Quantitative roles of ion channel dynamics on ventricular action potential

Figures & data

Table 1. Physical units used in the text

Time (t)	Voltage (V)	Capacitance (Cm)	Conductance	Concentration
Milliseconds (ms)	Millivolts(mV)	Picofarads (pF)	Nanosiemens per picofarad (nS/pF)	Millimol per liter (mmol/liter)

Table 2. Conductances of ion channels

Parameter	Value	Parameter	Value
$g_{Na}$	1.0044e+3	$g_{Ks}$	6.4916
$g_t$	16.4718	$g_{CaT}$	1.5854
$g_{hf}$	7.7282	$g_{Clb}$	1.5278
$g_{K1}$	6	$g_{BNa}$	0.0326
$g_{Kr}$	5.7017	$g_{BK}$	0.0500
$g_{CaL}$	6.2894	$g_{BCa}$	0.0025

Table 3. Membrane current and Ca²⁺ handling mechanism related parameters for equations above

Parameter	Value	Parameter	Value	Parameter	Value
$k_b^{-}$ (ms^−1)	3.4472	$v_{maxr}$(mM ms^−1)	0.0009	$k_{htrpn}^{+}$(mM^−1.ms^−1)	43.1286
$k_c^{+}$ (ms^−1)	0.0513	$K_m^{CMDN}$ (mM)	0.00238	$k_{htrpn}^{-}$(ms^−1)	7.1033e-4
$k_c^{-}$ (ms^−1)	0.0062	$K_m^{CSQN}$ (mM)	0.8	$k_{ltrpn}^{+}$(ms^−1)	0.0969
$k_a^{+}$(mM^−4 ms^−1)	5.78e+6	${\left[CMDN\right]}_{tot}$(mM)	0.05	$k_{ltrpn}^{-}$(ms^−1)	0.0013
$k_a^{-}$ (ms^−1)	0.5128	${\left[CSQN\right]}_{tot}$(mM)	15	${\left[\mathrm{H}\mathrm{T}\mathrm{R}\mathrm{P}\mathrm{N}\right]}_{\mathrm{t}\mathrm{o}\mathrm{t}}$(mM)	0.14
$k_b^{+}$(mM^−3 ms^−1)	2.1586e+7	${\mathrm{k}}_{\mathrm{E}\mathrm{G}\mathrm{T}\mathrm{A}}^{-}$ (mM)	0.00015	${\left[\mathrm{L}\mathrm{T}\mathrm{R}\mathrm{P}\mathrm{N}\right]}_{\mathrm{t}\mathrm{o}\mathrm{t}}$(mM)	0.07
v1 (ms^−1)	10.5921	$\mathrm{E}\mathrm{G}\mathrm{T}{\mathrm{A}}_{\mathrm{t}\mathrm{o}\mathrm{t}}$(mM)	10	$V_{myo}$(pL)	9.36
$K_{fb}$ (mM)	9.6176e-4	$V_{JSR}$(pL)	0.056	F (Faraday Constant-C/mol)	96,487
$K_{rb}$ (mM)	28.1467	$V_{ss}$(pL)	0.0012	T (Absolute temperature – K)	310.15
$K_{sr}$	2.3974	$V_{NSR}$(pL)	0.504	R (Ideal gas constant –mJ/mol K)	8314
$N_{fb}$	1.2	$A_{cap}$	0.8004
$N_{rb}$	1	${\tau }_{tr}$ (ms)	0.9258
$v_{maxf}$(mM ms^−1)	0.00004	${\tau }_{xfer}$(ms)	0.5234

Table 4. Initial conditions for state variables

Parameter	Initial value	Parameter	Initial value
$V$	−72	$P_{C_2}$	0.634
$n$	0.0041	$HTRPNCa$	0.139
$n_f$	0.67	$LTRPNCa$	0.00516
$n_s$	0.67	${\left[N{a}^{+}\right]}_i$	10.73519
$l$	2.1 × 10^−6	${\left[K^{+}\right]}_i$	139.275
$l_f$	0.99	${\left[C{a}^2+\right]}_i$	7.9 × 10^−5
$l_s$	0.99	${\left[C{a}^2+\right]}_{ss}$	8.737212 × 10^−5
$C{a}_i$	0.99	${\left[C{a}^2+\right]}_{JSR}$	6.607948 × 10^−2
$kt$	0.0021	${\left[C{a}^2+\right]}_{NSR}$	0.06600742
$k{t}_f$	0.98	$r$	0.3657
$k{t}_s$	0.64	$ct$	0.089
$y$	0.0035	$c{t}_i$	0.081
$P_{C_1}$	0.634	$C{l}_i$	30.03
$P_{O_1}$	4.327 × 10^−4	$s$	0.1776
$P_{O_2}$	6.06 × 10^−10	$r_i$	0.1

