iaf_tum_2000 – Leaky integrate-and-fire neuron model with exponential PSCs and integrated short-term plasticity synapse

Description

iaf_tum_2000 is a leaky integrate-and-fire neuron model with short-term synaptic plasticity and exponential shaped postsynaptic currents (PSCs). In particular, iaf_tum_2000 implements short-term depression and short-term facilitation according to [1] by solving Eqs. (3) and (4) from that paper in an exact manner.

iaf_tum_2000 differs from iaf_psc_exp by the addition of synaptic state variables \(x\), \(z\) and \(u\), which together with the membrane potential \(V_\text{m}\) and synaptic current \(I_\text{syn}\) obey the following dynamics:

\[ \begin{align}\begin{aligned}\frac{dV_\text{m}}{dt} &= -\frac{V_{\text{m}} - E_\text{L}}{\tau_{\text{m}}} + \frac{I_{\text{syn}} + I_\text{e}}{C_{\text{m}}}\\I_{\text{syn}} &= I_\text{syn,ex} + I_\text{syn,in}\\I_\text{syn,X} &= \sum_{j \in \Gamma_X} w_j y_j\\\frac{dx_j}{dt} &= \frac{z_j}{\tau_{\text{rec}}} - u_j x_j \delta(t - t_j)\\\frac{dy_j}{dt} &= -\frac{y_j}{\tau_{\text{syn},X}} + u_j x_j \delta(t - t_j)\\\frac{dz_j}{dt} &= \frac{y_j}{\tau_{\text{syn},X}} - \frac{y_j}{\tau_{\text{rec}}}\\\frac{du_j}{dt} &= -\frac{u}{\tau_{\text{fac}}} + U(1 - u) \delta(t - t_j)\end{aligned}\end{align} \]

where \(\Gamma_X\) is an index set over either excitatory (\(\text{X} = \text{ex}\)) or inhibitory (\(\text{X} = \text{in}\)) presynaptic neurons, \(k\) indexes the spike times of neuron \(j\), and \(d_j\) is the delay from neuron \(j\).

iaf_tum_2000 incorporates the tsodyks_synapse computations directly in the presynaptic neuron, that is, the synaptic state variables \(x,y,z,u\) are integrated in the presynaptic neuron instead of the synapse model. For a presynaptic neuron with \(K\) outgoing connections following the tsodyks_synapse dynamics, iaf_tum_2000 saves \(K-1\) integrations of the synaptic ODEs. This makes iaf_tum_2000 very computationally efficient in network simulations. Since the synaptic ODEs are linear, the postsynaptic current can be found as the sum of all presynaptic synaptic currents computed in the presynaptic neurons.

In order for synaptic depression or facilitation to take effect, both the presynaptic and postsynaptic neuron must be of type iaf_tum_2000.

Note

Connections between iaf_tum_2000 neurons must be through receptor_type 1.

Warning

iaf_tum_2000 does not support precise spike timing. Using precise spike timing will result in incorrect dynamics and must therefore be avoided.

Parameters

The following parameters can be set in the status dictionary.

Parameter

Unit

Math equivalent

Description

V_m

mV

\(V_{\text{m}}\)

Membrane potential

E_L

mV

\(E_\text{L}\)

Resting membrane potential

C_m

pF

\(C_{\text{m}}\)

Capacity of the membrane

tau_m

ms

\(\tau_{\text{m}}\)

Membrane time constant

t_ref

ms

\(t_{\text{ref}}\)

Duration of refractory period

V_th

mV

\(V_{\text{th}}\)

Spike threshold

V_reset

mV

\(V_{\text{reset}}\)

Reset potential of the membrane

tau_syn_ex

ms

\(\tau_{\text{syn, ex}}\)

Excitatory synaptic time constant

tau_syn_in

ms

\(\tau_{\text{syn, in}}\)

Inhibitory synaptic time constant

U

real

\(U\)

Parameter determining the increase in u with each spike [0,1]

tau_fac

ms

\(\tau_{\text{fac}}\)

Time constant for facilitation

tau_rec

ms

\(\tau_{\text{rec}}\)

Time constant for depression

x

real

\(x\)

Initial fraction of synaptic vesicles in the readily releasable pool [0,1]

y

real

\(y\)

Initial fraction of synaptic vesicles in the synaptic cleft [0,1]

u

real

\(u\)

Initial release probability of synaptic vesicles [0,1]

I_e

pA

\(I_\text{e}\)

Constant input current

V_min

mV

\(V_{\text{min}}\)

Absolute lower value for the membrane potenial (default \(-\infty\))

References

Transmits

SpikeEvent

See also

Neuron, Integrate-And-Fire, Current-Based, Synapse, Short-Term Plasticity

Examples using this model