Warning

This is A PREVIEW for NEST 3.0 and NOT an OFFICIAL RELEASE! Some functionality may not be available and information may be incomplete!

# Simulations with gap junctions¶

Note: This documentation describes the usage of gap junctions in NEST 2.12. A documentation for NEST 2.10 can be found in Hahne et al. 2016. It is however recommended to use NEST 2.12 (or later), due to several improvements in terms of usability.

## Introduction¶

Simulations with gap junctions are supported by the Hodgkin-Huxley neuron model hh_psc_alpha_gap. The synapse model to create a gap-junction connection is named gap_junction. Unlike chemical synapses gap junctions are bidirectional connections. In order to create one accurate gap-junction connection two NEST connections are required: For each created connection a second connection with the exact same parameters in the opposite direction is required. NEST provides the possibility to create both connections with a single call to nest.Connect via the make_symmetric flag (default value: False) of the connection dictionary:

import nest

a = nest.Create('hh_psc_alpha_gap')
b = nest.Create('hh_psc_alpha_gap')
# Create gap junction between neurons a and b
nest.Connect(a, b, {'rule': 'one_to_one', 'make_symmetric': True},
{'model': 'gap_junction', 'weight': 0.5})


In this case the reverse connection is created internally. In order to prevent the creation of incomplete or non-symmetrical gap junctions the creation of gap junctions is restricted to

• one_to_one connections with 'make_symmetric': True

• all_to_all connections with equal source and target populations and default or scalar parameters

## Create random connections¶

NEST random connection rules like fixed_total_number, fixed_indegree etc. cannot be employed for the creation of gap junctions. Therefore random connections have to be created on the Python level with e.g. the random module of the Python Standard Library:

import nest
import random
import numpy as np

# total number of neurons
n_neuron = 100

# total number of gap junctions
n_gap_junction = 3000

n = nest.Create('hh_psc_alpha_gap', n_neuron)

random.seed(0)

# draw n_gap_junction pairs of random samples from the list of all
# neurons and reshaped data into two corresponding lists of neurons
m = np.transpose(
[random.sample(n, 2) for _ in range(n_gap_junction)])

# connect obtained lists of neurons both ways
nest.Connect(m[0], m[1],
{'rule': 'one_to_one', 'make_symmetric': True},
{'model': 'gap_junction', 'weight': 0.5})


As each gap junction contributes to the total number of gap-junction connections of two neurons, it is hardly possible to create networks with a fixed number of gap junctions per neuron. With the above script it is however possible to control the approximate number of gap junctions per neuron. E.g. if one desires gap_per_neuron = 60 the total number of gap junctions should be chosen as n_gap_junction = n_neuron * gap_per_neuron / 2.

Note: The (necessary) drawback of creating the random connections on the Python level is the serialization of the connection procedure in terms of computation time and memory in distributed simulations. Each compute node participating in the simulation needs to draw the identical full set of random numbers and temporarily represent the total connectivity in variable m. Therefore it is advisable to use the internal random connection rules of NEST for the creation of connections whenever possible. For more details see Hahne et al. 2016.

## Adjust settings of iterative solution scheme¶

For simulations with gap junctions NEST uses an iterative solution scheme based on a numerical method called Jacobi waveform relaxation. The default settings of the iterative method are based on numerical results, benchmarks and previous experience with gap-junction simulations (see Hahne et al. 2015) and should only be changed with proper knowledge of the method. In general the following parameters can be set via kernel parameters:

nest.SetKernelStatus({'use_wfr': True,
'wfr_comm_interval': 1.0,
'wfr_tol': 0.0001,
'wfr_max_iterations': 15,
'wfr_interpolation_order': 3})


For a detailed description of the parameters and their function see (Hahne et al. 2016, Table 2).