Table 5. Extracellular ion concentrations

Parameter	${\left[\mathrm{N}{\mathrm{a}}^{+}\right]}_{\mathrm{o}}$	${\left[{\mathrm{K}}^{+}\right]}_{\mathrm{o}}$	${\left[\mathrm{C}{\mathrm{a}}^2+\right]}_{\mathrm{o}}$	${\left[\mathrm{C}{\mathrm{l}}^{-}\right]}_{\mathrm{o}}$
Value (mM)	140	5.4	1.5	140

Figure 1. Simulated AP (dark blue) and simulated Ca²⁺ activation function,l, (dark green) between 60–120 ms. In 80 mV, time constant of Ca²⁺ activation ${\tau }_l$ is increased by δτ (light green). Slowing down the Ca²⁺ activation (%60 for this plot) increases AP duration by δAP (light blue)

Figure 2. Functions for time-dependent (a) activation of I_CaL; (b) activation of I_Na; (c) fast-inactivation of I_Na; (d) slow-inactivation of I_Na; (e) fast-inactivation of I_CaL; (f) Ca²⁺ depedendent-inactivation of I_CaL; (g) activation of I_Ks; (h) activation of I_to; (i) fast-inactivation of I_to; (j) slow-inactivation of I_to. Red marks show epoch points of phase 0, blue marks show epoch points of phase 1, green marks show epoch points of phase 2 and pink marks show epoch points of phase 3. Light blue squares are phase points on each curve

Figure 3. Sign convention of the contribution analysis method. The traces of (a) show sign of contribution value of Na⁺ gating variables under the effect of Na⁺ Nernst potential while membrane is in depolarization state. The traces of (b) show sign of contribution value of Ca²⁺ gating variables under the effect of Ca²⁺ Nernst potential in repolarization state and the traces of (c) show sign of contribution value of K⁺ gating variables under the effect of K⁺ Nernst potential in repolarization state

Figure 4. Contribution results after the simulations are defined as a heatmap between −0.01 and 0.01. Each phase (P_0,1,2,3) is divided into four equal interval of interests (IoI_1,2,3,4) calculated as aggregated epochs. Each time dependent function in the model that has a role to shape cardiac action potential is measured and their roles are quantified in the table

Figure 5. Contribution quantification for Na⁺ current activation “n”, fast inactivation “nf” and slow inactivation ‘ns’during ventricular AP depolarization (phase 0 is between 67.44 and70.92 ms), early repolarization (phase 1 is between 70.92 and76 ms), plateau (phase 2 is between 76 and 90.76 ms) and late repolarization (phase 3 is between 90.76 and110 ms). Regions for the action potential duration of %20 (AP20), %50 (AP50) and %90 (AP90) are also shown. All phases are divided into four equal IoI regions as color coded

Figure 6. Contribution quantification for Ca²⁺ current activation “l”, fast inactivation “lf” and Ca²⁺ dependent inactivation “Cai” during ventricular AP depolarization (phase 0), early repolarization (phase 1), plateau (phase 2) and late repolarization (phase 3). Regions for the action potential duration of %20 (AP20), %50 (AP50) and %90 (AP90) are also shown. All phases are divided into four IoI regions as color coded

Figure 7. Contribution quantification for K⁺ current activation “kt”, fast inactivation “ktf” and slow inactivation “kts” during ventricular AP depolarization (phase 0), early repolarization (phase 1), plateau (phase 2) and late repolarization (phase 3). Regions for the action potential duration of %20 (AP20), %50 (AP50) and %90 (AP90) are also shown. All phases are divided into four IoI regions as color coded

Figure 8. Contribution quantification for rapidly activating delayed rectifier K⁺ current activation “r” and slowly activating delayed rectifier K⁺ current activation “s” during ventricular AP depolarization (phase 0), early repolarization (phase 1), plateau (phase 2) and late repolarization (phase 3). Regions for the action potential duration of %20 (AP20), %50 (AP50) and %90 (AP90) are also shown. All phases are divided into four IoI regions as color coded