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The slime mould Dictyostelium discoideum is a widely studied paradigm for biological pattern formation. To provide an explanation for the apparently paradoxical behaviour of Dictyostelium amoebae in the symmetric chemoattractant waves which govern their aggregation, we extend the standard model for chemotaxis of a cell population by explicitly considering adaptation of the chemotactic signalling pathway. In the limiting cases of very fast and very slow adaptation kinetics the model equations reduce to the standard model which predicts cell movement opposite to the observed direction. Adaptation on an intermediate timescale, however, provides cells with a "short-term memory" of experienced chemoattractant concentrations which can fully account for the experimental observation of cell translocation opposite to the direction of propagation of the chemoattractant waves.

Despite spectacular progress in biophysics, molecular biology and biochemistry our ability to predict the dynamic behavior of multicellular systems under different conditions is very limited. An important reason for this is that still not enough is known about how cells change their physical and biological properties by genetic or metabolic regulation, and which of these changes affect the cell behavior. For this reason, it is difficult to predict the system behavior of multicellular systems in case the cell behavior changes, for example, as a consequence of regulation or differentiation. The rules that underlie the regulation processes have been determined on the time scale of evolution, by selection on the phenotypic level of cells or cell populations. We illustrate by detailed computer simulations in a multi-scale approach how cell behavior controlled by regulatory networks may emerge as a consequence of an evolutionary process, if either the cells, or populations of cells are subject to selection on particular features. We consider two examples, migration strategies of single cells searching a signal source, or aggregation of two or more cells within minimal multiscale models of biological evolution. Both can be found for example in the life cycle of the slime mold Dictyostelium discoideum. However, phenotypic changes that can lead to completely different modes of migration have also been observed in cells of multi-cellular organisms, for example, as a consequence of a specialization in stem cells or the de-differentiation in tumor cells. The regulatory networks are represented by Boolean networks and encoded by binary strings. The latter may be considered as encoding the genetic information (the genotype) and are subject to mutations and crossovers. The cell behavior reflects the phenotype. We find that cells adopt naturally observed migration strategies, controlled by networks that show robustness and redundancy. The model simplicity allow us to unambiguously analyze the regulatory networks and the resulting phenotypes by different measures and by knockouts of regulatory elements. We illustrate that in order to maintain a cells' phenotype in case of a knockout, the cell may have to be able to deal with contradictory information. In summary, both the cell phenotype as well as the emerged regulatory network behave as their biological counterparts observed in nature.