Here analytical and simulation results are presented characterizing the recoding arising when overlapping patterns of sensor input impinge on an array of model neurons with branched thresholded dendritic trees. Thus, the neural units employed are intended to capture the integrative behavior of pyramidal cells that sustain isolated Na + or NMDA spikes in their branches. Given a defined set of sensor vectors, equations were derived for the probability of firing of both branches and neurons and for the expected overlap between the neural firing patterns triggered by two afferent patterns of given overlap. Thus, both the sparseness of the neural representation and the orthogonalization of overlapping vectors were computed. Simulations were then performed with an array of 1000 neurons comprising 30,000 branches to verify the analytical results and confirm their applicability to systems (which include any practicable artificial system) in which the combinatorically possible branches and neurons are severely subsampled. A means of readout and a measure of discrimination performance were provided so that the accuracy of discrimination among overlapping sensor vectors could be optimized as a function of neuron structure parameters. Good performance required both orthogonalization of the afferent patterns, so that discrimination was accurate and free of interference, and maintenance of a minimum level of neural activity, so that some neurons fired in response to each sensor pattern. It is shown that the discrimination performance achieved by arrays of neurons with branched dendritic trees could not be reached with single-compartment units, regardless of how many of the latter are used. The analytical results furnish a benchmark against which to measure further enhancements in the performance of subsequent simulated systems incorporating local neural mechanisms which, while often less amenable to closed-form analysis, are ubiquitous in biological neural circuitry.

Neocortical layer 5 intrinsically bursting (IB) pyramidal neurons were simulated using compartment model methods. Morphological data as well as target neurophysiological responses were taken from a series of published studies on the same set of rat visual cortex pyramidal neurons (Mason, A. and Larkman, A. J., 1990. J. Neurosci . 9,1440-1447; Larkman, A. J. 1991. J. Comp. Neurol . 306, 307-319). A dendritic distribution of ion channels was found that reproduced the range of in vitro responses of layer 5 IB pyramidal neurons, including the transition from repetitive bursting to the burst/tonic spiking mode seen in these neurons as input magnitude increases. In light of available data, the simulation results suggest that in these neurons bursts are driven by an inward flow of current during a high threshold Ca 2+ spike extending throughout both the basal and apical dendritic branches.