Pitchfork bifurcation in a receptor theory-based model of the serotonergic system

Abnormalities in the serotonergic system are thought to be a potent cause of several mental diseases. Past research has shown that autoreceptors are the key component. It is thought that the autoreceptor constructs a negative feedback circuit on this system and realizes homeostatic control on its neural activity. This study is mainly organized from the above mentioned knowledge. In this paper, we construct two possible models of the serotonergic system based on receptor theory and provide some predictions for this system with each model. In the first model, we predict that the deficit of serotonin synthesis causes destabilization of the amount of autoreceptors; autoreceptors show an explosive increase if serotonin synthesis drops below a certain threshold value. In the second model, we indicate that the serotonergic system changes its stable property from a monostable one to a bistable one by certain factors. We clarify these factors and show that this changing process is named pitch-fork bifurcation. Additionally, we also suggest another notable phenomena which would appear when we consider a stochastic perturbation on the receptor expressions. Lastly, we suggest some experimental ideas towards the verification of the validity of these models.