Receptors

Here we present the documentation of our receptor library. These receptors can act as the postsynaptic receptors in a neuron to neuron connection, when connecting neurons of appropriate types, e.g. an inhibitory projection works with a GABAergic receptor and a dopamine receptor requires that the presynaptic neuron is dopaminergic.

NeurobloxPharma.Glu_AMPA_Synapse — Type

Glu_AMPA_Synapse(; E_syn=0,  G_syn=3, V_shift=10, V_range=35, τ₁=0.1, τ₂=5, g=1)

An AMPA receptor model activated by glutamate. Equations and default parameter values are based on [1, 2].

\[\frac{dG}{dt} = -\frac{G}{τ_2} + z \\ \frac{dz}{dt} = -\frac{z}{τ_1} + \frac{G_\text{syn}}{1 + e^{-4.394(\frac{V-V_\text{shift}}{V_\text{range}})}}\]

Arguments :

E_syn [mV, reversal potential]
G_syn [mV, receptor conductance]
V_shift [mV, transmitter threshold]
V_range [mV, transmitter sensitivity]
τ₁ [ms, decay timescale for receptor conductance]
τ₂ [ms, decay timescale for receptor conductance]
g [conductance gain]

References :

C Koch, I Segev, TJ Sejnowski, TA Poggio, eds. (1998), Methods in Neuronal Modeling: From Ions to Networks, Computational

Neuroscience Series. (A Bradford Book, Cambridge, MA, USA), 2 edition.

SR Wicks, CJ Roehrig, CH Rankin (1996), A Dynamic Network Simulation of the Nematode Tap Withdrawal Circuit: Predictions

Concerning Synaptic Function Using Behavioral Criteria. The J. Neurosci. 16, 4017–4031.

NeurobloxPharma.Glu_AMPA_STA_Synapse — Type

Glu_AMPA_STA_Synapse(; E_syn=0,  G_syn=3, V_shift=10, V_range=35, τ₃=2000, τ₄=0.1, kₛₜₚ=0.5, g=1)

An AMPA receptor model activated by glutamate, which also includes short-term augmentation dynamics. Equations and default parameter values are based on [1, 2].

\[\frac{d G_\text{stp}}{dt} = -\frac{G_\text{stp}}{τ_3} + (k_\text{stp} - G_\text{stp}) \frac{z_\text{stp}}{5} \\ \frac{d z_\text{stp}}{dt} = -\frac{z_\text{stp}}{τ_4} + \frac{G_\text{syn}}{1 + e^{-4.394(\frac{V-V_\text{shift}}{V_\text{range}})}}\]

Arguments :

E_syn [mV, reversal potential]
G_syn [mV, receptor conductance]
V_shift [mV, transmitter threshold]
V_range [mV, transmitter sensitivity]
τ₁ [ms, decay timescale for receptor conductance]
τ₃ [ms, decay timescale for receptor conductance]
kₛₜₚ [mV, asymptotic upper bound of Gₛₜₚ]
g [conductance gain]

References :

C Koch, I Segev, TJ Sejnowski, TA Poggio, eds. (1998), Methods in Neuronal Modeling: From Ions to Networks, Computational

Neuroscience Series. (A Bradford Book, Cambridge, MA, USA), 2 edition.

SR Wicks, CJ Roehrig, CH Rankin (1996), A Dynamic Network Simulation of the Nematode Tap Withdrawal Circuit: Predictions

Concerning Synaptic Function Using Behavioral Criteria. The J. Neurosci. 16, 4017–4031.

NeurobloxPharma.MsnAMPAR — Type

MsnAMPAR(; E_syn=0.0, τ₁=0.1, τ₂=5.0, g=1.0)

MSN AMPA synapse based on the base Glu_AMPA_Synapse, extended with a D2 modulation input. D2 modulation is implemented as a multiplicative gain on the synaptic drive: G_asymp_eff = M_AMPA2 * G_asymp. For this linear synapse, this is equivalent to scaling the resulting AMPA conductance (and thus the downstream AMPA current computed in the neuron), consistent with the multiplicative D2 attenuation used in the MSN microcircuit model.

\[\frac{dG}{dt} = -\frac{G}{\tau_2} + z \\ \frac{dz}{dt} = -\frac{z}{\tau_1} + M_{AMPA2}\,G_{asymp}\]

Arguments:

E_syn [mV]: Reversal potential (kept for API consistency).
τ₁ [ms]: Time constant of the auxiliary variable z.
τ₂ [ms]: Decay time constant of G.
g [-]: Conductance gain (kept for API consistency; not used directly in this gate-only synapse).

