Immobile and mobile calcium buffers shape the calcium signal close to a channel by reducing and localizing the transient calcium increase to physiological compartments. In this paper, we focus on the impact of mobile buffers in shaping steadystate calcium gradients in the vicinity of an open channel, i.e. within its "calcium microdomain." We present a linear approximation of the combined reaction-diffusion problem, which can be solved explicitly and accounts for an arbitrary number of calcium buffers, either endogenous or added exogenously. It is valid for small saturation levels of the present buffers and shows that within a few hundred nanometers from the channel, standing calcium gradients develop in hundreds of microseconds after channel opening. It is shown that every buffer can be assigned a uniquely defined length-constant as a measure of its capability to buffer calcium close to the channel. The lengthconstant clarifies intuitively the significance of buffer binding and unbinding kinetics for understanding local calcium signals. Hence, we examine the parameters shaping these steady-state gradients. The model can be used to check the expected influence of single channel calcium microdomains on physiological processes such as excitation-secretion coupling or excitation-contraction coupling and to explore the differential effect of kinetic buffer parameters on the shape of these microdomains. Key words: Ca 2ϩ microdomains; Ca 2ϩ diffusion; Ca 2ϩ buffers; buffer kinetics; diffusion modeling; synaptic transmissionCalcium is involved in a multitude of fast intracellular signal transduction mechanisms ranging from excitation -contraction coupling to synaptic transmission (Augustine et al., 1985;Cheng et al., 1993;Bruns and Jahn, 1995; C lapham, 1995). To achieve a high bandwidth of signal transmission at specific sites, the cell needs to localize the calcium signals in time and space. Mobile calcium buffers are elegant tools to achieve this temporal and spatial f unctional compartmentalization (Roberts, 1994): mobile calcium buffers act as calcium shuttles or sinks to produce steep gradients in a close neighborhood of channels. In these "calcium microdomains," [C a 2ϩ ] readily reaches many tens of micromolar levels to activate low-affinity processes. Complementary to this, the microdomains dissipate very rapidly by virtue of the mobilities of the buffers.Recent experimental studies (Eilers et al., 1995;Yuste and Denk, 1995) have used imaging techniques to observe the temporal and spatial dynamics of [Ca 2ϩ ] in different cell types. Unfortunately, currently available imaging technology does not simultaneously provide a sufficiently high resolution in time and space. Temporal resolution is sacrificed to get a decent spatial resolution, or vice versa. This dilemma, in concert with the insight that "Ca 2ϩ signaling takes the local route" (Augustine and Neher, 1992b), has in turn triggered a huge body of simulation studies that attempt to calculate the expected time course of calcium concentration increases...

Kenyon cells are the intrinsic interneurons of the mushroom bodies in the insect brain, a center for olfactory and multimodal processing and associative learning. These neurons are small (3–8 microns soma diameter) and numerous (340,000 and 400,000 in the bee and cockroach brains, respectively). In Drosophila, Kenyon cells are the dominant site of expression of the dunce, DC0, and rutabaga gene products, enzymes in the cAMP cascade whose absence leads to specific defects in olfactory learning. In honeybees, the volume of the mushroom body neurophils may depend on the age or social status of the individual. Although the anatomy of these neurons has been known for nearly a century, their physiological properties and the principles of information processing in the circuits that they form are totally unknown. This article provides a first such characterization. The activity of Kenyon cells was recorded in vivo from locust brains with intracellular and local field potential electrodes during olfactory processing. Kenyon cells had a high input impedance (approximately 1 G omega at the soma). They produced action potentials upon depolarization, and consistently showed spike adaptation during long depolarizing current pulses. They generally displayed a low resting level of spike activity in the absence of sensory stimulation, despite a large background of spontaneous synaptic activity, and showed no intrinsic bursting behavior. Presentation of an airborne odor, but not air alone, to an antenna evoked spatially coherent field potential oscillations in the ipsilateral mushroom body, with a frequency of approximately 20 Hz. The frequency of these oscillations was independent of the nature of the odorant. Short bouts of oscillations sometimes occurred spontaneously, that is, in the absence of odorant stimulation. Autocorrelograms of the local field potentials in the absence of olfactory stimulation revealed small peaks at +/- 50 msec, suggesting an intrinsic tendency of the mushroom body networks to oscillate at 20 Hz. Such oscillatory behavior could not be seen from local field potential recordings in the antennal lobes, and may thus be generated in the mushroom body, or via feedback interactions with downstream neurons in the protocerebrum. During the odor-induced oscillations, the membrane potential of Kenyon cells oscillated around the resting level, under the influence of excitatory inputs phase- locked to the field activity. Each phasic wave of depolarization in a Kenyon cell could be amplified by intrinsic excitable properties of the dendritic membrane, and sometimes led to one action potential, whose timing was phase-locked to the population oscillations.(ABSTRACT TRUNCATED AT 400 WORDS)

