7. Signal Transmission and Neuronal Coding

In the preceding chapters, a theoretical description of neurons and neuronal populations has been developed. We are now ready to apply the theoretical framework to one of the fundamental problems of Neuroscience - the problem of neuronal coding and signal transmission. We will address the problem as three different questions, viz.,

(i)

How does a population of neurons react to a fast change in the input? This question, which is particularly interesting in the context of reaction time experiments, is the topic of Section 7.2.

(ii)

What is the response of an asynchronously firing population to an arbitrary time-dependent input current? This question points to the signal transfer properties as a function of stimulation frequency and noise. In Section 7.3 we calculate the signal transfer function for a large population as well as the signal-to-noise ratio in a finite population of, say, a few hundred neurons.

(iii)

What is the `meaning' of a single spike? If a neuronal population receives one extra input spike, how does this affect the population activity? On the other hand, if a neuron emits a spike, what do we learn about the input? These questions, which are intimately related to the problem of neural coding, are discussed in Section 7.4.

The population integral equation of Chapter 6.3 allows us to discuss these questions from a unified point of view. We focus in this chapter on a system of identical and independent neurons, i.e., a homogeneous network without lateral coupling. In this case, the behavior of the population as a whole is identical to the averaged behavior of a single neuron. Thus the signal transfer function discussed in Section 7.3 or the coding characteristics discussed in Section 7.4 can also be interpreted as single-neuron properties. Before we dive into the main arguments we derive in Section 7.1 the linearized population equation that will be used throughout this chapter.