Types of neurons

Spiking neurons

Rate neurons

Multi-state neurons

Astrocytes

In the following section, we introduce the different types of neuron models implemented in NEST, describe their dynamics and technical details. A generic description of the numerical update algorithm can be found here: Neuron update algorithms.

Spiking neurons

Geometry

Point neurons

The most common type of neuron model in NEST. Point neurons are simplified models of biological neurons that represent the neuron as a single point where all inputs are processed, without considering the complex neuronal morphology (such as dendrites and axons).

Multi-compartment neurons

Neurons are subdivided into multiple compartments that can represent different parts of the neuronal morphology, like soma, basal and apical dendrites. Inputs can be received in all compartments and are mediated across compartments via electric coupling.

For more information see our project NEST-NEAT, a Python library for the study, simulation and simplification of morphological neuron models.

Multi-compartment neurons

• cm_default – A neuron model with user-defined dendrite structure. Currently, AMPA, GABA or AMPA+NMDA receptors.

Spiking mechanism

Spiking neuron models process synaptic inputs and generate discrete output events, which are called action potentials or spikes. The mechanisms by which these spikes are generated can be classified with the following distinctions.

Hard threshold

General info

When the membrane potential reaches a certain threshold, the neuron deterministically “fires” an action potential. Neuron models with hard threshold do not contain intrinsic dynamics that produce the upswing of a spike. Some of the neurons in this class do not reset the membrane potential after a spike. Note that the threshold itself can be dynamic (see Adaptation section below).

Hard threshold

• amat2_psc_exp – Non-resetting leaky integrate-and-fire neuron model with exponential PSCs and adaptive threshold

• eprop_iaf_adapt_bsshslm_2020 – Current-based leaky integrate-and-fire neuron model with delta-shaped or exponentially filtered postsynaptic currents and threshold adaptation for e-prop plasticity

• eprop_iaf_bsshslm_2020 – Current-based leaky integrate-and-fire neuron model with delta-shaped or exponentially filtered postsynaptic currents for e-prop plasticity

• glif_cond – Conductance-based generalized leaky integrate and fire (GLIF) model (from the Allen Institute)

• glif_psc_double_alpha – Current-based generalized leaky integrate-and-fire (GLIF) models with double alpha-function (from the Allen Institute)

• iaf_bw_2001_exact – Leaky integrate-and-fire-neuron model with conductance-based synapses and additional NMDA receptors.

• iaf_chs_2007 – Spike-response model used in Carandini et al. 2007

• iaf_chxk_2008 – Conductance-based leaky integrate-and-fire neuron model supporting precise spike times used in Casti et al. 2008

• iaf_cond_alpha – Simple conductance based leaky integrate-and-fire neuron model

• iaf_cond_alpha_mc – Multi-compartment conductance-based leaky integrate-and-fire neuron model

• iaf_cond_beta – Simple conductance based leaky integrate-and-fire neuron model

• iaf_cond_exp – Simple conductance based leaky integrate-and-fire neuron model

• iaf_cond_exp_sfa_rr – Conductance based leaky integrate-and-fire model with spike-frequency adaptation and relative refractory mechanisms

• iaf_psc_alpha – Leaky integrate-and-fire model with alpha-shaped input currents

• iaf_psc_alpha_multisynapse – Leaky integrate-and-fire neuron model with multiple ports

• iaf_psc_alpha_ps – Current-based leaky integrate-and-fire neuron with alpha-shaped postsynaptic currents using regula falsi method for approximation of threshold crossing

• iaf_psc_delta – Leaky integrate-and-fire model with delta-shaped input currents

• iaf_psc_delta_ps – Current-based leaky integrate-and-fire neuron model with delta-shaped postsynaptic currents - precise spike timing version

• iaf_psc_exp – Leaky integrate-and-fire neuron model with exponential-shaped input currents

• iaf_psc_exp_htum – Leaky integrate-and-fire model with separate relative and absolute refractory period