Inputs:

G_asymp [-]: Presynaptic synaptic drive / conductance target.
M_AMPA2 [-]: D2 modulation factor (e.g., 1 - β2*ϕ2). Default 1.0 means no modulation.

Outputs:

G: AMPA conductance-like gate variable.

References:

Destexhe, A., Mainen, Z. F., & Sejnowski, T. J. (1998). Kinetic models of synaptic transmission. Methods in Neuronal Modeling (2nd ed.).
Humphries, M. D., Lepora, N., Wood, R., & Gurney, K. (2009). Dopamine-modulated dynamic cell assemblies generated by the GABAergic striatal microcircuit. Frontiers in Computational Neuroscience.

NeurobloxPharma.GABA_A_Synapse — Type

GABA_A_Synapse(; E_syn=-70, G_syn=11.5, τ₁=0.1, τ₂=70, g=1, V_shift=0, V_range=35)

A GABA A receptor model using the same type of damped oscillator dynamics as Glu_AMPA_Synapse. Equations and default parameter values are based on [1, 2].

\[\frac{dG}{dt} = -\frac{G}{τ_2} + z \\ \frac{dz}{dt} = -\frac{z}{τ_1} + \frac{G_\text{syn}}{1 + e^{-4.394(\frac{V-V_\text{shift}}{V_\text{range}})}}\]

Arguments :

E_syn [mV, reversal potential]
G_syn [mV, receptor conductance]
V_shift [mV, transmitter threshold]
V_range [mV, transmitter sensitivity]
τ₁ [ms, decay timescale for receptor conductance]
τ₂ [ms, decay timescale for receptor conductance]
g [conductance gain]

References :

C Koch, I Segev, TJ Sejnowski, TA Poggio, eds. (1998), Methods in Neuronal Modeling: From Ions to Networks, Computational

Neuroscience Series. (A Bradford Book, Cambridge, MA, USA), 2 edition.

SR Wicks, CJ Roehrig, CH Rankin (1996), A Dynamic Network Simulation of the Nematode Tap Withdrawal Circuit: Predictions

Concerning Synaptic Function Using Behavioral Criteria. The J. Neurosci. 16, 4017–4031.

NeurobloxPharma.GABA_B_Synapse — Type

GABA_B_Synapse(; E_syn=-75, τ₁=200.1, τ₂=200, G_syn=0.007, V_shift=0, V_range=2, g=1)

A GABA B receptor model using damped oscillator dynamics. Equations and default parameter values are based on [1].

\[\frac{dG}{dt} = -\frac{G}{τ_2} + z \\ \frac{dz}{dt} = -\frac{z}{τ_1} + \frac{G_\text{syn}}{1 + e^{-4.394(\frac{V-V_\text{shift}}{V_\text{range}})}}\]

Arguments :

E_syn [mV, reversal potential]
G_syn [mV, receptor conductance]
V_shift [mV, transmitter threshold]
V_range [mV, transmitter sensitivity]
τ₁ [ms, decay timescale for receptor conductance]
τ₂ [ms, decay timescale for receptor conductance]
g [conductance gain]

See also MoradiNMDAR.

NeurobloxPharma.MsnNMDAR — Type

MsnNMDAR(; E=-0.7, k=0.007, V_0=-100, g_VI=1,
                τ_A=1.47, τ_B=391.64, τ_g=50,
                Mg_O=1, IC_50=4.1, T=295.15, F=96485.332, R=8.314,
                z_Mg=2, δ=0.8, spk_coeff=0.05,
                G_syn=3.0, V_shift=10.0, V_range=35.0, τ₁=0.1)

MSN NMDA receptor model using the simplified Moradi-style kinetics, extended with a D1 modulation input. D1 modulation is implemented as a multiplicative gain on the exported NMDA synaptic current: I = M_NMDA1 * I_base, consistent with dopamine modulation used in the MSN microcircuit model.

