Predicting the Distribution of Spiral Waves from Cell Properties in a Developmental-Path Model of Dictyostelium Pattern Formation

The slime mold Dictyostelium discoideum is one of the model systems of biological pattern formation. One of the most successful answers to the challenge of establishing a spiral wave pattern in a colony of homogeneously distributed D. discoideum cells has been the suggestion of a developmental path the cells follow (Lauzeral and coworkers). This is a well-defined change in properties each cell undergoes on a longer time scale than the typical dynamics of the cell. Here we show that this concept leads to an inhomogeneous and systematic spatial distribution of spiral waves, which can be predicted from the distribution of cells on the developmental path. We propose specific experiments for checking whether such systematics are also found in data and thus, indirectly, provide evidence of a developmental path.Author Summary: Spatio-temporal pattern formation is a core discipline of theoretical biology. Formation of large-scale patterns from local interactions can very prominently be observed in the swarming behavior of fish and birds, in animal markings or bacterial growth patterns. It also plays a critical role in the life cycle of the social amoeba Dictyostelium discoideum. A homogeneous colony of amoebae is partitioned into subgroups that will form migrating slugs by a collective phase of chemotactic signaling, exhibiting typical and well-known patterns for this sort of excitable dynamics (circular and spiral waves). The mechanism of spatial localization of aggregation centers (that is, the centers of periodic circular and spiral waves) is unclear, despite its crucial role to the organism's procreation. Here we demonstrate for an established computational model of D. discoideum that the initial properties of potentially very few cells have a driving influence on the resulting asymptotic collective state of the colony. Analogous processes take place in diverse situations such as, e.g., heart cells (where spiral waves occur in potentially fatal ventricular fibrillation), so that a deeper understanding of this additional layer of self-organized pattern formation would be beneficial to a wide range of applications.