MTKNeuralToolkit

CalciumTracker

A configuration struct enabling Calcium dynamics within a compartment. When passed to build_compartment, it instantiates a CalciumPool and connects it to all channels that expose a ca_port.

Fields

• decay::Union{Float64, Function}: Either a time constant for linear decay, or a function that takes the current Calcium concentration and returns the decay rate.
• Ca_init::Float64: The initial intracellular Calcium concentration.

Keyword argument constructor for CalciumTracker.

Compartment

A struct representing a single neural compartment (e.g., a soma, axon hillock, or dendritic segment). It wraps the generated ModelingToolkit System along with metadata about its physical and electrical properties, and exposes a tuple of interfaces for acausal network connections.

Fields

• sys::System: The underlying MTK system representing the compartment's equations.
• interfaces::NamedTuple: Exposed boundary variables and pins (e.g., V, p_pin, n_pin, I_ext, I_syn).
• V_init::F: The initial membrane voltage.
• topology::Union{Scalar, Vectorized}: The electrical topology of the compartment.
• geometry::G: The physical geometry used for scaling biophysical parameters.
• morphology::M: The spatial morphology used for rendering or spatial simulations.

CouplingSpec

A specification struct used to wire an acausal coupling (e.g., a Gap Junction) between two compartments.

Fields

• comp_i::Compartment: The first compartment to be coupled.
• comp_j::Compartment: The second compartment to be coupled.
• coupling::System: The MTK coupling system component (e.g., GapJunction).

Network

A struct representing the complete assembled neural network. It encapsulates the fully connected MTK System and a vector of input variables for simulation drivers.

Fields

• sys::System: The final compiled MTK system representing the entire network.
• inputs::Vector{Any}: A collection of symbolic input variables for external stimulation.

NoCalcium

A configuration struct indicating that a compartment has no Calcium dynamics. When passed to build_compartment, it bypasses the creation of a CalciumPool.

SynapseSpec

A specification struct used to wire a synapse between a presynaptic voltage and a postsynaptic current. It provides the mapping needed by wire_synapses! to inject currents into the correct compartments.

Fields

• pre_V: The symbolic voltage variable of the presynaptic compartment.
• post_V: The symbolic voltage variable of the postsynaptic compartment.
• post_I_syn: The symbolic current variable of the postsynaptic compartment where the synapse will inject.
• synapse::System: The MTK synapse system component (e.g., ExpSynapse, CholSynapse).
• post_comp::Union{Compartment, Nothing}: The postsynaptic compartment struct (used for block synapse grounding logic).

Outer constructor for SynapseSpec that defaults post_comp to nothing. Useful for scalar synapses where block grounding logic is not required.

AlphaSynapse(; name, g_max=1.0, τ=5.0, E_rev=0.0, V_th=-20.0, slope=2.0)

An alpha-function synapse implemented via a cascade of two first-order filters (s1 and s2). This produces the classic unimodal alpha-function response in synaptic conductance following a sustained presynaptic depolarization.

The current injected into the postsynaptic compartment is: I_syn = g_max * s2 * (E_rev - V_post)

Arguments

• g_max: Maximum synaptic conductance.
• τ: Time constant for both cascaded filters.
• E_rev: Reversal potential of the synapse.
• V_th: Threshold voltage for presynaptic activation.
• slope: Slope of the presynaptic sigmoid activation.

CholSynapse(; name, g_max=30.0, E_rev=-80.0, k_minus=0.01, V_th=-35.0, delta=5.0, geometry=NoGeometry())

A continuous cholinergic synapse model. The synaptic state variable s represents the fraction of open receptors. It rises towards a steady-state s_inf governed by the presynaptic voltage, and decays exponentially.

The synaptic current is calculated as the current injected into the postsynaptic membrane: I_syn = g_max * s * (E_rev - V_post)

Arguments

• g_max: Maximum synaptic conductance (scaled by geometry if provided).
• E_rev: Reversal potential of the synapse (e.g., -80 mV for inhibitory).
• k_minus: Rate constant for receptor unbinding (controls decay time).
• V_th: Half-activation voltage for the presynaptic sigmoid.
• delta: Slope of the presynaptic sigmoid activation.
• geometry: AbstractGeometry struct for scaling g_max.

