Short-term facilitation example

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The iaf_tum_2000 neuron [1] is a model with short-term synaptic plasticity. Short-term plasticity can either strengthen or weaken a synapse and acts on a timescale of milliseconds to seconds. This example illustrates short-term facilitation, which is a transient increase in synaptic strength caused by influx of calcium into the axon terminal after spike generation. Facilitation results in an increase of neurotransmitters being released by each succeeding presynaptic spike.

In the iaf_tum_2000 model, a fraction \(u\) of the available synaptic resources \(x\) is used by each presynaptic spike (see Eq. 3 and 4 or Eq. 2.1 and 2.2 in [1] or [2], respectively). A parameter \(U \in [0, 1]\) determines the increase in \(u\) with each spike. In a facilitating synapse, \(u\) is increased with each presynaptic spike, which reflects the accumulation of calcium ions caused by spikes arriving in the presynaptic terminal, and returns to the baseline value with a time constant \(\tau_\mathrm{fac}\).

In this example, we reproduce Figure 1B in [2]. We connect two iaf_tum_2000 neurons. The presynaptic neuron is driven by DC input and we record the voltage trace of the postsynaptic neuron. Short-term facilitation is enabled by setting \(U\) to a small value, which causes a slow saturation of the synaptic efficacy, enabling a facilitating behavior.

For an example on short-term depression, see Short-term depression example.

Note

The iaf_tum_2000 neuron model combined with static_synapse provides a more efficient implementation of the model studied in [1] and [2] than the combination of iaf_psc_exp with tsodyks_synapse.

References

[1] (1,2,3)

Tsodyks M, Uziel A, Markram H (2000). Synchrony generation in recurrent networks with frequency-dependent synapses. The Journal of Neuroscience, 20,RC50:1-5. URL: https://infoscience.epfl.ch/record/183402

[2] (1,2,3,4,5)

Tsodyks M, Pawelzik K, Markram H (1998). Neural networks with dynamic synapses. Neural computation, http://dx.doi.org/10.1162/089976698300017502

See Also

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

import matplotlib.pyplot as plt
import nest
import numpy as np

First we make sure that the NEST kernel is reset and the resolution of the simulation is 0.1 ms. We also define the simulation time.

nest.ResetKernel()
nest.resolution = 0.1  # simulation step size [ms]

T_sim = 1200.0  # simulation time [ms]

We set the neuronal membrane parameters according to [2].

tau_m = 60.0  # membrane time constant [ms]
R_m = 1.0  # membrane input resistance [GΩ]
C_m = tau_m / R_m  # membrane capacitance [pF]
V_th = 15.0  # threshold potential [mV]
V_reset = 0.0  # reset potential [mV]
t_ref = 2.0  # refractory period [ms]

We create one current generator and configure a stimulus that will drive the presynaptic neuron. Configuration of the current generator includes the definition of the start and stop times and the amplitude of the injected current.

stim_start = 50.0  # start time of DC input [ms]
stim_end = 1050.0  # end time of DC input [ms]
f = 20.0 / 1000.0  # frequency used in [2] [mHz]
dc_amp = V_th * C_m / tau_m / (1 - np.exp(-(1 / f - t_ref) / tau_m))  # DC amplitude [pA]

dc_gen = nest.Create(
    "dc_generator",
    1,
    params={"amplitude": dc_amp, "start": stim_start, "stop": stim_end},
)

Next, we set the synaptic parameters according to [2].

x = 1.0  # initial fraction of synaptic vesicles in the readily releasable pool
u = 0.0  # initial release probability of synaptic vesicles
U = 0.03  # fraction determining the increase in u with each spike
tau_psc = 1.5  # decay constant of PSCs (tau_inact in [2]) [ms]
tau_rec = 130.0  # recovery time from synaptic depression [ms]
tau_fac = 530.0  # time constant for facilitation [ms]

We create two iaf_tum_2000 neurons. Since this model integrates the synaptic dynamics in the presynaptic neuron, the synaptic parameters, except for weight and delay, are provided together with the neuron parameters to the model.

nrns = nest.Create(
    "iaf_tum_2000",
    2,
    params={
        "C_m": C_m,
        "tau_m": tau_m,
        "tau_syn_ex": tau_psc,
        "tau_syn_in": tau_psc,
        "V_th": V_th,
        "V_reset": V_reset,
        "E_L": V_reset,
        "V_m": V_reset,
        "t_ref": t_ref,
        "U": U,
        "tau_psc": tau_psc,
        "tau_rec": tau_rec,
        "tau_fac": tau_fac,
        "x": x,
        "u": u,
    },
)

We connect the DC generator to the presynaptic neuron.

nest.Connect(dc_gen, nrns[0])

We then connect the pre- and postsynaptic neurons. We use a static_synapse to transfer the synaptic current computed in the presynaptic neuron. The synaptic weight and delay are passed with the static synapse’s syn_spec. Note that iaf_tum_2000 neurons must be connected via receptor_type 1.

weight = 1540.0  # synaptic weight [pA]
delay = 0.1  # synaptic delay [ms]

nest.Connect(
    nrns[0],
    nrns[1],
    syn_spec={
        "synapse_model": "static_synapse",
        "weight": weight,
        "delay": delay,
        "receptor_type": 1,
    },
)

We add a voltmeter to sample the membrane potentials from the postsynaptic neuron in intervals of 1.0 ms. Note that the connection direction for the voltmeter reflects the signal flow in the simulation kernel; a voltmeter observes the neuron instead of receiving events from it.

voltmeter = nest.Create("voltmeter", params={"interval": 1.0, "label": "Voltmeter"})
nest.Connect(voltmeter, nrns[1])

Finally, we simulate the system with simulation time T_sim and plot a voltage trace to produce the figure.

nest.Simulate(T_sim)
nest.voltage_trace.from_device(voltmeter)
plt.show()