  Signaling networks are designed to sense an environmental stimulus and adapt
to it. We propose and study a minimal model of signaling network that can sense
and respond to external stimuli of varying strength in an adaptive manner. The
structure of this minimal network is derived based on some simple assumptions
on its differential response to external stimuli. We employ stochastic
differential equations and probability distributions obtained from stochastic
simulations to characterize differential signaling response in our minimal
network model. We show that the proposed minimal signaling network displays two
distinct types of response as the strength of the stimulus is decreased. The
signaling network has a deterministic part that undergoes rapid activation by a
strong stimulus in which case cell-to-cell fluctuations can be ignored. As the
strength of the stimulus decreases, the stochastic part of the network begins
dominating the signaling response where slow activation is observed with
characteristic large cell-to-cell stochastic variability. Interestingly, this
proposed stochastic signaling network can capture some of the essential
signaling behaviors of a complex apoptotic cell death signaling network that
has been studied through experiments and large-scale computer simulations. Thus
we claim that the proposed signaling network is an appropriate minimal model of
apoptosis signaling. Elucidating the fundamental design principles of complex
cellular signaling pathways such as apoptosis signaling remains a challenging
task. We demonstrate how our proposed minimal model can help elucidate the
effect of a specific apoptotic inhibitor Bcl-2 on apoptotic signaling in a
cell-type independent manner. We also discuss the implications of our study in
elucidating the adaptive strategy of cell death signaling pathways.
