Coding efficiency and information rates in transmembrane signaling

A variety of cell types responds to hormonal stimuli by repetitive spikes in the intracellular concentration of calcium ([Ca²⁺]i) which have been demonstrated to encode information in their frequency, amplitude, and duration. These [Ca²⁺]i-spike trains are able to specifically regulate distinct cellular functions. Using a mathematical model for receptor-controlled [Ca²⁺]i oscillations in hepatocytes we investigate the encoding of fluctuating hormonal signals in [Ca²⁺]i-spike trains. The transmembrane information transfer is quantified by using an information-theoretic reverse-engineering approach which allows to reconstruct the dynamic hormonal stimulus from the [Ca²⁺]i-spike trains. This approach allows to estimate the accuracy of coding as well as the rate of transmembrane information transfer. We found that up to 87% of the dynamic stimulus information can be encoded in the [Ca²⁺]i-spike train at a maximum information transfer rate of 1.1 bit per [Ca²⁺]i-spike. These numerical results for humoral information transfer are in the same order as in a number of sensory neuronal systems despite several orders of magnitude different time scales of operation suggesting a universal principle of information processing in both biological systems.