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Table 4:
Common Symbols and Notations in This Article.
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,yi0 
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,yi0 
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:
Parameters Used for Simulations in This Article.
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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