Opioid Addiction Affects Neuronal Synchronization in the Hippocampus: A Computational Model

Drug addiction can affect the limbic system. Many computational models for drug addiction have been proposed, but most are for the reward system and behavioral models (Redish et al.,2004 and Gutkin et al.,2006). There are a few cellular mathematical models for drug addiction in the hippocampus that are very detailed (Borjkhani et al.,2018). We study a functional model for the synapses in the hippocampus to investigate the effect of opioid (Morphine) addiction on neuronal synchronization. We consider Pankratova et al.,2019 computational model. The model considers an astrocyte in synapses of two postsynaptic neurons in the hippocampus and studies the synchronization of the two neurons. In the model, we consider that Morphine addiction affects this tripartite synapses. The model consists of six differential equations for each neuron. One of the equations expresses the dynamics of the mean-field amount of released neurotransmitters based on presynaptic Poisson spike train and the astrocytic released glutamates in the synaptic cleft. Also, there is one differential equation for the mean-field amount of excitatory postsynaptic currents(EPSCs) based on presynaptic Poisson spike train and the D serine released from astrocyte. The four other equations indicate the Hodgkin-Huxley model (one of them for membrane voltage and the three other for gating variables), which its synaptic current input has been created by integrating EPSCs. Two differential equations describe the function of the astrocyte existed in synapses of the two neurons. One equation indicates the dynamics of the mean-field amount of astrocytic released glutamates based on the mean-field amount of the neurotransmitters of both neurons. The other equation expresses the dynamics of the mean-field amount of astrocytic released D serine based on the mean-field amount of the neurotransmitters of both neurons. Morphine addiction can affect three positions in synapses: presynaptic, astrocytic, and postsynaptic cells. It can cause an increase in neurotransmitters' concentration due to the disinhibitory mechanism of opioid receptors on presynaptic inhibitory neurons. Also, it can decrease the activity of astrocytic transporters causing fewer neurotransmitters reuptake by astrocyte. Morphine activates the opioid receptors on the postsynaptic neuron that increase NMDA's currents. In the model, we consider that Morphine influences the frequency of the Poisson spike train, the steady-state amount of neurotransmitters, and the gain of astrocytic glutamates. The amplitude of the EPCSs is also affected due to the Morphine addiction. The coefficient of synchronization is the ratio of synchronous spikes to the total spike number of both neurons. The results indicate that morphine addiction increases the synchrony of neurons. Thus, it can represent memory formation. In future works, we will study the withdrawal state in this model to analyze the neuronal synchronization and how the cues can result in relapse and how to control it.