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Table 1 List of parameter values. The abbreviation ‘cstd’ indicates that the value was constrained to reproduce experimental dynamics of DCN

From: A model of on/off transitions in neurons of the deep cerebellar nuclei: deciphering the underlying ionic mechanisms

Parameter

Value

Reference

Calcium ions dynamics

\(R_{c}\)

\(5 \times 10^{ - 4}~\mbox{cm}\)

[26]

δ

\(3 \times 10^{ - 4}~\mbox{cm}\)

k

\(10^{ - 2}~\mbox{cm/s}\)

\([ B ]_{T}\)

\(1.5 \times 10^{2}~\mu \mbox{M}\)

\(K_{D}\)

\(1~\mu \mbox{M}\)

Membrane potential dynamics

C

\(1~\mu \mbox{F/cm}^{2}\)

[25]

Membrane ion currents

Maximum conductances and permeabilities

\(g_{\text{L}}\)

\(2 \times 10^{1}~\mu \mbox{S/cm}^{2}\)

cstd

\(g_{\text{NaV}}\)

\(5 \times 10^{3}~\mu \mbox{S/cm}^{2}\)

\(g_{\text{Kdr}}\)

\(4.5 \times 10^{3}~\mu \mbox{S/cm}^{2}\)

\(g_{\text{TCN}}\)

\(4.5 \times 10^{1}~\mu \mbox{S/cm}^{2}\)

\(g_{\text{KCa}}\)

\(10~\mu \mbox{S/cm}^{2}\)

\(P_{\text{CaH}}\)

\(2 \times 10^{ - 4}~\mbox{cm/s}\)

\(P_{\text{CaT}}\)

\(7 \times 10^{ - 4}~\mbox{cm/s}\)

Nernst potential

\(E_{\text{L}}\)

\(- 60~\mbox{mV}\)

cstd

\(E_{\text{Na}}\)

\(+ 86~\mbox{mV}\)

[4]

\(E_{\text{K}}\)

\(- 80~\mbox{mV}\)

\(-83~\mbox{mV}\) in [28]

\(E_{\text{Cl}}\)

\(- 75~\mbox{mV}\)

\(-75~\mbox{mV}\) [2] and \(-74.3~\mbox{mv}\) in [28]; however, see [5]

\(E_{\text{TCN}}\)

\(- 34~\mbox{mV}\)

[4]

Steady-state (in)activation parameters (mV)

\(V_{m_{\text{NaV}}}\)

−32

cstd

\(k_{m_{\text{NaV}}}\)

8.5

\(V_{h_{\text{NaV}}}\)

−55

\(k_{h_{\text{NaV}}}\)

5.5

[4]

\(V_{m_{\text{Kdr}}}\)

−25

[29]

\(k_{m_{\text{Kdr}}}\)

11.5

\(V_{m_{\text{CaH}}}\)

−22

cstd

\(k_{m_{\text{CaH}}}\)

4.53

\(V_{m_{\text{CaT}}}\)

−56

[30]

\(k_{m_{\text{CaT}}}\)

6.2

\(V_{h_{\text{CaT}}}\)

−80

\(k_{h_{\text{CaT}}}\)

4

Parameters of time constants

\(\tau _{n_{\text{Kdr}}0}\)

\(0~\mbox{s}\)

cstd

\(\tau _{n_{\text{Kdr}}1}\)

\(5.4 \times 10^{ - 3}~\mbox{s}\)

\(\alpha _{\tau _{n_{\text{Kdr}}}}\)

6 × 10−1

\(V_{\tau_{n_{\text{Kdr}}1}} = V_{\tau_{n_{\text{Kdr}}2}}\)

\(- 30~\mbox{mV}\)

\(k_{\tau_{n_{\text{Kdr}}1}} = k_{\tau_{n_{\text{Kdr}}2}}\)

\(25~\mbox{mV}\)

\(\tau _{h_{\text{NaV}}0}\)

\(5 \times 10^{ - 3}~\mbox{s}\)

\(\tau _{h_{\text{NaV}}1}\)

\(3 \times 10^{ - 2}~\mbox{s}\)

\(\alpha _{\tau _{h_{\text{NaV}}}}\)

1

\(V_{\tau_{h_{\text{NaV}}1}} = V_{\tau_{h_{\text{NaV}}2}}\)

\(- 65~\mbox{mV}\)

\(k_{\tau_{h_{\text{NaV}}1}} = k_{\tau_{h_{\text{NaV}}2}}\)

\(7~\mbox{mV}\)

\(\tau _{m_{\text{CaT}}0}\)

\(2 \times 10^{ - 4}~\mbox{s}\)

[30]

\(\tau _{m_{\text{CaT}}1}\)

3.33 × 10−4

\(V_{\tau_{m_{\text{CaT}}1}}\)

\(- 131~\mbox{mV}\)

\(k_{\tau_{m_{\text{CaT}}1}}\)

\(16.7~\mbox{mV}\)

\(\alpha _{\tau _{m\text{CaT}}}\)

1

\(V_{\tau_{m_{\text{CaT}}2}}\)

\(- 15.8~\mbox{mV}\)

\(k_{\tau_{m_{\text{CaT}}2}}\)

\(18.2~\mbox{mV}\)

\(\tau _{h_{\mathrm{CaH}}0}\)

\(1.2 \times 10^{ - 2}~\mbox{s}\)

cstd (to produce a \(C^{1}\) function for \(\tau _{h_{\mathrm{CaT}}}\))

\(\tau _{h_{\mathrm{CaH}}1}\)

\(2~\mbox{s}\)

\(\alpha _{\tau _{h_{\mathrm{CaT}}}}\)

1

\(V_{\tau_{h_{\mathrm{CaH}}1}} = V_{\tau_{h_{\mathrm{CaH}}2}}\)

\(- 81~\mbox{mV}\)

\(k_{\tau_{h_{\mathrm{CaH}}1}} = k_{\tau_{h_{\mathrm{CaH}}2}}\)

\(8~\mbox{mV}\)