CdpStC_MA2020_GoC

class braincell.ion.CdpStC_MA2020_GoC(size, temp=Quantity(298.15, 'K'), Nannuli=10.9495, cainull=Quantity(4.5e-05, 'mM'), mginull=Quantity(0.59, 'mM'), Buffnull1=Quantity(0., 'mM'), rf1=Quantity(0.0134329, '1 / (mM * ms)'), rf2=Quantity(0.0397469, 'kHz'), Buffnull2=Quantity(60.9091, 'mM'), rf3=Quantity(0.1435, '1 / (mM * ms)'), rf4=Quantity(0.0014, 'kHz'), BTCnull=Quantity(0., 'mM'), b1=Quantity(5.33, '1 / (mM * ms)'), b2=Quantity(0.08, 'kHz'), DMNPEnull=Quantity(0., 'mM'), c1=Quantity(5.63, '1 / (mM * ms)'), c2=Quantity(0.000107, 'kHz'), PVnull=Quantity(0.08, 'mM'), m1=Quantity(107., '1 / (mM * ms)'), m2=Quantity(0.00095, 'kHz'), p1=Quantity(0.8, '1 / (mM * ms)'), p2=Quantity(0.025, 'kHz'), CAM_start=Quantity(0.03, 'mM'), K1Coff=Quantity(0.04, 'kHz'), K1Con=Quantity(5.4, '1 / (mM * ms)'), K2Coff=Quantity(0.00925, 'kHz'), K2Con=Quantity(15., '1 / (mM * ms)'), K1Noff=Quantity(2.5, 'kHz'), K1Non=Quantity(142.5, '1 / (mM * ms)'), K2Noff=Quantity(0.75, 'kHz'), K2Non=Quantity(175., '1 / (mM * ms)'), kpmp1=Quantity(0.003, '1 / (mM * ms)'), kpmp2=Quantity(1.75e-05, 'kHz'), kpmp3=Quantity(7.255e-05, 'kHz'), TotalPump=Quantity(1.e-09, 'mol / cm^2'), Co=None, Ci_initializer=None, species_initializers=None, solver=None, substeps=None, name=None, **channels)

Golgi-cell calcium pool: pump, generic buffers, PV, and CaM.

Undivided import of the Golgi-cell CdpStC calcium pool: Ci (the NMODL ca/cai pool) is buffered by two generic first-order buffers, the indicator dyes BTC and DMNPE, and parvalbumin (PV), extruded by a membrane pump, and additionally binds calmodulin (CaM) through the same four-site cooperative scheme documented in CdpStC_CAMOnly_MA2020_GoC. This is the combination that CdpStC_CAMOnly_MA2020_GoC (CaM branch only) and CdpStC_NoCAM_MA2020_GoC (pump/buffer/PV branch only) each keep half of.

Parameters:

• size (int | Sequence[int] | integer | Sequence[integer]) – The size of the simulation target, typically the number of neurons or compartments. Forwarded unchanged to Calcium.

• temp (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Absolute temperature used by the Nernst equation in E. Defaults to 25 degrees Celsius, converted to kelvin via u.celsius2kelvin before being stored.

• Nannuli (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Radial-shell count inherited from the NEURON multi-shell diffusion template; only shapes the single effective volume fraction vrat. Defaults to 10.9495.

• cainull (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Baseline/initial free calcium concentration Ci. Defaults to 45e-6 mM.

• mginull (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Baseline/initial magnesium concentration mg. Defaults to 0.59 mM.

• Buffnull1 (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Total concentration of the first generic buffer, Buff1 + Buff1_ca. Defaults to 0.0 mM.

• rf1 (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Forward and backward rate constants of the Buff1 binding step. Default 0.0134329 /(mM*ms) and 0.0397469 /ms.

• rf2 (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Forward and backward rate constants of the Buff1 binding step. Default 0.0134329 /(mM*ms) and 0.0397469 /ms.

• Buffnull2 (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Total concentration of the second generic buffer, Buff2 + Buff2_ca. Defaults to 60.9091 mM.

• rf3 (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Forward and backward rate constants of the Buff2 binding step. Default 0.1435 /(mM*ms) and 0.0014 /ms.

