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Title: Modeling of metabolic mutation evolutionary processes using branching random walks Authors:  Vladimir Kutsenko - Lomonosov Moscow State University (Russia) [presenting]
Yulia Makarova - Lomonosov Moscow State University (Russia)
Elena Yarovaya - Lomonosov Moscow State University (Russia)
Abstract: Recent researches demonstrate that the development of complex metabolic mechanisms in bacteria can be caused by a series of mutations that change the nutrition behavior. We study the bacteria population with a mutation leading to a complete change in nutrition behavior. We propose two models of such population evolution based on continuous-time branching random walks (BRWs) on the multidimensional lattices. The underlying random walk is assumed to be symmetric, homogeneous in space and irreducible. The first model based on BRW with one type of particles allows describing the evolution of mutant bacteria. At the initial time, the lattice is empty. We assume that immigration of particles occurs with a constant intensity at each lattice point. After immigration, a particle (a mutant bacterium) can split into two, die or jump to another lattice points. The second model based on the two-type BRW allows analyzing the distribution of both mutant and non-mutant bacteria at every lattice point. Initially at any lattice point may be only a finite number of first-type particles (non-mutant bacteria). In this model, a particle (a mutant or a non-mutant bacterium) can die or generate two particles of any type. The asymptotic behavior of the first moments of particles of both types at every lattice point was studied.