Self-organizing Mechanism for Development of Space-filling Neuronal Dendrites
Figure 2
Schematic Representation of the Cell Compartment Model
(A,B) An activator–suppressor system. Intracellular activator promotes growth of dendrite and produces the suppressor or accelerates secretion of the suppressor from intracellular organelles (“1” in (A)). On the other hand, the suppressor is secreted from the cell and diffuses in extracellular compartments. Binding of its receptor on the plasma membrane triggers signaling to inhibit synthesis of the activator (“2” in (A)). These reactions underlie inhibitory dendro-dendritic interactions (B).
(C) Black: core of the cell; dark gray: cell boundary. The cell compartment is represented by collective circular domains around the core with radius R (gray circles).
(D) Dynamics of core of the cell (c). The activator promotes cell growth when its concentration is higher than threshold (Tr). a(u) = 0.49 (u ≤ Tr) or a(u) = 0.49 − 2.5(u – Tr) (u > Tr). Upper graph: Both c = 0 and c = 1 are stable equilibrium points. Lower graph: When a(u) < 0, c = a(u) and c = 1 are stable equilibrium points and c = 0 becomes an unstable equilibrium point. Very small positive noise was added to c, so c → 1 quickly. These settings make it possible to store the history of growth of c, because c = 1 is a stable equilibrium point all the time.