Recoding Patterns of Sensory Input: Higher-Order Features and the Function of Nonlinear Dendritic Trees

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.