CdpCR_MA2020_GrC

class braincell.ion.CdpCR_MA2020_GrC(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'), CRnull=Quantity(0.9, 'mM'), nT1=Quantity(1.8, '1 / (mM * ms)'), nT2=Quantity(0.053, 'kHz'), nR1=Quantity(310., '1 / (mM * ms)'), nR2=Quantity(0.02, 'kHz'), nV1=Quantity(7.3, '1 / (mM * ms)'), nV2=Quantity(0.24, 'kHz'), 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)

Granule-cell calcium pool: pump, generic buffers, Calretinin.

Reuses the pump and generic-buffer (Buff1, Buff2, BTC, DMNPE) network of CdpStC_MA2020_GoC, but replaces its parvalbumin and calmodulin branches with a two-site-per-lobe cooperative Calretinin (CR) binding scheme plus one separate, uncoupled “vestigial” CR site. Parvalbumin is absent from this mechanism; Calretinin is the endogenous calcium buffer.

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.

• CRnull (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Total concentration of unbound Calretinin, the initializer for CR. Defaults to 0.9 mM.

• nT1 (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Forward and backward rate constants of a Calretinin site’s first calcium-binding step, on either lobe. Default 1.8 /(mM*ms) and 0.053 /ms.

• nT2 (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Forward and backward rate constants of a Calretinin site’s first calcium-binding step, on either lobe. Default 1.8 /(mM*ms) and 0.053 /ms.

• nR1 (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Forward and backward rate constants of a Calretinin site’s second, cooperative calcium-binding step, on either lobe. Default 310.0 /(mM*ms) and 0.02 /ms.

• nR2 (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Forward and backward rate constants of a Calretinin site’s second, cooperative calcium-binding step, on either lobe. Default 310.0 /(mM*ms) and 0.02 /ms.

• nV1 (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Forward and backward rate constants of the separate vestigial Calretinin site, CR -> CR_1V. Default 7.3 /(mM*ms) and 0.24 /ms.

• nV2 (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Forward and backward rate constants of the separate vestigial Calretinin site, CR -> CR_1V. Default 7.3 /(mM*ms) and 0.24 /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-one differential species: Ci, mg, the four generic-buffer species (Buff1, Buff1_ca, Buff2, Buff2_ca), the BTC and DMNPE pairs, the ten Calretinin species (CR, CR_1C_0N, CR_2C_0N, CR_2C_1N, CR_1C_1N, CR_0C_1N, CR_0C_2N, CR_1C_2N, CR_2C_2N, CR_1V), and pump. Defaults to None (no overrides); unset generic-buffer species default to their steady-state occupancy at cainull, CR defaults to CRnull, every other Calretinin species defaults to 0.0 mM, and pump defaults to TotalPump.

• 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-one 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 and generic-buffer reactions this class reuses (sources and conserves are the same tuple objects, and several helper methods delegate to it directly).

CdpCAM_MA2024_PC

Sibling Purkinje-network variant built on the same base but adding Calbindin instead of Calretinin.

braincell.ion._base.KineticIon

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

Notes

Ported from GrC/ion/CdpCR_MA20_GrC.mod, part of the granule cell subtype 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; 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.

Nineteen reactions couple the twenty-two species: the two pump steps, four generic-buffer steps (Buff1, Buff2, BTC, DMNPE; unlike CdpStC_MA2020_GoC there is no PV branch here), thirteen Calretinin reactions, and no calmodulin branch at all. The thirteen Calretinin reactions form a two-site-per-lobe cooperative lattice: nine states index how many of Calretinin’s two “C-lobe” sites (0, 1 or 2) and two “N-lobe” sites (0, 1 or 2) are calcium-bound (CR is the (0, 0) state, CR_2C_2N the fully bound state), every first-site binding step on either lobe uses the nT1/nT2 rate pair, and every second, cooperative-site binding step uses the faster nR1/nR2 pair. A tenth, separate Calretinin species, CR_1V, binds calcium directly from CR via its own nV1/nV2 rate pair and does not couple further into the nine-state lattice.

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., Tognolina, M., Laforenza, U., Moccia, F., & D’Angelo, E. (2020). Parameter tuning differentiates granule cell subtypes enriching transmission properties at the cerebellum input stage. Communications Biology, 3(1), 222. doi:10.1038/s42003-020-0953-x