Abstract
In the auditory system, tonotopy is postulated to be the substrate for a place code, where sound frequency is encoded by the location of the neurons that fire during the stimulus. Though conceptually simple, the computations that allow for the representation of intensity and complex sounds are poorly understood. Here, a mathematical framework is developed in order to define clearly the conditions that support a place code. To accommodate both frequency and intensity information, the neural network is described as a space with elements that represent individual neurons and clusters of neurons. A mapping is then constructed from acoustic space to neural space so that frequency and intensity are encoded, respectively, by the location and size of the clusters. Algebraic operations -addition and multiplication- are derived to elucidate the rules for representing, assembling, and modulating multi-frequency sound in networks. The resulting outcomes of these operations are consistent with network simulations as well as with electrophysiological and psychophysical data. The analyses show how both frequency and intensity can be encoded with a purely place code, without the need for rate or temporal coding schemes. The algebraic operations are used to describe loudness summation and suggest a mechanism for the critical band. The mathematical approach complements experimental and computational approaches and provides a foundation for interpreting data and constructing models.
Highlights
Many sensory systems are organized topographically so that adjacent neurons have small differences in the receptive fields
One way of encoding sensory information in the brain is with a so-called place code
The rigorous, formal process ensures that the conditions for a place code and the associated computations are defined precisely
Summary
Many sensory systems are organized topographically so that adjacent neurons have small differences in the receptive fields. The result is that minute changes in the sensory features causes an incremental shift in the spatial distribution of active neurons. This is has led to the notion of a place code where the location of the active neurons provides information about sensory attributes. The substrate for a place code is tonotopy, where the preferred frequency of each neuron varies systematically along one axis [1]. Tonotopy originates in the cochlea [2, 3] and is inherited by progressively higher order structures along the auditory pathway [4]. The importance of a place code [5] is underscored by the fact that cochlear implants, arguably the most successful brain-machine interface, enable deaf patients to discriminate tone pitch by delivering brief electrical pulses at points of the cochlea corresponding to specific frequencies [6, 7]
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