Reliable encoding of stimulus intensities within random sequences of intracellular Ca2+ spikes.

Ca(2+) is a ubiquitous intracellular messenger that regulates diverse cellular activities. Extracellular stimuli often evoke sequences of intracellular Ca(2+) spikes, and spike frequency may encode stimulus intensity. However, the timing of spikes within a cell is random because each interspike interval has a large stochastic component. In human embryonic kidney (HEK) 293 cells and rat primary hepatocytes, we found that the average interspike interval also varied between individual cells. To evaluate how individual cells reliably encoded stimuli when Ca(2+) spikes exhibited such unpredictability, we combined Ca(2+) imaging of single cells with mathematical analyses of the Ca(2+) spikes evoked by receptors that stimulate formation of inositol 1,4,5-trisphosphate (IP3). This analysis revealed that signal-to-noise ratios were improved by slow recovery from feedback inhibition of Ca(2+) spiking operating at the whole-cell level and that they were robust against perturbations of the signaling pathway. Despite variability in the frequency of Ca(2+) spikes between cells, steps in stimulus intensity caused the stochastic period of the interspike interval to change by the same factor in all cells. These fold changes reliably encoded changes in stimulus intensity, and they resulted in an exponential dependence of average interspike interval on stimulation strength. We conclude that Ca(2+) spikes enable reliable signaling in a cell population despite randomness and cell-to-cell variability, because global feedback reduces noise, and changes in stimulus intensity are represented by fold changes in the stochastic period of the interspike interval.