  Signal transduction is an important and basic mechanism to cell life
activities. The stochastic state transition of receptor induces the release of
signaling molecular, which triggers the state transition of other receptors. It
constructs a nonlinear sigaling network, and leads to robust switchlike
properties which are critical to biological function. Network architectures and
state transitions of receptor affect the performance of this biological
network. In this work, we perform a study of nonlinear signaling on biological
polymorphic network by analyzing network dynamics of the Ca$^{2+}$ induced
Ca$^{2+}$ release mechanism, where fast and slow processes are involved and the
receptor has four conformational states. Three types of networks,
Erd\"os-R\'enyi network, Watts-Strogatz network and BaraB\'asi-Albert network,
are considered with different parameters. The dynamics of the biological
networks exhibit different patterns at different time scales. At short time
scale, the second open state is essential to reproduce the quasi-bistable
regime, which emerges at a critical strength of connection for all three states
involved in the fast processes and disappears at another critical point. The
pattern at short time scale is not sensitive to the network architecture. At
long time scale, only monostable regime is observed, and difference of network
architectures affects the results more seriously. Our finding identifies
features of nonlinear signaling networks with multistate that may underlie
their biological function.
