Scheme of the double enzymatic cycle of addition/removal reactions of chemical groups via Michelis-Menten kinetic equations as shown in Eq. (1) in the case of phosphoric groups.
Stationary distributions for the A and states in the double phosphorylation cycle when detailed balance (13) holds with and . In the top figure we set the reaction velocities and (symmetric case), whereas in the bottom figure we increase the and value to 1.15. The number of molecules is N T = 40. The transition from a unimodal distribution to a bimodal distribution is clearly visible.
In grey we show the region where components of the vector field (11) are ≃1 using the parameter values of Fig. 2 (bottom). The blue lines enclose the region where the first component is nearby 1, whereas the red ones enclose the corresponding region for the second component.
Plot of the rotor field for the potential H using the following parameter values: v M1 = v M2 = 1, , N T = 40 and (left picture) or (right picture).
(Left picture): Plot of the zero-order approximation for the probability distribution using the decomposition (17) for the vector field associated to the CME. (Right picture): Plot of the stationary distribution computed by directly solving the CME (2). We use the parameter values of the case I in Table I.
The same as in Fig. 5 using parameter values of case II in Table I.
The same as in Fig. 5 using the parameter values of the case III in Table I.
Current vector field computed by using definiton (5) and the stationary solution of the CME with case IV parameters. The distribution is bimodal (cf. Figure 9) and the current lines tend to be orthogonal to the distribution gradient near the maximal value.
The same as in Fig. 5 using parameter values of case IV in Table I.
Main parameters used in the simulations.
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