# Location: BG_composite_M2 @ fcefc10a7dd7 / BG_M2_composite_Exported.m

Author:
Shelley Fong <s.fong@auckland.ac.nz>
Date:
2021-10-27 11:22:54+13:00
Desc:
Permanent Source URI:
https://models.cellml.org/workspace/700/rawfile/fcefc10a7dd7e17af448dbb9d7bab2ee8a2746f1/BG_M2_composite_Exported.m

```function [VOI, STATES, ALGEBRAIC, CONSTANTS] = mainFunction()
% This is the "main function".  In Matlab, things work best if you rename this function to match the filename.
[VOI, STATES, ALGEBRAIC, CONSTANTS] = solveModel();
end

function [algebraicVariableCount] = getAlgebraicVariableCount()
% Used later when setting a global variable with the number of algebraic variables.
% Note: This is not the "main method".
algebraicVariableCount =32;
end
% There are a total of 14 entries in each of the rate and state variable arrays.
% There are a total of 29 entries in the constant variable array.
%

function [VOI, STATES, ALGEBRAIC, CONSTANTS] = solveModel()
% Create ALGEBRAIC of correct size
global algebraicVariableCount;  algebraicVariableCount = getAlgebraicVariableCount();
% Initialise constants and state variables
[INIT_STATES, CONSTANTS] = initConsts;

% Set timespan to solve over
tspan = [0, 10];

% Set numerical accuracy options for ODE solver
options = odeset('RelTol', 1e-06, 'AbsTol', 1e-06, 'MaxStep', 1);

% Solve model with ODE solver
[VOI, STATES] = ode15s(@(VOI, STATES)computeRates(VOI, STATES, CONSTANTS), tspan, INIT_STATES, options);

% Compute algebraic variables
[RATES, ALGEBRAIC] = computeRates(VOI, STATES, CONSTANTS);
ALGEBRAIC = computeAlgebraic(ALGEBRAIC, CONSTANTS, STATES, VOI);

% Plot state variables against variable of integration
[LEGEND_STATES, LEGEND_ALGEBRAIC, LEGEND_VOI, LEGEND_CONSTANTS] = createLegends();
figure();
plot(VOI, STATES);
xlabel(LEGEND_VOI);
l = legend(LEGEND_STATES);
set(l,'Interpreter','none');
end

function [LEGEND_STATES, LEGEND_ALGEBRAIC, LEGEND_VOI, LEGEND_CONSTANTS] = createLegends()
LEGEND_STATES = ''; LEGEND_ALGEBRAIC = ''; LEGEND_VOI = ''; LEGEND_CONSTANTS = '';
LEGEND_CONSTANTS(:,1) = strpad('kappa_sig1 in component muscarinic_parameters (fmol_per_sec)');
LEGEND_CONSTANTS(:,2) = strpad('kappa_sig2 in component muscarinic_parameters (fmol_per_sec)');
LEGEND_CONSTANTS(:,3) = strpad('kappa_sig3 in component muscarinic_parameters (fmol_per_sec)');
LEGEND_CONSTANTS(:,4) = strpad('kappa_sig4 in component muscarinic_parameters (fmol_per_sec)');
LEGEND_CONSTANTS(:,5) = strpad('kappa_act1 in component muscarinic_parameters (fmol_per_sec)');
LEGEND_CONSTANTS(:,6) = strpad('kappa_act2 in component muscarinic_parameters (fmol_per_sec)');
LEGEND_CONSTANTS(:,7) = strpad('kappa_hyd in component muscarinic_parameters (fmol_per_sec)');
LEGEND_CONSTANTS(:,8) = strpad('kappa_reassoc in component muscarinic_parameters (fmol_per_sec)');
