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In neurobiology, an Inhibitory Post-Synaptic Current (IPSC), and its complementary process Excitatory Post-Synaptic Current (EPSC), are thought to be the foundational concepts that underlie the basic features of neurotransmission in mammalian cells.
For example, in elementary neurochemistry an IPSC may inhibit the formation of an action potential by changing the ion content in the cell, thus perturbing the resting potential of the cell so that voltage gated ion channels are less likely activated. That is, a voltage-gated ion channel opens when the membrane potential exceeds or reaches a certian threshold amplitude. The strength of this voltage signal is determined by the gradient of the ions across the membrane, which is really a potential difference over a distance (the width of the plasma membrane). Thus, on the post-synaptic side of the cleft, when a biologically induced current is applied, a flow of ions occurs over the membrane. This flow alters the ion content of the cleft, consequently changing the gradient of ions over the membrane, which in turn either inhibits or excites the nascent response of the voltage gated channel.
Such inhibitory/excitatory responses are highly nuanced and largely based on the particular channel type in the membrane of the neuron and the particular action of the neuron under investigation. See below for some introductory articles.
Dudel J., Voltage dependence of amplitude and time course of inhibitory synaptic current in crayfish muscle. Pflugers Arch. 1977 Oct 19;371(1-2):167-74.
Akasu T, Koketsu K., Electrogenesis of the slow inhibitory postsynaptic potential in bullfrog sympathetic ganglia. Jpn J Physiol. 1983;33(2):279-300.
White RL, Gardner D., Physostigmine prolongs the elementary event underlying decay of inhibitory postsynaptic currents in Aplysia. J Neurosci. 1983 Dec;3(12):2607-13.