Figure 3

Time-dependent buffering: the "muffling" of Ca⁺⁺ ions. A, Muffling is brought about by binding and flux. The concentration of free Ca⁺⁺ ions in a small volume element (dx × dy × dz) is changed instantaneously by addition Δe₀ further free Ca⁺⁺ ions (red arrow). The "error" imposed by this acute Ca⁺⁺ load either persists, or it is reduced over time. Reduction (blue arrows) may occur via Ca⁺⁺ flux across the boundaries of the volume element (right arrow), or by binding of Ca⁺⁺ to Ca⁺⁺ buffers within the volume element (lower arrow); the time-dependent, combined effect of binding and flux is termed "muffling". B, Prototypes of muffling. From top to bottom: 1, Zero muffling in the absence of both flux and binding; 2, Muffling via flux across its boundaries (e.g. diffusion), without binding to buffers within the volume element; 3, Muffling via binding to buffers inside the volume element, without flux; 4, Muffling due to both binding and flux. Note that peak size and magnitude of muffling action are not correlated. C, Measures for time-dependent "error reduction", or "muffling". A measure that reflects both the size and the duration of the error e(t) is the integral (red area). Similarly, a measure that reflects both the size and the duration of the "error reduction" or "muffling" m(t) is given by the integral (blue area). The proportions between ε(t) and μ(t) can be used to define a "muffling coefficient" and "muffling ratio" (see main text of BufferingII). These measures are the time-dependent analogs of the time-independent "buffering coefficient" and "buffering ratio" (Buffering I).