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Table 2 Functions associated with activation and inactivation variables for system ( 1a )–( 1g ). We use the variable y when an expression corresponds to a set of variables

From: Timescales and Mechanisms of Sigh-Like Bursting and Spiking in Models of Rhythmic Respiratory Neurons

Gating variables

Steady-state activation and inactivation

Time constants

\(m_{\mathrm{Na}}\)

\(y_{\infty}(V)= 1/(1+\exp (-(V-V_{y1/2})/k_{y}))\)

\(\tau_{y}(V)=\tau_{y\max}/\cosh (-(V-V_{\tau y1/2})/ k_{\tau y})\)

\(h_{\mathrm{Na}}\)

\(m_{\mathrm{NaP}}\)

\(h_{\mathrm{Na}}\)

\(m_{\mathrm{Ca}}\)

\(\tau_{m_{\mathrm{Ca}}}=0.5~\mbox{ms}\)

\(h_{\mathrm{Ca}}\)

\(\tau_{h_{\mathrm{Ca}}}=18~\mbox{ms}\)

\(m_{\mathrm{K}}\)

\({m_{\mathrm{K}}}_{\infty}= \alpha _{\infty}/(\alpha_{\infty}+\beta_{\infty})\)

\(\tau_{m_{\mathrm {K}}}=1/(\alpha_{\infty}+\beta_{\infty})\)

\(\alpha_{\infty}= A_{\alpha }\cdot(V+B_{\alpha})/(1-\exp(-(V+B_{\alpha})/k_{\alpha}))\), \(\beta _{\infty}=A_{\beta}\cdot\exp(-(V+B_{\beta})/k_{\beta})\)

\(m_{\mathrm{CAN}}\)

\(m_{\mathrm{CAN}}=1/(1+(K_{\mathrm {CAN}}/\mathrm{Ca}_{\mathrm{i}})^{n})\)