A Statistical View on Calcium Oscillations.

in Advances in experimental medicine and biology (2020), 1131

Transient rises and falls of the intracellular calcium concentration have been observed in numerous cell types and under a plethora of conditions. There is now a growing body of evidence that these whole ... [more ▼]

Transient rises and falls of the intracellular calcium concentration have been observed in numerous cell types and under a plethora of conditions. There is now a growing body of evidence that these whole-cell calcium oscillations are stochastic, which poses a significant challenge for modelling. In this review, we take a closer look at recently developed statistical approaches to calcium oscillations. These models describe the timing of whole-cell calcium spikes, yet their parametrisations reflect subcellular processes. We show how non-stationary calcium spike sequences, which e.g. occur during slow depletion of intracellular calcium stores or in the presence of time-dependent stimulation, can be analysed with the help of so-called intensity functions. By utilising Bayesian concepts, we demonstrate how values of key parameters of the statistical model can be inferred from single cell calcium spike sequences and illustrate what information whole-cell statistical models can provide about the subcellular mechanistic processes that drive calcium oscillations. In particular, we find that the interspike interval distribution of HEK293 cells under constant stimulation is captured by a Gamma distribution. [less ▲]

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

in Science Signaling (2014), 7(331), 59

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 ... [more ▼]

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. [less ▲]

Calcium signals driven by single channel noise.

in PLoS computational biology (2010), 6(8),

Usually, the occurrence of random cell behavior is appointed to small copy numbers of molecules involved in the stochastic process. Recently, we demonstrated for a variety of cell types that intracellular ... [more ▼]

Usually, the occurrence of random cell behavior is appointed to small copy numbers of molecules involved in the stochastic process. Recently, we demonstrated for a variety of cell types that intracellular Ca2+ oscillations are sequences of random spikes despite the involvement of many molecules in spike generation. This randomness arises from the stochastic state transitions of individual Ca2+ release channels and does not average out due to the existence of steep concentration gradients. The system is hierarchical due to the structural levels channel--channel cluster--cell and a corresponding strength of coupling. Concentration gradients introduce microdomains which couple channels of a cluster strongly. But they couple clusters only weakly; too weak to establish deterministic behavior on cell level. Here, we present a multi-scale modelling concept for stochastic hierarchical systems. It simulates active molecules individually as Markov chains and their coupling by deterministic diffusion. Thus, we are able to follow the consequences of random single molecule state changes up to the signal on cell level. To demonstrate the potential of the method, we simulate a variety of experiments. Comparisons of simulated and experimental data of spontaneous oscillations in astrocytes emphasize the role of spatial concentration gradients in Ca2+ signalling. Analysis of extensive simulations indicates that frequency encoding described by the relation between average and standard deviation of interspike intervals is surprisingly robust. This robustness is a property of the random spiking mechanism and not a result of control. [less ▲]

Clustering of InsP3 receptors by InsP3 retunes their regulation by InsP3 and Ca2+.

in Nature (2009), 458(7238), 655-9

The versatility of Ca2+ signals derives from their spatio-temporal organization. For Ca2+ signals initiated by inositol-1,4,5-trisphosphate (InsP3), this requires local interactions between InsP3 ... [more ▼]

The versatility of Ca2+ signals derives from their spatio-temporal organization. For Ca2+ signals initiated by inositol-1,4,5-trisphosphate (InsP3), this requires local interactions between InsP3 receptors (InsP3Rs) mediated by their rapid stimulation and slower inhibition\ by cytosolic Ca2+. This allows hierarchical recruitment of Ca2+ release events as the InsP3 concentration increases. Single InsP3Rs respond first, then clustered InsP3Rs open together giving a local 'Ca2+ puff', and as puffs become more frequent they ignite regenerative Ca2+ waves. Using nuclear patch-clamp recording, here we demonstrate that InsP3Rs are initially randomly distributed with an estimated separation of 1 m. Low concentrations of InsP3 cause InsP3Rs to aggregate rapidly and reversibly into small clusters of about four closely associated InsP3Rs. At resting cytosolic [Ca2+], clustered InsP3Rs open independently, but with lower open probability, shorter open time, and less InsP3 sensitivity than lone InsP3Rs. Increasing cytosolic [Ca2+] reverses the inhibition caused by clustering, InsP3R gating becomes coupled, and the duration of multiple openings is prolonged. Clustering both exposes InsP3Rs to local Ca2+ rises and increases the effects of Ca2+. Dynamic regulation of clustering by InsP3 retunes InsP3R sensitivity to InsP3 and Ca2+, facilitating hierarchical recruitment of the elementary events that underlie all InsP3-evoked Ca2+ signals. [less ▲]

The role of IP3R clustering in Ca2+ signaling.

in Genome informatics. International Conference on Genome Informatics (2008), 20

Ca(2+) is the most important second messenger controlling a variety of intracellular processes by oscillations of the cytosolic Ca(2+) concentration. These oscillations occur by Ca(2+) release from the ... [more ▼]

Ca(2+) is the most important second messenger controlling a variety of intracellular processes by oscillations of the cytosolic Ca(2+) concentration. These oscillations occur by Ca(2+) release from the endoplasmic reticulum (ER) into the cytosol through channels and the re-uptake of Ca(2+) into the ER by pumps. A common channel type present in many cell types is the inositol trisphosphate receptor (IP(3)R), which is activated by IP(3) and Ca(2+) itself leading to Ca(2+) induced Ca(2+) release (CICR). We have shown in an experimental study, that Ca(2+) oscillations are sequences of random spikes that occur by wave nucleation. We use here our recently developed model for Ca(2+) dynamics in 3 dimension to illuminate the role of IP(3)R clustering within spatial extended systems. [less ▲]

Statistical properties and information content of calcium oscillations.

in Genome informatics. International Conference on Genome Informatics (2007), 18

Calcium is the most important second messenger in living cells serving as a critical link between a large variety of extracellular stimuli and the intracellular target. Often, the Ca(2+) signal is carried ... [more ▼]

Calcium is the most important second messenger in living cells serving as a critical link between a large variety of extracellular stimuli and the intracellular target. Often, the Ca(2+) signal is carried by [Ca(2+)] oscillations. Our recent studies have demonstrated that in contrast to traditional ideas Ca(2+) oscillations do not occur by simple synchronization of channel clusters opening and closing in an oscillatory fashion but originate from microscopic fluctuation caused by the stochastic binding of the ligands Ca(2+) and IP(3) to the receptor's binding sites. They are orchestrated spatially on the cell level by wave nucleation. In this paper we analyze the stochastic data and show how internal properties can be determined from global observations. Further, we analyze the information content of spontaneous and stimulated oscillations. [less ▲]