From c9879c4e42644711c4270e74301ab281eccdc988 Mon Sep 17 00:00:00 2001 From: Michael Clerx Date: Mon, 24 Jun 2024 19:29:21 +0100 Subject: [PATCH] Added more documentation to O'Hara INaK. --- c/ohara-2011.mmt | 102 +++++++++++++++++++++++++++++------------------ 1 file changed, 64 insertions(+), 38 deletions(-) diff --git a/c/ohara-2011.mmt b/c/ohara-2011.mmt index f9525ef..5aa9f96 100644 --- a/c/ohara-2011.mmt +++ b/c/ohara-2011.mmt @@ -1,6 +1,6 @@ [[model]] name: ohara-2011 -version: 20240529 +version: 20240624 mmt_authors: Michael Clerx display_name: O'Hara et al., 2011 desc: """ @@ -772,70 +772,93 @@ INaCa_ss = 0.2 * inaca.fNaCa * inaca.gNaCa * allo * (JncxNa + 2 * JncxCa) use membrane.V use extra.Na_o, sodium.Na_i, sodium.Na_ss use extra.K_o, potassium.K_i, potassium.K_ss -k1p = 949.5 [1/s] +MgATP = 9.8 [mM] # Original + in [mM] + desc: Intracellular MgATP concentration +MgADP = 0.05 [mM] # Original + in [mM] + desc: Intracellular MgADP concentration +eP = 4.2 [mM] # Original + in [mM] + desc: The total concentration of inorganic phosphate (free + bound) +H = 1e-4 [mM] # Corrected (see below) + in [mM] + desc: Intracellular H+ + note: Corrected to 1e-7 [M] (pH 7) from original value of 1e-7 [mM] +Khp = 1.698e-7 [mM] # This value is suspicious! Smith and crampin paper says 6.77. Cellml says 1.69e-4 + in [mM] + desc: Dissociation constant relating [HPi] and [H] +Kxkur = 292 [mM] # Original + in [mM] + desc: Dissociation constant relating [KPi] and [K]i +Knap = 224 [mM] # Original + in [mM] + desc: Dissociation constant relating [NaPi] and [Na]i +# Table 1 parameters in Smith & Cramin +k1p = 949.5 [1/s] # Refit from 1050 in [1/s] -k1m = 182.4 [1/s/mM] +k1m = 182.4 [1/s/mM] # Refit from 172.1 in [1/s/mM] -k2p = 687.2 [1/s] +k2p = 687.2 [1/s] # Refit from 481 in [1/s] -k2m = 39.4 [1/s] +k2m = 39.4 [1/s] # Refit from 40 in [1/s] -k3p = 1899 [1/s] +k3p = 1899 [1/s] # Refit from 2000 in [1/s] -k3m = 79300 [1/s/mM^2] +k3m = 79300 [1/s/mM^2] # Original in [1/s/mM^2] -k4p = 639 [1/s] +k4p = 639 [1/s] # Refit from 320 in [1/s] -k4m = 40 [1/s] +k4m = 40 [1/s] # Original in [1/s] -Knai0 = 9.073 [mM] - in [mM] -Knao0 = 27.78 [mM] +Knao0 = 27.78 [mM] # Refit from 15.5 in [mM] -Kki = 0.5 [mM] + desc: Extracellular Na+ dissociation constant at 0mV +Knai0 = 9.073 [mM] # Refit from 2.49 in [mM] -Kko = 0.3582 [mM] + desc: Intracellular Na+ dissociation constant at 0mV +Kko = 0.3582 [mM] # Refit from 0.213 in [mM] -delta = -0.155 -MgADP = 0.05 [mM] + desc: Extracellular K+ dissociation constant +Kki = 0.5 [mM] # Original in [mM] -MgATP = 9.8 [mM] - in [mM] -Kmgatp = 1.698e-7 [mM] - in [mM] -H = 1e-4 [mM] - in [mM] - note: Corrected to 1e-7 [M] (pH 7) from original value of 1e-7 [mM] -eP = 4.2 [mM] - in [mM] -Khp = 1.698e-7 [mM] - in [mM] -Knap = 224 [mM] - in [mM] -Kxkur = 292 [mM] - in [mM] -P = eP / (1 + H / Khp + Na_i / Knap + K_i / Kxkur) + desc: Intracellular K+ dissociation constant +Kmgatp = 1.698e-7 [mM] # Refit from 2.51 in [mM] + desc: Intracellular MgATP dissociation constant +delta = -0.155 # Refit from -0.031 + desc: """A constant that "determines how the voltage dependence is + partitioned between intra and extracellular Na+ dissociation + reactions.""" +# Equations 14: Voltage-dependent Na+ dissociation constants Knai = Knai0 * exp(delta * V * phys.FRT / 3) in [mM] Knao = Knao0 * exp((1 - delta) * V * phys.FRT / 3) in [mM] +# Equations 30: Forward (clockwise) rates a1 = k1p * (Na_i / Knai)^3 / ((1 + Na_i / Knai)^3 + (1 + K_i / Kki)^2 - 1) in [Hz] -b1 = k1m * MgADP - in [Hz] a2 = k2p in [Hz] -b2 = k2m * (Na_o / Knao)^3 / ((1 + Na_o / Knao)^3 + (1 + K_o / Kko)^2 - 1) - in [Hz] a3 = k3p * (K_o / Kko)^2 / ((1 + Na_o / Knao)^3 + (1 + K_o / Kko)^2 - 1) in [Hz] -b3 = k3m * P * H / (1 + MgATP / Kmgatp) - in [Hz] a4 = k4p * MgATP / Kmgatp / (1 + MgATP / Kmgatp) in [Hz] +# Equations 31: Backward (anticlockwise) rates +b1 = k1m * MgADP + in [Hz] +b2 = k2m * (Na_o / Knao)^3 / ((1 + Na_o / Knao)^3 + (1 + K_o / Kko)^2 - 1) + in [Hz] +b3 = k3m * P * H / (1 + MgATP / Kmgatp) + in [Hz] b4 = k4m * (K_i / Kki)^2 / ((1 + Na_i / Knai)^3 + (1 + K_i / Kki)^2 - 1) in [Hz] +# Equation 33 +P = eP / (1 + H / Khp + Na_i / Knap + K_i / Kxkur) + in [mM] +# Terms used to calculate the steady-state occupancies of the four states +# Based on the "diagram method" described in [2], these terms are the sums of +# the reaction rates of all (non-cyclical) paths leading to each state x1 = a4 * a1 * a2 + b1 * b4 * b3 + a2 * b4 * b3 + b3 * a1 * a2 in [Hz^3] note: Corrected from the original code (b1 in second term) @@ -845,8 +868,11 @@ x3 = a2 * a3 * a4 + b3 * b2 * b1 + b2 * b1 * a4 + a3 * a4 * b1 in [Hz^3] x4 = b4 * b3 * b2 + a3 * a4 * a1 + b2 * a4 * a1 + b3 * b2 * a1 in [Hz^3] +# Cycle rate (obtaining by writing any one of the four flux equations: they all +# give the same result so that the pump count is conserved). r = (a1 * a2 * a3 * a4 - b1 * b2 * b3 * b4) / (x1 + x2 + x3 + x4) in [1/s] +# INaK current JnakNa = 3 * r in [1/s] JnakK = -2 * r