Adaptation to Optimal Cell Growth through Self-Organized Criticality

A simple cell model consisting of a catalytic reaction network is studied to show that cellular states are self-organized in a critical state for achieving optimal growth; we consider the catalytic network dynamics over a wide range of environmental conditions, through the spontaneous regulation of nutrient transport into the cell. Furthermore, we find that the adaptability of cellular growth to reach a critical state depends only on the extent of environmental changes, while all chemical species in the cell exhibit correlated partial adaptation. These results are in remarkable agreement with the recent experimental observations of the present cells.

Figure 1

Adaptive dynamics of nutrient uptake. (a) Nutrient uptake $F_0$ plotted as a function of the environmental nutrient concentration $S$. The results of ten randomly generated reaction networks are overlaid. The dotted line denotes the maximal nutrient uptake for the case $\alpha =0$, beyond which the cell can no longer grow continuously. The parameters were set as $N=10000$, $\rho =2.5\times {10}^{-2}$, and $\alpha =2$. (b) The concentration of transporter $x_1$ is plotted as a function of the total concentration of non-nutrient chemicals $1-x_0$. The relationships obtained by ten random networks shown in (a) are presented. The solid line represents a slope of 2 for reference.

Figure 2

Rank-ordered concentration distribution of chemical species. Distributions for different values of $S$ are superimposed by using different colors. The solid line has a slope of $-1$ for reference. The other parameter values are identical to those shown in Fig. 1.

Figure 3

Adaptation dynamics of the nutrient uptake $F_0$ after the environmental nutrient concentration $S$ is changed. At $t=0$, $S$ is increased twice, and the responses corresponding to $S=100\to 200$, $S=200\to 400$, and $S=400\to 800$ are overlaid. The other parameter values are identical to those shown in Fig. 1.