A Kinetic Model of Dopamine- and Calcium-Dependent Striatal Synaptic Plasticity
Figure 12
Bi-stability of PKA-PP2A-Thr75 positive feedback.
(A, B) Bifurcation diagrams created by identification of steady states using the Newton method and determination of stabilities using the eigenvalues of the Jacobian. Large points indicate stable steady states and small points indicate unstable steady states. (A) Bifurcation diagram for the altered cAMP, with fixed parameters of calcium and
Cdk5. The subsystem has one stable state when cAMP is less than
or greater than
. At middle range of cAMP, three steady states exist: two stable states and one unstable state. (B) Bifurcation diagram for the altered Cdk5, with fixed parameters of
calcium and
cAMP. The subsystem has one stable state when Cdk5 is less than
or greater than
. At middle range of Cdk5, three steady states exist: two stable states and one unstable state. (C) Steady state level of PKA in the 2D parameter space of cAMP and Cdk5. The calcium concentration was fixed at
. The blue and red planes are steady states of PKA at low and high levels, respectively. The black dots indicate steady states with Cdk5 fixed at
or cAMP fixed at
, as plotted in panels A and B. (D) PKA trajectories from several initial conditions at a cAMP level of
and Cdk5 level of
. The trajectories funnel toward a stable steady state. The dotted line indicates PKA levels at an unstable steady state.