Biopolym. Cell. 2020; 36(5):341-347.
Simulation modeling of cAMP induced Dictyostelium aggregation by using object-oriented Pharo programming language
1Nizheradze K. A.
  1. Bogomolets National Medical University
    13, Shevchenko Blvd., Kyiv, Ukraine, 01601


Aim. Periodically emitted spiral waves of cAMP determine the directed movement of individual amoebae of Dictyostelium discoideum towards the aggregation centers, which are the sources of these waves. Overall behavior of cell population that includes at this stage the thousands of independent organisms, could be reproduced and visualized through 2D simulation modeling. Methods. Object-oriented Pharo programming language was applied to create the model. As the source of random numbers the explicit inversive congruential generator was used. The following processes were attributed to developing population of individual amoebae: appearance of randomly distributed initial cells/spores; the search of feeding substrate; mitosis; forming (depending on the local environment) of the active aggregation centers; periodical emittances of cAMP spiral waves from the aggregation centers; directed movement of the amoebae, which were captured by the cAMP wave, towards aggregation center. Results. In course of the simulation of the feeding and subsequent mitosis, small initial population of amoebae was multiplied and distributed in the borders of specified area. When reaching a finite population density, the appearance of few active aggregation centers took place. Spiral cAMP waves periodically propagated from these centers in 2D area of the model. The cells, which were “covered” by the wave, begun their movement to the corresponding aggregation center, intermitted with the periods of the rest. During migration, the cells formed the characteristic “streams”. Conclusion. This model could provide additional important information in the study of the phases and underlying mechanisms of self-organizing cell populations.
Keywords: cAMP waves, cell aggregation, object-oriented programming language


[1] Bonner JT. Evolution of development in the cellular slime molds. Evol Dev. 2003;5(3):305-13.
[2] Kessin RH. Dictyostelium: evolution, cell biology, and the development of multicellularity. Cambridge: “Cambridge University Press”, 2001; 294 p.
[3] Vidal-Henriquez E, Gholami A. Spontaneous center formation in Dictyostelium discoideum. Sci Rep. 2019;9(1):3935.
[4] MacKay SA. Computer simulation of aggregation in Dictyostelium discoideum. J Cell Sci. 1978;33:1-16.
[5] Parhizkar M, Di Marzo Serugendo G. Agent-based models for first- and second-order emergent collective behaviours of social amoeba Dictyostelium discoideum aggregation and migration phases. Artif Life Robotics. 2018;23: 498–507.
[6] Ducasse S, Chloupis D, Hess N, Zagidulin D. Pharo by Example 5. “ & Square Bracket Associates”, 2017; 352 p.
[7] Hellekalek P. Good random number generators are (not so) easy to find. Math Comput Simulat. 1998;46(5-6):485-505.
[8] Nizheradze KA. Binding of wheat germ agglutinin to extracellular network produced by cultured human fibroblasts. Folia Histochem Cytobiol. 2000;38(4):167-73.
[9] Martiel JL, Goldbeter A. A Model Based on Receptor Desensitization for Cyclic AMP Signaling in Dictyostelium Cells. Biophys J. 1987;52(5):807-28.
[10] Bhowmik A, Rappel WJ, Levine H. Excitable waves and direction-sensing in Dictyostelium discoideum: steps towards a chemotaxis model. Phys Biol. 2016;13(1):016002.
[11] Goldbeter A. Oscillations and waves of cyclic AMP in Dictyostelium: a prototype for spatio-temporal organization and pulsatile intercellular communication. Bull Math Biol. 2006;68(5):1095-109.
[12] Kravchenko AO, Kosach VR, Shkarina KA, Zaiets IV, Tykhonkova IO, Khoruzhenko AI. Optimization of in vitro model for analysis of tumor cell migration dynamics. Biopolym Cell. 2018; 34(6):477–86.
[13] Nizheradze KA, Efimov AS. Study of the dynamics of epithelioid outgrowth of skin explants of healthy people and the patients with insulin-dependent diabetes mellitus. Dopov Nac Akad Nauk Ukr. 1993;(9):165-71.
[14] Goldbeter A, Gérard C, Gonze D, Leloup JC, Dupont G. Systems biology of cellular rhythms. FEBS Lett. 2012;586(18):2955-65.