Modeling Chemotactic Cell Sorting during Dictyostelium discoideum Mound Formation

Abstract

Coordinated cell movement is a major mechanism of the multicellular development of most organisms. The multicellular morphogenesis of the slime mould Dictyostelium discoideum, from single cells into a multicellular fruiting body, results from differential chemotactic cell movement. During aggregation cells differentiate into prestalk and prespore cells that will form the stalk and spores in the fruiting body. These cell types arise in a salt and pepper pattern after what the prestalk cells chemotactically sort out to form a tip. The tip functions as an organizer because it directs the further development. It has been difficult to get a satisfactory formal description of the movement behavior of cells in tissues. Based on our experiments, we consider the aggregate as a drop of a viscous fluid and show that this consideration is very well suited to mathematically describe the motion of cells in the tissue. We show that the transformation of a hemispherical mound into an elongated slug can result from the coordinated chemotactic cell movement in response to scroll waves of the chemoattractant cAMP. The model calculations furthermore show that cell sorting can result from differences in chemotactic cell movement and cAMP relay kinetics between the two cell types. During this process, the faster moving and stronger signaling cells collect on the top of the mound to form a tip. The mound then extends into an elongated slug just as observed in experiments. The model is able to describe cell movement patterns in the complex multicellular morphogenesis of Dictyostelium rather well and we expect that this approach may be useful in the modeling of tissue transformations in other systems.

Modelling cell movement, cell differentiation, cell sorting and proportion regulation in Dictyostelium discoideum aggregations

“…In reality, Dictyostelium cells do not move at a constant speed. For example, it has been shown that in Dictyostelium discoideum aggregations, cells speed depends on the chemoattractant and on its spatial and temporal gradients [17,20,34,35]. The cells also speed-up or slow-down as a consequence of cell-cell mechanical interactions or interactions with the substratum and the so-called slime sheath that surrounds the slug [38].…”

“…One can observe the cAMP pulses propagating from the centre, with a period of approximately 7.5 minutes. In reality, PSP and PST cells differ in many aspects: PST cells are faster (stronger chemotactic forces), more excitable (produce more cAMP), and less adhesive (lower viscosity) [17,20]. This led us to investigate the case of different speeds, chemotactic sensitivities, and mechanical interactions.…”

“…As for isolated PSP fragments, the spatiotemporal dynamics of cAMP is determined by Eqs. (17). Finally, we assume that the PST cells move faster than the PSP cells (see Table B.4).…”

“…Over the last two decades, mathematical models (of continuous and discrete type, or a combination of the two) have been derived to analyse various aspects of Dictyostelium discoideum morphogenesis [14,15,16,17,18,19,20,21,22]. For example, it has been shown that the aggregation of single cells is driven mainly by chemotaxis to cyclic adenosine-3',5'-monophosphate (cAMP) [14,15,16].…”

“…For example, it has been shown that the aggregation of single cells is driven mainly by chemotaxis to cyclic adenosine-3',5'-monophosphate (cAMP) [14,15,16]. Other studies on mound formation and slug motion emphasised also the importance of mechanical interactions between cells [16,17,18,19,20,21,22]. Models aimed to describe the process of culmination in Dictyostelium discoideum showed that cAMP signalling and mechanical interactions, combined with cell differentiation, are sufficient to produce the cell movements which lead to the formation of the fruiting body [23].…”