• rf4 (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Forward and backward rate constants of the Buff2 binding step. Default 0.1435 /(mM*ms) and 0.0014 /ms.

• BTCnull (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Total concentration of the BTC indicator dye buffer, BTC + BTC_ca. Defaults to 0.0 mM.

• b1 (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Forward and backward rate constants of the BTC binding step. Default 5.33 /(mM*ms) and 0.08 /ms.

• b2 (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Forward and backward rate constants of the BTC binding step. Default 5.33 /(mM*ms) and 0.08 /ms.

• DMNPEnull (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Total concentration of the caged-calcium buffer DMNPE, DMNPE + DMNPE_ca. Defaults to 0.0 mM.

• c1 (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Forward and backward rate constants of the DMNPE binding step. Default 5.63 /(mM*ms) and 0.107e-3 /ms.

• c2 (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Forward and backward rate constants of the DMNPE binding step. Default 5.63 /(mM*ms) and 0.107e-3 /ms.

• PVnull (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Total concentration of parvalbumin, PV + PV_ca + PV_mg. Defaults to 0.08 mM.

• m1 (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Forward and backward rate constants of the PV calcium binding step. Default 1.07e2 /(mM*ms) and 9.5e-4 /ms.

• m2 (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Forward and backward rate constants of the PV calcium binding step. Default 1.07e2 /(mM*ms) and 9.5e-4 /ms.

• p1 (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Forward and backward rate constants of the PV magnesium binding step. Default 0.8 /(mM*ms) and 2.5e-2 /ms.

• p2 (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Forward and backward rate constants of the PV magnesium binding step. Default 0.8 /(mM*ms) and 2.5e-2 /ms.

• CAM_start (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Baseline/initial concentration of unbound calmodulin, CAM0. Defaults to 0.03 mM.

• K1Coff (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Backward and forward rate constants of the first C-lobe calcium-binding step. Default 0.04 /ms and 5.4 /(mM*ms).

• K1Con (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Backward and forward rate constants of the first C-lobe calcium-binding step. Default 0.04 /ms and 5.4 /(mM*ms).

• K2Coff (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Backward and forward rate constants of the second C-lobe calcium-binding step. Default 0.00925 /ms and 15.0 /(mM*ms).

• K2Con (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Backward and forward rate constants of the second C-lobe calcium-binding step. Default 0.00925 /ms and 15.0 /(mM*ms).

• K1Noff (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Backward and forward rate constants of the first N-lobe calcium-binding step. Default 2.5 /ms and 142.5 /(mM*ms).

• K1Non (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Backward and forward rate constants of the first N-lobe calcium-binding step. Default 2.5 /ms and 142.5 /(mM*ms).

• K2Noff (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Backward and forward rate constants of the second N-lobe calcium-binding step. Default 0.75 /ms and 175.0 /(mM*ms).

• K2Non (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Backward and forward rate constants of the second N-lobe calcium-binding step. Default 0.75 /ms and 175.0 /(mM*ms).

• kpmp1 (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Forward and backward rate constants of the pump + Ci -> pumpca binding step. Default 3e-3 /(mM*ms) and 1.75e-5 /ms.

• kpmp2 (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Forward and backward rate constants of the pump + Ci -> pumpca binding step. Default 3e-3 /(mM*ms) and 1.75e-5 /ms.

• kpmp3 (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Rate constant of the irreversible extrusion step, pumpca -> pump. Defaults to 7.255e-5 /ms.

• TotalPump (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Areal pump-site density; the conserved sum of pump + pumpca per unit membrane area. Defaults to 1e-9 mol/cm2.

• Co (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable | None) – Extracellular calcium concentration. Defaults to None, which falls back to Calcium.default_Co inside KineticIon._init_kinetic_ion().

• Ci_initializer (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable | None) – Initializer for the Ci species. Defaults to None, which falls back to cainull.

• species_initializers (dict[str, object] | None) – Per-species initializer overrides, keyed by one of this class’s twenty-three differential species (the fourteen of CdpStC_NoCAM_MA2020_GoC plus the nine CaM species CAM0, CAM1C, CAM2C, CAM1N2C, CAM1N, CAM2N, CAM2N1C, CAM1C1N, CAM4). Defaults to None (no overrides); unset buffer/PV species default to their steady-state occupancy at cainull/mginull, pump defaults to TotalPump, CAM0 defaults to CAM_start, and every other CaM species defaults to 0.0 mM.

