| Abstract: |
| In a broader context, the experimental investigation postulates that toxic neuropeptides/neurotransmitters are causing damage to the functionality of synapses during neurotransmission processes. In this paper, we are aiming to propose a novel mathematical model that studies the dynamics of synaptic damage in terms of concentrations of toxic neuropeptides/neurotransmitters during neurotransmission processes. Our primary objective is to employ Wardrop`s first and second principles within a neural network of the brain. In order to comprehensively incorporate Wardrop`s first and second principles into the neural network of the brain, we introduce two novel concepts: \textit{neuropeptide`s (neurotransmitter`s) equilibrium} and \textit{synapses optimum}. The \textit{neuropeptide/neurotransmitter equilibrium} refers to \textit{a distribution of toxic neuropeptides/neurotransmitters that leads to uniform damage across all synaptic links}. Meanwhile, \textit{synapses optimum} is \textit{the most desirable distribution of toxic neuropeptides/neurotransmitters that minimizes the cumulative damage experienced by all synapses}. In the context of a neural network within the brain, an analogue of the price of anarchy is \textit{the price of cognition} which is \textit{the most unfavorable ratio between the overall impairment caused by toxic neuropeptide`s (neurotransmitter`s) equilibrium in comparison to the optimal state of synapses (synapses optimum)}. To put it differently, \textit{the price of cognition} measures \textit{the loss of cognitive ability resulting from increased concentrations of toxic neuropeptides/neurotransmitters}. Additionally, a replicator equation is proposed within this framework that leads to the establishment of the synapses optimum during the neurotransmission process. It is important to note that our model serves as a high-level simplification and abstraction of the natural neurotransmission process involving interactions between two neurons. Nevertheless, we envision that this mathematically abstract model can serve as a source of motivation to instigate novel experimental, mathematical, and computational research avenues in the field of contemporary neuroscience. |
|