Computational modeling of calcium signaling from the nanoscale to multicellular systems

Calcium signaling is one of the most important signaling mechanisms controlling e.g. the contraction of muscle cells, the release of neurotransmitter from neurons and astrocytes, transcription inside the nucleus and metabolic processes in liver and pancreas [8, 44, 36]. Due to the general importance in cell biology, Ca2+ signals of a variety of forms have been the subject of much recent experimental research. A recent and particularly powerful approach towards the understanding of Ca2+ signaling is the combination of highly resolved fluorescent imaging methods and detailed mathematical modeling. Models for Ca2+ signaling are probably the most advanced and realistic modes in all areas of biological physics. Hence theoretical predictions are quantitative in nature and allow direct comparison with experiments.;Ca2+ signaling patterns exhibit a hierarchical structure varying from single-channel release events (10's of nanometers) to Ca2+ waves sweeping over entire organs like the liver to globally orchestrate the efficient release of enzymes [48]. This multi-scale organization renders it an ideal tool for studying basic concepts of pattern formation, especially since access to the most important experimental parameters is given. The aim of this dissertation is to develop mathematical models that quantitatively describe the characteristics of elementary Ca2+ elements (called Ca2+ -puffs) on the nano-scale as well as the organization of global waves and oscillations on the cell and organ scale. We used oocytes, eggs and astrocytes as model cells for our theoretical studies. Particularly on the microscopic scale we report significant progress in modeling Ca 2+ release events that are accurate in time course and spatial shape.;Experimental investigations have revealed recently that Ca 2+ signaling differentiates during the development of oocytes into mature eggs. The fertilization specific Ca2+ signal in mature eggs is characterized by a fast rise of intracellular Ca2+ and a slow decay on the time scale of minutes [46, 21]. The extended elevated Ca2+ signal during egg activation is important because it protects the egg against polyspermy that could cause death of the egg. The mechanism of Ca 2+ signaling differentiation during oocyte maturation, however, is largely unknown and is a subject of current research. We utilize mathematical modeling in conjunction with parallel experimental investigations (Khaled Machaca) to generate hypotheses for the changes in the Ca 2+ signaling machinery during oocyte maturation.;Astrocytes, a subtype of glial cells, play an active role in processing information in the brain. These cells form small circuits that modulate dynamically neuronal synapses in their vicinity. In cell cultures it has been observed that the recruitment of astrocytes in circuits leads to coordinated Ca2+ oscillations. We use mathematical modeling to investigate the physiological conditions under which astrocytes can exhibit the observed organization of relative phases of their Ca 2+ oscillations. The results suggest that intercellular Ca 2+ waves are partially autocatalytic---a topic of current dispute.