global H OH x1 global k1f k1r k4f k4r global x1_13 x1_18 x1_47 global k1f_13 k1r_13 k4f_13 k4r_13 global a1f a1r a4f a4r global b1f b1r b4f b4r global R18w R18OH global s1f s1r s4f s4r global p1f p1r p4f p4r %__________________________________________________________________________ % CO2 Dissociation Constants K1 = 10^( (-3404.71/Tk) + 14.8435 - (0.032786*Tk) ); % Harned & Davis (1943) % {CO2aq+H2CO3} <-> HCO3- + H+ K2 = 10^( (-2902.39/Tk) + 6.4980 - (0.02379*Tk) ); % Harned & Scholes (1941) % HCO3- <-> CO32- + H+ Kw = 10^( (-6013.79/Tk) - (23.6521*log10(Tk)) + 64.7013 ); % Harned & Owen (1958) % H2O <-> H+ + OH- % Derive [H+] and [OH-] H = 10^(-pH); OH = Kw/H; % x1 = [HCO3-]/[DCP], x2 = [CO32-]/[DCP] % where [DCP] = [HCO3-] + [CO32-] x1 = 1 / (1 + (K2/H)); x2 = 1 - x1; %__________________________________________________________________________ % Kinetic Rate Constants for CO2 hydration & Hydroxylation k1f = 10^(329.850 - (110.541*log10(Tk)) - (17265.4/Tk)); % Pinsent et al. (1956) CO2 + H2O -> H2CO3 k1r = k1f / K1; k4f = 10^(13.635 - (2895/Tk)); % Pinsent et al. (1956) CO2 + OH- -> HCO3- k4r = (k4f*Kw)/K1; % Note that K4 = [HCO3-][H+]/[CO2] = K1/Kw %__________________________________________________________________________ % 13R and 18R for the Isotopic Reference Materials (VPDB, VSMOW) R13vpdb = 0.011180; R18vsmow = 0.0020052; % [Brand] and [Chang & Assonov] values in Daeron et al. (2016) % Table 1 R18vpdb = R18vsmow * 1.03091; % VPDB/VSMOW conversion factor (1.03091) by Coplen et al. (1983) %__________________________________________________________________________ % Carbon Isotope System % Equilibrium 13C Fractionations Eps13_dg = -(0.0049*Tc) - 1.31; % between CO2(aq) & CO2(g) Eps13_bg = -(0.1141*Tc) + 10.78; % between HCO3- & CO2(g) Eps13_cg = -(0.052*Tc) + 7.22; % between CO32- & CO2(g) % Zhang et al. (1995), all in EPSILON (permil) % EPSILON = (ALPHA - 1)*1000 % Conversion to ALPHA Alp13_dg = 1 + (Eps13_dg/1000); % between CO2(aq) & CO2(g) Alp13_bg = 1 + (Eps13_bg/1000); % between HCO3- & CO2(g) Alp13_cg = 1 + (Eps13_cg/1000); % between CO32- & CO2(g) % From these, the followings can be derived Alp13_db = Alp13_dg / Alp13_bg; % between CO2(aq) & HCO3- Alp13_bd = Alp13_bg / Alp13_dg; % between HCO3- & CO2(aq) Alp13_cd = Alp13_cg / Alp13_dg; % between CO32- & CO2(aq) Alp13_dc = Alp13_dg / Alp13_cg; % between CO2(aq) & CO32- Alp13_cb = Alp13_cg / Alp13_bg; % between CO32- & HCO3- Alp13_DCPd = (x1*Alp13_bg + x2*Alp13_cg) / Alp13_dg; K1_13 = K1 / Alp13_db; K2_13 = K2 * Alp13_cb; x1_13 = 1 / (1 + (K2_13/H)); % Rate constants, using KIF as adjustable parameters % Hydration k1f_13 = k1f / KIF13_CO2H2O; k1r_13 = k1f_13 / K1_13; % Hydroxylation k4f_13 = k4f / KIF13_CO2OH; k4r_13 = ((k4f_13)*Kw) / K1_13; %__________________________________________________________________________ % Oxygen Isotope System % Alp18_OHw = exp((0.00048*Tk) - 0.1823); % between OH- & H2O % % Green & Taube 1963 (see Laurent Devriendt et al. 2007) Alp18_OHw = (1.0214)^(-1); % Latest work of Zeebe suggest EQ 18O H2O-OH fractionation % between 1.019-1.0214 at 25C, for which the mid-point being % 1.0214. % What is needed here is 18O OH-H2O fractionation, so need to % inverse if Tc == 25 Alp18_bw = exp(30.58/1000); % between HCO3- & H2O UCHIKAWA/ZEEBE Alp18_cw = exp(24.50/1000); % between CO32- & H2O UCHIKAWA/ZEEBE else Alp18_bw = exp((2590/Tk^2) + 0.00189); % between HCO3- & H2O BECK Alp18_cw = exp((2390/Tk^2) + 0.00270); % between CO32- & H2O BECK end Alp18_dw = exp((2520/Tk^2) + 0.01212); % between CO2(aq) & H2O BECK % From these, the followings can be derived Alp18_cb = Alp18_cw / Alp18_bw; % between CO32- & HCO3- Alp18_bd = Alp18_bw / Alp18_dw; % between HCO3- & CO2(aq) Alp18_cd = Alp18_cw / Alp18_dw; % between CO32- & CO2(aq) %Alp18_db = Alp18_dw / Alp18_bw; % between CO2(aq) & HCO3- Alp18_DCPd = (x1*Alp18_bd) + (x2*Alp18_cd); % between DCP and co2(aq) Alp18_DCPw = (x1*Alp18_bw) + (x2*Alp18_cw); % between DCP and H2O %K1_18 = K1 / Alp18_db; K2_18 = K2 * Alp18_cb; x1_18 = 1 / (1 + (K2_18/H)); % Rate constants % forward ks for hydration & hydroxylation a1f = k1f / KIF18_a1; b1f = k1f / KIF18_b1; a4f = k4f / KIF18_a4; b4f = k4f / KIF18_b4; % backward ks for hydration & hydroxylation a1r = a1f / (K1 * Alp18_bw); b1r = b1f / (K1 * Alp18_bd); a4r = (a4f * Alp18_OHw * Kw) / (K1 * Alp18_bw); b4r = (b4f * Kw) / (K1 * Alp18_bd); % a1r = a1f / (K1 * Alp18_DCPw); % b1r = b1f / (K1 * Alp18_DCPd); % a4r = (a4f * Alp18_OHw * Kw) / (K1 * Alp18_DCPw); % b4r = (b4f * Kw) / (K1 * Alp18_DCPd); %__________________________________________________________________________ % Clumped Isotope System % Equilibrium D47 signature for HCO3- and CO32- (Tripati et al., 2015) D47_HCO3 = 0.713; D47_CO3 = 0.650; % Theoretical constraints by Hill et al. (2020). % Accounting for D47 offset in HCO3- and CO32- of Tripati at 25C % D47_CO3 = ((9.033152E-6)*Tc^2) - ((3.133305E-3)*Tc) + 7.90637E-1; % D47_HCO3 = ((9.391747E-6)*Tc^2) - ((3.313957E-3)*Tc) + 7.23313E-1; % No experimental constraint on D47 of CO2a(aq)/H2CO3. % Choose/Test 2 Options below % Option 1: 0.7441 D47_CO2 = D47_HCO3 + 0.0311; % Option 2 0.8509 % D47_CO2 = (71840/Tk^2) + 0.0427; % Option 1: Ab-initio calc by Hill et al. (2014) suggest D47 % of H2CO3 to be higher than HCO3- by 0.031 permil. % CAVEAT: Assume D47 of H2CO3 = D47 of CO2(aq) % Option 2: Wang et al. (2004). Linear fit on theoretically % constrained D47 of "16O13C18O (I)" vs Temp % (in Table 4) % CAVEAT: Assume D47 of CO2(g) = D47 of CO2(aq) % D47 of equilibrated DCP, based on mass balance D47eqDCP = (x1 * D47_HCO3) + (x2 * D47_CO3); % Equilibrium Constant for 13-18 clumping in CO2, HCO3-, CO32- & DCP % see Watkins & Hunt (2015) Eq-41 & 46 K47_CO2 = 1 + (D47_CO2/1000); K47_HCO3 = 1 + (D47_HCO3/1000); K47_CO3 = 1 + (D47_CO3/1000); K47_DCP = 1 + (D47eqDCP/1000); % Clumped isotope fractionation between CO32- & HCO3- Alp47_cb = (1 + (D47_CO3/1000)) / (1 + (D47_HCO3/1000)); K2_47 = K2 * Alp47_cb * Alp13_cb * Alp18_cb; x1_47 = 1 / (1 + (K2_47/H)); % Rate constants (after Guo et al. for KIE47) % forward ks for hydration & hydroxylation p1f = (k1f_13*a1f) / (k1f) / (KIE47_p1); s1f = (k1f_13*b1f) / (k1f) / (KIE47_s1); p4f = (k4f_13*a4f) / (k4f) / (KIE47_p4); s4f = (k4f_13*b4f) / (k4f) / (KIE47_s4); % Kp1 = (K1 * K47_HCO3 * Alp18_bw) / Alp13_db; % Ks1 = (K1 * K47_HCO3 * Alp18_bd) / (K47_CO2 * Alp13_db); % Kp4 = (K1 * K47_HCO3 * Alp18_bw) / (Alp13_db * Alp18_OHw * Kw); % Ks4 = (K1 * K47_HCO3 * Alp18_bd) / (K47_CO2 * Alp13_db * Kw); Kp1 = (K1 * K47_DCP * Alp18_bw) / Alp13_db; Ks1 = (K1 * K47_DCP * Alp18_bd) / (K47_CO2 * Alp13_db); Kp4 = (K1 * K47_DCP * Alp18_bw) / (Alp13_db * Alp18_OHw * Kw); Ks4 = (K1 * K47_DCP * Alp18_bd) / (K47_CO2 * Alp13_db * Kw); % Reverse Rate Constants p1r = p1f / Kp1; s1r = s1f / Ks1; p4r = p4f / Kp4; s4r = s4f / Ks4; %__________________________________________________________________________ % Carbonic Anhydrase % Michaelis Menton Kinetics for CO2 hydration by bovine erythrocyte CA MM = 2.7*10^7; % MM = (k_cat)/KM % MM value based on yhe fit to UZ12 experimental data % (see Fig. 9 therein) k1f_enz = k1f + (MM)*(CA); cat_factor = (k1f_enz)/k1f; if CA_catalysis cat_factor = 20; end % CA enzymatic catalysis on CO2 hydration k1f = (k1f)*(cat_factor); k1f_13 = (k1f_13)*(cat_factor); a1f = (a1f)*(cat_factor); b1f = (b1f)*(cat_factor); p1f = (p1f)*(cat_factor); s1f = (s1f)*(cat_factor); k1r = (k1r)*(cat_factor); k1r_13 = (k1r_13)*(cat_factor); a1r = (a1r)*(cat_factor); b1r = (b1r)*(cat_factor); p1r = (p1r)*(cat_factor); s1r = (s1r)*(cat_factor);