neuron

README

Neuron = single spiking neuron

This is adapted from CCN Sims.

This simulation illustrates the basic properties of neural spiking activation, reflecting a balance of excitatory and inhibitory influences (including leak and synaptic inhibition).

In this model, the NetView only shows a single neuron which is "injected" with excitatory current (as neuroscientists might do with an electrode injecting current into a single neuron). If you do Run Cycles in the toolbar you will see it get activated, but to really understand what is going on, we need to see the relationship among multiple variables as shown in the TstCycPlot.

Plot of Neuron variables over time

• Press the TstCycPlot tab in the right panel to display the graph view display. If you haven't done Run Cycles yet, do it now so you can see the results of running with the default parameters.

Only the excitatory and leak currents are operating here, with their conductances (GbarE, GbarL) as shown in the control panel. You should see various lines plotted over 200 time steps (cycles) on the X axis.

Here is a quick overview of each of the variables -- we'll go through them individually next (see for more details on how to determine what is being graphed, and how to configure it):

• Ge (black line) = total excitatory input conductance to the neuron, which is generally a function of the number of open excitatory synaptic input channels at any given point in time (Ge(t)) and the overall strength of these input channels, which is given by GbarE. In this simple model, Ge(t)) goes from 0 prior to cycle 10, to 1 from 10-160, and back to 0 thereafter. Because GBarE = .3 (by default), the net value goes up to .3 from cycle 10-160. The timing of the input is controlled by the OnCycle and OffCycle parameters.

• Inet (red line) = net current (sum of individual excitation and leak currents), which is excitatory (upward) when the excitatory input comes on, and then oscillates as the action potential spikes fire. In general this reflects the net balance between the excitatory net input and the constant leak current (plus inhibition, which is not present in this simulation).

• Vm (blue line) = membrane potential, which represents integration of all inputs into neuron. This starts out at the resting potential of .3 (= -70mV in biological units), and then increases with the excitatory input. As you can see, the net current (Inet) shows the rate of change of the membrane potential while it is elevated prior to spiking. When Vm gets above about .5, a spike is fired, and Vm is then reset back to .3, starting the cycle over again.

• Act (green line) = activation. This shows the amount of activation (rate of firing), which is computed from the running-average measured inter-spike-interval (ISI). It is first computed after the second spike, as that is the only point when the ISI is available.

• Spike (purple line) = discrete spiking -- this goes to 1 when the neuron fires a discrete spike, and 0 otherwise.

• Gk (orange line) = conductance of sodium-gated potassium (k) channels, which drives adaptation -- this conductance increases during spikes, and decays somewhat in between, building up over time to cause the rate of spiking to adapt or slow down over time.

Spiking Behavior

The default parameters that you just ran show the spiking behavior of an axon Neuron. This is implementing a modified version of the Adaptive Exponential function (see CCN Textbook) or AdEx model, which has been shown to provide a very good reproduction of the firing behavior of real cortical pyramidal neurons. As such, this is a good representation of what real neurons do.

At the broadest level, you can see the periodic purple spikes that fire as the membrane potential gets over the firing threshold, and it is then reset back to the rest level, from which it then climbs back up again, to repeat the process again and again. Looking at the overall rate of spiking as indexed by the spacing between spikes (i.e., the ISI or inter-spike-interval), you can see that the spacing increases over time, and thus the rate decreases over time. This is due to the adaptation property of the AdEx model -- the spike rate adapts over time (note: we are using a different form of adaptation than used in the original AdEx model).

From the tug-of-war model, you should expect that increasing the amount of excitation coming into the neuron will increase the rate of firing, by enabling the membrane potential to reach threshold faster, and conversely decreasing it will decrease the rate of firing. Furthermore, increasing the leak or inhibitory conductance will tug more strongly against a given level of excitation, causing it to reach threshold more slowly, and thus decreasing the rate of firing.

This intuitive behavior is the essence of what you need to understand about how the neuron operates -- now let's see it in action.

Manipulating Parameters

Now we will use some of the parameters in the control panel to explore the properties of the point neuron activation function.

Excitatory

First, we will focus on GbarE, which controls the amount of excitatory conductance. In general, we are interested in seeing how the neuron membrane potential reflects a balance of the different inputs coming into it (here just excitation and leak), and how the spiking rate responds to the resulting membrane potential.

• Increase GbarE from .3 to .4 (and then do Run Cycles to see the effects). Then observe the effects of decreasing GbarE to .2 and all the way down to .1.

Question 2.1: Describe the effects on the rate of neural spiking of increasing GbarE to .4, and of decreasing it to .2, compared to the initial value of .3 (this is should have a simple answer).

Question 2.2: Is there a qualitative difference in the neural spiking when GbarE is decreased to .1, compared to the higher values -- what important aspect of the neuron's behavior does this reveal?

