Stability Analysis to Derive and Regulate Homeostatic Set Points for Negative Feedback Loops

Abstract

The dynamics of mutual excitation has been neglected by neurobiologists in comparison to studies of negative (homeostatic) feedback, perhaps because of a widespread misconception that negative feedback systems are intrinsically stable, whereas positive feedback systems with regenerative excitation are intrinsically unstable. Mutual excitation is widely believed to be responsible for epileptic seizures, and therefore to be avoided or suppressed in brain systems. On the contrary, each form of feedback can be stable, and with sufficiently high gain each can be destabilized to give respectively monotonic or oscillatory outputs. Feedforward excitation was proposed by Ramón y Cajal (1955) to exist as “avalanche conduction”, by which the axon collaterals of a small number of mitral cells might excite other mitral cells and these yet others, in the recruitment of a large number of cells to amplify a weak olfactory stimulus (Nicoll 1971), but he did not intend by invoking this “snow-ball” effect to allow feedback, because he believed that a neuron could not function properly if it were unable to distinguish input of other neurons from its own output (Freeman 1984). The work of Cajal’s student Lorente de No (1934) demonstrated the likelihood of feedback among cortical neurons, leading to theories of neural networks by McCulloch and Pitts (1943), and of nerve cell assemblies by Donald Hebb (1949). However, the resulting concept of “reverberatory circuits” was roundly criticized as epileptogenic, and was rejected as a basis for steady state neural activity or memory.KeywordsOlfactory BulbStimulus IntensityPulse ProbabilityLoop GainGlomerular LayerThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.