• iaf_psc_exp_ps – Current-based leaky integrate-and-fire neuron with exponential-shaped postsynaptic currents using regula falsi method for approximation of threshold crossing

• iaf_psc_exp_ps_lossless – Current-based leaky integrate-and-fire neuron with exponential-shaped postsynaptic currents predicting the exact number of spikes using a state space analysis

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

• mat2_psc_exp – Non-resetting leaky integrate-and-fire neuron model with exponential PSCs and adaptive threshold

Technical details

• Integrating neural models using exact integration

• Handling time-constant singularities in integrate-and-fire neurons

Soft threshold

General info

Neurons with a soft threshold model aspects of the voltage dependent conductances that underlie the biophysics of spike generation. Models either produce dynamics, which mimic the upswing of a spike or the whole spike wave form. Some models in this class contain a hard threshold that triggers an instantaneous reset of the membrane potential. This threshold is needed to finish the action potential and to avoid an unbounded growth of the membrane potential. The action-potential initiation is not affected by this and governed by continuous dynamics.

Soft threshold

• aeif_cond_alpha – Conductance based exponential integrate-and-fire neuron model

• aeif_cond_alpha_astro – Conductance based exponential integrate-and-fire neuron model with support for neuron-astrocyte interactions

• aeif_cond_alpha_multisynapse – Conductance based adaptive exponential integrate-and-fire neuron model

• aeif_cond_beta_multisynapse – Conductance based adaptive exponential integrate-and-fire neuron model

• aeif_cond_exp – Conductance based exponential integrate-and-fire neuron model

• aeif_psc_alpha – Current-based exponential integrate-and-fire neuron model

• aeif_psc_delta – Current-based adaptive exponential integrate-and-fire neuron model with delta synapse

• aeif_psc_delta_clopath – Adaptive exponential integrate-and-fire neuron

• aeif_psc_exp – Current-based exponential integrate-and-fire neuron model

• hh_cond_beta_gap_traub – Hodgkin-Huxley neuron with gap junction support and beta function synaptic conductances

• hh_cond_exp_traub – Hodgkin-Huxley model for Brette et al (2007) review

• hh_psc_alpha – Hodgkin-Huxley neuron model

• hh_psc_alpha_clopath – Hodgkin-Huxley neuron model with support for Clopath plasticity

• hh_psc_alpha_gap – Hodgkin-Huxley neuron model with gap-junction support

• ht_neuron – Neuron model after Hill & Tononi (2005)

• izhikevich – Izhikevich neuron model

Technical details

• How NEST generates spikes in Hodgkin-Huxley style models

• The Hill-Tononi Neuron and Synapse Models

Stochastic

Stochastic spiking models do not produce deterministic spike events: instead spike times are stochastic and described by a point process, with an underlying time dependent firing rate that is determined by the membrane potential of a neuron. Elevated membrane potential with respect to the resting potential increaes the likelihood of output spikes.

Stochastic

• gif_cond_exp – Conductance-based generalized integrate-and-fire neuron (GIF) model (from the Gerstner lab)

• gif_pop_psc_exp – Population of generalized integrate-and-fire neurons (GIF) with exponential postsynaptic currents and adaptation (from the Gerstner lab)

• gif_psc_exp – Current-based generalized integrate-and-fire neuron (GIF) model (from the Gerstner lab)

• gif_psc_exp_multisynapse – Current-based generalized integrate-and-fire neuron (GIF) model with multiple synaptic time constants (from the Gerstner lab)

• pp_cond_exp_mc_urbanczik – Two-compartment point process neuron with conductance-based synapses

• pp_psc_delta – Point process neuron with leaky integration of delta-shaped PSCs

Input mechanism

NEST supports various input mechanisms to neuron models. The majority of mechanisms are related to chemical synapses that couple neurons with a delay, but there are also electrical synapses, which couple neurons instantaneously.

