Excitation and inhibition are two of the fundamental interactions between neurons. In neural networks, these processes allow for competition and learning, and lead to the diverse variety of output behaviors found in Biology. Two simple network control systems based on these interactions are the feedforward and feedback inhibitory networks. Feedforward inhibition limits activity at the output depending on the input activity. Feedback networks induce inhibition at the output as a result of activity at the ouput [1]. The networks in this demonstration consist of neurons modeled by HodgkinHuxley kinetics, connected with either NMDAmediated excitatory synapses or mediated inhibitory synapses. The first neuron in the network is depolarized with a constant current of adjustable amplitude . Spikes in presynaptic cells trigger postsynaptic currents where and are the reversal potentials, is the potential of the postsynaptic cell, is the fraction of active ion channels, and are the maximum conductances, adjustable above. A simple model for describing the dynamics of is a two state (open or closed) system, described by where is the concentration of neurotransmitter, in this case either or , and α,β are the rate constants. As a simplification, it is assumed that a spike in the presynaptic cell triggers a pulse of neurotransmitter during which the concetration is constant for a duration of , and is zero otherwise. In this case, an analytic expression for exists [2]. The values of the rate constants used were and and and [2].
 Contributed by: Oliver K. Ernst
Snapshot 1: Example of feedforward inhibiton, where the repeated spiking of neuron 2 causes continual inhibition in neuron 3. Snapshot 2: Example of feedback inhibition, where spiking activity in neuron 3 leads to later selfinhibition in neuron 3, which in turns allows for excitiation again. Snapshot 3: Fine tuning of the synaptic currents may be used to explore the transition between inhibitory and excitatory realms. [1] O'Reilly, R. C., Munakata, Y., Frank, M. J., Hazy, T. E., and Contributors. Computational Cognitive Neuroscience, Wiki Book, 1st Edition, 2012. pp. 3149. URL: http://ccnbook.colorado.edu. [2] A. Destexhe, Z.F. Mainen, and T.J. Sejnowski, "An Efficient Method for Computing Synaptic Conductances Based on a Kinetic Model of Receptor Binding," Neural Computation, 6, 1994 pp. 1418.


