How Does Calcium Oscillate?

Ca2+ is the most important second messenger in living cells serving as a critical link between a variety of extracellular stimuli and their intraand intercellular responses. The external signals are translated most often into repeated increases of the cytosolic Ca2+ concentration. Due to their importance and frequent appearance, Ca2+ oscillations have been extensively studied in experiments and most of the involved physiological elements are identified. Despite this knowledge, the link between these microscopic elements and the cellular dynamics is only vaguely understood. An important mechanism for generating cytosolic Ca2+ transients is Ca2+ release by channels from internal storage compartments, mainly from the endoplasmic reticulum and the sacroplasmic reticulum. A common channel type present in many cells is the inositol 1,4,5-trisphosphate receptor (IP3R) which opens and closes randomly in dependence on binding and dissociation of IP3 and Ca2+. The open probability of IP3R exhibits a nonlinear dependence on the cytosolic Ca2+ concentration leading to Ca2+ induced Ca2+ release, the key element of Ca2+ signaling. An initial opening of a single channel increases the open probability of adjacent channels, and Ca2+ release spreads throughout the whole cell until channel inhibition caused by high Ca2+ concentrations terminates the release. This work uses an interdisciplinary approach combining experimental techniques from biology, analytical tools from theoretical physics and computer simulations to clarify the question of the oscillation mechanism and how cells can generate globally coordinated Ca2+ signals originated from local stochastic channel dynamics. In this context, the spatial inhomogeneous distribution of IP3Rs, forming channel clusters which are separated by 1-7 μm, plays a key role. Together with Ca2+ pumps, this induces huge concentration gradients close to open clusters, leading to a hierarchical organization of Ca2+ signals. In combination with the random behavior of single IP3Rs, this might generate a stochastic medium, which is known from pattern formation. Starting from this knowledge, Ca2+ oscillations are predicted to be stochastic as well as to consist of repetitive wave nucleation and hence to have a spatial character. This hypothesis is justified experimentally in the first part of this thesis by analyzing Ca2+ oscillations of four different cell types in terms of their mean periods and standard deviations exhibiting a linear dependence. Hence, Ca2+ signaling constructively uses thermal noise to build global signals. Thereby the molecular fluctuations are carried on the level of the cell by the hierarchical signaling structure rendering Ca2+ oscillations stochastic. This contradicts the current opinion of the last decades of Ca2+ being a representative cellular oscillator. Moreover, this makes Ca2+ a first natural example of array enhanced coherent resonance, a phenomenon theoretically predicted by statistical physics. The knowledge of the oscillation mechanism allows as well for determination of intrinsic cell properties by global observations. To illuminate the structure of the signaling mechanism, the data are also analyzed with respect to information processing. Furthermore, the temperature dependence of Ca2+ signaling in astrocytes is analyzed experimentally. The findings show that the reported difference between cultured astrocytes and astrocytes in acute brain slices are mainly caused by the different temperatures at which cells are used to be measured. This leads again to a more general interrogation as to how temperature is recognized. Are the decreased Ca2+ signals at higher temperature caused by an increased pump activity and hence spatially controlled or does temperature mainly change local properties like the channel dynamics? In the modeling part of this work, a physiological model for intracellular Ca2+ dynamics in three spatial dimensions is developed that takes the spatial arrangement of cells seriously. In contrast to most models of Ca2+ dynamics using ordinary differential equations, it uses a detailed channel model for the discrete release sites and takes into account diffusion and buffer interaction of Ca2+. The model is based on separation of the two involved length scales. On the microscopic scale, the IP3Rs are described by Markov chains, the dynamics of which depend on the local Ca2+ concentration. The Ca2+ concentration is determined on its part by the channel states acting as source terms of the corresponding reaction diffusion system (RDS) describing the macroscopic scale. The two model segments are coupled by a hybrid version of a Gillespie algorithm. For an efficient simulation tool, the RDS is linearized and solved analytically by a three component Green’s functions describing cytosolic free Ca2+, mobile and immobile Ca2+ buffers, respectively. The linear RDS allows for an elegant parallel algorithm enabling detailed physiological simulation of intracellular Ca2+ dynamics. In dependence on physiological motivated parameters, the developed Green’s cell algorithm generates in a natural way the whole spectrum of experimentally known Ca2+ signals and fits the experimental data of the first part in an almost perfect manner.Thus, the temperature dependence of astrocytic Ca2+ signals are in line with an increased pump activity and highlights once more the spatial character of Ca2+ signaling. In simulations that go beyond the experimental possibilities, the role of IP3R clustering in Ca2+ signaling is studied and the influence of intrinsic channel properties on Ca2+ signals is analyzed. These investigations may lead to the design of new experiments. Although this work is inspired by Ca2+ dynamics, the general concept how cells can generate predictable behavior from noisy molecular properties may also hold for other signaling pathways, especially for those exhibiting spatial concentration gradients as well, such as cyclic adenosine monophosphate (cAMP). Moreover, the derived methods and modeling tools can be used in other scientific disciplines, too.