Introduction of my study

Background

We had studied regeneration phenomena through numerical simulation of connected chaotic elements [3], where cell types are regarded as various types of attractors within chemicals' state space, providing a unique view of cockroach leg regeneration. We had also modeled a multicellular organism using a Lindenmayer system (L-system) to derive a condition for the coexistence of various cell types [1,2], wherein an algebraic method was used to analyze the model with parameters.

Present Study

Tissues of animals and plants are maintained through balanced cell growth, movement, and elimination. Although cells are exchanged perpetually, the whole structure of the tissue is maintained. This form of maintenance is called cell turnover. I proposed a bio-inspired model of patterns that regenerate through turnover. This model is derived from the Dachsous–Fat system, which has recently attracted much attention because it is considered to facilitate regeneration in insect legs. In this model, I parameterize the manner of the redistribution of Dachsous and Fat during cell division, and then derived equations in the parameters that enable the patterns to regenerate and maintain themselves through turnover ( [4] , [5] ).
Extending these models, I now propose a method for analyzing multicell-turnover models by using multivariate polynomials.
[1] Yoshida, H., et al. "A simple classification of the volvocine algae by formal 　languages,"Bulletin of Mathematical Biology, Vol. 67, pp. 1339-1354, 2005.

[2] Yoshida, H., Miwa, Y., and Kaneko, M. "Elliptic curves and Fibonacci numbers arising from Lindenmayer system with Symbolic Computation," Applicable Algebra in Engineering, Communication and Computing, Vol. 22, No. 2, pp. 147-164, 2011.

[3] Yoshida, H., et al. "Selection of initial conditions for recursive production of multicellular organisms," J. Theor. Biol. Vol. 233, pp.501-514, 2005.

[4] Yoshida, H. “A pattern to regenerate through turnover,” Biosystems, Vol. 110, pp. 43-50, 2012.

[5] Yoshida, H. et al. “An extended steepness model for leg-size determination based on Dachsous/Fat trans-dimer system,” Scientific Reports, Vol. 4, 4335, 2014.