Information content in stochastic pulse sequences of intracellular messengers

Abstract

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.