Figure 1.
Schematic diagrams of dopamine- and calcium-dependent synaptic plasticity.
(A) Dopamine-dependent synaptic plasticity (modified from [27]). (B) Calcium-dependent synaptic plasticity. The abbreviations used in superimposition are as follows: SN - substantia nigra; LFS - low-frequency stimulation; and HFS - high-frequency stimulation. The altered direction of synaptic efficacy depends on input intensity of dopamine and calcium.
Figure 2.
Block diagram of the signal transduction model in medium spiny neurons.
The red and blue arrows indicate activation and inhibition, respectively. Detailed information on the regulatory pathways is provided in the Materials and Methods section, and the rough sketch of the signal flow is as follows. Glutamate binds to its corresponding receptors and increases intracellular calcium. D1R binding to dopamine increases cAMP. Calcium and cAMP alter the number of AMPA membrane receptors via downstream cascades and, thereby, regulate the synaptic efficacy of the neuron. The bi-directional effect of calcium on receptor should be mentioned. The activation level (open probability) of
receptor displays a bell-shaped response curve to intracellular calcium concentrations. The
receptor activation level is maximal when intracellular calcium concentration is approximately
[107]. However, more (and less) calcium reduces
receptor activation. To represent this regulation, two complementary arrows represent activation and inhibition from calcium to
receptor in this diagram. In addition, one arrow originates from Ser137 and terminates at an arrow from PP2B to Thr34. Phosphorylation of Ser137 decreases the rate of Thr34 dephosphorylation by PP2B. Therefore, Ser137 contributes to disinhibition of the PP2B-Thr34 pathway [55]. The arrow from Ser137 represents this effect.
Figure 3.
Schematic diagram of the AMPA receptor trafficking model.
AMPA receptors are phosphorylated at Ser845 and Ser831 by PKA and CaMKII, respectively, and are also dephosphorylated by PP1 and PP2A. The phosphorylated AMPA receptors bind to anchor protein (Anchor) and are inserted into the cell membrane. In contrast, dephosphorylated AMPA receptors are removed from the membrane. AMPA receptors released from anchor protein are degraded and stored in cytosol (Bulk AMPAR).
Figure 4.
Transient time courses from two input sources.
(A) Calcium input and (B) magnification from 0 to 1 second. (C) Dopamine input and (D) magnification from 0 to 1 second.
Figure 5.
Transient activation responses of intracellular molecules from the original model.
Line colors denote four different conditions: calcium influx without dopamine input (cyan);
calcium influx without dopamine input (blue);
calcium influx coincident with
dopamine input (magenta); and
dopamine input in the absence of calcium influx (red). (A–O) Each plot indicates the activation state of each protein. (P) AMPARp indicates total concentration of phosphorylated AMPA receptor from at least one phosphorylation site.
Figure 6.
Dopamine- and calcium-dependent synaptic plasticity reproduced by the model.
(A) Transient time courses of synaptic efficacy induced by (solid line),
(dotted line), and
(dashed line) dopamine input coincident with
calcium input. (B) Transient time courses of synaptic efficacy induced by
(solid line),
(dotted line), and
(dashed line) calcium input without dopamine input. In all cases from (A) and (B), input was initiated at 0 seconds and synaptic efficacy was evaluated by the number of AMPA receptors in the post-synaptic membrane. (C) Synaptic plasticity as a function of dopamine input with
calcium input. The dopamine concentration was fixed at
in the depleted condition, but set to
steady state in the remaining conditions. (D) Synaptic plasticity as a function of calcium input. For (C) and (D), plasticity was evaluated by the ratio of the number of AMPA receptors in the post-synaptic membrane prior to and 10 minutes after stimulation onset.
Figure 7.
Contour plot of synaptic plasticity during dopamine and calcium input.
Panels (A–D) show results from four different conditions: (A) control with the original model; (B) fixation of CaMKII activity; (C) fixation of PKA activity; and (D) fixation of PP1 activity. The quantitative evaluation of synaptic plasticity was identical to Fig. 4. Green (corresponding to 1.0 in the right color-bar) indicates areas where synaptic efficacy was not altered. Hotter and colder colors indicate areas where LTP and LTD are induced, respectively.
