Further Work on the Shaping of Cortical Development and Function by Synchrony and Metabolic Competition

Abstract

This paper furthers our attempts to resolve two major controversies-whether gamma synchrony plays a role in cognition, and whether cortical columns are functionally important. We have previously argued that the configuration of cortical cells that emerges in development is that which maximizes the magnitude of synchronous oscillation and minimizes metabolic cost. Here we analyze the separate effects in development of minimization of axonal lengths, and of early Hebbian learning and selective distribution of resources to growing synapses, by showing in simulations that these effects are partially antagonistic, but their interaction during development produces accurate anatomical and functional properties for both columnar and non-columnar cortex. The resulting embryonic anatomical order can provide a cortex-wide scaffold for postnatal learning that is dimensionally consistent with the representation of moving sensory objects, and, as learning progressively overwrites the embryonic order, further associations also occur in a dimensionally consistent framework. The role ascribed to cortical synchrony does not demand specific frequency, amplitude or phase variation of pulses to mediate "feature linking." Instead, the concerted interactions of pulse synchrony with short-term synaptic dynamics, and synaptic resource competition can further explain cortical information processing in analogy to Hopfield networks and quantum computation.

Keywords: cortical computation; cortical development; cortical information flow; synaptic development; synchronous oscillation.

Figure 1

Results of fitting two exponential axonal density functions, of inverse length constants λ_α and λ_β, to a power function representing the ideal ultra-small world average density vs. distance relation. Top: The fraction, N_β = 1 − N_α of cells with axons of inverse length λ_β required to obtain best fit. Bottom: The average distance, X, from cell bodies of either type at which their axonal densities are equal.

Figure 2

Results of simulations showing alpha and beta cell positions maximizing ultra-small world post-synaptic connectivity, generated without regard to maximization of synchrony amplitude. Alpha cells red, beta cells blue.

Figure 3

Results of simulations showing alpha and beta cell positions maximizing synchrony amplitude generated with Hebbian connection symmetry alone.

Figure 4

Results of simulations showing alpha and beta cell positions maximizing ultra-small world post-synaptic connectivity early in development, then under the subsequent acquisition of Hebbian connection symmetry during the later stages of cell development.

Figure 5

Results of simulations showing alpha and beta cell positions maximizing ultra-small world post-synaptic connectivity under the following influence of Hebbian symmetry, and then late-stage distribution of synaptic growth resources optimizing the amplitude of synchrony.

Figure 6

A detail from the simulation with λ_α = 0.25, λ_β = 1.50, from Figure 5. Alpha cells red, beta cells blue. Six alpha cells surrounding a zone of beta cells have been picked out each at distances of separation from their nearest neighbors roughly the cross-over distance, X, of relative axonal density of alpha and beta cells. The fields of potential synaptic connection of these cells with beta cells and other alpha cells (Equations 8a,b) have been emphasized in gray.

Figure 7

The same system of six alpha cells and their fields of potential synaptic connection as in Figure 6. Connections to beta cells within the central zone are now colored red, green, and blue according to their origins from diametrically opposite alpha cells. Consequent to restriction of synaptic resources, connections have become established over only half the potential field, and these are arranged so diametrically opposite alpha cells make connections outwards at similar angles from a “singularity.” The inset shows the corresponding form of connections among the beta cells within the zone. Concurrently, the beta cells have established connections so they form a connected system analogous to a Möbius strip. This synergic distribution of resources to alpha-beta and beta-beta connections is that which maximizes synchronous resonance of the system. The inset also shows the mirror-image arrangement of connections in an adjacent column of beta cells.

Figure 8

Utilizing the analogy of the connections shown in Figure 7 to the distribution of OP from 0 to 180° over 360° about an OP singularity, an emergent pattern of OP is shown by arrangement in adjacent systems of alpha cells and their enclosed beta cells. This pattern in centered on one of the original six alpha cells in Figure 6. Those alpha cells to which the central cell makes strong connection are shown as enlarged red filled circles, and those beta cells with common OP connected to the central alpha are marked with black stars. These patterns are those that maximize synchronous resonance, and resemble patch cell connections, and “like to like” connections, respectively.

Figure 9

A section of the simulation result obtained with λ_α = 2.25, λ_β = 3.00 from Figure 4, magnified by a factor of 2.5, with the detail used in Figure 5 inserted as an inset. By rescaling, the cross-over distance, X, is normalized between the section and the inset. Alpha cell connections approximately distance X from near neighbors are then picked out by highlighting in red, in both the section and the inset, showing that similar connection structures can exist in both, but with marked interweaving in the “non-columnar” case.