Electrical

Gap junctions are direct electrical connections between neurons. The respective membrane potentials are instantaneously coupled to each other.

Chemical

Chemical synapses couple neurons in a delayed fashion, because of the conversion of electrical and chemical signals at the synapse. This process is captured by two major classes of models in NEST that either model synaptic inputs as currents or conductances.

Current-based (CUBA) models

Model post-synaptic responses to incoming spikes as changes in current. The response of the post-synaptic neuron is independent of the neuronal state. In NEST, current-based neuron models are labeled by psc (post-synaptic currents).

Current-based neuron models

• aeif_psc_alpha – Current-based exponential integrate-and-fire neuron model

• aeif_psc_delta – Current-based adaptive exponential integrate-and-fire neuron model with delta synapse

• aeif_psc_delta_clopath – Adaptive exponential integrate-and-fire neuron

• aeif_psc_exp – Current-based exponential integrate-and-fire neuron model

• amat2_psc_exp – Non-resetting leaky integrate-and-fire neuron model with exponential PSCs and adaptive threshold

• eprop_iaf – Current-based leaky integrate-and-fire neuron model with delta-shaped postsynaptic currents for e-prop plasticity

• eprop_iaf_adapt – Current-based leaky integrate-and-fire neuron model with delta-shaped postsynaptic currents and threshold adaptation for e-prop plasticity

• eprop_iaf_adapt_bsshslm_2020 – Current-based leaky integrate-and-fire neuron model with delta-shaped or exponentially filtered postsynaptic currents and threshold adaptation for e-prop plasticity

• eprop_iaf_bsshslm_2020 – Current-based leaky integrate-and-fire neuron model with delta-shaped or exponentially filtered postsynaptic currents for e-prop plasticity

• eprop_iaf_psc_delta – Current-based leaky integrate-and-fire neuron model with delta-shaped postsynaptic currents for e-prop plasticity

• eprop_iaf_psc_delta_adapt – Current-based leaky integrate-and-fire neuron model with delta-shaped postsynaptic currents and threshold adaptation for e-prop plasticity

• eprop_readout – Current-based leaky integrate readout neuron model with delta-shaped postsynaptic currents for e-prop plasticity

• eprop_readout_bsshslm_2020 – Current-based leaky integrate readout neuron model with delta-shaped or exponentially filtered postsynaptic currents for e-prop plasticity

• gif_pop_psc_exp – Population of generalized integrate-and-fire neurons (GIF) with exponential postsynaptic currents and adaptation (from the Gerstner lab)

• gif_psc_exp – Current-based generalized integrate-and-fire neuron (GIF) model (from the Gerstner lab)

• gif_psc_exp_multisynapse – Current-based generalized integrate-and-fire neuron (GIF) model with multiple synaptic time constants (from the Gerstner lab)

• glif_psc – Current-based generalized leaky integrate-and-fire (GLIF) models (from the Allen Institute)

• glif_psc_double_alpha – Current-based generalized leaky integrate-and-fire (GLIF) models with double alpha-function (from the Allen Institute)

• hh_psc_alpha – Hodgkin-Huxley neuron model

• hh_psc_alpha_clopath – Hodgkin-Huxley neuron model with support for Clopath plasticity

• hh_psc_alpha_gap – Hodgkin-Huxley neuron model with gap-junction support

• iaf_psc_alpha – Leaky integrate-and-fire model with alpha-shaped input currents

• iaf_psc_alpha_multisynapse – Leaky integrate-and-fire neuron model with multiple ports

• iaf_psc_alpha_ps – Current-based leaky integrate-and-fire neuron with alpha-shaped postsynaptic currents using regula falsi method for approximation of threshold crossing

• iaf_psc_delta – Leaky integrate-and-fire model with delta-shaped input currents

• iaf_psc_delta_ps – Current-based leaky integrate-and-fire neuron model with delta-shaped postsynaptic currents - precise spike timing version