\[\frac{dA}{dt} = \text{spk\_coeff}\,z - \frac{A}{\tau_A} \\ \frac{dB}{dt} = \text{spk\_coeff}\,z - \frac{B}{\tau_B} \\ \frac{dg}{dt} = B\,\frac{g_{VD}(V_{post}) - g}{\tau_g} \\ \frac{dz}{dt} = -\frac{z}{\tau_1} + \frac{G_{syn}}{1 + e^{-4.394\left(\frac{V_{pre}-V_{shift}}{V_{range}}\right)}} \\ g_{VD}(V) = k\,(V - V_0) \\ I = M_{NMDA1}\,(B-A)(g_{VI}+g)(V_{post}-E)\,\frac{1}{1 + \frac{\mathrm{Mg}_O e^{-\frac{z_{Mg}\,\delta\,F\,V_{post}}{R\,T}}}{IC_{50}}}\]

Arguments:

E [mV]: Reversal potential.
k [mV⁻¹]: Slope of the voltage-dependent conductance term g_VD(V).
V_0 [mV]: Voltage offset in g_VD(V).
g_VI [-]: Voltage-independent conductance offset used as (g_VI + g).
τ_A [ms]: Time constant for state A.
τ_B [ms]: Time constant for state B.
τ_g [ms]: Time constant for voltage-dependent conductance state g.
τ_M [ms]: Time constant for tracking M_NMDA1 into the synaptic current output.
Mg_O [mM]: Extracellular magnesium concentration.
IC_50 [mM]: Half-inhibition constant for Mg block at 0 mV.
T [K]: Absolute temperature for the Mg block term.
F [C/mol]: Faraday constant.
R [J/(K*mol)]: Gas constant.
z_Mg [-]: Magnesium valence (typically 2).
δ [-]: Dimensionless Mg block factor.
spk_coeff [-]: Gain applied to the presynaptic release proxy z.
G_syn [-]: Release strength in the presynaptic logistic transmitter proxy.
V_shift [mV]: Presynaptic voltage shift in the logistic transmitter proxy.
V_range [mV]: Presynaptic voltage range in the logistic transmitter proxy.
τ₁ [ms]: Decay time constant of the presynaptic release proxy z.

Inputs:

V_pre [mV]: Presynaptic membrane voltage (drives transmitter release proxy z).
V_post [mV]: Postsynaptic membrane voltage (drives g_VD and Mg block).
M_NMDA1 [-]: D1 modulation factor (e.g., 1 + β1*ϕ1). Default 1.0 means no modulation.

Computed properties:

I: D1-modulated NMDA synaptic current.

References:

Humphries, M. D., Lepora, N., Wood, R., & Gurney, K. (2009). Dopamine-modulated dynamic cell assemblies generated by the GABAergic striatal microcircuit. Frontiers in Computational Neuroscience.

NeurobloxPharma.MsnD1Receptor — Type

MsnD1Receptor(; K_D1=0.3, n_D1=1.0, τ_ϕ1=100.0, β1=0.5)

A minimal dopamine D1 receptor occupancy / modulation module for MSN models. This blox converts a dopamine level DA(t) into a slow D1 activation state ϕ1(t) using Hill steady-state occupancy with first-order relaxation, and exports a multiplicative NMDA gain M_NMDA1 that can be wired into an NMDA receptor blox.

\[\phi_{1,\infty}(DA) = \frac{DA^{n_{D1}}}{DA^{n_{D1}} + K_{D1}^{n_{D1}}} \\ \frac{d\phi_1}{dt} = \frac{\phi_{1,\infty}(DA) - \phi_1}{\tau_{\phi 1}} \\ M_{NMDA1} = 1 + \beta_1 \phi_1\]

Arguments:

K_D1 [-]: Half-saturation dopamine level for D1 (Hill constant).
n_D1 [-]: Hill coefficient for D1 occupancy.
τ_ϕ1 [ms]: Time constant for D1 activation dynamics.
β1 [-]: Maximal multiplicative gain of D1 on NMDA; output is 1 + β1*ϕ1.

Inputs:

DA [-]: Dopamine level (arbitrary units; must be consistent with K_D1).

Outputs:

M_NMDA1 [-]: D1 modulation factor for NMDA receptors.

