1.1 Elements of Neuronal Systems

Over the past hundred years, biological research has accumulated an enormous amount of detailed knowledge about the structure and function of the brain. The elementary processing units in the central nervous system are neurons which are connected to each other in an intricate pattern. A tiny portion of such a network of neurons is sketched in Fig. 1.1 which shows a drawing by Ramón y Cajal, one of the pioneers of neuroscience around 1900. We can distinguish several neurons with triangular or circular cell bodies and long wire-like extensions. This picture can only give a glimpse of the network of neurons in the cortex. In reality, cortical neurons and their connections are packed into a dense network with more than 10⁴ cell bodies and several kilometers of `wires' per cubic millimeter. In other areas of the brain the wiring pattern may look different. In all areas, however, neurons of different sizes and shapes form the basic elements.

The cortex does not consist exclusively of neurons. Beside the various types of neuron there is a large number of `supporter' cells, so-called glia cells, that are required for energy supply and structural stabilization of brain tissue. Since glia cells are not directly involved in information processing, we will not discuss them any further. We will also neglect a few rare subtypes of neuron, such as analog neurons in the mammalian retina. Throughout this book we concentrate on spiking neurons only.

**Figure 1.1:** This reproduction of a drawing of Ramón y Cajal shows a few neurons in the mammalian cortex that he observed under the microscope. Only a small portion of the neurons contained in the sample of cortical tissue have been made visible by the staining procedure; the density of neurons is in reality much higher. Cell b is a nice example of a pyramidal cell with a triangularly shaped cell body. Dendrites, which leave the cell laterally and upwards, can be recognized by their rough surface. The axons are recognizable as thin, smooth lines which extend downwards with a few branches to the left and right. From Ramòn y Cajal (1909).
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1.1.1 The Ideal Spiking Neuron

A typical neuron can be divided into three functionally distinct parts, called dendrites, soma, and axon; see Fig. 1.2. Roughly speaking, the dendrites play the role of the `input device' that collects signals from other neurons and transmits them to the soma. The soma is the `central processing unit' that performs an important non-linear processing step: If the total input exceeds a certain threshold, then an output signal is generated. The output signal is taken over by the `output device', the axon, which delivers the signal to other neurons.

The junction between two neurons is called a synapse. Let us suppose that a neuron sends a signal across a synapse. It is common to refer to the sending neuron as the presynaptic cell and to the receiving neuron as the postsynaptic cell. A single neuron in vertebrate cortex often connects to more than 10⁴ postsynaptic neurons. Many of its axonal branches end in the direct neighborhood of the neuron, but the axon can also stretch over several centimeters so as to reach to neurons in other areas of the brain.

**Figure 1.2:** A. Single neuron in a drawing by Ramón y Cajal. Dendrite, soma, and axon can be clearly distinguished. The inset shows an example of a neuronal action potential (schematic). The action potential is a short voltage pulse of 1-2 ms duration and an amplitude of about 100 mV. B. Signal transmission from a presynaptic neuron j to a postsynaptic neuron i. The synapse is marked by the dashed circle. The axons at the lower right end lead to other neurons (schematic figure).
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1.1.2 Spike Trains

The neuronal signals consist of short electrical pulses and can be observed by placing a fine electrode close to the soma or axon of a neuron; see Fig. 1.2. The pulses, so-called action potentials or spikes, have an amplitude of about 100 mV and typically a duration of 1-2 ms. The form of the pulse does not change as the action potential propagates along the axon. A chain of action potentials emitted by a single neuron is called a spike train - a sequence of stereotyped events which occur at regular or irregular intervals. Since all spikes of a given neuron look alike, the form of the action potential does not carry any information. Rather, it is the number and the timing of spikes which matter. The action potential is the elementary unit of signal transmission.

Action potentials in a spike train are usually well separated. Even with very strong input, it is impossible to excite a second spike during or immediately after a first one. The minimal distance between two spikes defines the absolute refractory period of the neuron. The absolute refractory period is followed by a phase of relative refractoriness where it is difficult, but not impossible to excite an action potential.

1.1.3 Synapses

The site where the axon of a presynaptic neuron makes contact with the dendrite (or soma) of a postsynaptic cell is the synapse. The most common type of synapse in the vertebrate brain is a chemical synapse. At a chemical synapse, the axon terminal comes very close to the postsynaptic neuron, leaving only a tiny gap between pre- and postsynaptic cell membrane, called the synaptic cleft. When an action potential arrives at a synapse, it triggers a complex chain of bio-chemical processing steps that lead to a release of neurotransmitter from the presynaptic terminal into the synaptic cleft. As soon as transmitter molecules have reached the postsynaptic side, they will be detected by specialized receptors in the postsynaptic cell membrane and open (either directly or via a biochemical signaling chain) specific channels so that ions from the extracellular fluid flow into the cell. The ion influx, in turn, leads to a change of the membrane potential at the postsynaptic site so that, in the end, the chemical signal is translated into an electrical response. The voltage response of the postsynaptic neuron to a presynaptic action potential is called the postsynaptic potential.

Apart from chemical synapses neurons can also be coupled by electrical synapses, so-called gap junctions. Specialized membrane proteins make a direct electrical connection between the two neurons. Not very much is known about the functional aspects of gap junctions, but they are thought to be involved in the synchronization of neurons.