Short term synaptic depression model—Analytical solution and analysis

Depressing synapse as a detector of frequency change

In this article we discuss the short-term synaptic depression using a mathematical model. We derive the model of synaptic depression caused by the depletion of synaptic vesicles for the case of infinitely short stimulation time and show that the analytical formulas for the postsynaptic potential (PSP) and kinetic functions take simple closed form. A solution in this form allows an analysis of the characteristics of depression as a function of the models parameters and the derivation of analytic formulas for measures of short time synaptic depression commonly used in experimental studies. Those formulas are used to validate the model by fitting it to two types of synapses described in the literature. Given the fitted parameters we discuss the behavior of the synapse in situations involving frequency change. We also indicate a possible role of depressing synapses in information processing as not only a filter of high frequency input but as a detector of the return from high frequency stimulation to the stimulation within frequency band specific for a given synapse.

P2X7 regenerative-loop potentiation of glutamate synaptic transmission by microglia and astrocytes

P2X7 purinergic receptors have been implicated in chronic neuropathic and neuroinflammatory pain as well as in depression. These receptors are predominantly found in the central nervous system on microglial cells and on glutamatergic nerve terminals. Here, we develop hypotheses concerning mechanisms by which transient high-frequency impulse firing in glutamatergic terminals, such as occurs in nociceptor terminals accompanying neuropathic/neuroinflammatory pain, can lead to long-lasting changes in neural network function that is mediated by surrounding glial cells. The hypothesis consists of two parts. In the first, glutamate released by low-frequency (2Hz) terminal action potentials is insufficient to generate postsynaptic action potentials, but these are generated by brief high-frequency input bursts. Glutamate released by these bursts is partly removed by transporters on the enveloping astrocyte processes and also excites AMPA receptors on these processes, which then release ATP. This ATP is partly metabolised to adenosine, which acts on presynaptic A1 receptors to inhibit glutamate release. The remaining ATP acts on the presynaptic P2X7 receptors to facilitate glutamate release by both the high-frequency burst of action potentials as well as by a continuous low-frequency (2Hz) action potential firing that occurs in the absence of a neuropathic/neuroinflammatory insult. The positive feedback of terminal glutamate release, triggering astrocyte ATP release and leading to further glutamate release through activation of P2X7 receptors, is then sufficient to allow the normal low-frequency (2Hz) action potentials to now elicit postsynaptic action potentials after the insult is removed. In the second part of this model, the high concentration of ATP derived from astrocytes at the terminal attracts microglia by chemotaxis. The P2X7 receptors on these microglia are then engaged, resulting in microglia secreting the cytokine TNFalpha. This acts on postsynaptic TNF-R1 receptors to increase the number of AMPA receptors there, thus enhancing the efficacy of synaptic transmission. The TNFalpha also acts on presynaptic TNF-R1 to increase the amount of glutamate released by each nerve terminal impulse. Experimental tests can be made of this hypothesis that P2X7 receptors on the presynaptic terminal and those on the microglia synergistically act to ensure feedback pathways that reset to a high level the efficacy of synaptic transmission, thus ensuring chronic neuropathic/neuroinflammatory pain even when the initial insult has subsided.