Models of aggregation in <em>dictyostelium discoideum</em>: On the track of spiral waves

Miguel A. Herrero; Leandro Sastre; Miguel A. Herrero; Leandro Sastre

doi:10.3934/nhm.2006.1.241

Networks and Heterogeneous Media

2006, Volume 1, Issue 2: 241-258. doi: 10.3934/nhm.2006.1.241

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Models of aggregation in dictyostelium discoideum: On the track of spiral waves

Miguel A. Herrero ^{1
,},
Leandro Sastre ^{2
,}

1.
Departamento de Matemática Aplicada, Facultad de Matemáticas, Universidad Complutense, Plaza de las Ciencias, 28040 Madrid
2.
Instituto de Investigaciones Biomédicas, CSIC/Universidad Autónoma de Madrid, Arturo Duperier 4, 28029 Madrid

Received: 01 January 2006 Revised: 01 February 2006
Primary: 34K11, 35B27 ; Secondary: 74Q15, 47N60.

This work is concerned with some aspects of the social life of the amoebae Dictyostelium discoideum (Dd). In particular, we shall focus on the early stages of the starvation-induced aggregation of Dd cells. Under such circumstances, amoebae are known to exchange a chemical messenger (cAMP) which acts as a signal to mediate their individual behaviour. This molecule is released from aggregation centres and advances through aggregation ﬁelds, ﬁrst as circular waves and later on as spiral patterns. We shall recall below some of the basic features of this process, paying attention to the mathematical models that have been derived to account for experimental observations.
- Biological models,
- Dictyostelium,
- pattern formation,
- target and spiral waves,
- effective equations
Citation: Miguel A. Herrero, Leandro Sastre. Models of aggregation in dictyostelium discoideum: On the track of spiral waves[J]. Networks and Heterogeneous Media, 2006, 1(2): 241-258. doi: 10.3934/nhm.2006.1.241

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Abstract

This work is concerned with some aspects of the social life of the amoebae Dictyostelium discoideum (Dd). In particular, we shall focus on the early stages of the starvation-induced aggregation of Dd cells. Under such circumstances, amoebae are known to exchange a chemical messenger (cAMP) which acts as a signal to mediate their individual behaviour. This molecule is released from aggregation centres and advances through aggregation ﬁelds, ﬁrst as circular waves and later on as spiral patterns. We shall recall below some of the basic features of this process, paying attention to the mathematical models that have been derived to account for experimental observations.
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