The Emergence of Miller's Magic Number on a Sparse Distributed Memory

Human memory is limited in the number of items held in one's mind—a limit known as “Miller's magic number”. We study the emergence of such limits as a result of the statistics of large bitvectors used to represent items in memory, given two postulates: i) the Sparse Distributed Memory; and ii) chunking through averaging. Potential implications for theoretical neuroscience are discussed

Biophysical Basis for Three Distinct Dynamical Mechanisms of Action Potential Initiation

Transduction of graded synaptic input into trains of all-or-none action potentials (spikes) is a crucial step in neural coding. Hodgkin identified three classes of neurons with qualitatively different analog-to-digital transduction properties. Despite widespread use of this classification scheme, a generalizable explanation of its biophysical basis has not been described. We recorded from spinal sensory neurons representing each class and reproduced their transduction properties in a minimal model. With phase plane and bifurcation analysis, each class of excitability was shown to derive from distinct spike initiating dynamics. Excitability could be converted between all three classes by varying single parameters; moreover, several parameters, when varied one at a time, had functionally equivalent effects on excitability. From this, we conclude that the spike-initiating dynamics associated with each of Hodgkin's classes represent different outcomes in a nonlinear competition between oppositely directed, kinetically mismatched currents. Class 1 excitability occurs through a saddle node on invariant circle bifurcation when net current at perithreshold potentials is inward (depolarizing) at steady state. Class 2 excitability occurs through a Hopf bifurcation when, despite net current being outward (hyperpolarizing) at steady state, spike initiation occurs because inward current activates faster than outward current. Class 3 excitability occurs through a quasi-separatrix crossing when fast-activating inward current overpowers slow-activating outward current during a stimulus transient, although slow-activating outward current dominates during constant stimulation. Experiments confirmed that different classes of spinal lamina I neurons express the subthreshold currents predicted by our simulations and, further, that those currents are necessary for the excitability in each cell class. Thus, our results demonstrate that all three classes of excitability arise from a continuum in the direction and magnitude of subthreshold currents. Through detailed analysis of the spike-initiating process, we have explained a fundamental link between biophysical properties and qualitative differences in how neurons encode sensory input

Optogenetic Stimulation Shifts the Excitability of Cerebral Cortex from Type I to Type II: Oscillation Onset and Wave Propagation.

Constant optogenetic stimulation targeting both pyramidal cells and inhibitory interneurons has recently been shown to elicit propagating waves of gamma-band (40-80 Hz) oscillations in the local field potential of non-human primate motor cortex. The oscillations emerge with non-zero frequency and small amplitude-the hallmark of a type II excitable medium-yet they also propagate far beyond the stimulation site in the manner of a type I excitable medium. How can neural tissue exhibit both type I and type II excitability? We investigated the apparent contradiction by modeling the cortex as a Wilson-Cowan neural field in which optogenetic stimulation was represented by an external current source. In the absence of any external current, the model operated as a type I excitable medium that supported propagating waves of gamma oscillations similar to those observed in vivo. Applying an external current to the population of inhibitory neurons transformed the model into a type II excitable medium. The findings suggest that cortical tissue normally operates as a type I excitable medium but it is locally transformed into a type II medium by optogenetic stimulation which predominantly targets inhibitory neurons. The proposed mechanism accounts for the graded emergence of gamma oscillations at the stimulation site while retaining propagating waves of gamma oscillations in the non-stimulated tissue. It also predicts that gamma waves can be emitted on every second cycle of a 100 Hz oscillation. That prediction was subsequently confirmed by re-analysis of the neurophysiological data. The model thus offers a theoretical account of how optogenetic stimulation alters the excitability of cortical neural fields