Alex Chernajvsky, John Moody
The existence of modularity in the organization of nervous systems (e.g. cortical columns and olfactory glomeruli) is well known. We show that localized activity patterns in a layer of cells, collective excitations, can induce the formation of modular structures in the anatomical connections via a Hebbian learning mechanism. The networks are spatially homogeneous before learning, but the spon(cid:173) taneous emergence of localized collective excitations and subse(cid:173) quently modularity in the connection patterns breaks translational symmetry. This spontaneous symmetry breaking phenomenon is similar to those which drive pattern formation in reaction-diffusion systems. We have identified requirements on the patterns of lateral connections and on the gains of internal units which are essential for the development of modularity. These essential requirements will most likely remain operative when more complicated (and bi(cid:173) ologically realistic) models are considered.
1 Present Address: Molecular and Cellular Physiology, Beckman Center, Stanford University,
Stanford, CA 94305.
2 Please address correspondence to John Moody.
Chernjavsky and Moody
1 Modularity in Nervous Systems
Modular organization exists throughout the nervous system on many different spa(cid:173) tial scales. On the very small scale, synapses appear to be clustered on dendrites. On the very large scale, the brain as a whole is composed of many anatomically and functionally distinct regions. At intermediate scales, the scales of networks and maps, the brain exhibits columnar structures.
The purpose of this work is to suggest possible mechanisms for the development of modular structures at the intermediate scales of networks and maps. The best known modular structure at this scale is the column. Many modality- specific variations of columnar organization are known, for example orientation selective columns, ocular dominance columns, color sensitive blobs, somatosensory barrels, and olfactory glomeruli. In addition to these anatomically well-established struc(cid:173) tures, other more speculative modular anatomical structures may exist. These include the frontal eye fields of association cortex whose modular structure is in(cid:173) ferred only from electrophysiology and the hypothetical existence of minicolumns and possibly neuronal groups.
Although a complete biophysical picture of the development of modular structures is still unavailable, it is well established that electrical activity is crucial for the development of certain modular structures such as complex synaptic zones and oc(cid:173) ular dominance columns (see Kalil 1989 and references therein). It is also generally conjectured that a Hebb-like mechanism is operative in this development. These observations form a basis for our operating hypothesis described below.
2 Operating Hypothesis and Modeling Approach Our hypothesis in this work is that localized activity patterns in a layer of cells induce the development of modular anatomical structure within the layer. We further hypothesize that the emergence of localized activity patterns in a layer is due to the properties of the intrinsic network dynamics and does not necessarily depend upon the system receiving localized patterns of afferent activity.
Our work therefore has two parts. First, we show that localized patterns of ac(cid:173) tivity on a preferred spatial scale, collective excitations, spontaneously emerge in homogeneous networks with appropriate lateral connectivity and cellular response properties when driven with arbitrary stimulus (see Moody 1990). Secondly, we show that these collective excitations induce the formation of modular structures in the connectivity patterns when coupled to a Hebbian learning mechanism.
The emergence of collective excitations at a preferred spatial scale in a homogeneous network breaks translational symmetry and is an example of spontaneous symmetry breaking. The Hebbian learning freezes the modular structure into the anatomy. The time scale of collective excitations is short, while the Hebbian learning process occurs over a longer time scale. The spontaneous symmetry breaking mechanism is similar to that which drives pattern formation in reaction-diffusion systems (Turing 1952, Meinhardt 1982). Reaction-diffusion models have been applied to pattern for-
Note on Development or Modularity in Simple Cortical Models