CdpCAM_MA2024_PC

class braincell.ion.CdpCAM_MA2024_PC(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'), CBnull=Quantity(0.16, 'mM'), nf1=Quantity(43.5, '1 / (mM * ms)'), nf2=Quantity(0.0358, 'kHz'), ns1=Quantity(5.5, '1 / (mM * ms)'), ns2=Quantity(0.0026, '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)

Purkinje-cell calcium pool: pump, buffers, Calbindin, PV, CaM.

Extends the Golgi-cell pump/generic-buffer/parvalbumin/calmodulin network of CdpStC_MA2020_GoC with a four-state Calbindin D-28k (CB) cooperative binding scheme. This is the same CdpStC scaffold with the CB subnetwork enabled and both CB and CaM species placed in the cytosolic compartment, per the imported source tree’s “Ion_dyn implementation notes”; the pump, generic-buffer, PV and CaM reactions are otherwise unchanged from CdpStC_MA2020_GoC.

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.

• CBnull (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Total concentration of Calbindin D-28k, CB + CB_f_ca + CB_ca_s + CB_ca_ca. Defaults to 0.16 mM.

• nf1 (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Forward and backward rate constants of Calbindin’s fast binding sites (used for both the CB -> CB_ca_s and CB_f_ca -> CB_ca_ca steps). Default 43.5 /(mM*ms) and 3.58e-2 /ms.

• nf2 (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Forward and backward rate constants of Calbindin’s fast binding sites (used for both the CB -> CB_ca_s and CB_f_ca -> CB_ca_ca steps). Default 43.5 /(mM*ms) and 3.58e-2 /ms.

• ns1 (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Forward and backward rate constants of Calbindin’s slow binding sites (used for both the CB -> CB_f_ca and CB_ca_s -> CB_ca_ca steps). Default 5.5 /(mM*ms) and 0.26e-2 /ms.

• ns2 (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Forward and backward rate constants of Calbindin’s slow binding sites (used for both the CB -> CB_f_ca and CB_ca_s -> CB_ca_ca steps). Default 5.5 /(mM*ms) and 0.26e-2 /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-seven differential species: the fourteen of CdpStC_NoCAM_MA2020_GoC, the four Calbindin species (CB, CB_f_ca, CB_ca_s, CB_ca_ca), and the nine CaM species (CAM0, CAM1C, CAM2C, CAM1N2C, CAM1N, CAM2N, CAM2N1C, CAM1C1N, CAM4). Defaults to None (no overrides); unset buffer/Calbindin/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-seven 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_MA2020_GoC

Golgi-cell mechanism supplying the pump, generic-buffer, PV and CaM reactions this class reuses (sources and conserves are the same tuple objects, and several helper methods delegate to it directly).

CdpCR_MA2020_GrC

Sibling Purkinje-network variant that substitutes Calretinin for Calbindin.

braincell.ion._base.KineticIon

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

Notes

Ported from PC/ion/CdpCAM_MA24_PC.mod, part of the human Purkinje cell model of (Masoli et al., 2024) [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; sources and conserves are the exact tuple objects defined on CdpStC_MA2020_GoC (same Ci-driving Source and same pump + pumpca = TotalPump * parea Conserve), and several geometry/current helpers (vrat, parea, dsq, dsqvol, _require_diam_arc_mean, _ci_source_flux, _as_initializer) explicitly delegate to CdpStC_MA2020_GoC rather than redefining the same logic.

Twenty-four reactions couple the twenty-eight species: the two pump steps and four of the six buffer/PV steps from CdpStC_NoCAM_MA2020_GoC (Buff1, Buff2, BTC, DMNPE; PV keeps only its two binding steps, unaffected by Calbindin), four Calbindin reactions forming its two-site fast/slow cooperative scheme (CB -> CB_ca_s via the fast rates nf1/nf2, CB -> CB_f_ca via the slow rates ns1/ns2, then both intermediates converging on CB_ca_ca via the complementary rate pair), and the same twelve calmodulin reactions documented in CdpStC_CAMOnly_MA2020_GoC.

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., Sanchez-Ponce, D., Vrieler, N., Abu-Haya, K., Lerner, V., Shahar, T., Nedelescu, H., Rizza, M. F., Benavides-Piccione, R., DeFelipe, J., Yarom, Y., Munoz, A., & D’Angelo, E. (2024). Human Purkinje cells outperform mouse Purkinje cells in dendritic complexity and computational capacity. Communications Biology, 7(1), 5. doi:10.1038/s42003-023-05689-y