The Coding Paradox

In the last quarter of the nineteenth century Eduard Hitzig and Gustav Fritsch discovered the localisation of cortical motor areas in dogs using electrical stimulation and Richard Caton was the first to record electrical activity from the brain. Electrophysiology started to develop rapidly and Edgar D. Adrian published a seminal study suggesting the all-or-none principle in nerve (1912). In the late Twenties Hans Berger in Germany demonstrated the first human electroencephalogram and opened the way to clinical applications of electrophysiology. Nevertheless, the English School was leading the investigations in electrophysiology in the first part of the century, and for his specific research on the function of neurons, Adrian shared the 1932 Nobel Prize for Medicine with Sir Charles Sherrington. Although most remembered for his scientific contributions to neurophysiology, Sherrington's research focused on spinal reflexes as well as on the physiology of perception, reaction, and behaviour. His transdisciplinary approach, in the sense that disciplines were not only used one next to the other but were really intermingled in his protocols, was an extraordinary example of non-reductionist view of neurophysiology.

A series of experimental achievements obtained in the 1950s delineated the theory that the essential carriers of neural information are perturbations of the membrane potential of the neurons, the most dramatic of which is called action potential or spike (see Shepherd, 1994, for all references to basic neuroscience). The term spike refers to the waveform of the potential when recorded by means of a high impedence microelectrode in the vicinity of the neuron (extracellular recording) or in its interior (intracellular recording). The waveform is characterised by a peak corresponding to an initial decay of the membrane potential immediately followed by a sudden reversal of the potential and its return to the initial level. Such process lasts about 1 ms for the overall majority of nerve cells for species ranging from invertebrates to mammals.

The spike is propagated through a specific neuronal appendix - the axon - in a way that it is 'regenerated' at the branching points. At the tip of the axonal branches the cell membrane is specialised and forms the so-called pre-synaptic membrane. The electrical current carried by the spike produces changes in the pre-synaptic membrane properties that affect the membrane of another nerve cell (the post-synaptic neuron). These changes may last up to a few tenths of a millisecond and may be mediated by electrical currents or chemical reactions. As a consequence of the synaptic transmission a small post-synaptic current is generated in the post-synaptic neuron and it is propagated through specialised appendices -the dendrites - towards the cell region containing the nucleus (where the genetic material [the nucleic acids] is located in association with regulatory scaffolding proteins). Whenever the perturbation of the cell membrane of a sensitive region near the nucleus is strong enough to modify its ionic currents a spike is generated and propagated through the axon. Then, the process goes on to the next postsynaptic cells. There are two main exceptions in this system: the entry and the output points. The sensory cells - the entry points - are specialised nerve cells able to transduce the energy of the surrounding world (light, heat, mechanical pressure, chemical ligand-receptor bindings) into spikes that will be transmitted along the nervous system. The output points of the system are the muscle and the glands that allow expression of the neural response to a stimulus - the behaviour - via motor and humoral responses. The cells of the effector organs have the possibility to transduce the afferent electrical currents into another physical energy (e.g. mechanical movement for muscles, release of hormones for the humoral system).

Other electrical processes, so-called after-potentials, may last hundredths of millisecond and other spike-triggered events involving intracellular biochemical reactions and modulation of genetic expression may last orders of magnitude longer (in the order of minutes to hours). This indicates that several time scales coexist and are intermingled in the process of neural information. The discussion of these phenomena goes beyond the scope of the present article and we will restrict to the discussion of the information transmitted by the action potentials.

The generation of a spike is the consequence of ionic currents that drive ions in and out the nerve cell. A neuron spends most of its energy to keep its membrane potential to a certain level as a function of its biophysical membrane properties. Despite some small fluctuations the membrane potential at rest is very stable. This stability holds for many biophysical perturbations but it has often been observed that many neurons may be characterised by a bistability, with two levels of resting potentials as a function of major changes in the state of the cell membrane. Notice that in a widespread jargon used by the neurophysiologists a neuron is said to fire whenever it generates an action potential. This jargon produces expressions like firing rate referred to the rate of spikes per second, firing pattern, etc.

All the spikes of a sequence produced by one and the same neuron look very similar given the same resting potential. Spikes are also similar for different neurons and such all-or-none feature has often inspired the digital analogy for brain processing. Far from being real, this is an extremely rough approach because spikes tend to occur at an average frequency of five spikes or less per second.

If one assumed a binary code at the millisecond scale for the spiking (say digit '1') and not-spiking (digit '0') state of a neuron this would lead to consider that a

Fig. 2 (a) Extracellular recording of action potentials by a microelectrode. (b) The action potentials waveforms have been sorted at the millisecond scale according to the their shape and three spike trains are obtained. (c) The three spike trains might be coded in a binary stream where '1' means spike

Fig. 2 (a) Extracellular recording of action potentials by a microelectrode. (b) The action potentials waveforms have been sorted at the millisecond scale according to the their shape and three spike trains are obtained. (c) The three spike trains might be coded in a binary stream where '1' means spike neuron would transmit '0' most of the time. Action potentials occur either singly or in bursts (a rapid succession of spikes) where spikes step on each other's tails. The sequence of the spikes of a neuron is referred to as spike train (Fig. 2).

If one assumed long-lasting chunks of time this would lead to elementary neural bits that would last tens or hundredths of millisecond, a duration that can hardly be accepted when considering the precision and the time scale of movement execution, which is the major observable output of neural processing.

The problem of the neural time scale reappears despite the attempt to remove all spike-triggered effects other than the spikes themselves. In fact, random variation, noise, and reliability arise almost universally in the nervous system and the questions of the definition and meaning of neural coding are far from being trivial to pose (Segundo, 1985). The term 'coding' has a strict definition in cryptology as it refers to a substitution scheme where the message to be encoded is replaced by a special set of symbols. The above definition seems to be a far weaker metaphor for representation of information in the nervous system. Firstly, substitution codes are essentially static because they are defined by fixed rules. If the rules change over time the message cannot be deciphered and will be misinterpreted (actually this problem appears clearly with human aging but it will not be discussed here). Secondly, it seems unlikely the existence of a small fixed set of symbols to be encoded or decoded in the nervous system. In the nervous system, time sequences, delays, relatively precise coincidence relationships seem to be critically important aspects of information processing and the possibility to fit them into substitution codes appears rather remote. The search for dynamical coding schemes at variable time scales is the main goal of the Neuroheuristic paradigm. To this respect the present knowledge of the neurosciences is not advanced enough to let us formulate a testable theory. Instead, the emergence of collective properties - the properties not contained by the sum of the parties - is becoming a meaningful question thanks to the possibility that appeared in the past decades to investigate the activity of a network of neurons both theoretically and experimentally.

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