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Neural Model

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Free C++ source code for the integrate and fire neuron model is available.

How Neurons are Modeled

Click here for a detailed list neuron properties.

Passive Properties
The neuron is modeled as a RC (resistor-capacitor) circuit, in which the user sets the time constant. The nominal input resistance is set at 1 megohm, but this can be altered by changing the relative electrical size. Doubling the size effectively halves the input resistance. The neuron is perturbed from its resting membrane potential by current passing across the membrane. There are 3 sources of current.

1. Current can be injected by the user as if through a microelectrode inserted into the neuron.
2. Current can pass into the neuron from another neuron to which it is coupled by an electrical synapse. The effect of current from either of these sources depends upon the electrical size of the neuron; the larger the size the smaller the voltage perturbation. This follows from Ohm's law, since the current itself does not change with neuron size.
3. Current can pass through a chemical synaptic conductance. The voltage perturbation produced by this current is independent of size, since in the simulation the synaptic current scales proportionately with size (i.e. ion channel density is assumed to remain constant as the neuron changes in size).

Spiking Properties

Basic spike mechanism
Each integrate-and-fire neuron has a spike threshold. If the membrane potential exceeds this threshold (i.e. is more positive), the neuron spikes. A spike is modeled as a brief (1 integration time step) shift in membrane potential to the defined spike peak amplitude. NOTE: no current flow is modeled during the depolarising phase of the spike, and thus the spike is largely "cosmetic". This is to increase the speed of the simulation, but it can reduce the realism of effects mediated by electrical and non-spiking chemical synapses. The main problem is that the spike is shorter in duration than it may be in reality, which means that less current flows in an electrical synapse. To help overcome this limitation a “strength” parameter is defined, which simply changes the effective spike amplitude, without changing the displayed amplitude. A spike in a neuron is followed by a sudden increase in membrane conductance with amplitude defined by the Afterspike Hyperpolarising Potential (AHP) conductance parameter. This conductance increase is to an ion with an equilibrium potential defined by the AHP equilibrium potential parameter, and would normally be set to a value appropriate for potassium ions. The AHP conductance then decays exponentially back to a zero value, with a defined AHP time constant. Following a spike there is also a brief defined absolute refractory period, during which the threshold is set infinitely high.

Spike Threshold Accommodation
A relative accommodation level can be defined for spike threshold. Accommodation means that spike threshold potential varies as membrane potential itself varies. An accommodation level of 0 means no accommodation; the threshold is fixed at its defined initial value. An accommodation level of 1 means that when the membrane potential changes, the threshold also changes so as to eventually exactly parallel the membrane potential, and maintain the same relative voltage difference as is defined between the resting potential and the initial threshold. However, the spike threshold does not change instantaneously, but rather approaches its new value with an exponential time course, as defined by the accommodation time constant. Thus rapid changes in membrane potential can induce spiking, even if the relative accommodation level is large, so long as the accommodation time constant is long.

 

1. Initial threshold level.
2. Accommodated threshold level.
3. Accommodation time constant.

Calcium conductance and bursting
A simple voltage and time-dependent inactivating calcium current is implemented which, if the appropriate parameters are defined, can give a neuron endogenous bursting or plateau capabilities. The calcium current has a defined equilibrium potential and maximum conductance. Activation and inactivation both have first-order kinetics (i.e. mh, as opposed to m3h for the Hodgkin-Huxley model). Each variable has a defined mid-point voltage at which it has a steady-state value of 0.5, a mid-point slope which describes the rate of change of the variable with voltage at the mid-point, and a time constant, which describes the rate at which the variable approaches its steady-state value.