LEGEND_CONSTANTS(:,9) = strpad('K_L in component muscarinic_parameters (per_fmol)');
LEGEND_CONSTANTS(:,10) = strpad('K_R in component muscarinic_parameters (per_fmol)');
LEGEND_CONSTANTS(:,11) = strpad('K_G in component muscarinic_parameters (per_fmol)');
LEGEND_CONSTANTS(:,12) = strpad('K_LR in component muscarinic_parameters (per_fmol)');
LEGEND_CONSTANTS(:,13) = strpad('K_RG in component muscarinic_parameters (per_fmol)');
LEGEND_CONSTANTS(:,14) = strpad('K_LRG in component muscarinic_parameters (per_fmol)');
LEGEND_CONSTANTS(:,15) = strpad('K_a_GTP in component muscarinic_parameters (per_fmol)');
LEGEND_CONSTANTS(:,16) = strpad('K_beta_gamma in component muscarinic_parameters (per_fmol)');
LEGEND_CONSTANTS(:,17) = strpad('K_a_GDP in component muscarinic_parameters (per_fmol)');
LEGEND_VOI = strpad('time in component environment (second)');
LEGEND_ALGEBRAIC(:,1) = strpad('q_L_init in component environment (fmol)');
LEGEND_CONSTANTS(:,18) = strpad('q_LRG_init in component environment (fmol)');
LEGEND_CONSTANTS(:,19) = strpad('q_LR_init in component environment (fmol)');
LEGEND_CONSTANTS(:,20) = strpad('q_R_init in component environment (fmol)');
LEGEND_CONSTANTS(:,21) = strpad('q_G_init in component environment (fmol)');
LEGEND_CONSTANTS(:,22) = strpad('q_RG_init in component environment (fmol)');
LEGEND_CONSTANTS(:,23) = strpad('q_a_GTP_init in component environment (fmol)');
LEGEND_CONSTANTS(:,24) = strpad('q_beta_gamma_init in component environment (fmol)');
LEGEND_CONSTANTS(:,25) = strpad('q_a_GDP_init in component environment (fmol)');
LEGEND_STATES(:,1) = strpad('q_R in component GiProtein (fmol)');
LEGEND_STATES(:,2) = strpad('q_G in component GiProtein (fmol)');
LEGEND_STATES(:,3) = strpad('q_RG in component GiProtein (fmol)');
LEGEND_STATES(:,4) = strpad('q_LR in component GiProtein (fmol)');
LEGEND_STATES(:,5) = strpad('q_LRG in component GiProtein (fmol)');
LEGEND_STATES(:,6) = strpad('q_a_GTP in component GiProtein (fmol)');
LEGEND_STATES(:,7) = strpad('q_beta_gamma in component GiProtein (fmol)');
LEGEND_STATES(:,8) = strpad('q_a_GDP in component GiProtein (fmol)');
LEGEND_STATES(:,9) = strpad('q_L in component LRGbinding (fmol)');
LEGEND_STATES(:,10) = strpad('q_R in component LRGbinding (fmol)');
LEGEND_STATES(:,11) = strpad('q_G in component LRGbinding (fmol)');
LEGEND_STATES(:,12) = strpad('q_LR in component LRGbinding (fmol)');
LEGEND_STATES(:,13) = strpad('q_RG in component LRGbinding (fmol)');
LEGEND_STATES(:,14) = strpad('q_LRG in component LRGbinding (fmol)');
LEGEND_ALGEBRAIC(:,2) = strpad('q_L in component environment (fmol)');
LEGEND_ALGEBRAIC(:,7) = strpad('q_LRG in component environment (fmol)');
LEGEND_ALGEBRAIC(:,5) = strpad('q_LR in component environment (fmol)');
LEGEND_ALGEBRAIC(:,3) = strpad('q_R in component environment (fmol)');
LEGEND_ALGEBRAIC(:,4) = strpad('q_G in component environment (fmol)');
