Research reportSpurious dynamics in somatosensory cortex
Introduction
Nonlinear dynamical systems—i.e. systems whose formal description would require nonlinear equations—are remarkable in their great propensity for very complex, ‘chaotic’ dynamical behaviors. Even very simple dynamical systems can exhibit chaotic dynamics, as was first recognized 100 years ago by Henri Poincaré in his study of an abstract solar system made up of just three bodies [1]. In the extreme, even first-order difference equations with just one variable (e.g. ‘population growth’ equation Nt+1=Nt (a−bNt)) can exhibit a full array of dynamical behaviors from stable to periodic to deterministic (but seemingly random) fluctuations [18]. And of course, conversely, the more variables and more functional connections among variables in a dynamical system, the greater should be the tendency for complex dynamics.
A cerebral cortical network is an extremely complex dynamical system. Many of its dynamical behaviors are there, obviously, to carry out the information-processing tasks for which the network was created by evolution. However, in addition to these ‘intended’ dynamical behaviors, just the sheer complexity of the network's structure and membrane biophysics should generate other, ‘unintended’ dynamical behaviors, whether useful or detrimental. Such spurious dynamics, the by-product of the network's structural and functional complexity, can conceivably be very pervasive and contribute prominently to cortical physiology, affecting information processing and ultimately sensory perception.
To get some idea what kinds of spurious dynamical behaviors might be expected in a cortical network, we studied dynamics of a basic model of a local cortical network. In view of our present lack of understanding of the nature and mechanisms of information processing carried out by cortical networks, such models probably are closer to real cortical networks in their spurious dynamics than in their functional dynamics.
We find that many complex and intriguing features of cortical dynamics observed experimentally can be readily reproduced in such naive models, suggesting that these features might be emerging spontaneously out of the general complexity of the network as a whole, rather than being produced deliberately by any special mechanisms. In this paper we describe the major lessons we have learned from studying such models concerning the nature of spurious dynamics, their contribution to stimulus-evoked behaviors of somatosensory cortical neurons, and their possible contribution to stimulus representation and perception.
Section snippets
Generic cortical network model
The model was constructed to represent the upper layers of an approximately 0.8 mm diameter cortical region, made up of 196 minicolumns, each with two excitatory and two inhibitory cells [7]. Each minicolumn was assigned a somatotopically positioned receptive field (RF). Cells in the network were interlinked extensively via lateral connections. Each cell, whether excitatory or inhibitory, received connections from 15 excitatory and 15 inhibitory cells. These connections were drawn at random,
Somatosensory cortical network model
To relate the model's dynamics more closely to experimentally observed cortical dynamics, we developed another model, specifically a model of the somatosensory cortical network [8], [13]. This model is a multistage network (Fig. 3), composed of skin, thalamic, and cortical fields, with the cortical field composed of the input layer (representing cortical layer 4) and the upper layer (representing upper cortical layers 2–3). The cortical field contains two classes of modules: minicolumns and
Conclusions
We draw a number of lessons from our studies of model cortical networks. First, one major source of dynamics in cortical networks is likely to be the sheer structural complexity of these networks, regardless of specific details. This should be sufficient for emergence of quasiperiodic or even chaotic dynamics, although it appears from our studies that such spurious dynamical behaviors will be greatly constrained in their complexity. This constraint is fortuitous, considering that a crucial
Acknowledgements
This work was supported, in part, by ONR grant N00014-95-1-0113.
References (26)
- et al.
Assessment of the capacity of human subjects and S-I neurons to distinguish opposing directions of stimulus motion across the skin
Brain Res. Rev.
(1985) - et al.
Spatial organization of the peripheral input to area 1 cell columns: I. The detection of ‘segregates’
Brain Res. Rev.
(1988) - et al.
Spatial organization of the peripheral input to area 1 cell columns: II. The forelimb representation achieved by a mosaic of segregates
Brain Res. Rev.
(1988) - et al.
Nonlinear dynamical properties of a somatosensory cortical model
Inform. Sci.
(2001) - et al.
The brain as a dynamic physical system
Neuroscience
(1994) - Barrow-Green J. Poincaré and the Three Body Problem. History of Mathematics, vol. 11. Providence RI: Am. Math. Soc.,...
- et al.
Demonstration of discrete place-defined columns—segregates—in the cat SI
J. Comp. Neurol.
(1990) - et al.
Minicolumnar organization within somatosensory cortical segregates: I. Development of afferent connections
Cereb. Cortex
(1994) - et al.
Stimulus–response diversity in local neuronal populations of the cerebral cortex
NeuroReport
(1996) - et al.
Local receptive field diversity within cortical neuronal populations