References:

Humphries, M. D., Lepora, N., Wood, R., & Gurney, K. (2009). Dopamine-modulated dynamic cell assemblies generated by the GABAergic striatal microcircuit. Frontiers in Computational Neuroscience.

NeurobloxPharma.MsnD2Receptor — Type

MsnD2Receptor(; K_D2=0.3, n_D2=1.0, τ_ϕ2=100.0, β2=0.3)

A minimal dopamine D2 receptor occupancy / modulation module for MSN models. This blox converts dopamine level DA(t) into a slow D2 activation state ϕ2(t) using Hill steady-state occupancy with first-order relaxation, and exports a multiplicative AMPA gain M_AMPA2 (typically an attenuation) that can be wired into an AMPA receptor blox.

\[\phi_{2,\infty}(DA) = \frac{DA^{n_{D2}}}{DA^{n_{D2}} + K_{D2}^{n_{D2}}} \\ \frac{d\phi_2}{dt} = \frac{\phi_{2,\infty}(DA) - \phi_2}{\tau_{\phi 2}} \\ M_{AMPA2} = 1 - \beta_2 \phi_2\]

Arguments:

K_D2 [-]: Half-saturation dopamine level for D2 (Hill constant).
n_D2 [-]: Hill coefficient for D2 occupancy.
τ_ϕ2 [ms]: Time constant for D2 activation dynamics.
β2 [-]: Gain of D2 on the target receptor (AMPA in the referenced MSN microcircuit); output is 1 - β2*ϕ2.

Inputs:

DA [-]: Dopamine level (arbitrary units; must be consistent with K_D2).

Outputs:

M_AMPA2 [-]: D2 modulation factor for AMPA receptors.

References:

Humphries, M. D., Lepora, N., Wood, R., & Gurney, K. (2009). Dopamine-modulated dynamic cell assemblies generated by the GABAergic striatal microcircuit. Frontiers in Computational Neuroscience.

NeurobloxPharma.HTR5 — Type

HTR5(;)

A 5-HT / kinase-condition selector for the Baxter et al. (1999) Aplysia sensory neuron model. This blox is intentionally not a biophysical receptor current model. Instead, it acts as a mode switch that outputs binary (0/1) flags corresponding to the four experimental conditions used in the paper: Control, PKA-only, PKC-only, and 5-HT (PKA+PKC). These outputs can be wired into a neuron blox that implements the corresponding parameter “corner” values.

Mode mapping (recommended to hold constant during a simulation):

mode = 0 → Control → (PKA, PKC) = (0, 0)
mode = 1 → PKA only → (PKA, PKC) = (1, 0)
mode = 2 → PKC only → (PKA, PKC) = (0, 1)
mode = 3 → 5-HT (PKA+PKC) → (PKA, PKC) = (1, 1)

Arguments:

(none)

Inputs:

mode [-]: Condition index (0..3). Non-integers are thresholded with piecewise ifelse.

Outputs:

PKA [-]: Binary kinase flag (0/1).
PKC [-]: Binary kinase flag (0/1).
CTRL [-]: 1 if in control mode, else 0.
PKA_only [-]: 1 if in PKA-only mode, else 0.
PKC_only [-]: 1 if in PKC-only mode, else 0.
HT_flag [-]: 1 if in 5-HT mode, else 0.
mode_index [-]: Debug index (0..3) after thresholding.

References:

Baxter, D. A., Byrne, J. H. (1999). Serotonergic modulation of two potassium currents in Aplysia sensory neurons. Journal of Neurophysiology, 82(6), 2914–2926. (doi:10.1152/jn.1999.82.6.2914)

NeurobloxPharma.CaTRPM4R — Type

CaTRPM4R(; ḡ=0.1, E_CAN=0.0, K_d=87.0,
          τ_can=400.0, X_base=0.0, X_CCh=500.0,
          use_Vdep=1.0, V_fix=-60.0)

A TRPM4 / I_CAN receptor-current module with nanodomain Ca coupling. TRPM4 is Ca-impermeable; its opening is regulated by Ca in a local nanodomain produced by nearby Ca sources (e.g., VGCC). This blox models:

a nanodomain Ca signal can(t) driven by inward Ca current I_Ca and relaxing to Ca_bulk;
a two-state TRPM4 activation gate m(t) with voltage-dependent rates and Ca-dependent scaling of the forward rate; and
an Ohmic TRPM4 current output I = ḡ * m * (V - E_CAN).

