Oscillations in the concentration of free cytosolic Ca 2+ are an important and ubiquitous control mechanism in many cell types. It is thus correspondingly important to understand the mechanisms that underlie the control of these oscillations and how their period is determined. We show that Class I Ca 2+ oscillations (i.e., oscillations that can occur at a constant concentration of inositol trisphosphate) have a common dynamical structure, irrespective of the oscillation period. This commonality allows the construction of a simple canonical model that incorporates this underlying dynamical behavior. Predictions from the model are tested, and confirmed, in three different cell types, with oscillation periods ranging over an order of magnitude. The model also predicts that Ca 2+ oscillation period can be controlled by modulation of the rate of activation by Ca 2+ of the inositol trisphosphate receptor. Preliminary experimental evidence consistent with this hypothesis is presented. Our canonical model has a structure similar to, but not identical to, the classic FitzHugh-Nagumo model. The characterization of variables by speed of evolution, as either fast or slow variables, changes over the course of a typical oscillation, leading to a model without globally defined fast and slow variables. ) are a ubiquitous signaling mechanism, occurring in many cell types and controlling a wide array of cellular functions (1-6). In many cases, the signal is carried by the oscillation frequency; for example, Ca 2+ oscillation frequency is known to control contraction of pulmonary and arteriole smooth muscle (7,8), as well as gene expression and differentiation (9-11). Although there are cell types where the frequency of Ca 2+ oscillation appears to be less important than the mean [Ca 2+ ] (12), an understanding of how Ca 2+ oscillation frequency is controlled remains critical to our understanding of many important cellular processes. Interestingly, it appears that the signal may not be carried by the absolute oscillation frequency but rather by a change in frequency (13), leading to a signaling system that is robust to intercellular variability, even within the same cell type. A concept similar to that of the Ca 2+ toolbox is important in the mathematical modeling of Ca 2+ dynamics. Models try to extract fundamental mechanisms, omitting less important details so that the basic skeleton-the basic toolbox components-can become clear. In the construction of such skeleton models, the concept of dynamical structure becomes important. The behavior of a model can be qualitatively described by a set of bifurcations and attracting or repelling sets, and this description is essentially independent of the exact model equations and parameters used to realize the underlying dynamical structure (in that there can be many different equations and parameters that have the same dynamical structure).One important question is how cells can generate Ca 2+ oscillations of widely differing periods, even though they appear to be using the same elements o...

(7,8). On the other hand, oscillatory changes in [IP 3 ] i have been suggested by the observed cyclical translocation of a GFPtagged pleckstrin homology domain of PLC-␦ (GFP-PHD) (9, 10). However, in other experiments using more specific IP 3 biosensors, IP 3 was shown to accumulate gradually with little or no fluctuation during Ca 2ϩ oscillations (11). These discrepant observations may be attributable to differences between various IP 3 biosensors and a lack of quantitation.There are two types of IP 3 biosensors, GFP-PHD and IP 3 Rbased FRET sensors. GFP-PHD binds to both PIP 2 and IP 3 ; thus it has been thought that changes in [IP 3 ] i could be monitored indirectly by the release of membrane-bound GFP-PHD (9). IP 3 R-based FRET biosensors consist of the ligand-binding domain of IP 3 R and a pair of fluorescent proteins, cyan fluorescent protein and yellow fluorescent protein. Since the successful monitoring of IP 3 with LIBRA (12), the first IP 3 R-based FRET biosensor, several different groups have used similar biosensors for IP 3 monitoring (11,13,14). In principle, quantitative measurements of [IP 3 ] i are not possible with GFP-PHD. In addition, it is recognized that GFP-PHD may be released from the plasma membrane by decreases in available PIP 2 (15), which could be attributed to PIP 2 hydrolysis or the occupation by other molecules. IP 3 R-based FRET biosensors offer significant benefits for monitoring IP 3 based on their high selectivity for IP 3 and ratiometric measurement.In this study, we developed a series of improved IP 3 biosensors that exhibit high pH stability and varying IP 3 affinities. They also possess higher selectively and afford a larger dynamic range than that of original LIBRA. In combination with these * This work was supported by Grant-in-aid for Scientific Research 16390532 (to A. T.), by HAITEKU (2007) from the Ministry of Education, Culture, Sports, Science and Technology of Japan, and the Japan Science and Technology Agency. The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

