Unicellular organisms exhibit elaborate collective behaviors in response to environmental cues. These behaviors are controlled by complex biochemical networks within individual cells and coordinated through cell-to-cell communication. Describing these behaviors requires new mathematical models that can bridge scales-from biochemical networks within individual cells to spatially structured cellular populations. Here we present a family of "multiscale" models for the emergence of spiral waves in the social amoeba Dictyostelium discoideum. Our models exploit new experimental advances that allow for the direct measurement and manipulation of the small signaling molecule cyclic adenosine monophosphate (cAMP) used by Dictyostelium cells to coordinate behavior in cellular populations. Inspired by recent experiments, we model the Dictyostelium signaling network as an excitable system coupled to various preprocessing modules. We use this family of models to study spatially unstructured populations of "fixed" cells by constructing phase diagrams that relate the properties of population-level oscillations to parameters in the underlying biochemical network. We then briefly discuss an extension of our model that includes spatial structure and show how this naturally gives rise to spiral waves. Our models exhibit a wide range of novel phenomena. including a density-dependent frequency change, bistability, and dynamic death due to slow cAMP dynamics. Our modeling approach provides a powerful tool for bridging scales in modeling of Dictyostelium populations.

Cellular slime molds, including the well-studied Dictyostelium discoideum, are amoebae whose life cycle includes both a single-cellular and a multicellular stage. To achieve the multicellular stage, individual amoebae aggregate upon starvation to form a fruiting body made of dead stalk cells and reproductive spores, a process that has been described in terms of cooperation and altruism. When amoebae aggregate they do not perfectly discriminate against nonkin, leading to chimeric fruiting bodies. Within chimeras, complex interactions among genotypes have been documented, which should theoretically reduce genetic diversity. This is however inconsistent with the great diversity of genotypes found in nature. Recent work has shown that a little-studied component of D. discoideum fitness--the loner cells that do not participate in the aggregation--can be selected for depending on environmental conditions and that, together with the spores, they could represent a bet-hedging strategy. We suggest that in all cellular slime molds the existence of loners could resolve the apparent diversity paradox in two ways. First, if loners are accounted for, then apparent genotypic skew in the spores of chimeras could simply be the result of different investments into spores versus loners. Second, in an ecosystem with multiple local environments differing in their food recovery characteristics and connected globally via weak-to-moderate dispersal, coexistence of multiple genotypes can occur. Finally, we argue that the loners make it impossible to define altruistic behavior, winners or losers, without a clear description of the ecology.

Collective behavior in cellular populations is coordinated by biochemical signaling networks within individual cells. Connecting the dynamics of these intracellular networks to the population phenomena they control poses a considerable challenge because of network complexity and our limited knowledge of kinetic parameters. However, from physical systems, we know that behavioral changes in the individual constituents of a collectively behaving system occur in a limited number of well-defined classes, and these can be described using simple models. Here, we apply such an approach to the emergence of collective oscillations in cellular populations of the social amoeba Dictyostelium discoideum. Through direct tests of our model with quantitative in vivo measurements of single-cell and population signaling dynamics, we show how a simple model can effectively describe a complex molecular signaling network at multiple size and temporal scales. The model predicts novel noise-driven single-cell and population-level signaling phenomena that we then experimentally observe. Our results suggest that like physical systems, collective behavior in biology may be universal and described using simple mathematical models.