Table 4:
SymbolMeaning
$C$ Membrane capacitance ($μF/cm2$
$v$ Membrane potential ($mV$
$VNa,VK,VL$ Ionic reversal potential for Na$+$, K$+$and leak ($mV$
$Iapp$ Applied current to the membrane ($nA/cm2$
$m,h,n$ Dimensionless gating variables for Na$+$ and K$+$ channels
$αx,βxx∈{m,n,h}$ Voltage-dependent rate constant ($1/msec$
$x$ Vector of state variables
$M=[M1,M2,⋯,M8]$ Eight-component state vector for the Na$+$ gates
$[m00,m10,m20,m30,$ Components for the Na$+$gates
$m01,m11,m21,m31]⊺$
$N=[N1,N2,⋯,N5]$ Five-component state vector for the K$+$ gates
$[n0,n1,n2,n3,n4]⊺$ Components for the K$+$ gates
$Mtot,Ntot$ Total number of Na$+$ and K$+$ channels
$X$ 4-dimensional manifold domain for 4D HH model
$Y$ 14-dimensional manifold domain for 14D HH model
$Δk$ $k$-dimensional simplex in $Rk+1$ given by $y1+…+yk+1=1,yi≥0$
$M$ Multinomial submanifold within the 14D space
$ANa$, $AK$ State-dependent rate matrix
$D$ State diffusion matrix
$S$, $S1$, $S2$, $SNa$, $SK$ Noise coefficient matrices
$ξ$ Vector of independent $δ$-correlated gaussian white noise with zero mean and unit variance
$X=[X1,X2,…,Xd]$ A $d$-dimensional random variable for sample path
$W=[W1,W2,…,Wn]$ A Wiener trajectory with $n$ components
$δ(·)$ The Dirac delta function
$δij$ The Kronecker delta
$Fn$ Empirical cumulative distribution function with $n$ observations (in section 5, we use $m,n$ as sample sizes)
SymbolMeaning
$C$ Membrane capacitance ($μF/cm2$
$v$ Membrane potential ($mV$
$VNa,VK,VL$ Ionic reversal potential for Na$+$, K$+$and leak ($mV$
$Iapp$ Applied current to the membrane ($nA/cm2$
$m,h,n$ Dimensionless gating variables for Na$+$ and K$+$ channels
$αx,βxx∈{m,n,h}$ Voltage-dependent rate constant ($1/msec$
$x$ Vector of state variables
$M=[M1,M2,⋯,M8]$ Eight-component state vector for the Na$+$ gates
$[m00,m10,m20,m30,$ Components for the Na$+$gates
$m01,m11,m21,m31]⊺$
$N=[N1,N2,⋯,N5]$ Five-component state vector for the K$+$ gates
$[n0,n1,n2,n3,n4]⊺$ Components for the K$+$ gates
$Mtot,Ntot$ Total number of Na$+$ and K$+$ channels
$X$ 4-dimensional manifold domain for 4D HH model
$Y$ 14-dimensional manifold domain for 14D HH model
$Δk$ $k$-dimensional simplex in $Rk+1$ given by $y1+…+yk+1=1,yi≥0$
$M$ Multinomial submanifold within the 14D space
$ANa$, $AK$ State-dependent rate matrix
$D$ State diffusion matrix
$S$, $S1$, $S2$, $SNa$, $SK$ Noise coefficient matrices
$ξ$ Vector of independent $δ$-correlated gaussian white noise with zero mean and unit variance
$X=[X1,X2,…,Xd]$ A $d$-dimensional random variable for sample path
$W=[W1,W2,…,Wn]$ A Wiener trajectory with $n$ components
$δ(·)$ The Dirac delta function
$δij$ The Kronecker delta
$Fn$ Empirical cumulative distribution function with $n$ observations (in section 5, we use $m,n$ as sample sizes)
Table 5:
SymbolMeaningValue
$C$ Membrane capacitance 1 $μF/cm2$
$g¯Na$ Maximal sodium conductance 120 $μS/cm2$
$g¯K$ Maximal potassium conductance 36 $μS/cm2$
$gleak$ Leak conductance 0.3 $μS/cm2$
$VNa$ Sodium reversal potential for Na$+$ 50 $mV$
$VK$ Potassium reversal potential for K$+$ $-$77 $mV$
$Vleak$ Leak reversal potential $-$54.4 $mV$
$Iapp$ Applied current to the membrane 10 $nA/cm2$
$A$ Membrane area $100μm2$
$Mtot$ Total number of Na$+$ channels 6,000
$Ntot$ Total number of K$+$ channels 18,00
SymbolMeaningValue
$C$ Membrane capacitance 1 $μF/cm2$
$g¯Na$ Maximal sodium conductance 120 $μS/cm2$
$g¯K$ Maximal potassium conductance 36 $μS/cm2$
$gleak$ Leak conductance 0.3 $μS/cm2$
$VNa$ Sodium reversal potential for Na$+$ 50 $mV$
$VK$ Potassium reversal potential for K$+$ $-$77 $mV$
$Vleak$ Leak reversal potential $-$54.4 $mV$
$Iapp$ Applied current to the membrane 10 $nA/cm2$
$A$ Membrane area $100μm2$
$Mtot$ Total number of Na$+$ channels 6,000
$Ntot$ Total number of K$+$ channels 18,00

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