How glutamatergic synapse loss affects the firing rhythm of DG-CA3 model related with Alzheimer’s disease

. 2021 Aug 16;16(1):167–181. doi: 10.1007/s11571-021-09705-x

Channel	Definition	Explicit expression
$I_{Na}$	$g_{Na} m_{\infty} {(V_{P})}^{3} h (V_{P} - V_{Na})$	$m_{\infty} (V_{P}) = α_{m} (V_{P}) / (α_{m} (V_{P}) + β_{m} (V_{P}))$ $α_{m} (V_{P}) = 0.32 (V_{P} + 54) / (1 - exp (- (V_{P} + 54) / 4))$ $β_{m} (V_{P}) = 0.28 (V_{P} + 27)$ /( $exp ((V_{P} + 27) / 5) - 1)$ $τ_{h} (V_{P}) = 1 / (α_{h} (V_{P}) + β_{h} (V_{P}))$ $α_{h} (V_{P}) = 0.128 exp (- (V_{P} + 50) / 18)$
$I_{K}$	$g_{K} n^{4} (V_{P} - V_{K})$	$β_{h} (V_{P}) = 4 / 1 + exp (- (V_{P} + 27) / 5)$ $n_{\infty} (V_{P}) = α_{n} (V_{P}) / (α_{n} (V_{P}) + β_{n} (V_{P}))$
$I_{L}$	$g_{L} (V_{P} - V_{L})$	$τ_{n} (V_{P}) = 1 / (α_{n} (V_{P}) + β_{n} (V_{P}))$ $α_{n} (V_{P}) = 0.032 (V_{P} + 52) / (1 - exp (- (V_{P} + 52) / 5))$ $β_{n} (V_{P}) = 0.5 exp (- (V_{P} + 57) / 40)$

Channel

Definition

Explicit expression

I_{Na}

g_{Na} m_{\infty} {(V_{P})}^{3} h (V_{P} - V_{Na})

$m_{\infty} (V_{P}) = α_{m} (V_{P}) / (α_{m} (V_{P}) + β_{m} (V_{P}))$

$α_{m} (V_{P}) = 0.32 (V_{P} + 54) / (1 - exp (- (V_{P} + 54) / 4))$

$β_{m} (V_{P}) = 0.28 (V_{P} + 27)$ /( $exp ((V_{P} + 27) / 5) - 1)$

$τ_{h} (V_{P}) = 1 / (α_{h} (V_{P}) + β_{h} (V_{P}))$

$α_{h} (V_{P}) = 0.128 exp (- (V_{P} + 50) / 18)$

I_{K}

g_{K} n^{4} (V_{P} - V_{K})

$β_{h} (V_{P}) = 4 / 1 + exp (- (V_{P} + 27) / 5)$

$n_{\infty} (V_{P}) = α_{n} (V_{P}) / (α_{n} (V_{P}) + β_{n} (V_{P}))$

I_{L}

g_{L} (V_{P} - V_{L})

$τ_{n} (V_{P}) = 1 / (α_{n} (V_{P}) + β_{n} (V_{P}))$

$α_{n} (V_{P}) = 0.032 (V_{P} + 52) / (1 - exp (- (V_{P} + 52) / 5))$

$β_{n} (V_{P}) = 0.5 exp (- (V_{P} + 57) / 40)$