Reliable Encoding of Stimulus Intensities Within Random Sequences of Intracellular Ca 2+ Spikes

Mathematical analysis of Ca 2+ signals in single cells reveals how cells can encode stimulus intensity in the frequency of Ca 2+ spikes. Repetitive Ca 2+ spikes occur in many cells in response to stimuli that activate an intracellular signaling cascade that involves Ca 2+ released from internal stores. These repetitive spikes are believed to represent the intensity of the stimulus, such that increasing the stimulus increases the frequency of the spikes. But the time between spikes (interspike interval) is random within a cell, and cells in a population exhibit variable spiking frequencies. Thurley et al . performed single-cell Ca 2+ imaging of primary liver cells and human embryonic kidney (HEK) 293 cells to examine the properties of Ca 2+ spikes in response to extracellular ligands under various conditions. Mathematical analysis revealed that, although the interspike interval had a random element, there was a consistent fold change in this interval across populations of cells responding to different amounts of the ligands. Thus, a common change to a random element enables the cells to properly interpret signal intensity from the frequency of repetitive Ca 2+ 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 (IP 3 ). 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 dependen