• iaf_psc_exp – Leaky integrate-and-fire neuron model with exponential-shaped input currents

• iaf_psc_exp_ps – Current-based leaky integrate-and-fire neuron with exponential-shaped postsynaptic currents using regula falsi method for approximation of threshold crossing

• iaf_psc_exp_ps_lossless – Current-based leaky integrate-and-fire neuron with exponential-shaped postsynaptic currents predicting the exact number of spikes using a state space analysis

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

• ignore_and_fire – Ignore-and-fire neuron model for generating spikes at fixed intervals irrespective of inputs

• mat2_psc_exp – Non-resetting leaky integrate-and-fire neuron model with exponential PSCs and adaptive threshold

• pp_psc_delta – Point process neuron with leaky integration of delta-shaped PSCs

Conductance-based (COBA) models

Model post-synaptic responses to incoming spikes as changes in conductances. The response of the post-synaptic neuron depends on the neuronal state. These models capture more realistic synaptic behavior, as they account for the varying impact of synaptic inputs depending on the membrane potential, which can change over time. In NEST, conductance-based neuron models are labeled by cond.

Conductance-based neuron models

• aeif_cond_alpha – Conductance based exponential integrate-and-fire neuron model

• aeif_cond_alpha_astro – Conductance based exponential integrate-and-fire neuron model with support for neuron-astrocyte interactions

• aeif_cond_alpha_multisynapse – Conductance based adaptive exponential integrate-and-fire neuron model

• aeif_cond_beta_multisynapse – Conductance based adaptive exponential integrate-and-fire neuron model

• aeif_cond_exp – Conductance based exponential integrate-and-fire neuron model

• gif_cond_exp – Conductance-based generalized integrate-and-fire neuron (GIF) model (from the Gerstner lab)

• gif_cond_exp_multisynapse – Conductance-based generalized integrate-and-fire neuron (GIF) with multiple synaptic time constants (from the Gerstner lab)

• glif_cond – Conductance-based generalized leaky integrate and fire (GLIF) model (from the Allen Institute)

• hh_cond_beta_gap_traub – Hodgkin-Huxley neuron with gap junction support and beta function synaptic conductances

• hh_cond_exp_traub – Hodgkin-Huxley model for Brette et al (2007) review

• iaf_bw_2001 – Leaky integrate-and-fire-neuron model with conductance-based synapses and additional NMDA receptors with simplified dynamics.

• iaf_bw_2001_exact – Leaky integrate-and-fire-neuron model with conductance-based synapses and additional NMDA receptors.

• iaf_chxk_2008 – Conductance-based leaky integrate-and-fire neuron model supporting precise spike times used in Casti et al. 2008

• iaf_cond_alpha – Simple conductance based leaky integrate-and-fire neuron model

• iaf_cond_alpha_mc – Multi-compartment conductance-based leaky integrate-and-fire neuron model

• iaf_cond_beta – Simple conductance based leaky integrate-and-fire neuron model

• iaf_cond_exp – Simple conductance based leaky integrate-and-fire neuron model

• iaf_cond_exp_sfa_rr – Conductance based leaky integrate-and-fire model with spike-frequency adaptation and relative refractory mechanisms

• pp_cond_exp_mc_urbanczik – Two-compartment point process neuron with conductance-based synapses

Post-synaptic input responses

Synaptic inputs can be modeled using different kernels to represent how the current or conductance changes over time after a synaptic event. The type of post-synaptic input (exp, delta, alpha, beta) are indicated at the end of the neuron model name (e.g., iaf_psc_delta)

Delta

Exp

Alpha

Beta

Adaptation mechanism

General info

Unlike a fixed threshold, an adaptive threshold increases temporarily following each spike and gradually returns to its baseline value over time. This mechanism models phenomena such as spike-frequency adaptation, where a neuron’s responsiveness decreases with sustained high-frequency input. A different mechanism to implement similar adaptation behavior is via a spike-triggered hyperpolarizing adaptation current.

