Modeling of glutamate transporters and receptors

About 11% of the world’s diseases are neurological, with about one billion people worldwide affected according to the World Health Organization. The development of new treatments and drugs requires a thorough understanding of central nervous system (CNS) functions for design of new drugs with minimal side effects. However, due to the complexity of the nervous system, elucidating many basic parameters and functional properties turns out to be challenging. In this work we present the application of a particular mathematical approach, called the Boundary Function Method, to determine unknown neurophysiological parameters. Neurons are the cells responsible for the basic functions of the nervous system. They communicate with each other and with different parts of the body via signaling molecules called neurotransmitters that are released to act at receptors. Glutamate is the predominant excitatory neurotransmitter in the mammalian human CNS. However, the prolonged exposure of receptors to glutamate leads to excitotoxicity and neuron death. Excitatory amino acid transporters (EAATs) play an important role by transporting glutamate in astrocytes from the extracellular space after neuronal signaling and limiting its toxic effects. To date five different subtypes of EAATs have been found in mammals, namely EAAT1 - 5. In human forebrain the major transporter on neurons is EAAT3 and the major transporter on astrocytes is EAAT2. Epilepsy, Alzheimer’s disease, stroke, and other diseases are associated with changes in glutamate transporter functions and expression. However, some basic properties of EAATs are still not known. For example, the turnover rate of EAATs, i.e., the average time it takes to transport a glutamate molecule, differs in the literature by several orders of magnitude. This uncertainty is due to a discrepancy between the complexity of the existing models and the limited available experimental data. The naïve statistical approach to analyzing this problem previously used by various researchers was not suited for the analysis of such problems. The lack of mathematical apparatus often results in unreliable estimates of model parameter values which results in the mentioned above discrepancies. The use of more advanced methods of analysis has allowed us to derive a new model of the process of interest and to resolve the issue of reliably estimating the transporters turnover rate