ORIGINAL PAPER Effectors of the frequency of calcium oscillations in HEK-293 cells: wavelet analysis and a computer model David Szekely Æ Sarah C. Brennan Æ Hee-Chang Mun Æ Arthur D. Conigrave Æ Philip W. Kuchel Received: 26 February 2009 / Revised: 22 April 2009 / Accepted: 29 April 2009 / Published online: 3 June 2009 Ó European Biophysical Societies’ Association 2009 Abstract Oscillations of the intracellular concentration of Ca 2? in cultured HEK-293 cells, which heterologously expressed the calcium-sensing receptor, were recorded with the fluorophore Fura-2 using fluorescence microscopy. HEK-293 cells are extremely sensitive to small perturba- tions in extracellular calcium concentrations. Resting cells were attached to cover slips and perifused with saline solution containing physiologically relevant extracellular Ca 2? concentrations in the range 0.5–5 mM. Acquired digitized images of the cells showed oscillatory fluctua- tions in the intracellular Ca 2? concentration over the time course, and were processed as a function of the change in Fura-2 excitation ratio and frequency at 12–37°C. Newly developed data processing techniques with wavelet analy- sis were used to estimate the frequency at which the rectified sinusoidal oscillations occurred; we estimated *4 min -1 under normal conditions. Temperature varia- tions revealed an Arrhenius relationship in oscillation frequency. A critical Ca 2? concentration of *2 mM was estimated, below which oscillations did not occur. These data were used to develop a kinetic model of the system that was simulated using Mathematica; kinetic parameter values were adjusted to match the experimentally observed oscillations of intracellular Ca 2? concentration as a func- tion of extracellular Ca 2? concentration, and temperature; and from these, limit cycles were obtained and control coefficients were estimated for all parameters. Keywords Analytical kinetic model  Calcium-induced oscillations  Calcium-sensing receptor  Control coefficient  Fourier analysis  Fura-2 fluorescence microscopy  Limit cycle  Metabolic control analysis  Wavelet analysis Abbreviations 1D One-dimensional 2D Two-dimensional ATP Adenosine triphosphate CaR Calcium sensing receptor C f p Control coefficient, frequency with respect to parameter value DOG Derivative of a Gaussian EGTA Ethylene glycol tetra acetic acid ER Endoplasmic reticulum GTP Guanosine triphosphate HEK-293 Human embryonic kidney cells, Graham’s experiment number 293 IP 3 Inositol trisphosphate IP 3 R IP 3 receptor K d Dissociation constant K M Michaelis constant PKC Protein kinase C PMCA Plasma membrane Ca 2? -ATPase SERCA Sarcoplasmic/endoplasmic reticulum Ca 2? -ATPase t Time ‘‘Proteins, membranes and cells: the structure-function nexus.’’ Contributions from the annual scientific meeting (including a special symposium in honour of Professor Alex Hope of Flinders University, South Australia) of the Australian Society for Biophysics held in Canberra, ACT, Australia, 28 September–1 October 2008. D. Szekely  S. C. Brennan  H.-C. Mun  A. D. Conigrave  P. W. Kuchel (&) School of Molecular and Microbial Biosciences, University of Sydney, Building G08, Sydney, NSW 2006, Australia e-mail: p.kuchel@mmb.usyd.edu.au P. W. Kuchel Centre for Mathematical Biology, University of Sydney, Sydney, NSW 2006, Australia 123 Eur Biophys J (2009) 39:149–165 DOI 10.1007/s00249-009-0469-2