Topology and graph theory applied to cortical anatomy may help explain working memory capacity for three or four simultaneous items

• Published in: Brain Research Bulletin 2003-04, Vol.60 (1), p.25-42
• Main Author: Glassman, Robert B
• Format: Article
• Language: English
• Subjects: Animals; Association; Biological and medical sciences; Cerebral Cortex - anatomy & histology; Cerebral Cortex - physiology; Cognition - physiology; Column; Combinatorial; Cortex; Fundamental and applied biological sciences. Psychology; Humans; Memory, Short-Term - physiology; Models, Neurological; Module; Nerve Net; Planar
• ISSN: 0361-9230; 1873-2747
• DOI: 10.1016/S0361-9230(03)00030-3

Cognitive experimentation suggests that at any single instant only three or four items (“chunks”) are simultaneously prominent as a working memory (WM) trace, if we disregard the rehearsal component of WM. The reason for small WM capacity may concern combinatorial manageability. How might the neural representations of these few coactive chunks occupy a spatially distributed set of areas of the sheet-like cortex, while providing both order and flexibility to associate items in WM? Each attribute of each simultaneously active WM item must have broad access to the representational facilities of the cortical sheet, comprising tens of thousands of modular “cortical columns.” The two hypothesized neural levels of WM during any moment of cognition comprise (a) “binding” together of many distributed attribute representations within each respective WM chunk, and (b) combinatorial play among three or four WM chunk-representations. Anatomical and functional evidence of cortical unity through its depth suggests that cortex may be viewed as essentially planar in its distribution of activations. Thus, a moment’s WM is hypothesized here to reside in myriad activated cortical planar “patches,” each subdivided into up to four amoeboid “subpatches.” Two different lines of topological reasoning suggest orderly associations of such representations. (1) The four-color principle of map topology, and the related K 4 is planar theorem of graph theory, imply that if a small cortical area is dynamically subdivided into no more than four, discretely bounded planar subareas, then each such segment has ample free access to each of the others. (2) A hypothetical alternative to such associative adjacency of simultaneously active cortical representations of chunk-attributes is associative overlap, whereby, in dense cortical neuropil, activated subpatches behave like Venn diagrams of intersecting sets. As the number of Venn-like coactive subpatches within a patch increases, maintaining ad hoc associativity among all combinations requires exponentially proliferating intersections. Beyond four, serpentine subpatch shapes are required, which could easily lead to pathologies of omission or commission. As hypothesized by many researchers, the binding of the widely distributed cortical modules that represent a given chunk may involve synchrony or coherence of a single EEG frequency. Elsewhere, I have conjectured that such a binding frequency for a single chunk may bear a harmonic relationship w