ExpSynapse(; name, g_max=1.0, τ=5.0, E_rev=0.0, V_th=-20.0, slope=2.0)

A simple exponential decay synapse. The synaptic gating variable s is driven by a continuous sigmoidal function of the presynaptic voltage and decays exponentially with time constant τ.

The current injected into the postsynaptic compartment is: I_syn = g_max * s * (E_rev - V_post)

Arguments

• g_max: Maximum synaptic conductance.
• τ: Decay time constant of the synapse.
• E_rev: Reversal potential of the synapse.
• V_th: Threshold voltage for presynaptic activation.
• slope: Slope of the presynaptic sigmoid activation.

fixed_reversal Component: A pure constant voltage source (Nernst battery).

GlutSynapse(; name, g_max=30.0, E_rev=-70.0, k_minus=0.025, V_th=-35.0, delta=5.0, geometry=NoGeometry())

A continuous glutamatergic synapse model. Behaves identically to CholSynapse but uses default parameters typical for fast excitatory glutamatergic receptors.

Arguments

• g_max: Maximum synaptic conductance (scaled by geometry if provided).
• E_rev: Reversal potential of the synapse (e.g., -70 mV or higher for excitatory).
• k_minus: Rate constant for receptor unbinding.
• V_th: Half-activation voltage for the presynaptic sigmoid.
• delta: Slope of the presynaptic sigmoid activation.
• geometry: AbstractGeometry struct for scaling g_max.

NMDASynapse(; name, g_max=1.0, τ=100.0, E_rev=0.0, V_th=-20.0, Mg_conc=1.0, slope=2.0)

An N-Methyl-D-Aspartate (NMDA) receptor synapse. It includes the classic voltage-dependent Magnesium block that reduces conductance at hyperpolarized potentials. The gating variable s decays with a slow time constant τ.

The current injected into the postsynaptic compartment is: I_syn = g_max * s * mg_block(V_post) * (E_rev - V_post)

Arguments

• g_max: Maximum synaptic conductance.
• τ: Slow decay time constant typical of NMDA receptors.
• E_rev: Reversal potential of the synapse (usually near 0 mV).
• V_th: Threshold voltage for presynaptic activation.
• Mg_conc: Extracellular Magnesium concentration determining block strength.
• slope: Slope of the presynaptic sigmoid activation.

STDPSynapse(; name, g_max=1.0, E_rev=0.0, V_th=0.0, slope=2.0, τ_s=5.0, 
            τ_plus=20.0, τ_minus=20.0, A_plus=0.1, A_minus=0.1, 
            w_init=0.5, w_max=1.0, w_min=0.0)

A continuous, smooth approximation of Spike-Timing-Dependent Plasticity (STDP) with soft bounds. It uses a continuous spike-detector function (sigmoid) and trace variables (x for pre, y for post) to approximate the relative timing of spikes without requiring discrete event handling.

The weight w evolves continuously according to: dw/dt = A_plus * (w_max - w) * x * σ(V_post) - A_minus * (w - w_min) * y * σ(V_pre)

where x and y are exponentially decaying traces, and σ(V) is a sigmoid acting as a continuous spike detector. This formulation is purely acausal and ODE-based, making it incredibly robust for standard differential equation solvers while demonstrating classic STDP behavior.

SpikingCapacitor Component: Capacitor that automatically resets its voltage when a threshold is crossed

SynapsePort

A boundary connector that exposes the postsynaptic current variable (I_syn) and binds it to the positive pin (p.i) of a standard electrical port.

This component is typically used internally by compartment builders to route synaptic currents into a postsynaptic compartment's CurrentSource.