\[\frac{d\,can}{dt} = -X \, I_{Ca,inward} + \frac{Ca_{bulk} - can}{\tau_{can}} \\ \alpha(V) = 0.0057\,e^{0.0060V}, \quad \beta(V) = 0.033\,e^{-0.019V} \\ \alpha'(V,can) = \alpha(V)\frac{can}{can + K_d} \\ \frac{dm}{dt} = \alpha'(V,can)(1-m) - \beta(V)m \\ I_{TRPM4} = \bar{g}\,m\,(V - E_{CAN})\]

Arguments:

ḡ [mS/cm²]: Maximal TRPM4 conductance (tunable).
E_CAN [mV]: Reversal potential for CAN current (often near 0 mV; set here to 0 mV by default).
K_d [µM]: Ca binding dissociation constant for TRPM4 activation (paper reports ~87 µM).
τ_can [ms]: Nanodomain Ca relaxation time constant.
X_base [-]: Coupling gain from inward Ca current to nanodomain Ca in control.
X_CCh [-]: Coupling gain under CCh (carbachol-like) condition.
use_Vdep [-]: 1 uses instantaneous V for gating; 0 clamps gating voltage to V_fix.
V_fix [mV]: Clamp voltage for gating when use_Vdep=0.

Inputs:

V [mV]: Postsynaptic membrane voltage.
I_Ca [µA/cm²]: Ca influx current (proxy) from Ca sources (not TRPM4 current).
Ca_bulk [µM]: Bulk/bath baseline Ca level for nanodomain relaxation.
CCh [-]: 0/1 (or 0..1) condition flag that interpolates X between X_base and X_CCh.

Computed properties:

I [µA/cm²]: TRPM4 / I_CAN current.
can_pos [-]: max(can,0) for debugging/inspection.
m_open [-]: Open probability (same as m).
Vm_gate [mV]: Effective voltage used for gating (clamped or not).
X_used [-]: Effective coupling gain used in the current condition.

References:

Combe, C. L., Canavier, C. C., & Gasparini, S. (2023). (TRPM4 / I_CAN in CA1 pyramidal cells). eLife. (doi:10.7554/eLife.84387)

NeurobloxPharma.Alpha7ERnAChR — Type

Alpha7ERnAChR(; Ḡ_α7=0.001, Ca_o=2.0, RTF_Ca=13.32,
              α=0.1, α1=0.01, β=5.0, γ=0.1, d2=5.0, d3=5.0,
              ACh_baseline=0.0,
              use_PAM=0.0, β_PAM=0.1, d3_PAM=0.1,
              v_IP3R_s=170.0, v_RyR_s=57.0, v_leak_s=0.0001, v_SERCA_s=0.3,
              K_IP3=1e-4, K_act=3e-4, K_inact=2e-4, K_RyR=1e-4, K_SERCA=1e-4,
              ρ_ER=0.185,
              τ_IP3=200.0, IP3_rest=0.0, k_IP3_from_Ca=0.0)

An α7 nicotinic ACh receptor model coupled to an intracellular ER Ca store module. This blox combines:

α7 receptor gating via a 3-state Markov scheme (C, O, D) driven by ACh with optional PAM (positive allosteric modulator) that reduces exit rates from the open state; and
ER Ca handling with IP3R, RyR, leak, and SERCA fluxes that contribute a net ER→cytosol Ca flux J_ER to be added into the postsynaptic neuron’s cytosolic Ca equation.

