Integration of postsynaptic potentials

Integration involves weighing up the balance of EPSPs and IPSPs within a cell and the outcome determines how excited the neuron is at any given moment. In order to sort out all the PSPs that it receives, a neuron needs to have a way of combining them together. In general, the dendrites of a neuron function to combine PSPs as well as to receive them and this function is made possible by their passive cell membrane. This contrasts with the membrane of an axon, which is described as being active because it contains the voltage-sensitive channels responsible for generating spikes.

It is difficult to study the way in which PSPs travel in the dendrites of most neurons because of their complex branching structure. However, an axon or a muscle cell conducts potentials that are below the threshold for a spike in the same way as a long, unbranching dendrite would, and can be used to illustrate the properties of a signal as it is conducted along a length of passive membrane (Fig. 2.8a). These properties can be examined by using a pair of microelectrodes, one to inject pulses of current and the second to record voltage changes at different distances away from the point of injection.

Two important changes occur as a postsynaptic potential is conducted along a passive membrane. One is that its amplitude decreases as it travels away from its point of origin. Signal size is not directly proportional to the distance, but declines exponentially. This can be understood by considering the flow of electrical current along and across the cell membrane (Fig. 2.8b). When the cell membrane is passive, an axon or dendrite behaves electrically like an insulated cable and this type of current flow was studied by the engineers who first constructed long submarine cables to carry telegraph messages. The passive conducting properties of axons and dendrites are therefore often described as their cable properties.

The electrical model of a cell membrane in Fig. 2.8b consists of a network of electrical resistors, each of which offers a pathway for the flow of current. The current spread along the axon will be greater if the membrane resistance is high in relation to the internal resistance because less current will then flow out through the membrane. The cell membrane is indeed a relatively poor conductor of electricity, being composed chiefly of lipid, which is a good electrical insulator. Ion channels are the major route for current flow across the membrane and without them even less current would be siphoned away from the pathway along the length of the axon. The electrical resistance of the cytoplasm depends on the diameter of the axon, with wider axons being better conductors than narrow ones. Signals are therefore conducted passively for greater distances along wide axons and den-drites than along narrow ones.

The way in which a signal changes in size along the length of an axon or dendrite is expressed as the space constant, which is defined as the distance over which a signal decays to 37 per cent of its original amplitude

Neurons Png

Figure 2.8 Cable properties of a length of axon or dendrite. (a) Two electrodes are inserted into the axon, one to inject a pulse of current and the second, which is moved successively further from the first, to record membrane potential. Drawings of voltage responses to a square current pulse are drawn for three locations. Note how the signal changes in size and shape as distance from its point of origin increases. (b) Electrical circuit for the membrane. (c) Graph to show how membrane potential declines with distance, including the definition of space constant for a cable.

Figure 2.8 Cable properties of a length of axon or dendrite. (a) Two electrodes are inserted into the axon, one to inject a pulse of current and the second, which is moved successively further from the first, to record membrane potential. Drawings of voltage responses to a square current pulse are drawn for three locations. Note how the signal changes in size and shape as distance from its point of origin increases. (b) Electrical circuit for the membrane. (c) Graph to show how membrane potential declines with distance, including the definition of space constant for a cable.

(Fig. 2.8c). The space constant may be as great as 1 cm in a really wide axon, such the giant axon of a squid which has a diameter of 1 mm. It is difficult to measure the space constant in small neurons, but values from 0.2 to 1 mm have been estimated for typical mammalian dendrites. These values are large in relation to most neurons, which means that postsynaptic potentials will readily carry along the length of the average dendrite.

The second change that happens to a signal as it travels along a passive membrane is that its waveform becomes more rounded. This can be seen by comparing a square-shaped pulse of electrical current injected into an axon at one point with the responses at two locations further along (Fig. 2.8a). This change in shape is due to electrical capacitance of the membrane, a property that occurs because the relatively high-resistance membrane separates two low-resistance solutions having unlike charges (negative inside, positive outside). A capacitor stores electrical charges and a store, whether an electrical capacitor or a bucket of water, takes time to fill and empty. As the signal decreases in size with distance, it also takes longer to alter the charge on the membrane capacitor and this is why the waveform recorded in an axon or dendrite changes more slowly as the distance from the origin of the signal increases. A measure of the effect an axon or dendrite has on the time course of a signal due to its capacitance is given by its time constant, which is defined as the time taken for a constant current pulse to change the membrane potential to 37 per cent short of its final value.

