Presentation Information
[POS-65]Mathematical Modeling for the Habituation in True Slime Molds Based on a Simplified Reaction-Diffusion System
*Kota Nishi1, Atsushi Tero1, Yukinori Nishigami2, Toshiyuki Nakagaki2 (1. Kyushu Univ. (Japan), 2. Hokkaido Univ. (Japan))
Keywords:
unicellular organisms,learning,mathematical modeling,simplified reaction-diffusion system
Habituation is a type of learning defined as a decrease in behavioral response to a repeated stimulus. The learning occurs in various organisms, and it is considered to be a critical function that filters unimportant stimuli. Boisseau et al. (2016) demonstrated the hallmarks of habituation in the plasmodium of Physarum polycephalum, true slime mold. The plasmodium is an amoeba-like unicellular organism. The organism forms protrusions at the leading edge due to the endoplasmic sol flow, and it locomotes. Boisseau et al. (2016) reported that the time to cross an agar region containing quinine, a chemical repellent, decreased when the plasmodium repeatedly crossed the area. In addition, they showed that the time to cross the quinine region recovered after it crossed the agar region without quinine. These results correspond to the hallmarks of habituation. In our study, we made a mathematical model to understand the mechanisms which realize the hallmarks in the plasmodium.
We considered the plasmodium locomotion on a straight line. First, we assumed that the extending velocity of its tip is proportional to the volumetric flow rate of sol toward the leading edge. The volumetric flow rate of sol is proportional to the sol pressure difference between the front and rear parts of the plasmodium because the sol flow can be approximated by Hagen-Poiseuille flow. As a result, we obtained a tip locomotion model controlled by two variables, the sol pressure at front and rear parts . Next, we derived the temporal dynamics of the sol pressures from a reaction-diffusion system of a chemical related to the pressure generation. Note that the diffusion term is discretely represented due to considering a chemical diffusion between two points, the front and rear parts. In addition, the parameters of reaction term switches depending on the presence or absence of stimulus. Ultimately, we obtained a model of linear ordinary differential equations with three variables, the tip position and the sol pressure at front and rear parts.
Our simulation results reproduced the experimental results well. From our model, we found that the followings are important for the habituation behavior in the plasmodium: the dimensionality compression structure that transforms the sol pressures of two variables into the extending velocity of one variable, and the chemical diffusion.
Reference: Boisseau, R. P., et al. (2016). Proc. R. Soc. B, 283(1829).
We considered the plasmodium locomotion on a straight line. First, we assumed that the extending velocity of its tip is proportional to the volumetric flow rate of sol toward the leading edge. The volumetric flow rate of sol is proportional to the sol pressure difference between the front and rear parts of the plasmodium because the sol flow can be approximated by Hagen-Poiseuille flow. As a result, we obtained a tip locomotion model controlled by two variables, the sol pressure at front and rear parts . Next, we derived the temporal dynamics of the sol pressures from a reaction-diffusion system of a chemical related to the pressure generation. Note that the diffusion term is discretely represented due to considering a chemical diffusion between two points, the front and rear parts. In addition, the parameters of reaction term switches depending on the presence or absence of stimulus. Ultimately, we obtained a model of linear ordinary differential equations with three variables, the tip position and the sol pressure at front and rear parts.
Our simulation results reproduced the experimental results well. From our model, we found that the followings are important for the habituation behavior in the plasmodium: the dimensionality compression structure that transforms the sol pressures of two variables into the extending velocity of one variable, and the chemical diffusion.
Reference: Boisseau, R. P., et al. (2016). Proc. R. Soc. B, 283(1829).