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CbStOuNeuron

The Model

The membrane voltage V_m is governed by

$$C_m \frac{V_m}{dt} = -\frac{V_m-E_m}{R_m} - \sum_{c=1}^{N_c} ... ...{exc}) + g_{noise}^{inh}(t)(V_m -E_{noise}^{inh}) + I_{inject}$$

with the following meanings of symbols

• C_m membrane capacity (Farad)
• E_m reversal potential of the leak current (Volts)
• R_m membrane resistance (Ohm)
• N_c total number of channels (active + synaptic)
• g_c(t) current conductance of channel c (Siemens)
• E_rev^c reversal potential of channel c (Volts)
• N_s total number of current supplying synapses
• I_s(t) current supplied by synapse s (Ampere)
• G_s total number of coductance based synapses
• g_s(t) coductance supplied by synapse s (Siemens)
• E_rev^(s) reversal potential of synapse s (Volts)
• g_noise^exz(t) excitatory coductance given Ornstein Uhlenbeck process noise
• E_noise^exc reversal potential for excitatory Ornstein Uhlenbeck process noise
• g_noise^inh(t) inhibitory coductance given Ornstein Uhlenbeck process noise
• E_noise^inh reversal potential for inhibitory Ornstein Uhlenbeck process noise
• I_inject injected current (Ampere)

At time t=0 V_m ist set to V_init .

The value of E_m is calculated to compensate for ionic currents such that V_m actually has a resting value of $V_\mathit{resting}$ .

Spiking and reseting the membrane voltage

If the membrane voltage V_m exceeds the threshold V_tresh the CbNeuronSt sends a spike to all its outgoing synapses and the membrane voltage follows a predefined spike templage during the absolute refractory period of length T_refract if doReset = 1.

If the flag doReset=0 the spike template is not applied and the above equation is also applied during the absolute refractory period but the event of threshold crossing is transmitted as a spike to outgoing synapses. This is usfull if one includes channels which produce a real action potential (see HH_K_Channel and HH_Na_Channel) but one still just wants to communicate the spikes as events in time.

Implementation

The exponential Euler method is used for numerical integration.

Read/writable Fields

ge (S) :

exc and inh conductances (noise)

gi (S) :

exc and inh conductances (noise)

ge0 (S) :

exc and inh mean conductances (noise)

gi0 (S) :

exc and inh mean conductances (noise)

tau_e (S) :

time constants and std for exc and inh conductances (noise)

tau_i (S) :

time constants and std for exc and inh conductances (noise)

sig_e (S) :

time constants and std for exc and inh conductances (noise)

sig_i (S) :

time constants and std for exc and inh conductances (noise)

Ee (V) :

Reversal potential for exc and inh currents (noise)

Ei (V) :

Reversal potential for exc and inh currents (noise)

STempHeight (Volt) :

Height

Vthresh (V) :

If V_m exceeds V_thresh a spike is emmited.

Vreset (V) :

The voltage to reset V_m to after a spike.

doReset (flag) :

Flag which determines wheter V_m should be reseted after a spike

Trefract (sec) :

Length of the absolute refractory period.

nummethod (flag) :

Numerical method for the solution of the differential equation: Exp. Euler = 0, Crank-Nicolson = 1

type :

Type (e.g. inhibitory or excitatory) of the neuron

Cm (F) :

The membrane capacity C_m

Rm (Ohm) :

The membrane resistance R_m

Vresting (V) :

The resting membrane voltage.

Vinit (V) :

Initial condition forV_m at time t=0.

VmScale (V) :

Defines the difference between Vresting and the Vthresh for the calculation of the iongate tables and the ionbuffer Erev.

Inoise (W²) :

Variance of the noise to be added each integration time constant.

Iinject (A) :

Constant current to be injected into the CB neuron.

Readonly Fields

Em (V) :

The reversal potential of the leakage channel

Vm (V) :

The membrane voltage

OuInoise :

noise input current

OuGnoise :

noise input conductance

Isyn :

synaptic input current

Gsyn :

synaptic input conductance

nIncoming :

Number of incoming synapses

nOutgoing :

Number of outgoing synapses

nBuffers :

Number of ion buffers

nChannels :

Number of channels

(C) 2003, Thomas Natschläger

last modified 07/10/2006