also able to reproduce perception by the slug of a temperature gradient or light: we show that, independently of the initial orientation, after some transient process the slug starts moving along the temperature gradient or towards the light source. We were also able to reproduce the well known experimental phenomenon of bidirectional phototaxis, as well as a number of other experimental findings. I will discuss the biological mechanisms accounting for the tactic orientations.
Note, that slug behaviour in our model is due to the collective behaviour of the amoebae. Individual amoebae can neither respond to a shallow temperature gradient, nor measure the direction of incidence of light.