Linearized Buffered Ca²⁺Diffusion in Microdomains and Its Implications for Calculation of [Ca²⁺] at the Mouth of a Calcium Channel

Abstract

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...

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