TABLE A1.
Population parameters for initial model represented in Fig. 1
| Population | Size | Resting Threshold, mV | THO Variability, mV | Membrane Time Constant | Post-Spike Increase in GK+ | Post-Spike GK+ Time Constant, ms | Adaptation Threshold Increase | Adaptation, ms | Noise Amplitude | DC, mV | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Variable names | N | THO | TMEM | B | TGK | C | TTH | |||||||||||
| PRG I | 100 | 10.0 | 1.0 | 9.0 | 20.0 | 7.0 | 0.0 | 500.0 | 0.9 | 0.0 | ||||||||
| PRG rIE | 100 | 10.0 | 1.0 | 9.0 | 20.0 | 7.0 | 0.0 | 500.0 | 0.9 | 12.0 | ||||||||
| PRG cIE | 100 | 10.0 | 1.0 | 9.0 | 20.0 | 7.0 | 0.0 | 500.0 | 1.0 | 5.0 | ||||||||
| PRG E | 100 | 10.0 | 1.0 | 6.0 | 27.0 | 2.5 | 0.0 | 500.0 | 0.9 | 0.0 | ||||||||
| PRG E-Other | 100 | 10.0 | 1.0 | 9.0 | 20.0 | 7.0 | 0.0 | 500.0 | 0.9 | 20.0 | ||||||||
| PRG EI | 100 | 10.0 | 1.0 | 9.0 | 20.0 | 7.0 | 0.0 | 500.0 | 0.9 | 0.0 | ||||||||
| PRG NRM+ | 100 | 10.0 | 1.0 | 9.0 | 20.0 | 7.0 | 0.0 | 500.0 | 0.03 | 25.0 | ||||||||
| PRG NRM− | 100 | 10.0 | 1.0 | 9.0 | 20.0 | 7.0 | 0.0 | 500.0 | 0.09 | 15.0 | ||||||||
| I-DRIVER | 300 | see Table A2 | ||||||||||||||||
| I-Dec | 300 | 10.0 | 1.0 | 6.0 | 25.5 | 6.63 | 0.5 | 500.0 | 0.1 | 28.0 | ||||||||
| I-Aug-BS | 300 | 10.0 | 1.0 | 6.0 | 25.0 | 3.8 | 0.0 | 5000.0 | 0.5 | 5.0 | ||||||||
| VRC IE | 99 | 10.0 | 1.0 | 9.0 | 5.6 | 5.0 | 0.0 | 1000.0 | 0.54 | 7.0 | ||||||||
| E-Dec-P | 99 | 8.0 | 1.0 | 9.0 | 27.0 | 2.5 | 0.8 | 2000.0 | 0.1 | 7.0 | ||||||||
| E-Dec-T | 300 | 8.0 | 1.0 | 9.0 | 27.0 | 2.5 | 0.8 | 2000.0 | 0.06 | 16.5 | ||||||||
| E-Aug-early | 300 | 10.0 | 1.0 | 6.0 | 27.0 | 2.5 | 0.0 | 500.0 | 0.1 | 21.0 | ||||||||
| E-Aug-late | 300 | 10.0 | 1.0 | 9.0 | 27.0 | 2.5 | 0.0 | 500.0 | 0.1 | 27.0 | ||||||||
| E-Aug-BS | 300 | 10.0 | 1.0 | 9.0 | 27.0 | 2.5 | 0.0 | 500.0 | 0.23 | 27.0 | ||||||||
| Pump+ | 300 | 0.0 | 0.0 | 6.0 | 25.0 | 3.8 | 0.08 | 500.0 | 0.1 | 0.0 | ||||||||
| Pump− | 300 | 0.0 | 0.0 | 6.0 | 25.0 | 3.8 | 0.08 | 500.0 | 0.1 | 0.0 | ||||||||
| Phrenic (Phr) | 300 | 10.0 | 1.0 | 6.0 | 25.0 | 3.8 | 0.08 | 500.0 | 0.1 | 7.0 | ||||||||
| Exp Motor | 300 | 10.0 | 1.0 | 9.0 | 27.0 | 2.5 | 0.0 | 500.0 | 0.023 | 0.0 | ||||||||
Parameter values for initial model network populations. Variable names used by MacGregor (1987) are in italics. All values representing voltages are relative to the resting potential, which is considered equal to zero. N is the number of neurons simulated in each population. THO, the resting threshold, is normally distributed in the population around the value of THO with a standard deviation equal to the “THO variability” value. TMEM is the membrane time constant. B is the amplitude of the post-spike increase in potassium conductance. TGK is the time constant of the potassium conductance decay following an action potential. C and TTH define the change in threshold associated with spike adaptation. C is the ratio of the threshold increase to the membrane potential increase; its value is between 0 and 1. TTH is the time constant of the rise in threshold with spike adaptation. Noise Amplitude. Each cell has an internal noise generator that acts like two synapses, one with an equilibrium potential of 70 mV above resting and the other with −70 mV. Each acts like it has an incoming firing probability of 0.05 per time step, and a synapse time constant of 1.5 ms. This parameter is the conductance that gets added to the synapse conductance on each (virtual) spike. DC. An injected current will raise the membrane potential by an amount that is inversely proportional to the membrane conductance. Instead of being specified directly as a current, this parameter is specified in mV, and it is interpreted as the current that is required to raise the membrane potential by the specified number of mV when the membrane conductance has its resting value. The effect on the membrane potential at other membrane conductances will be inversely proportional to the conductance. Note also that as in other types of IF neuron models, our neuron models do not actually generate action potential-like spikes but only identified moments of spikes, so “spiking” shown in all neuron simulations are represented graphically by assigning vertical spike-like lines at computed times of threshold crossing.