Keller, Evelyn F.; Segel, Lee A. Initiation of slime mold aggregation viewed as an instability. (English) Zbl 1170.92306 J. Theor. Biol. 26, No. 3, 399-415 (1970). Summary: The chemotactic interaction of amoebae, as mediated by acrasin, is evidenced in a variety of ways, the most dramatic of which is aggregation. In this paper we present a mathematical formulation of the general interaction, and provide a detailed analysis of the aggregation process. By analogy with many problems in the physical world, aggregation is viewed as a breakdown of stability caused by intrinsic changes in the basic parameters which characterize the system. This point of view provides a description of aggregation which does not require that any cells be distinguished, but rather assumes a homogeneous population. Cited in 10 ReviewsCited in 1366 Documents MSC: 92C17 Cell movement (chemotaxis, etc.) 35Q92 PDEs in connection with biology, chemistry and other natural sciences PDF BibTeX XML Cite \textit{E. F. Keller} and \textit{L. A. Segel}, J. Theor. Biol. 26, No. 3, 399--415 (1970; Zbl 1170.92306) Full Text: DOI OpenURL References: [1] Bonner, J.T., The cellular slime molds, (1967), Princeton University Press Princeton [2] Bonner, J.T.; Dodd, M.R., Biol. bull, 122, 13, (1962) [3] Bonner, J.T.; Hoffman, M.E., J. embryol. exp. morphol, 11, 571, (1963) [4] Bonner, J.T.; Barkley, D.S.; Hall, E.M.; Konijn, T.M.; Mason, J.W.; O’Keefe, G.; Wolfe, P.B., Develop. biol, (1969), Submitted to [5] Chandrasekhar, S., Hydrodynamic and hydromagnetic stability, (1961), Clarendon Press Oxford · Zbl 0142.44103 [6] Chang, Y.Y., Science, N.Y, 160, 57, (1968) [7] Heineken, F.G.; Tsuchiya, H.M.; Aris, R., Math. biosciences, 1, 95, (1967) [8] Konijn, T.M., Develop. biol, 12, 487, (1965) [9] Konijn, T.M.; Van De Meene, J.G.; Bonner, J.T.; Barkley, D.S., (), 1152 [10] Konijn, T.M., Biol. bull, 134, 302, (1968) [11] Prigogine, I.; Nicolis, G., J. chem. phys, 46, 3542, (1967) [12] Segel, L.A., (), 165 [13] Shaffer, B.M., J. exp. biol, 33, 645, (1956) [14] Shaffer, B.M., Am. nat, 91, 19, (1957) [15] Shaffer, B.M., Q. J. microsc. sci, 99, 103, (1958) [16] Shaffer, B.M., Adv. morphogenesis, 2, 109, (1962) [17] Turing, A.M., Phil. trans. R. soc. series B, 237, 37, (1952) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.