Information Content in Stochastic Pulse Sequences of Intracellular Messengers

Many cell signaling pathways rely on oscillatory messenger concentrations even to transduce aperiodic environmental changes. The universal second messenger calcium, Ca²⁺ often exhibits pulsatile behavior in the presence of constant concentrations of external ligands such as hormones or neurotransmitters. The analysis of intracellular Ca²⁺ pulses that involve Ca²⁺ release through inositol 1,4,5-trisphosphate (IP₃) receptors led to a model with stochastic pulse firing at rate, λ and deterministic inhibition with recovery at rate, ρ. Here we combine this model with recent observations that established an exponential relationship between λ and the external ligand concentration, C. We compute analytically the mutual information between C and the interpulse time, t, or the number of pulses, N, in the λ/ρ ≪ 1 and λ/ρ ≫ 1 limits. We obtain that both I(C, t) and I(C, N) are largest in the second limit with a difference of at most ~1bit. Thus, the resolution with which the values of C can be discriminated at most doubles in one limit with respect to the other. The components of the model and the exponential dependence of the firing rate with C are features common to noise-driven excitable systems. Our results thus hold in this more general setting that applies widely in biology.