The effect of a spike on the postsynaptic neuron can be recorded with an intracellular electrode which measures the potential difference u(t) between the interior of the cell and its surroundings. This potential difference is called the membrane potential. Without any spike input, the neuron is at rest corresponding to a constant membrane potential. After the arrival of a spike, the potential changes and finally decays back to the resting potential, cf. Fig. 1.3A. If the change is positive, the synapse is said to be excitatory. If the change is negative, the synapse is inhibitory.
At rest, the cell membrane has already a strong negative polarization of about -65mV. An input at an excitatory synapse reduces the negative polarization of the membrane and is therefore called depolarizing. An input that increases the negative polarization of the membrane even further is called hyperpolarizing.
Let us formalize the above observation. We study the time course ui(t) of the membrane potential of neuron i. Before the input spike has arrived, we have ui(t) = urest. At t = 0 the presynaptic neuron j fires its spike. For t > 0, we see at the electrode a response of neuron i
Consider two presynaptic neurons j = 1, 2, which both send spikes to the postsynaptic neuron i. Neuron j = 1 fires spikes at t1(1), t1(2),..., similarly neuron j = 2 fires at t2(1), t2(2),.... Each spike evokes a postsynaptic potential or , respectively. As long as there are only few input spikes, the total change of the potential is approximately the sum of the individual PSPs,
On the other hand, linearity breaks down if too many input spikes arrive during a short interval. As soon as the membrane potential reaches a critical value , its trajectory shows a behavior that is quite different from a simple summation of PSPs: The membrane potential exhibits a pulse-like excursion with an amplitude of about 100 mV, viz., an action potential. This action potential will propagate along the axon of neuron i to the synapses of other neurons. After the pulse the membrane potential does not directly return to the resting potential, but passes through a phase of hyperpolarization below the resting value. This hyperpolarization is called `spike-afterpotential'.
Single EPSPs have amplitudes in the range of one millivolt. The critical value for spike initiation is about 20 to 30 mV above the resting potential. In most neurons, four spikes - as shown schematically in Fig. 1.3C - are thus not sufficient to trigger an action potential. Instead, about 20-50 presynaptic spikes have to arrive within a short time window before postsynaptic action potentials are triggered.
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