Models with adaptation

• aeif_cond_alpha – Conductance based exponential integrate-and-fire neuron model

• aeif_cond_alpha_astro – Conductance based exponential integrate-and-fire neuron model with support for neuron-astrocyte interactions

• aeif_cond_alpha_multisynapse – Conductance based adaptive exponential integrate-and-fire neuron model

• aeif_cond_beta_multisynapse – Conductance based adaptive exponential integrate-and-fire neuron model

• aeif_cond_exp – Conductance based exponential integrate-and-fire neuron model

• aeif_psc_alpha – Current-based exponential integrate-and-fire neuron model

• aeif_psc_delta – Current-based adaptive exponential integrate-and-fire neuron model with delta synapse

• aeif_psc_delta_clopath – Adaptive exponential integrate-and-fire neuron

• aeif_psc_exp – Current-based exponential integrate-and-fire neuron model

• amat2_psc_exp – Non-resetting leaky integrate-and-fire neuron model with exponential PSCs and adaptive threshold

• eprop_iaf_adapt_bsshslm_2020 – Current-based leaky integrate-and-fire neuron model with delta-shaped or exponentially filtered postsynaptic currents and threshold adaptation for e-prop plasticity

• gif_cond_exp – Conductance-based generalized integrate-and-fire neuron (GIF) model (from the Gerstner lab)

• gif_cond_exp_multisynapse – Conductance-based generalized integrate-and-fire neuron (GIF) with multiple synaptic time constants (from the Gerstner lab)

• gif_pop_psc_exp – Population of generalized integrate-and-fire neurons (GIF) with exponential postsynaptic currents and adaptation (from the Gerstner lab)

• gif_psc_exp – Current-based generalized integrate-and-fire neuron (GIF) model (from the Gerstner lab)

• gif_psc_exp_multisynapse – Current-based generalized integrate-and-fire neuron (GIF) model with multiple synaptic time constants (from the Gerstner lab)

• glif_cond – Conductance-based generalized leaky integrate and fire (GLIF) model (from the Allen Institute)

• glif_psc – Current-based generalized leaky integrate-and-fire (GLIF) models (from the Allen Institute)

• glif_psc_double_alpha – Current-based generalized leaky integrate-and-fire (GLIF) models with double alpha-function (from the Allen Institute)

• ht_neuron – Neuron model after Hill & Tononi (2005)

• izhikevich – Izhikevich neuron model

• mat2_psc_exp – Non-resetting leaky integrate-and-fire neuron model with exponential PSCs and adaptive threshold

• pp_psc_delta – Point process neuron with leaky integration of delta-shaped PSCs

Technical details

• NEST implementation of the aeif models

Auxilliary neurons

NEST provides a number of auxilliary neuron models that can be used for specific purposes such as repeating or ignoring particular incoming spike patterns. Use cases for such functionality include testing or benchmarking simulator performance, or the creation of shared spiking input patterns to neurons.

Auxillary neurons

ignore-and-fire – Used for benchmarking

parrot_neuron – Neuron that repeats incoming spikes

parrot_neuron_ps – Neuron that repeats incoming spikes - precise spike timing version

Precise spike timing

By default, the dynamics of neuronal models are evaluated on a fixed time grid that can be specified before simulation.

Precise neuron models instead calculate precise rather than grid-constrained spike times. These models are more computationally heavy, but provide better resolution to spike times than a grid-constrained model. Spiking neuron networks are often chaotic systems such that an infinitesimal shift in spike time might lead to changes in the overall network dynamics. In NEST, we label models with precise spike times with ps.

See our guide on precise spike timing.

