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

## Description¶

pp_cond_exp_mc_urbanczik is an implementation of a two-compartment spiking point process neuron with conductance-based synapses as it is used in 1. It is capable of connecting to an Urbanczik synapse.

The model has two compartments: soma and dendrite, labeled as s and p, respectively. Each compartment can receive spike events and current input from a current generator. Additionally, an external (rheobase) current can be set for each compartment.

Synapses, including those for injection external currents, are addressed through the receptor types given in the receptor_types entry of the state dictionary. Note that in contrast to the single-compartment models, all synaptic weights must be positive numbers! The distinction between excitatory and inhibitory synapses is made explicitly by specifying the receptor type of the synapse. For example, receptor_type=dendritic_exc results in an excitatory input and receptor_type=dendritic_inh results in an inhibitory input to the dendritic compartment.

## Multicompartment models and synaptic delays¶

Note that in case of multicompartment models that represent the dendrite explicitly, the interpretation of the synaptic delay in NEST requires careful consideration. In NEST, the delay is at least one simulation time step and is assumed to be located entirely at the postsynaptic side. For point neurons, it represents the time it takes for an incoming spike to travel along the postsynaptic dendrite before it reaches the soma, see panel a). Conversely, if the synaptic weight depends on the state of the postsynaptic neuron, the delay also represents the time it takes for the information on the state to propagate back through the dendrite to the synapse.

For multicompartment models in NEST, this means the delay is positioned directly behind the incoming synapse, that is, before the first dendritic compartment on the postsynaptic side, see panel b). Therefore, the delay specified in the synapse model does not account for any delay that might be associated with information traveling through the explicitly modeled dendritic compartments.

In the Urbanczik synapse, the change of the synaptic weight is driven by an error signal, which is the difference between the firing rate of the soma (derived from the somatic spike train $$S_{post}$$) and the dendritic prediction of the firing rate of the soma (derived from the dendritic membrane potential $$V$$). The original publication 1 does not assume any delay in the interaction between the soma and the dendritic compartment. Therefore, we evaluate the firing rate and the dendritic prediction at equal time points to calculate the error signal at that time point. Due to the synaptic delay $$d$$, the synapse combines a delayed version of the error signal with the presynaptic spike train ($$S_{pre}$$), see panel c).

Figure 40 a) Two point neurons (red circles pre and post) connected via a synapse. In NEST, the delay is entirely on the postsynaptic side, and in the case of point neurons, it is interpreted as the dendritic delay. b) Two two-compartment neuron models composed of a somatic (green) and a dendritic (blue) compartment. The soma of the presynaptic neuron is connected to the dendrite of the postsynaptic neuron. The synaptic delay is located behind the synapse and before the dendrite. c) Time trace of the State variables that enter the Urbanczik-Senn rule. Due to the synaptic delay $$d$$, the presynaptic spike train (top) is combined with a delayed version of the postsynaptic quantities; the dendritic membrane potential (middle) and the somatic spike train (bottom).

## Parameters¶

The following parameters can be set in the status dictionary. Parameters for each compartment are collected in a sub-dictionary; these sub-dictionaries are called “soma” and “dendritic”, respectively. In the list below, these parameters are marked with an asterisk.

 V_m* mV Membrane potential E_L* mV Leak reversal potential C_m* pF Capacity of the membrane E_ex* mV Excitatory reversal potential E_in* mV Inhibitory reversal potential g_L* nS Leak conductance tau_syn_ex* ms Rise time of the excitatory synaptic alpha function tau_syn_in* ms Rise time of the inhibitory synaptic alpha function I_e* pA Constant input current g_sp nS Coupling between soma and dendrite g_ps nS Coupling between dendrite and soma t_ref ms Duration of refractory period

Remarks:

The neuron model uses standard units of NEST instead of the unitless quantities used in 1.

Note

All parameters that occur for both compartments are stored as C arrays, with index 0 being soma.

SpikeEvent