The neuronal signal consists of short voltage pulses called action potentials or spikes. These pulses travel along the axon and are distributed to several postsynaptic neurons where they evoke postsynaptic potentials. If a postsynaptic neuron receives several spikes from several presynaptic neurons within a short time window, its membrane potential may reach a critical value and an action potential is triggered. This action potential is the output signal which is, in turn, transmitted to other neurons.
The sequence of action potentials contains the information that is conveyed from one neuron to the next - but what is the code used by the neurons? Even though it is a question of fundamental importance the problem of neuronal coding is still not fully resolved. We have reviewed three concepts of rate codes, viz. spike count over some time window, spike density in a histogram, and population activity in an ensemble of neurons. All three concepts have been successfully used in experimental data analysis. All of these concepts are, however, problematic when they are interpreted as the actual code used for neuronal information transmission. A constructive criticism of rate codes may come from a presentation of potential spike codes, if their usefulness in terms of computational power or ease of implementation in biological hardware can be shown. It should be clear that modeling cannot give definite answers to the problem of neuronal coding. The final answers have to come from experiments. One task of modeling may be to discuss possible coding schemes, study their computational potential, exemplify their utility, and point out their limitations.
It is difficult to draw a clear border line between pulse and rate codes. Whatever the name of the code, it should offer a neural system the possibility to react quickly to changes in the input. This seems to be a minimum requirement if fast behavioral reaction times are to be accounted for.
If pulse coding is relevant, a description of information processing in the brain must be based on spiking neuron models. If all information is contained in the mean firing rate, then models on the level of rates suffice. Since we do not want to take any decision a priori about the neuronal code, we concentrate in this book on models of spiking neurons. In some cases, for example for stationary input, it will turn out that the spiking neuron models can be strictly reduced to rate models; in other cases such a reduction is not possible. By modeling on the level of spiking neurons, the question of neuronal coding can thus be kept open.
Phenomenological spiking neuron models similar to the model discussed in Section 1.3.1 have a long tradition in theoretical neuroscience, e.g., (McCulloch and Pitts, 1943; Stein, 1967b; Hill, 1936; Lapicque, 1907; Stein, 1965; Geisler and Goldberg, 1966; Weiss, 1966). They are reviewed in Holden (1976), Tuckwell (1988), and Maass and Bishop (1998).
An excellent discussion of the problem of neuronal coding can be found in the book `SPIKES - Exploring the neural code' by Rieke et al. (1996). The debate of spikes versus rates is also highlighted in several papers (Maass and Bishop, 1998; Abbott, 1994; Abeles, 1994; Theunissen and Miller, 1995; Shadlen and Newsome, 1994; Softky, 1995).
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