• solver (str | None) – Integrator name used for the reaction network. Defaults to None, which falls back to default_solver ("backward_euler").

• substeps (int | None) – Number of solver substeps run inside one parent update. Defaults to None, which falls back to default_substeps (1).

• name (str | None) – Runtime ion instance name. Defaults to None.

• **channels – Channel instances to attach to this ion, forwarded unchanged to Calcium.

Raises:

• ValueError – If species_initializers names a species outside the twenty-three listed above, or if temp is explicitly passed as None, or substeps is less than 1 (the latter two raised by KineticIon._init_kinetic_ion()).

• AttributeError – Raised during state initialization or reset, or from parea/dsq, if this ion’s compartment geometry (diam_arc_mean) has not been attached yet.

See also

Calcium

Base calcium ion family this class attaches the reaction network to.

CdpStC_CAMOnly_MA2020_GoC

Sibling decomposition keeping only the CaM network this class also includes.

CdpStC_NoCAM_MA2020_GoC

Sibling decomposition keeping only the pump/buffer/PV network this class also includes.

CdpCAM_MA2024_PC

Purkinje-cell mechanism reusing this class’s pump/buffer network unchanged and adding Calbindin.

CdpCR_MA2020_GrC

Granule-cell mechanism reusing this class’s pump/buffer network unchanged and substituting Calretinin for parvalbumin.

braincell.ion._base.KineticIon

Template this class instantiates; documents the NMODL-style semantics shared by all Cdp* mechanisms.

Notes

Ported from GoC/ion/CdpStC_MA20_GoC.mod, part of the cerebellar Golgi cell model of (Masoli et al., 2020) [4]; its header names Anwar, Hong & De Schutter [1] as the reference for the mechanism, credits the extended buffer parameters to Schmidt et al. (2003) [2], and records the pump rate as tuned to data from Maeda et al. (1999) [3]. uses_total_current = True and one Source drives Ci from the channel current supplied at each step: _ci_source_flux returns zero when no current is supplied, and otherwise total_current * pi * diam_arc_mean / (2 * faraday_constant). NEURON’s raw GoC ica is efflux-positive, but BrainCell channel currents follow the repo-wide inward-positive convention, so a positive total_current here increases Ci.

One Conserve constrains pump + pumpca = TotalPump * parea, with pumpca recovered algebraically rather than integrated; pump is the only pump state among the twenty-three differential species.

Twenty reactions couple the twenty-four species: the two pump steps and the six buffer/PV steps described in CdpStC_NoCAM_MA2020_GoC, plus twelve reactions forming the same two-lobe cooperative calmodulin scheme described in CdpStC_CAMOnly_MA2020_GoC (CAM0 through CAM4, reached via either the C-lobe-first or N-lobe-first binding order). Buffer- and PV-bound species initialize at the equilibrium occupancy implied by their dissociation constants and cainull/mginull, not at zero.

References

[1]

Anwar, H., Hong, S., & De Schutter, E. (2012). Controlling Ca2+-activated K+ channels with models of Ca2+ buffering in Purkinje cells. The Cerebellum, 11(3), 681-693. doi:10.1007/s12311-010-0224-3

[2]

Schmidt, H., Stiefel, K. M., Racay, P., Schwaller, B., & Eilers, J. (2003). Mutational analysis of dendritic Ca2+ kinetics in rodent Purkinje cells: role of parvalbumin and calbindin D28k. The Journal of Physiology, 551(1), 13-32. doi:10.1113/jphysiol.2002.035824

[3]

Maeda, H., Ellis-Davies, G. C. R., Ito, K., Miyashita, Y., & Kasai, H. (1999). Supralinear Ca2+ signaling by cooperative and mobile Ca2+ buffering in Purkinje neurons. Neuron, 24(4), 989-1002. doi:10.1016/S0896-6273(00)81045-4

[4]

Masoli, S., Ottaviani, A., Casali, S., & D’Angelo, E. (2020). Cerebellar Golgi cell models predict dendritic processing and mechanisms of synaptic plasticity. PLOS Computational Biology, 16(12), e1007937. doi:10.1371/journal.pcbi.1007937