LEGEND_ALGEBRAIC(:,6) = strpad('q_RG in component environment (fmol)');
LEGEND_ALGEBRAIC(:,8) = strpad('q_a_GTP in component environment (fmol)');
LEGEND_ALGEBRAIC(:,10) = strpad('q_beta_gamma in component environment (fmol)');
LEGEND_ALGEBRAIC(:,12) = strpad('q_a_GDP in component environment (fmol)');
LEGEND_CONSTANTS(:,26) = strpad('R in component constants (J_per_K_per_mol)');
LEGEND_CONSTANTS(:,27) = strpad('T in component constants (kelvin)');
LEGEND_CONSTANTS(:,28) = strpad('F in component constants (C_per_mol)');
LEGEND_ALGEBRAIC(:,29) = strpad('vact1 in component GiProtein (fmol_per_sec)');
LEGEND_ALGEBRAIC(:,30) = strpad('vact2 in component GiProtein (fmol_per_sec)');
LEGEND_ALGEBRAIC(:,31) = strpad('vhyd in component GiProtein (fmol_per_sec)');
LEGEND_ALGEBRAIC(:,32) = strpad('vreassoc in component GiProtein (fmol_per_sec)');
LEGEND_ALGEBRAIC(:,14) = strpad('mu_R in component GiProtein (J_per_mol)');
LEGEND_ALGEBRAIC(:,16) = strpad('mu_G in component GiProtein (J_per_mol)');
LEGEND_ALGEBRAIC(:,18) = strpad('mu_RG in component GiProtein (J_per_mol)');
LEGEND_ALGEBRAIC(:,20) = strpad('mu_LR in component GiProtein (J_per_mol)');
LEGEND_ALGEBRAIC(:,22) = strpad('mu_LRG in component GiProtein (J_per_mol)');
LEGEND_ALGEBRAIC(:,24) = strpad('mu_a_GTP in component GiProtein (J_per_mol)');
LEGEND_ALGEBRAIC(:,26) = strpad('mu_beta_gamma in component GiProtein (J_per_mol)');
LEGEND_ALGEBRAIC(:,28) = strpad('mu_a_GDP in component GiProtein (J_per_mol)');
LEGEND_ALGEBRAIC(:,9) = strpad('mu_L in component LRGbinding (J_per_mol)');
LEGEND_ALGEBRAIC(:,11) = strpad('mu_R in component LRGbinding (J_per_mol)');
LEGEND_ALGEBRAIC(:,13) = strpad('mu_G in component LRGbinding (J_per_mol)');
LEGEND_ALGEBRAIC(:,15) = strpad('mu_LR in component LRGbinding (J_per_mol)');
LEGEND_ALGEBRAIC(:,17) = strpad('mu_RG in component LRGbinding (J_per_mol)');
LEGEND_ALGEBRAIC(:,19) = strpad('mu_LRG in component LRGbinding (J_per_mol)');
LEGEND_ALGEBRAIC(:,21) = strpad('vsig1 in component LRGbinding (fmol_per_sec)');
LEGEND_ALGEBRAIC(:,23) = strpad('vsig2 in component LRGbinding (fmol_per_sec)');
LEGEND_ALGEBRAIC(:,25) = strpad('vsig3 in component LRGbinding (fmol_per_sec)');
LEGEND_ALGEBRAIC(:,27) = strpad('vsig4 in component LRGbinding (fmol_per_sec)');
LEGEND_CONSTANTS(:,29) = strpad('vol in component LRGbinding (pL)');
LEGEND_RATES(:,1) = strpad('d/dt q_R in component GiProtein (fmol)');
LEGEND_RATES(:,3) = strpad('d/dt q_RG in component GiProtein (fmol)');
LEGEND_RATES(:,2) = strpad('d/dt q_G in component GiProtein (fmol)');
LEGEND_RATES(:,4) = strpad('d/dt q_LR in component GiProtein (fmol)');
LEGEND_RATES(:,5) = strpad('d/dt q_LRG in component GiProtein (fmol)');
LEGEND_RATES(:,6) = strpad('d/dt q_a_GTP in component GiProtein (fmol)');
LEGEND_RATES(:,7) = strpad('d/dt q_beta_gamma in component GiProtein (fmol)');
