The aKP Cycle Model
(A) In its macroscopic determinist approximation, the model consists of a simple reaction scheme. The nonphosphorylated (S) and phosphorylated (S*) forms are present with fractions 1 − f and f, respectively, and are interconverted with rates K and P by the kinase and a phosphatase. Enzymes are activity dependent through calcium, and f is the readout variable.
(B) Kinase (thick line) and phosphatase (thin line) calcium activation functions. Dashed line indicates Ca0, the basal Ca (0.1 μM).
(C) Rapid plastic modifications in f in response to Ca pulses from Ca0 to 6 μM (upper traces) and 3 μM (lower traces) in the stochastic (individual traces: thin black trace; mean trace [n = 20]: thick black trace) and deterministic (thick gray trace) models.
(D) Relaxation of f at Ca0 from different f values. Inset: enlargement of three relaxation traces during 24 h illustrates the low evolution rate of f.