Steady-state approximations for Hodgkin-Huxley cell models: Reduction of order for uterine smooth muscle cell model
Fig 5
Steady-state approximation comparisons with ODE solutions for I − V curves and Vm results from FTM simulations; L-type (Panel A) and Na+ (Panel B) channels.
Full ODE solutions displayed with black traces (labeled ‘FTM’) and hybrid SS-ODE or full SS solutions with dotted/coloured traces as noted. Presented plots similar as for BK and T-type, with upper panes displaying currents (scaled to maximum inbound) solved out to T = 10 or 100 ms (inset), and lower panes Vm or ΔVm as labeled. (Panel A) CaL channel, d activation and f1, f2 inactivation variables. ICaL shown (upper pane) for full ODE (black trace, FTM) and SS approximated variables as noted (blue-, red- and cyan-dotted). SS approximations for only f2 not performed. Vm presented (lower pane) and not ΔVm due to obvious deviations; note same trace legend as upper pane (black FTM and coloured SS combinations). SSP simulations with varied conductances (inset) for two SS approximations and improved Vm fit to FTM: d and f1 both SS (cyan trace) with gCaL reduced; only d approximated with SS (red trace) with gCaL reduced as well as gNa and gK1 both increased (see text for details). (Panel B). Na+ channel, m and h activation/inactivation variables. Upper pane presents currents for full ODE, hybrid SS and full SS solutions out to T = 10 and 100 ms (inset), and lower pane result for SSP showing ΔVm (relative) and Vm (inset) with same ODE and SS combinations as noted in upper legend: full ODE (black trace), both m and h activation/inactivation variables SS (blue dotted) and m or h SS (red and cyan dotted, respectively). See SSP description for numerical details.