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Models of IP₃ and Ca²⁺ Oscillations: Frequency Encoding and Identification of Underlying Feedbacks

Antonio Politi ^*, Lawrence D. Gaspers , Andrew P. Thomas  and Thomas Höfer ^*

^* Department of Theoretical Biophysics, Institute of Biology, Humboldt University Berlin, 10115 Berlin, Germany; and Department of Physiology and Pharmacology, University of Medicine and Dentistry of New Jersey, Newark, New Jersey

Correspondence: Address reprint requests to Thomas Höfer, Dept. of Theoretical Biophysics, Institute of Biology, Humboldt University Berlin, Invalidenstrasse 42, 10115 Berlin, Germany. Tel.: 4930-2093-8592-8698; Fax: 4930-2093-8813; E-mail: thomas.hoefer{at}biologie.hu-berlin.de.

Hormones that act through the calcium-releasing messenger, inositol 1,4,5-trisphosphate (IP₃), cause intracellular calcium oscillations, which have been ascribed to calcium feedbacks on the IP₃ receptor. Recent studies have shown that IP₃ levels oscillate together with the cytoplasmic calcium concentration. To investigate the functional significance of this phenomenon, we have developed mathematical models of the interaction of both second messengers. The models account for both positive and negative feedbacks of calcium on IP₃ metabolism, mediated by calcium activation of phospholipase C and IP₃ 3-kinase, respectively. The coupled IP₃ and calcium oscillations have a greatly expanded frequency range compared to calcium fluctuations obtained with clamped IP₃. Therefore the feedbacks can be physiologically important in supporting the efficient frequency encoding of hormone concentration observed in many cell types. This action of the feedbacks depends on the turnover rate of IP₃. To shape the oscillations, positive feedback requires fast IP₃ turnover, whereas negative feedback requires slow IP₃ turnover. The ectopic expression of an IP₃ binding protein has been used to decrease the rate of IP₃ turnover experimentally, resulting in a dose-dependent slowing and eventual quenching of the Ca²⁺ oscillations. These results are consistent with a model based on positive feedback of Ca²⁺ on IP₃ production.

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