The exported α7 current is treated as Ca-only:

\[I_{\alpha7} = \bar{G}_{\alpha7}\,O\,(V_m - E_{Ca}), \quad E_{Ca} = RTF_{Ca}\ln\left(\frac{Ca_o}{Ca_i}\right)\]

ER flux bookkeeping (positive ER→cytosol, negative uptake):

\[J_{ER} = J_{IP3R} + J_{RyR} + J_{leak} - J_{SERCA}\]

Arguments (α7 gating):

Ḡ_α7 [µA/(mV·cm²)]: Maximal α7 conductance density (current units compatible with neuron balance).
Ca_o [mM]: Extracellular Ca concentration (typically fixed).
RTF_Ca [mV]: Nernst factor for divalent ions (≈ 13.32 mV at ~37°C).
α [(µM⁻¹ ms⁻¹)]: ACh-dependent C→O rate coefficient (assumes ACh in µM).
α1 [ms⁻¹]: C→D desensitization rate.
β [ms⁻¹]: O→C closing rate.
γ [ms⁻¹]: D→O recovery rate.
d2 [ms⁻¹]: D→C recovery rate.
d3 [ms⁻¹]: O→D desensitization rate.
ACh_baseline [µM]: Baseline ACh level added to the ACh input.
use_PAM [-]: If 1, enable PAM effect using β_PAM and d3_PAM.
β_PAM [ms⁻¹]: PAM-modified closing rate (used when PAM is active).
d3_PAM [ms⁻¹]: PAM-modified desensitization rate from O (used when PAM is active).

Arguments (ER store / IP3):

v_IP3R_s, v_RyR_s, v_leak_s, v_SERCA_s [s⁻¹]: Maximal flux rates (internally converted to ms⁻¹).
K_IP3, K_act, K_inact, K_RyR, K_SERCA [mM]: Half-saturation constants (stored in mM).
ρ_ER [-]: ER/cyt volume scaling factor used in the Ca_ER ODE.
τ_IP3 [ms]: Time constant for IP3 relaxation.
IP3_rest [mM]: Rest (clamp) value of IP3.
k_IP3_from_Ca [(mM/ms)/mM]: Optional coupling from cytosolic Ca to IP3 production.

Inputs:

V_m [mV]: Membrane potential.
Ca_i [mM]: Cytosolic Ca concentration (owned by the postsynaptic neuron).
ACh [µM]: Phasic cholinergic input (added to ACh_baseline).
PAM [-]: External PAM flag (0/1) that can override/enable PAM modulation.

Outputs:

I_α7 [µA/cm²]: α7 Ca current.
J_ER [mM/ms]: Net ER→cytosol Ca flux contribution to add to neuron Ca_i dynamics.
O_open [-]: Open-state fraction O (debug).
Ca_ER_out [mM]: ER Ca store concentration (debug).
IP3_out [mM]: IP3 level (debug).
h_IP3_out [-]: IP3R inactivation gate (debug).
JIP3R, JRyR, Jleak, JSERCA: Optional debug flux components if wired/used downstream.

References:

King, J. R., et al. (2017). (α7 nAChR / Ca signaling framework used here). Molecular Pharmacology. (doi:10.1124/mol.117.111401)

NeurobloxPharma.MuscarinicR — Type

MuscarinicR(; ḡ_NCM=1.0, E_NCM=0.0,
              α_Ca=0.2, α_max=10.0, β_m=1.0, gate_exp=1.0,
              τ_CaNCM=1333.0, Ca_min=1.0e-5, Ca_scale=1000.0,
              τ_M=200.0, M_baseline=0.0,
              f_Na=0.576923)

Muscarinic-activated non-specific cation current (INCM / INaNCM / I_KNCM) module with Ca-dependent gating and slow muscarinic activation dynamics.

This blox is intended to be wired into an ion-conserving neuron (e.g., MuscarinicNeuron) that keeps explicit Na/K concentration state variables. The module exports:

the total membrane current I_NCM (added to the membrane current balance), and
a Na/K apportionment of that same current (I_NaNCM, I_KNCM) for ion bookkeeping.

Biophysical assumptions:

The NCM current is modeled as an Ohmic non-specific cation current (typically reversing near 0 mV).
Channel opening is Ca-dependent via a two-state gate m(t).
Muscarinic drive M(t) is low-pass filtered into an effective activation ϕ_M(t).

