Jesse Palma†, Massimiliano Versace1, and Stephen Grossberg*

Department of Cognitive and Neural Systems, Center for Adaptive Systems, and Center of Excellence for Learning in Education, Science, and Technology, Boston University, Boston, MA 02215

†palma@cns.bu.edu, 1versace@cns.bu.edu, *steve@cns.bu.edu 

How can networks of spiking neurons be designed to carry out prescribed transformations of input patterns? Many of the most crucial aspects of brain dynamics depend upon such transformations, including working memory, categorization, decision making, and learning. Earlier theorems about rate-based neural models have shown how such transformations depend upon the choice of nonlinear signal functions, notably the feedback and output signals of cells which obey membrane, or shunting, equations as they interact in recurrent on-center/off-center networks (Grossberg 1973; Grossberg and Levine, 1975; Ellias and Grossberg, 1975). Hundreds of subsequent studies have built upon this foundation. What processes control the shape of such nonlinear signal functions within biophysically detailed models of spiking neurons? Findings about the behavioral and pharmacological dynamics of acetylcholine (Hsieh et al. 2000; Descarries et al., 1997) and its neuromodulatory effect on after-hyperpolarization (AHP) currents (Vogalis et al., 2003; McCormick and Williamson, 1989; Giocomo and Hasselmo, 2007) provide evidence for how modulatory signals could control cortical transfer functions for mode shifts in cortical network dynamics. Our work demonstrates how these AHP currents, which hyperpolarize the membrane following action potentials mainly via calcium-dependent potassium channels, can control the shape of sigmoidal signal functions, notably their threshold and slope. Simulated neurons are composed of somatic, proximal dendritic and distal dendritic compartments governed by Hodgkin-Huxley dynamics (Hodgkin and Huxley, 1952) with parameters based on previous cortical models (Grossberg and Versace 2008; Traub and Miles, 2001). Somatic compartments contain fast, medium, and slow AHP currents with properties observed in mammalian neocortex (Storm, 1987; Lee et al., 2005; Abel et al., 2004; Lorenzon and Foehring, 1992). Rise and fall rates of excitatory postsynaptic potentials (EPSP) in the model are derived from recordings of currents through alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptors on neocortical pyramidal cells (Watt et al., 2000). Simulations under a wide range of stimulation spike trains (8-522 Hz) confirm transfer functions of an asymmetric sigmoid form, as often observed physiologically (Freeman, 1979; Ho and Destexhe, 2000). Our analysis reveals simple rules that govern conductance changes in the three AHP currents as they combine to generate desired changes in sigmoidal signaling. These rules suggest how nonlinear signals from individual neurons may be modified to achieve different network operating characteristics.

Supported in part by Hewlett-Packard Company (DARPA prime contract HR0011-09-3-0001), HRL Laboratories LLC (subcontract #801881-BS under DARPA prime contract HR0011-09-C-0011), and the National Science Foundation (NSF SBE-0354378).