AMSN | To simplify the analysis, we ignored the leak term and considered a linear transfer function, 8(2) 2 z for Which we calculated the fixed point rates 7L D1 and km. |
AMSN | As in the ‘additive’ scenario, we performed a simplified analysis of the dynamics of Eqs 21 and 22 without leak term and a linear transfer function and found the fixed point rates 7L D1 and |
AMSN | In this regime, the striatal network settles into stable fixed points (cf. |
D1 MSNs require overall stronger input from cortex than D2 MSNs | We confirmed this by evaluating the fixed points of the linearized dynamics of the D1 and D2 MSNs in a mean field model (Eqs 25—27, Fig 1B—grey and black traces). |
Mean field model | Linearizing around the fixed point With the Iacobian ma-triX: |
Mean field model | Where allows to analyze the stability by calculating the eigenvalues of the fixed point . |
Mean field model | We found the ei-genvalues to be real and negative for all values of the fixed points . |
Model limitations | Thirdly, our model explores the striatal dynamics at steady states, since the model showed stable fixed points . |
Supporting Information | (A) Fixed points for D1 and D2 MSNs plotted for different levels of dopamine. |
Introduction | a feedback loop) and their states form a partial fixed point of the Boolean model. |
Introduction | (A partial fixed point is a subset of nodes and a respective state for each of these nodes such that updating any node in the subset leaves its state unchanged, regardless of the state of the nodes outside the subset.) |
Introduction | It is noteworthy that stable motifs are preserved for other updating schemes because of their dynamical property of being partial fixed points . |
Stable motif control implies network control | The stable motifs’ states are partial fixed points of the logical model, and as such, they act as “points of no return” in the dynamics. |
The control targets transcend the logical modeling framework | Thus, the fixed point attractors of the Boolean model are preserved in the ODE model. |
f0 = (NOT B AND NOT A) OR (D AND NOT A) OR (D AND NOT B) OR NOT E | These stable motifs are strongly connected components and partial fixed points of the logical network. |