By systematically searching the parameter range for GbarE between .1 and .2, you should be able to locate the point at which the membrane potential just reaches threshold.

Question 2.3: To 2 decimal places (e.g., 0.15), what value of GbarE puts the neuron just over threshold, such that it spikes at this value, but not at the next value below it?

• Note: If you want to see the precise numbers for the values in the graph, click on the TstCycLog. Be sure to press UpdateView if you run again, to update to current results. You don't need these yet but may want to look at them anyway -- the precise numbers you need here are for the GbarE parameter, but it might be useful to see the underlying Vm values.

Question 2.4 (advanced): Using one of the equations for the equilibrium membrane potential from the Neuron chapter, compute the exact value of excitatory input conductance required to keep Vm in equilibrium at the spiking threshold. Show your math. This means rearranging the equation to have excitatory conductance on one side, then substituting in known values. (note that: Gl is a constant = .3; Ge is 1 when the input is on; inhibition is not present here and can be ignored) -- this should agree with your empirically determined value.

Leak

You can also manipulate the value of the leak conductance, , which controls the size of the leak current -- recall that this pulls the opposite direction as the excitatory conductance in the neural tug-of-war.

• Press the Defaults button on the control panel to restore the default parameters, then manipulate the GbarL parameter in .1 increments (.4, .5, .2 etc) and observe the effects on neural spiking.

Question 2.5: What value of GbarL just prevents the neuron from being able to spike (in .1 increments) -- explain this result in terms of the tug-of-war model relative to the GbarE excitatory conductance.

Question 2.6 (advanced): Use the same technique as in question 2.4 to directly solve for the value of GbarL that should put the neuron right at it's spiking threshold -- show your math.

Driving / Reversal Potentials

• Press Defaults in the toolbar to restore the default parameters. Then manipulate the ErevE and ErevL parameters and observe their effects on the spiking rate.

You should see that decreasing ErevE reduces the spiking rate, because it makes the excitatory input pull less strongly up on the membrane potential. Increasing ErevL produces greater spiking by making leak pull less strongly down.

Rate Coded Activations

Next, we'll see how the discrete spiking behavior of the neuron corresponds to a continuous rate-coded value. The green Act line in the graphs has been tracking the actual rate of spiking to this point, based on the inverse of the ISI.

TODO: more about conversion to Act

Noise

TODO: use new Ge, Gi noise

An important aspect of spiking in real neurons is that the timing and intervals between spikes can be quite random, although the overall rate of firing remains predictable. This is obviously not evident with the single constant input used so far, which results in regular firing. However, if we introduce noise by adding randomly generated values to the net input, then we can see a more realistic level of variability in neural firing. Note that this additional noise plays a similar role as the convolution of noise with the XX1 function in the noisy XX1 function, but in the case of the noisy XX1 we have a deterministic function that incorporates the averaged effects of noise, while here we are actually adding in the random values themselves, making the behavior stochastic.

• Change the variance of the noise generator (Noise in the control panel) from 0 to .2, and do Run Cycles. You should see the Ge black line is now perturbed significantly with the noise.

It can be difficult to tell from a single run whether the spike timing is random -- the neuron still fires with some regularity.

• Do many Runs and observe the extent of variability in spikes as the plot updates.

Even with this relatively high level of noise, the spike timing is not completely uniform -- the spikes still form clusters at relatively regulalry-spaced intervals. If you increase Noise all the way to .5, the spikes will be more uniformly distributed. However, note that even with the high levels of variability in the specific spike timing, the overall rate of spiking recorded by Act at the end of the input does not change that much. Thus, the rate code is a highly robust reflection of the overall net input.

In the brain (or large networks of simulated spiking neurons), there are high levels of variability in the net input due to variability in the spike firing of the different inputs coming into a given neuron. As measured in the brain, the statistics of spike firing are captured well by a Poisson distribution, which has variability equal to the mean rate of spiking, and reflects essentially the maximum level of noise for a given rate of spiking. Neurons are noisy.

Adaptation

TODO: explain actual KNa form more..

Cortical pyramidal neurons exhibit the property of spike rate adaptation. We are now using a more advanced form of adaptation than the form from the original AdEx model, based on sodium-gated potassium channels (K_na), which is turned on by the KNaAdpat parameter in the control panel. You can explore the basic effect of adaptation by turning this on and off.

You should observe that spiking is perfectly regular throughout the entire period of activity without adaptation, whereas with adaptation the rate decreases significantly over time. One benefit of adaptation is to make the system overall more sensitive to changes in the input -- the biggest signal strength is present at the onset of a new input, and then it "habituates" to any constant input. This is also more efficient, by not continuing to communicate spikes at a high rate for a constant input signal that presumably has already been processed after some point.

Documentation

Overview

neuron: This simulation illustrates the basic properties of neural spiking and rate-code activation, reflecting a balance of excitatory and inhibitory influences (including leak and synaptic inhibition).