Reduced Calcium Soma-Dendrite (RCSD)

The default model for the brian2, NEURON, and Diffrax backends. RCSD implements two-compartment neuron models with calcium dynamics, providing biophysically detailed excitatory and inhibitory cell types.

from livn.models.rcsd import ReducedCalciumSomaDendrite

model = ReducedCalciumSomaDendrite()

Cell types

Excitatory: Booth-Rinzel-Kiehn motoneuron

A two-compartment motoneuron model with the following ion channels:

• Na⁺: Fast sodium (soma only)
• K⁺: Delayed rectifier (soma)
• Ca²⁺: L-type (dendrite) and N-type (both compartments)
• KCa: Calcium-dependent potassium (both compartments)

Calcium dynamics include influx via Ca²⁺ channels and extrusion via first-order kinetics, driving the KCa current. Soma and dendrite are coupled via gap-junction conductance.

params = model.params("BoothRinzelKiehn-MN")

Inhibitory: Pinsky-Rinzel interneuron

A fast-spiking interneuron with Ca²⁺ dynamics, KCa current, and simplified K⁺/Na⁺ gating compared to the excitatory cell.

params = model.params("PinskyRinzel-PVBC")

Dual-compartment stimulation

Because each neuron has a soma and dendrite compartment, stimulus_coordinates returns interleaved coordinates, doubling the number of stimulation targets:

coords = model.stimulus_coordinates(system.neuron_coordinates)
# Shape: [2 * n_neurons, 4] - soma0, dend0, soma1, dend1, ...

The dendritic compartment is offset from the soma by dx = 0.9 × L, where L = 120 µm for motoneurons and L = 37.6 µm for interneurons.

Synaptic dynamics

RCSD defines four synapse types with distinct kinetics:

Synapse	Type	Rise time	Decay time	Voltage-dependent
AMPA	Excitatory	~0.1 ms	~2 ms	No
NMDA	Excitatory	~5 ms	~30 ms	Yes (Mg²⁺ block)
GABA_A	Inhibitory	~0.5 ms	~5 ms	No
GABA_B	Inhibitory	~50 ms	~200 ms	No

Synaptic weights are specified per projection (pre-population → post-population), target section, and synapse type:

weights = {
    "EXC_EXC-hillock-AMPA-weight": 0.001,
    "EXC_INH-hillock-AMPA-weight": 2.9,
    "INH_EXC-soma-GABA_A-weight": 9.4,
}
env.set_weights(weights)

Synaptic plasticity (STDP)

RCSD supports spike-timing-dependent plasticity via specialized synapse mechanisms:

• Excitatory: StdpLinExp2Syn, StdpLinExp2SynNMDA
• Inhibitory: StdpLinExp2SynInh

See the Plasticity reference and the Plasticity guide for usage details.

Opsin configuration

RCSD includes built-in opsin (channelrhodopsin) support for optical stimulation. The opsin_config() method controls which opsin mechanism is inserted and where:

model = ReducedCalciumSomaDendrite()
model.opsin_config()
# {'mechanism': 'RhO3c', 'sections': ['soma'], 'wavelength_nm': 473.0}

Override in a subclass to customize or disable:

class NoOpsin(ReducedCalciumSomaDendrite):
    def opsin_config(self):
        return None  # disable opsins

Background noise

RCSD uses an Ornstein-Uhlenbeck process (Gfluct3) to model fluctuating synaptic conductances. The noise is spatially split: the soma receives inhibitory noise only, while the dendrite receives excitatory noise only.

noise_params = {
    "g_e0": 1.0,       # mean excitatory conductance
    "g_i0": 1.2,       # mean inhibitory conductance
    "std_e": 0.33,      # excitatory conductance std
    "std_i": 0.36,      # inhibitory conductance std
    "tau_e": 33.0,      # excitatory time constant (ms)
    "tau_i": 28.5,      # inhibitory time constant (ms)
}
env.set_noise(noise_params)

Diffrax backend

When used with the Diffrax backend, RCSD provides a MotoneuronCulture Equinox module for differentiable simulation. It supports both current and conductance input modes and returns (time, soma_voltage, dend_voltage, soma_current, dend_current, final_state).

model = ReducedCalciumSomaDendrite()
module = model.diffrax_module()