Selection for spiral waves in the social amoebae  Dictyostelium

Abstract

Starving Dictyostelium amoebae emit pulses of the chemoattractant cAMP that are relayed from cell to cell as circular and spiral waves. We have recently modeled spiral wave formation in Dictyostelium. Our model suggests that a secreted protein inhibitor of an extracellular cAMP phosphodiesterase selects for spirals. Herein we test the essential features of this prediction by comparing wave propagation in wild type and inhibitor mutants. We find that mutants rarely form spirals. The territory size of mutant strains is approximately 50 times smaller than wild type, and the mature fruiting bodies are smaller but otherwise normal. These results identify a mechanism for selecting one wave symmetry over another in an excitable system and suggest that the phosphodiesterase inhibitor may be under selection because it helps regulate territory size.

Geometric diagnostics of complex patterns: Spiral defect chaos

“…Examples include meandering spirals and defect chaos in chemical systems, [1][2][3]28 spirals in the oscillation amplitude of whirling hexagons in rotating non-Boussinesq convection, 27 spirals in vertically vibrated material, 10 patterns of bacterial colonies, 6,7 calcium waves, 11,12 spiral waves in the heart, 49 and in aggregating amoebaes. 13,14 …”

“…8,9 Other examples are spirals arising in vibrationally excited waves on the surface of granular material, 10 in calcium waves in oocytes 11 and hippocampus, 12 and in the aggregation patterns of the amoeba Dictyostelium. 13,14 These patterns often evolve chaotically in time and arise in transitions from simpler structures, and may in turn undergo further transitions to other, possibly more complex structures. To gain detailed understanding of such spatio-temporally chaotic states and their transitions, it is important to have quantitative measures that extract the relevant features of the patterns.…”

Modeling oscillations and waves of cAMP in Dictyostelium discoideum cells

“…Any process that helps to build up defects associated with spatial heterogeneities is likely to favor the formation of spirals. As shown by theoretical and experimental studies, one such factor could be the phosphodiesterase inhibitor released by the amoebae into the extracellular medium [31,40], since this factor indirectly controls the level of cAMP. The effect of this inhibitor is implicitly included in the developmental path shown in Fig.…”

Noise can play an organizing role for the recurrent dynamics in excitable media

“…The established wave pattern then initiates a movement of cells toward the origin of the wave, resulting in cell aggregation; these cells will later differentiate to form sophisticated fruiting bodies and complete the organism's life cycle. Detailed experimental studies of the patterns of cAMP signaling reveal the standard phenomenology (1-3, 16) of a 2D excitable medium (5,(17)(18)(19). The basic questions these experiments raise, which are common to studies of all excitable systems, are about the origin of wave pattern initiation and selection.…”

“…We were motivated by the experiments on Dictyostelium by Lee and coworkers (17)(18)(19), who studied the initiation and evolution of the cAMP signaling patterns under various conditions. Our model is a coarsely discretized version of a stochastic partial differential equation with the Brusselatorlike kinetics (29) and diffusive excitatory coupling:…”