Fig. 4: Nested hysteresis.
a Iterative construction of the kinetic scheme of nested hysteresis, generalizable to any value of n. In each diagram, the gray ovals indicate the subsystems (corresponding to binding and unbinding to the first n − 1 sites), which are assumed to relax much faster than the other transitions. b Occupation over time for each of n = 3 binding sites (black, blue, and orange), in a particular stochastic realization of nested hysteresis (parameters: n = 3, s = 10, x = 2). Dotted arrows in the schematic indicate the pattern of influences between the binding sites. c Illustration of a parameter choice (inset, color indicates rate—magenta = 104, blue = 100, cyan = 1) for which the dependence on x of the probability of the fully bound state approaches a Hill function with H = 7 very closely.
