Derivation of rigorous conditions for high cell-type diversity by algebraic approach

Hiroshi Yoshida, Hirokazu Anai, Katsuhisa Horimoto

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


The development of a multicellular organism is a dynamic process. Starting with one or a few cells, the organism develops into different types of cells with distinct functions. We have constructed a simple model by considering the cell number increase and the cell-type order conservation, and have assessed conditions for cell-type diversity. This model is based on a stochastic Lindenmayer system with cell-to-cell interactions for three types of cells. In the present model, we have successfully derived complex but rigorous algebraic relations between the proliferation and transition rates for cell-type diversity by using a symbolic method: quantifier elimination (QE). Surprisingly, three modes for the proliferation and transition rates have emerged for large ratios of the initial cells to the developed cells. The three modes have revealed that the equality between the development rates for the highest cell-type diversity is reduced during the development process of multicellular organisms. Furthermore, we have found that the highest cell-type diversity originates from order conservation.

Original languageEnglish
Pages (from-to)486-495
Number of pages10
Issue number2
Publication statusPublished - Sept 2007
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modelling and Simulation
  • General Biochemistry,Genetics and Molecular Biology
  • Applied Mathematics


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