Figure 11.

ATP/ADP invariance explained through a fast-slow analysis. The arrows indicate direction and relative magnitude of motion. (A) The burst trajectory is projected into the plane of the ATP/ADP and $V$ variables. The silent-to-active transition (rightmost dashed vertical line) occurs at the knee of the s-shaped bifurcation diagram (the saddle-node bifurcation), whereas the active-to-silent transition (leftmost dashed vertical line) occurs at the termination of the periodic spiking branch (the homoclinic bifurcation). The glucose concentration is $G=8\text{ mM}$. The color coding is purple = slow motion, green = fast motion, and yellow = very fast motion. (B) When the glucose level is increased to $G=13\text{ mM}$ the burst trajectory covers the same path along the fast subsystem bifurcation diagram. For this reason, the peak, nadir, and mean values of ATP/ADP are the same at both glucose levels. The only difference is the speed at which the trajectory moves through the silent phase and the active phase of the burst. In both (A) and (B), $g_{\text{K}\left(\text{Ca}\right)}=10$ pS. To see this figure in color, go online.