\[\frac{d\,Ca_{pool}}{dt} = \frac{\max(Ca_i, Ca_{min}) - Ca_{pool}}{\tau_{CaNCM}} \\ M_{eff} = \mathrm{clip}_{[0,1]}(M_{baseline} + M) \\ \frac{d\,\phi_M}{dt} = \frac{M_{eff} - \phi_M}{\tau_M} \\ \alpha_m(Ca_{pool}) = \min\bigl(\alpha_{Ca}\,(Ca_{pool}\,Ca_{scale}),\,\alpha_{max}\bigr) \\ \frac{dm}{dt} = \alpha_m(Ca_{pool})\,(1-m) - \beta_m\,m \\ I_{NCM} = \bar g_{NCM}\,\max(\phi_M,0)\,m^{\mathrm{gate\_exp}}\,(V_m - E_{NCM}) \\ I_{NaNCM} = f_{Na}\,I_{NCM}, \qquad I_{KNCM} = (1-f_{Na})\,I_{NCM}\]

Arguments:

ḡ_NCM [µA/(mV·cm²)]: Maximal NCM conductance density (tunable).
E_NCM [mV]: NCM reversal potential (often near 0 mV).
α_Ca [-]: Gain for Ca-dependent opening rate α_m.
α_max [ms⁻¹]: Upper bound (saturation) for α_m.
β_m [ms⁻¹]: Ca-independent closing rate for the two-state gate.
gate_exp [-]: Exponent applied to m in the current expression (often 1).
τ_CaNCM [ms]: Time constant for low-pass Ca pool Ca_pool.
Ca_min [mM]: Floor applied to Ca to avoid numerical issues at extremely low Ca.
Ca_scale [-]: Scale mapping neuron Ca_i (mM) into the effective Ca scale used by α_m.
τ_M [ms]: Time constant for muscarinic activation low-pass ϕ_M.
M_baseline [mM]: Baseline muscarinic tone added to the input M.
f_Na [-]: Fraction of I_NCM assigned to Na for ion bookkeeping (K fraction is 1-f_Na).

Inputs:

V_m [mV]: Postsynaptic membrane potential.
Ca_i [mM]: Cytosolic calcium concentration (owned by the postsynaptic neuron).
M [-]: Muscarinic drive (0..1 recommended; baseline is added internally).

Outputs:

I_NCM [µA/cm²]: Total NCM membrane current.
I_NaNCM [µA/cm²]: Na component of I_NCM for ion bookkeeping.
I_KNCM [µA/cm²]: K component of I_NCM for ion bookkeeping.
m_open [-]: Gate open probability (debug; equals m).
Ca_pool_out [-]: Filtered Ca pool (debug; equals Ca_pool).
M_act [-]: Filtered muscarinic activation (debug; equals ϕ_M).

References:

Fransen, E., Alonso, A. A., & Hasselmo, M. E. (2002). Simulations of the Role of the Muscarinic-Activated Calcium-Sensitive Nonspecific Cation Current INCM in Entorhinal Neuronal Activity during Delayed Matching Tasks. Journal of Neuroscience, 22(3), 1081-1097.

NeurobloxPharma.Beta2nAChR — Type

Beta2nAChR(; ḡ_ACh=5.0, E_ACh=0.0, τ_act=5.0, τ_des_base=500.0, ...)

β2-containing nicotinic acetylcholine receptor (nAChR) model for VTA neurons.

Models distinct effects of pulsatile ACh input versus tonic nicotine on receptor activation and desensitization using a 4-state scheme.

\[g_{eff} = \bar{g}_{ACh} \cdot ACh_{act} \cdot (1 - ACh_{des})\]

Arguments:

ḡ_ACh [mS/cm²]: Maximal conductance (5-10 for DA, 1.5-4 for GABA neurons).
E_ACh [mV]: Reversal potential (0 mV for non-specific cation channel).
τ_act [ms]: Activation time constant.
τ_des_base, τ_des_scale, K_t: Desensitization time constant parameters.
EC50, IC50 [µM]: Half-maximal concentrations for activation/desensitization.
n_act, n_des [-]: Hill coefficients.
w [-]: Nicotine potency relative to ACh.

Inputs:

V [mV]: Postsynaptic membrane voltage.
inp_ACh [µM]: Pulsatile ACh input.
inp_Nic [µM]: Tonic nicotine concentration.

Outputs:

I [µA/cm²]: nAChR current (outward positive, g*(V-E)).

References:

Morozova, E. O., et al. (2020). Distinct Temporal Structure of Nicotinic ACh Receptor Activation Determines Responses of VTA Neurons to Endogenous ACh and Nicotine. eNeuro, 7(4). (doi:10.1523/ENEURO.0418-19.2020)