Inference of Probabilities over a Stochastic IL-System by Quantifier Elimination

An algebraic approach based on quantifier elimination is proposed for the inference of probabilistic parameters over stochastic Lindenmayer systems with interaction, IL-systems. We are concerned with a multi-cellular organism as an instance of a stochastic IL system. The organism starts with one or a few cells, and develops different types of cells with distinct functions. We have constructed a simple model with cell-type order conservation and have assessed conditions for high cell-type diversity. This model is based on the stochastic IL-system for three types of cells. The cell-type order conservation corresponds to interaction terms in the IL-system. In our model, we have successfully inferred algebraic relations between the probabilities for cell-type diversity by using a symbolic method, quantifier elimination (QE). Surprisingly, three modes for the proliferation and transition rates emerged for various ratios of the initial cells to the developed cells. Furthermore, we have found that the high cell-type diversity pattern originates from the cell-type order conservation. Thus, QE has yielded analysis of the IL-system, which has revealed that, during the developing process of multi-cellular organisms, complex but explicit relations exist between cell-type diversity patterns and developmental rates.

Authors and Affiliations

1. Faculty of Mathematics, Organization for the Promotion of Advanced Research, Kyushu University, Hakozaki 6–10–1, Higashi-ku, Fukuoka, 812–8581, Japan

   Hiroshi Yoshida

2. Computational Biology Research Centre (CBRC), National Institute of Advanced Industrial Science and Technology (AIST), Aomi 2–42, Koto-ku, Tokyo, 135–0064, Japan

   Katsuhisa Horimoto

3. IT Core Laboratories, Fujitsu Laboratories Ltd./CREST, JST., Kamikodanaka 4–1–1, Nakahara-ku, Kawasaki, 211–8588, Japan

   Hirokazu Anai

Corresponding author

Correspondence to Hiroshi Yoshida.

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