) (6).Plasmid Construction-A CFP/YFP fusion construct was made by cutting EYFP out of pEYFP-N1 (Clontech) using BamHI and XbaI and ligating into pECFP-C1 (Clontech) cut with the same enzymes. The multiple cloning site of this vector was then removed by cutting with BspEI and BamHI and replaced with a linker generated from two synthetic oligonucleotides. The forward sequence of this linker was TCC GGA AAG CTC GAG GCA GTA AGA TCT GGC TCC GCC GAC GAT GAC GAT AAG GCC GGA TCT GTC GAC GCA GTC GGA TCC, where the reconstituted BspEI and BamHI sites have been included for clarity and the sequence has been parsed into codons. This fusion construct was referred to as pCY-N. The linker plus EYFP sequence of pCY-N was then cut out with BsrGI and ligated into pECFP-mem (Clontech) cut with the same enzyme. Finally the multiple cloning site originating from pECFP-mem was removed by cutting with Eco47III and SmaI and religating. The resultant construct, mCY, codes for ECFP preceded by the N-terminal 20 amino acids of neuromodulin (a membrane-targeting signal) and followed by the above linker and EYFP.To construct LIBRA (luminous inositol trisphosphate-binding domain for ratiometric analysis) the IP 3 -binding domain of the rat type 3 IP 3 R (amino acids 1-604) was amplified by PCR using pCB-EGFP: IP 3 R3 (7) as the template and incorporating XhoI sites at either end. This sequence was then ligated into the XhoI site in the linker region of mCY using standard methods. LIBRA⌬N was constructed in the same way using amino acids 227-604 of the rat type 3 IP 3 R (8). The forward PCR primers used were ACG CAT ACT CGA GAT GAA TGA AAT GTC CAG C for LIBRA and AAG CAT ACT CGA GTT CCG GGA CCA TCT GGA G for LIBRA⌬N. The same reverse primer, AGC GTA TCT CGA GCT TCC GGT TGT TGT GCA G, was used for both PCR reactions. The correctness of all constructs was confirmed by restriction digestion and sequencing.Cell Culture and Transfection-SH-SY5Y cells purchased from Deutsche Sammlung von Mikroorganismen und Zellkulturen GmbH (Braunschweig, Germany) were cultured in Dulbecco's modified Eagle's medium (Invitrogen) with low glucose (100 mg/ml), supplemented with 10% newborn calf serum, 584 mg/ml L-glutamine, 110 mg/ml sodium pyruvate, 100 units/ml penicillin and 100 g/ml streptomycin. Cells were transfected with plasmids using LipofectAMINE

Abstract. In many cell types, low concentrations of inositol 1,4,5-trisphosphate (IP3) release only a portion of the intraceUular IP3-sensitive Ca 2÷ store, a phenomenon known as "quantal" Ca 2+ release. It has been suggested that this effect is a result of reduced activity of the IP3-dependent Ca 2÷ channel with decreasing calcium concentration within the IP3-sensitive store ([Ca2÷]s). To test this hypothesis, the properties of IP 3-dependent Ca 2÷ release in single saponin-permeabilized HSY cells were studied by monitoring [Ca2+]s using the Ca2+-sensitive fluorescent dye mag-fura-2. In permeabilized cells, blockade of the sarco/ER Ca 2+-ATPase pump in stores partially depleted by IP3 induced further Ca 2+ release via an IP3-dependent route, indicating that Ca e÷ entry via the sarco/ER Ca2+-ATPase pump had been balanced by Ca 2÷ loss via the IP3-sensitive channel before pump inhibition. IP3-dependent Mn 2÷ entry, monitored via quenching of luminal magfura-2 fluorescence, was readily apparent in filled stores but undetectable in Ca2+-depleted stores, indicating markedly reduced IP3-sensitive channel activity in the latter. Also consistent with reduced responsiveness of Ca2÷-depleted stores to IP3, the initial rate of refilling of these stores was unaffected by the presence of 0.3 ~M IP3, a concentration that was clearly effective in eliciting Ca 2+ release from filled stores. Analysis of the rate of Ca e÷ release at various IP3 concentrations indicated a significant shift of the IP 3 dose response toward higher [IP3] T RE physiologic effects of numerous hormones, growth factors, and neurotransmitters are mediated by a rise in intracellular (cytosolic) calcium concentration