Models with precise spike times

• iaf_chxk_2008 – Conductance-based leaky integrate-and-fire neuron model supporting precise spike times used in Casti et al. 2008

• iaf_psc_alpha_ps – Current-based leaky integrate-and-fire neuron with alpha-shaped postsynaptic currents using regula falsi method for approximation of threshold crossing

• iaf_psc_delta_ps – Current-based leaky integrate-and-fire neuron model with delta-shaped postsynaptic currents - precise spike timing version

• iaf_psc_exp_ps – Current-based leaky integrate-and-fire neuron with exponential-shaped postsynaptic currents using regula falsi method for approximation of threshold crossing

• iaf_psc_exp_ps_lossless – Current-based leaky integrate-and-fire neuron with exponential-shaped postsynaptic currents predicting the exact number of spikes using a state space analysis

• parrot_neuron_ps – Neuron that repeats incoming spikes - precise spike timing version

• poisson_generator_ps – Simulated neuron firing with Poisson process statistics - precise spike timing version with arbitrary dead times

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Rate neurons

Rate neurons can approximate biologically realistic neurons but they are also used in artificial neuronal networks (also known as recurrent neural networks RNNs).

Most rate neurons in NEST are implemented as templates based on the non-linearity and noise type.

Type of non-linearity

You can specify the type of non-linearity, which in NEST are provided as C++ templates.

The following non-linearity types are available:

Templates with non-linearity

• gauss_rate – Rate neuron model with Gaussian gain function

• lin_rate – Linear rate model

• sigmoid_rate – Rate neuron model with sigmoidal gain function

• sigmoid_rate_gg_1998 – rate model with sigmoidal gain function

• tanh_rate – rate model with hyperbolic tangent non-linearity

• threshold_lin_rate – Rate model with threshold-linear gain function

Where is Non-linearity applied?

The boolean parameter linear_summation determines whether the input from different presynaptic neurons is first summed linearly and then transformed by a nonlinearity (True), or if the input from individual presynaptic neurons is first nonlinearly transformed and then summed up (False). Default is True.

You can set this parameter in the parameter dictionary of the rate neuron.

Noise application

Input noise

ipn: Noise is added to the input rate

rate_neuron_ipn – Base class for rate model with input noise

Output noise

opn: Noise is applied to the output rate

rate_neuron_opn – Base class for rate model with output noise

Use rate neurons in your simulation

The rate models are instantiated from the templates. To use a rate neuron, the naming convention is <non-linearity>_rate_<noise_type>

For example:

nest.Create("gauss_rate_opn")

If using the rate_transformer_node (see below), you can use the following syntax rate_transformer_<non-linearity>

Example:

nest.Create("rate_transformer_tanh")

Mean field theory

General info

Rate models can also be used as mean-field descriptions for the population-rate dynamics of spiking networks.

• siegert_neuron – model for mean-field analysis of spiking networks

Technical details

• Siegert neuron integration

Rate transformer

If you want to transform rates in a non-linear manner, but do not want any neuronal dynamics processing these rates, then you can use the rate transformer node.

The rate_transformer_node applies a non-linearity to a sum of incoming rates, transforming them before passing on to other nodes.

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Multi-state neurons

Neurons with two or three discrete states. These are the simplest neuron models with threshold activation. Binary neurons have On / Off behavior used in theoretical neuroscience and disease theory.

Multi-state neurons

• erfc_neuron – Binary stochastic neuron with complementary error function as activation function

• ginzburg_neuron – Binary stochastic neuron with sigmoidal activation function

• mcculloch_pitts_neuron – Binary deterministic neuron with Heaviside activation function

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Astrocytes

General info

NEST offers an astrocyte model for interactions with neurons, including TripartiteConnect to support the creation of a pre-synaptic, a post-synaptic and a third-factor population.

Astrocyte models

• aeif_cond_alpha_astro – Conductance based exponential integrate-and-fire neuron model with support for neuron-astrocyte interactions

• astrocyte_lr_1994 – An astrocyte model based on Li & Rinzel (1994)

• sic_connection – Synapse type for astrocyte-neuron connections

Technical details

• NEST implementation of the astrocyte_lr_1994 model