Spiking Networks

Several neuron types produce discrete "spikes," that is, instantaneous firing events. When they do, the neuron and the lines leading out from it (the "axon") turn a different color (by default yellow). This framework is used to create more biologically realistic simulations. In these neurons, the activation--the number in the neuron--is interpreted as a voltage potential, and when that number passes a threshold the neuron "fires," and typically the activation then drops to a lower value.

Currently two neurons are spiking neurons:

Integrate and Fire
Izhikivech

The question arises with spiking neurons of how this discrete "event" can be interpreted by the neurons it connects to. This is handled using a special interface in all synapses fanning out from the spiking neuron. When you double click on one of these synapses, the dialog is as it normally would be for a synapse of that type, but an additional tab is added, a "spike response" tab. This tab determines how spike events will be converted into activation.

In general, when a spike arrives at a post-synaptic cell (the target neuron of the spiking neuron), a "wave" of activation is created. This is modeled using a "response funnction" which characterizes a synaptic current, the influx of chemicals into a target cell which occurs when vesicles are released from a source neuron.

Formally, while the weighted inputs to a target neuron are usually computed by taking the sum of the source activation times weights at time t, if the source neuron is a spiking cell that term is replaced by:

weight(t) x response function(t) x [target neuron activation - synaptic resting potential]

The bracketed term is only computed if "scale by PSP" is selected."

 

Scale by PSP

If set to true, the response of the response function is multiplied by the differences between the post-synaptic resting potential and the activation of the post-synaptic cell, as described above.

Synaptic Resting Potential

The resting potential used if scale by PSP is selected.

Spike Response Function

Determines the wave form of the response to a spike. There are currently three (parameters are listed in italics):

Step

Before the spike the step function persists at base-line value, 0. After the
spike the wave form's response height increases by a constant amount for a specific
number of iterations or time-steps called the response time. After the
response time has passed the function returns to its base-line value.

Jump and Decay

This response function produces an instantaneous jump in height, jump height, followed by an exponential decay back to a base-line response at a rate which is
proportional to the decay constant, decay rate.

Rise and Decay

The response rises up to a maximum value, maximum response, and then decays back to a base-line value, 0, at a rate which is proportional to the decay constant. The global time step can be set when this function is selected.