Principles underlying mammalian neocortical scaling

Abstract

The neocortex undergoes a complex transformation from mouse to whale. Whereas synapse density remains the same, neuron density decreases as a function of gray matter volume to the power of around -1/3, total convoluted surface area increases as a function of gray matter volume to the power of around 8/9, and white matter volume disproportionately increases as a function of gray matter volume to the power of around 4/3. These phylogenetic scaling relationships (including others such as neuron number, neocortex thickness, soma radius, and number of cortical areas) are clues to understanding the principles driving neocortex organization, but there is currently no theory that can explain why these neocortical quantities scale as they do. Here I present a two-part model that explains these neocortical allometric scaling laws. The first part of the model is a special case of the physico-mathematical model recently put forward to explain the quarter power scaling laws in biology. It states that the neocortex is a space-filling neural network through which materials are efficiently transported, and that synapse sizes do not vary as a function of gray matter volume. The second part of the model states that the neocortex is economically organized into functionally specialized areas whose extent of area-interconnectedness does not vary as a function of gray matter volume. The model predicts, among other things, that the number of areas and the soma radius increase as a function of gray matter volume to the power of 1/3 and 1/9, respectively, and empirical support is demonstrated for each. Also, the scaling relationships imply that, although the percentage of the total number of neurons to which a neuron connects falls as a function of gray matter volume with exponent -1/3, the network diameter of the neocortex is invariant at around two. Finally, I discuss how a similar approach may have promise in explaining the scaling relationships for the brain and other organs as a function of body mass.

Natural world physical, brain operational, and mind phenomenal space–time

“…From a functional perspective, the spatiotemporal brain organization is necessitated by evolutionary pressure [78]: In the space-constrained skull, more computational efficiency is obtained by grouping together (space aspect) neurons with similar function and denser interactions on a particular time scale (temporal aspect), so that the overall number of interconnections is minimized [79][80][81]. Indeed in the course of the evolution of the brain, the number of neurons has considerably increased, whereas their connections have become less direct [79,82,83], thus minimizing costs of interconnection between neural sites, and yielding efficient communication between them [84][85][86][87].…”

“…Neurophysics [504] contends that within the transition there is also a brief period when the drastic and abrupt increase in degrees of freedom of neuronal assemblies is accompanied by a sudden increase in entropy and information 82 , followed by a quick reduction in the degrees of freedom of neuronal assemblies and rapid decrease in entropy and information [44,45] (see Fig 10).…”

“…Indeed, research shows that oxygen utilization (Blood Oxygen Level) increases as the spatial-temporal pattern loses stability, suggesting that the demands on neural resources to sustain a given pattern stability also increase [510]. Therefore, each phenomenal object, scene or thought has 82 The parallel increase of information and entropy requires additional clarification. From the viewpoint of information theory [505], the information content of a series of states is highest if the entropy is maximal, which means that the predictability of the state of any part of the system from the states of the other parts is low, as well as the predictability of the state at any time from the state at other times.…”

Common scaling laws for city highway systems and the mammalian neocortex

“…These neocortical scaling laws appear to be a consequence of selection pressure for a sheet-like structure (namely, gray matter) to economically maintain a high level of interconnectedness [1,2,19,20]. We might therefore expect to find similar scaling laws for any sheetlike structure under similar selection pressures, in which case the neocortex would be just an instance of a more general kind of structure.…”

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A variety of scaling laws are known for the mammalian neocortex relating gray matter volume, total number of synapses [1,2], white matter volume [3][4][5][6][7][8][9], number of neurons [6,[10][11][12], surface area [4,5,[13][14][15][16], axon caliber [1,17], and number of cortical areas or compartments [18]. These neocortical scaling laws appear to be a consequence of selection pressure for a sheet-like structure (namely, gray matter) to economically maintain a high level of interconnectedness [1,2,19,20].

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