VectorizedExpSynapse(; name, N_pre, N_post, W, g_max=1.0, τ=5.0, E_rev=0.0, V_th=-20.0, slope=2.0)

A vectorized block of exponential synapses representing a dense N_post by N_pre projection. It accepts an entire weight matrix W mapping presynaptic gating variables to postsynaptic currents.

The synaptic state s is a vector of length N_pre. The postsynaptic current vector is computed via: I_syn[i] = g_max * sum_j(W[i, j] * s[j]) * (E_rev - V_post[i])

Arguments

• N_pre: Number of presynaptic elements.
• N_post: Number of postsynaptic elements.
• W: A matrix of connection weights (dimensions N_post x N_pre).
• g_max: Maximum global synaptic conductance.
• τ: Decay time constant.
• E_rev: Reversal potential of the synapse.
• V_th: Threshold voltage for presynaptic activation.
• slope: Slope of the presynaptic sigmoid activation.

build_acausal_network(compartments; coupling_specs, synapse_specs, drivers, name)

Assembles a collection of Compartments into a complete Network system. It handles grounding, wiring driving stimuli, gap junctions (via CouplingSpec), and chemical synapses (via SynapseSpec).

Arguments

• compartments::Vector{<:Compartment}: The compartments making up the network.
• coupling_specs: A vector of CouplingSpec structs for acausal electrical connections.
• synapse_specs: A vector of SynapseSpec structs for directed chemical synapses.
• drivers: A vector of (target, stim) tuples, where target is a compartment or index, and stim is an MTK block, vector, or number.
• name::Symbol: The name of the overall network system.

Returns

• A Network struct containing the assembled MTK System.

build_compartment(capacitor, channels; name, V_init, topology, ion_config, geometry, morphology)

Builds a Compartment by connecting a Capacitor, current injectors, and a collection of ion channels. This forms the fundamental electrical unit of a neuron. All positive terminals (p) are connected together to the membrane potential, and all negative terminals (n) are connected to ground.

Arguments

• capacitor: A Capacitor system defining the membrane capacitance.
• channels: A vector of ion channel systems (e.g., GenericChannel, CaVChannel).
• name::Symbol: The name of the compartment system.
• V_init::Float64: Initial membrane voltage (default -65.0 mV).
• topology: Scalar() or Vectorized(N) (default Scalar()).
• ion_config: NoCalcium() or CalciumTracker() to handle ion pools.
• geometry: Geometry struct for biophysical scaling (default NoGeometry()).
• morphology: Morphology struct for spatial data (default NoMorphology()).

Returns

• A Compartment struct containing the assembled System and its exposed interfaces.

build_synapse_block(pre_comp, post_comp, W; name, synapse_type, kwargs...)

Helper function to create a SynapseSpec using a vectorized synapse block. It automatically determines the pre- and postsynaptic dimensions based on the weight matrix W and binds it to the provided compartments.

Arguments

• pre_comp::Compartment: The presynaptic compartment.
• post_comp::Compartment: The postsynaptic compartment.
• W: The weight matrix (dimensions N_post x N_pre).
• name::Symbol: The name for the synapse block system.
• synapse_type: The vectorized synapse component to use (defaults to VectorizedExpSynapse).
• kwargs...: Additional keyword arguments passed to synapse_type (e.g., g_max, E_rev).

Returns

• A SynapseSpec configured for the network builder.

wire_ions!(eqs, systems, channels, config, topology, name)

Internal helper function to wire ion dynamics into a compartment's equations and systems list. Uses multiple dispatch to handle different ion configurations.

• If config is NoCalcium, it does nothing.
• If config is CalciumTracker, it creates a CalciumPool and connects it to all channels in the compartment that expose a ca_port.

wire_synapses!(eqs, systems, specs)

Internal helper function that wires a collection of SynapseSpecs into the network equations. It binds the presynaptic and postsynaptic voltage variables to the synapse, and pre-collects convergent synapses by their target current variable to write a single summed equation per target.

Returns a tuple of (driven_syn_targets, block_driven_targets) used for grounding unconnected inputs.