Narrow Results

Symmetries in the external world constrain the evolution of neuronal circuits that allow organisms to sense the environment and act within it. Many small “modular” circuits can be viewed as approximate discretizations of the relevant symmetries, relating their forms to the functions they perform. The recent development of a formal theory of dynamics and bifurcations of networks of coupled differential equations permits the analysis of some aspects of network behavior without invoking specific model equations or numerical simulations. We review basic features of this theory, compare it to equivariant dynamics, and examine the subtle effects of symmetry when combined with network structure. We illustrate the relation between form and function through examples drawn from neurobiology, including locomotion, peristalsis, visual perception, balance, hearing, location detection, decision-making, and the connectome of the nematode Caenorhabditis elegans.

Classical conditioning rapidly produces enduring frequency-specific modification of receptive fields (RF) in the auditory cortex (ACx) which favor the processing of the frequency of the conditioned stimulus (CS). Responses to the CS are increased whereas responses to the pre-training best frequency (BF) and other frequencies are decreased; tuning is often completely shifted so that the frequency of the CS becomes the BF. Such plasticity is observed both for single tone and for two-tone discrimination training. CS-specific RF plasticity may be reversed by extinction training. Sensitization training produces only general increases in responsiveness. Habituation produces frequency-specific decreased responses in the RF. Tuning shifts similar to those produced by conditioning can be produced by iontophoretic application of muscarinic agonists or cholinesterase antagonists to the ACx and pairing one tone with application of ACh to the auditory cortex produces receptive field plasticity which is specific to the frequency of the paired tone. Dual medial geniculate (MG) input to the auditory cortex consists of a frequency-specific non-plastic nucleus (MGv) and a broadly-tuned plastic nucleus (MGm). A preliminary model of receptive field plasticity and behavioral learning is presented. It links MGv and MGm influences on auditory cortex with cholinergic neuromodulation, and makes several predictions, some of which have recently been supported.