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 .
The networks in this demonstration consist of neurons modeled by Hodgkin-Huxley kinetics, connected with either NMDA-mediated 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
are the reversal potentials,
is the potential of the post-synaptic 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
is the concentration of neurotransmitter, in this case either
, 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 . The values of the rate constants used were
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 self-inhibition 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.
 O'Reilly, R. C., Munakata, Y., Frank, M. J., Hazy, T. E., and Contributors. Computational Cognitive Neuroscience,
Wiki Book, 1st Edition, 2012. pp. 31-49. URL: http://ccnbook.colorado.edu.
 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,