The Ca2+ binding kinetics of fura-2, DM-nitrophen, and the endogenous Ca2+ buffer, which determine the time course of Ca2+ changes after photolysis of DM-nitrophen, were studied in bovine chromaffin cells. The in vivo Ca2+ association rate constants of fura-2, DM-nitrophen, and the endogenous Ca2+ buffer were measured to be 5.17 x 10(8) M-1 s-1, 3.5 x 10(7) M-1 s-1, and 1.07 x 10(8) M-1 s-1, respectively. The endogenous Ca2+ buffer appeared to have a low affinity for Ca2+ with a dissociation constant around 100 microM. A fast Ca2+ uptake mechanism was also found to play a dominant role in the clearance of Ca2+ after flashes at high intracellular free Ca2+ concentrations ([Ca2+]), causing a fast [Ca2+]i decay within seconds. This Ca2+ clearance was identified as mitochondrial Ca2+ uptake. Its uptake kinetics were studied by analyzing the Ca2+ decay at high [Ca2+]i after flash photolysis of DM-nitrophen. The capacity of the mitochondrial uptake corresponds to a total cytosolic Ca2+ load of approximately 1 mM.

Recent experimental studies have investigated the kinetic competition between calcium chelators and the secretion apparatus at a fast central synapse. Simultaneously, mathematical modelling studies indicate the importance of a quantitative knowledge of the binding kinetics of the chelators in studying fast physiological processes operating on a millisecond time scale. Using the temperature-jump relaxation method, I have studied the in vitro kinetics of Bis-Fura-2, Furaptra, Fluo-3, Calcium-Green-1, Calcium-Green-5N, Calcium-Orange-5N as well as EGTA, BAPTA and H-EDTA in conditions which are identical to those implemented in our patch clamp recordings, i.e. 100-140 mM CsCl, 20-40 mM Cs-HEPES, 8 mM NaCl, pH = 7.2 at 22 degrees C. The results can be summarized as follows: all fluorescent indicators have on rates in the range of 10(8)-10(9) M-1s-1. They differ significantly with respect to their off-rates from each other according to their affinities, ranging from 100 s-1 up to 26,000 s-1. BAPTA is kinetically almost indistinguishable from Fura-2. EGTA and H-EDTA have small binding rate constants for calcium in the range of 3 x 10(6) M-1s-1 since, at pH 7.20, protons need to be dissociated from the chelators before they can bind calcium ions.

The linear response function technique is used to analyze two 1300‐km tracks of SEASAT altimeter data and corresponding bathymetry in the Musician Seamounts region north of Hawaii. Bathymetry and geoid height are highly correlated in the 50‐ to 300‐km wavelength range. A predictive filter is developed which can operate on SEASAT altimetry in poorly surveyed oceanic regions to indicate the presence of major bathymétrie anomalies. Modeling of the bathymetry‐geoid correlation in the Musician region is attempted using the elastic plate model. The flexural rigidity D of the plate is not well constrained by our data but appears to lie in the range 5×1021 N m ‐ 5×1022 N m at the time of loading. Since the Musician Seamounts and the crust on which they lie are both Late Cretaceous in age, this value represents the effective flexural rigidity of very young lithosphere that was ‘frozen in’ at the time of voicanism, The modeling indicates that the general form of a predictive filter will strongly depend on various geologic parameters, especially the effective flexural rigidity. Hence, some a priori geologic constraints are necessary to estimate successfully the bathymetry from the altimeter data. Alternately, if high‐quality bathymetry is available, a crude estimate of the age of loading (i.e., voicanism) can be made from the altimeter data.