When the cell membrane is responding passively, the potential change is graded in amplitude with the size of the electrical stimulus, in approximate accordance with Ohm's law. A number of these graded potentials can therefore sum, giving a resultant potential with an amplitude that is proportional to the current flow. The way in which the passive membrane of a neuron sums together different synaptic inputs is shown in Fig. 2.9.

In Fig. 2.9a a neuron is shown receiving one excitatory synapse, and the EPSP it produces is recorded by a microelectrode inserted into the cell body. A single EPSP depolarises the membrane, but not as far as the spike threshold for the postsynaptic neuron. If the presynaptic neuron spikes twice, the second EPSP sums with the first, and the postsynaptic neuron is more excited than by a single EPSP. A third EPSP is then able to carry the membrane potential past threshold. The ability to sum several postsynap-tic potentials occurring in rapid succession depends on the time constant of the membrane. The capacitative properties of the postsynaptic

Post Synactic Neuron

Figure2.9 Integration of postsynaptic potentials. In each section, an experiment to show a particular type of integration is shown schematically, together with the appearance of recordings on an oscilloscope screen. (a) Temporal summation of EPSPs. (b) Spatial summation of an EPSP with an IPSP. (c) Comparison of EPSPs at two locations along a long dendrite.

Summation Postsynaptic Potentials

Figure2.9 Integration of postsynaptic potentials. In each section, an experiment to show a particular type of integration is shown schematically, together with the appearance of recordings on an oscilloscope screen. (a) Temporal summation of EPSPs. (b) Spatial summation of an EPSP with an IPSP. (c) Comparison of EPSPs at two locations along a long dendrite.

membrane slow the voltage changes so that an EPSP will decay more slowly than the synaptic current that gave rise to it. Consequently, a second EPSP following soon after the first, will add its depolarisation to that remaining from the first EPSP. Several EPSPs in rapid succession are thus able to depolarise the membrane to threshold even though a single one is insufficient to do so. This is called temporal summation.

In Fig 2.9b a neuron is shown receiving an excitatory synapse on one dendrite and an inhibitory synapse on another dendrite some distance away. When both presynaptic neurons produce spikes simultaneously, an EPSP will be generated in the one postsynaptic dendrite at the same time as an IPSP is generated in the other dendrite. As these two potentials spread towards the recording electrode, they will meet and sum, producing a much reduced depolarisation in this case. Similarly, if two excitatory synapses are active at the same time, the postsynaptic neuron will be more strongly excited than if just one synapse were active. This integration of PSPs from different sites is called spatial summation. The ability to sum synaptic potentials occurring at different sites within the neuron depends on the space constant of the membrane. This is particularly important because the postsynaptic membrane itself is not usually capable of generating spikes; it is not electrically excitable. So the summed potential change produced by synaptic activity must spread passively to the nearest patch of membrane that is capable of generating action potentials. This is called the spike-initiating zone, and it is usually at some little distance from the synapses. For neurons with long axons, it is located close to the origin of the axon.

In this way, the sites of synaptic action and the sites of spike generation are restricted to different parts of the neuron, and are all linked together by the passive spread of graded potentials. This arrangement offers great scope for varying the integrative properties of neurons by varying the space constant, the dendritic geometry and the sites of synaptic input. For instance, the closer a given synaptic input is to the spike-initiating zone, the more influence it will generally have on the output, because its postsynap-tic potentials will have decayed less than those of other inputs further away by the time they reach the spike-initiating zone. This is illustrated in Fig. 2.9 c, where two excitatory synapses are shown at different distances from the base of a long thin dendrite. An EPSP from the synapse towards the base of the dendrite will have decayed far less than one from the more distant synapse when recorded close to the spike-initiating zone. Similarly, an inhibitory synapse close to the spike initiating zone can effectively veto excitation that arises further out on the dendritic tree.

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