Figure 8.
The role of the CK1-Cdk5 pathway.
The maximum response of (A) Cdk5 and (B) PP2A activities to different levels of calcium input. (C) Altered transient responses of phosphorylated Thr75 by removing the Ck1-Cdk5 pathway. The solid lines are responses from the original model. Dotted lines are the responses from the modified model, where the CK1-Cdk5 pathway was removed from the original model. Different levels of calcium input are denoted by different colors: red for calcium input; and blue for
calcium input.
Figure 9.
Responses of PKA and PP1 in the absence of DARPP-32.
(A–B) Maximal responses of active PKA to various levels of dopamine and calcium input, respectively. (C–D) Maximal responses of active PP1 to various levels of dopamine and calcium input, respectively. For all panels, black lines indicate results from the original model (control), and green lines indicate results from the modified model, where DARPP-32 is fixed at (DARPP-32 knockout condition).
Figure 10.
Synaptic plasticity in the absence of DARPP-32.
(A) Synaptic plasticity due to varying strengths of dopamine input combined with calcium input. (B) Synaptic plasticity due to varying strengths of calcium input without dopamine input. Black lines indicate results from the original model (control), and green lines indicate results from the modified model, where DARPP-32 is fixed at
(DARPP-32 knockout condition). (C) Contour plot of synaptic plasticity in the DARPP-32 knockout condition as a function of calcium and dopamine input.
Figure 11.
Hysteresis of PKA-PP2A-DARPP-32 positive feedback loop.
(A) Schematic diagram of the sub-network forming the PKA-PP2A-DARPP-32 positive feedback loop. Blocks indicate different molecular states. Specifically, DARPP-32 has four phosphorylation cites (Thr34, Thr75, Ser102, and Ser137), which are indicated by different colors in this diagram. Round arrowheads are enzymatic actions and red dots indicate phosphorylated states. (B) Active PKA changes at steady states, with gradual changes in cAMP concentration at fixed concentrations of calcium at and Cdk5 at
. First, cAMP concentration was set to
, and active PKA steady state was calculated by COPASI. Subsequently, cAMP concentration was increased by a step of
to
, and steady state level of active PKA was calculated at each setting. Next, cAMP concentration was reduced by a step of
to
, and steady state of active PKA was analyzed again. The arrows along the lines show the direction of the trajectory in the two-dimensional space of cAMP conditions and steady states of active PKA.
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.
Figure 13.
Robustness of the PKA-PP2A-DARPP-32 positive feedback loop.
(A–C) Robustness of the threshold-like PKA activation as a function of total concentration of Cdk5 in the sub-system shown in Fig. 9, when three parameters were independently altered: (A) A dissociation constant Kd in a reaction where Thr75 is dissociated from inhibited PKA, was given by (blue),
(cyan),
(green),
(orange),
(magenta) or
(red); (B) A catalytic constant
in a reaction where active PKA phosphorylates PP2A, is given by 10 times (black), 5 times (blue), 2 times (green), control (yellow), 0.5 times (orange), 0.2 times (magenta), 0.1 times (red), larger than the control value in the original model (yellow); and (C) A catalytic constant
in a reaction where active PP2A dephosphorylates Thr75, is given by 10 times (black), 5 times (blue), 2 times (green), control (yellow), 0.5 times (orange), 0.2 times (magenta), 0.1 times (red), larger than the control value in the original model (yellow). Please note that the dissociation constant Kd in panel (A) was set at
in our original model while it was said to be
in an experimental study [57].
Figure 14.
Transient responses at high basal dopamine levels.
Time courses of (A) cAMP, (B) PKA, (C) PP1 and (D) AMPA receptor in the post-synaptic membrane, respectively, when basal dopamine level was altered. The cyan lines indicate calcium influx, the blue lines indicate
calcium influx without dopamine input, and the magenta lines indicate
calcium influx together with
dopamine input. The solid lines indicate the
basal dopamine (control) condition, the dotted lines indicate the
condition, and the dashed lines indicate the
basal dopamine (dopamine depletion) condition.