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Physico-chemical model of a protocell. (English) Zbl 0571.92003
A physico-chemical model of a self-maintaining unity or protocell is constructed on the basis of reaction and diffusion processes. The surface motion of the protocell is taken into account explicitly by a so-called Stefan condition, which leads to a nonlinear feedback to the reaction and diffusion processes.
The spatio-temporal dynamics in the neighbourhood of the steady states is investigated in the framework of linear stability analysis with the use of an expansion in terms of spherical harmonics \(Y_ l^ m\). It is shown that modes with \(l\geq 2\) become successively unstable with increasing nutrient supply. The leading instability with \(l=2\) initiates a process of the nonlinear dynamics which is interpreted as the onset of division. A stabilizing effect of surface tension is also discussed.

MSC:
92B05 General biology and biomathematics
92Cxx Physiological, cellular and medical topics
35A99 General topics in partial differential equations
35B35 Stability in context of PDEs
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