Mikolaj Cieslak, Przemyslaw Prusinkiewicz
Background. Lindenmayer systems (L-systems) provide a useful framework for modelling the development of multicellular structures and organisms. The parametric extension of L-systems allows for incorporating molecular-level processes into the models. Until now, the dynamics of these processes has been expressed using differential equations, implying continuously-valued concentrations of the substances involved. This assumption is not satisfied, however, when the numbers of molecules are small. A further extension that accounts for the stochastic effects arising in this case is thus needed.
Results. We integrate L-systems and the Gillespie Stochastic Simulation Algorithm to simulate stochastic processes in fixed and developing linear structures. We illustrate the resulting formalism with stochastic implementations of diffusion-decay, reaction-diffusion, and auxin-transport-driven morphogenetic processes.
Conclusions. Our method and software can be used to simulate molecular and higher-level spatially explicit stochastic processes in static and developing structures, and study their behaviour in the presence of stochastic perturbations.
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