Inactivation gates for the fast Na current (I_Na), “h” and “j”, are partially closed at normal quiescent membrane potentials in the O'Hara-Rudy dynamic (ORd) model. This was the result of using Sakakibara et al.¹⁠ nonfailing human ventricular I_Na data (17° C) and correcting for temperature using Nagatomo et al.²⁠ HEK-expressed hH1 data and for time after patch-clamp commencement using Hanck & Sheets³⁠ data (see manuscript page 6 for details). This is ultimately why the maximum conductance was set to 75 mS/μF, substantially larger than in other models. There are no independent human I_Na data available to determine whether the temperature/time corrections applied were in fact quantitatively accurate. The partial unavailability amounts to a functional reserve of I_Na. Perhaps it is true. This could explaining super-normality⁴⁠ and reserve of I_Na channels as implied by Lin et al.⁵⁠.

With hyperkalemia, “h” and “j” gates are further closed as resting membrane voltage depolarizes through the steep portion of the steady state inactivation curves. In single cells, this reduces the action potential upstroke velocity within the physiological range. However, in 3-dimensional tissue, where cells experience a large electrical load, this might cause conduction block at lower levels of hyperkalemia than observed experimentally.

A solution to this problem may be to replace ORd I_Na with ten Tusscher et al.⁶⁠ I_Na in such simulations. The ten Tusscher I_Na steady state inactivation curves were based on Nagatomo et al.²⁠ hH1 data extrapolated to 37° C, not corrected for time after patch-clamp commencement. The resulting inactivation gates are less sensitive to resting membrane voltage elevation under hyperkalemic conditions because steady state inactivation curves are ~10 mV depolarized relative to ORd.

Below are the equations describing the ten Tusscher I_Na model⁶⁠:

a_m=1.0/(1.+exp((-60.0-Vm)/5.0))
b_m=0.1/(1.0+exp((Vm+35.0)/5.0))+0.10/(1.0+exp((Vm-50.0)/200.0))
tau_m=a_m*b_m
m_inf=1.0/((1.0+exp((-56.86-Vm)/9.03))*(1.0+exp((-56.86-Vm)/9.03)))

if (Vm>=-40.0) {
a_h=0.0
b_h=0.77/(0.13*(1.+exp(-(Vm+10.66)/11.1)))
}
else {
a_h=0.057*exp(-(Vm+80.0)/6.8)
b_h=2.7*exp(0.079*Vm)+(3.1e5)*exp(0.3485*Vm)
}
tau_h=1.0/(a_h+b_h)
h_inf=1.0/((1.+exp((Vm+71.55)/7.43))*(1.0+exp((Vm+71.55)/7.43)))

if (Vm>=-40) {
a_j=0.0
b_j =0.6*exp((0.057)*Vm)/(1.0+exp(-0.1*(Vm+32.0)))
}
else {
a_j=((-2.5428e4)*exp(0.2444*Vm Vm 6.948e-6)*exp(-0.04391*Vm))*(Vm+37.78)/(1.0+exp(0.311*(Vm+79.23)))
b_j=0.02424*exp(-0.01052*Vm)/(1.+exp(-0.1378*(Vm+40.14)))
}
tau_j=1.0/(a_j+b_j)
j_inf=h_inf

dm/dt=(m_inf-m)/tau_m
dh/dt=(h_inf-h)/tau_h
dj/dt=(j_inf-j)/tau_j

GNa=14.838
INa=GNa*m3*h*j*(Vm-ENa)


1. Sakakibara, Y. et al. Sodium current in isolated human ventricular myocytes. The American journal of physiology 265, H1301–9 (1993).
2. Nagatomo, T. et al. Temperature dependence of early and late currents in human cardiac wild-type and long Q-T DeltaKPQ Na+ channels. The American journal of physiology 275, H2016–24 (1998).
3. Hanck, D. A. & Sheets, M. F. Time-dependent changes in kinetics of Na+ current in single canine cardiac Purkinje cells. The American journal of physiology 262, H1197–207 (1992).
4. Spear, J. F. & Moore, E. N. Supernormal Excitability and Conduction in the His-Purkinje System of the Dog. Circulation Research 35, 782–792 (1974).
5. Lin, X. et al. Subcellular heterogeneity of sodium current properties in adult cardiac ventricular myocytes. Heart Rhythm (2011).doi:10.1016/j.hrthm.2011.07.016
6. ten Tusscher, K. H. W. J., Noble, D., Noble, P. J. & Panfilov, a V. A model for human ventricular tissue. American journal of physiology. Heart and circulatory physiology 286, H1573–89 (2004).