LEGEND_RATES(:,8) = strpad('d/dt q_a_GDP in component GiProtein (fmol)');
LEGEND_RATES(:,9) = strpad('d/dt q_L in component LRGbinding (fmol)');
LEGEND_RATES(:,10) = strpad('d/dt q_R in component LRGbinding (fmol)');
LEGEND_RATES(:,11) = strpad('d/dt q_G in component LRGbinding (fmol)');
LEGEND_RATES(:,12) = strpad('d/dt q_LR in component LRGbinding (fmol)');
LEGEND_RATES(:,13) = strpad('d/dt q_RG in component LRGbinding (fmol)');
LEGEND_RATES(:,14) = strpad('d/dt q_LRG in component LRGbinding (fmol)');
LEGEND_STATES  = LEGEND_STATES';
LEGEND_ALGEBRAIC = LEGEND_ALGEBRAIC';
LEGEND_RATES = LEGEND_RATES';
LEGEND_CONSTANTS = LEGEND_CONSTANTS';
end

function [STATES, CONSTANTS] = initConsts()
VOI = 0; CONSTANTS = []; STATES = []; ALGEBRAIC = [];
CONSTANTS(:,1) = 238142;
CONSTANTS(:,2) = 266.437;
CONSTANTS(:,3) = 3304.28;
CONSTANTS(:,4) = 53920.1;
CONSTANTS(:,5) = 0.00103925;
CONSTANTS(:,6) = 1.69088e-05;
CONSTANTS(:,7) = 0.0682376;
CONSTANTS(:,8) = 76.6955;
CONSTANTS(:,9) = 0.190462;
CONSTANTS(:,10) = 0.0844987;
CONSTANTS(:,11) = 0.00948347;
CONSTANTS(:,12) = 5.77509;
CONSTANTS(:,13) = 16.2165;
CONSTANTS(:,14) = 17.9264;
CONSTANTS(:,15) = 0.0164815;
CONSTANTS(:,16) = 0.0731915;
CONSTANTS(:,17) = 0.00880903;
CONSTANTS(:,18) = 1e-16;
CONSTANTS(:,19) = 1e-16;
CONSTANTS(:,20) = 0.00072;
CONSTANTS(:,21) = 0.00836;
CONSTANTS(:,22) = 1e-16;
CONSTANTS(:,23) = 1e-16;
CONSTANTS(:,24) = 1e-16;
CONSTANTS(:,25) = 1e-16;
STATES(:,1) = 1e-16;
STATES(:,2) = 1e-16;
STATES(:,3) = 1e-16;
STATES(:,4) = 1e-16;
STATES(:,5) = 1e-16;
STATES(:,6) = 1e-16;
STATES(:,7) = 1e-16;
STATES(:,8) = 1e-16;
STATES(:,9) = 1e-16;
STATES(:,10) = 1e-16;
STATES(:,11) = 1e-16;
STATES(:,12) = 1e-16;
STATES(:,13) = 1e-16;
STATES(:,14) = 1e-16;
CONSTANTS(:,26) = 8.31;
CONSTANTS(:,27) = 310;
CONSTANTS(:,28) = 96485;
CONSTANTS(:,29) = 34.4;
if (isempty(STATES)), warning('Initial values for states not set');, end
end

function [RATES, ALGEBRAIC] = computeRates(VOI, STATES, CONSTANTS)
global algebraicVariableCount;
statesSize = size(STATES);
statesColumnCount = statesSize(2);
if ( statesColumnCount == 1)
STATES = STATES';
ALGEBRAIC = zeros(1, algebraicVariableCount);
utilOnes = 1;
else
statesRowCount = statesSize(1);
ALGEBRAIC = zeros(statesRowCount, algebraicVariableCount);
RATES = zeros(statesRowCount, statesColumnCount);
utilOnes = ones(statesRowCount, 1);
end
ALGEBRAIC(:,3) = STATES(:,10)+STATES(:,1)+CONSTANTS(:,20);
ALGEBRAIC(:,11) =  CONSTANTS(:,26).*CONSTANTS(:,27).*log( CONSTANTS(:,10).*ALGEBRAIC(:,3));
ALGEBRAIC(:,4) = STATES(:,11)+STATES(:,2)+CONSTANTS(:,21);
ALGEBRAIC(:,13) =  CONSTANTS(:,26).*CONSTANTS(:,27).*log( CONSTANTS(:,11).*ALGEBRAIC(:,4));
ALGEBRAIC(:,6) = STATES(:,13)+STATES(:,3)+CONSTANTS(:,22);
ALGEBRAIC(:,17) =  CONSTANTS(:,26).*CONSTANTS(:,27).*log( CONSTANTS(:,13).*ALGEBRAIC(:,6));
ALGEBRAIC(:,21) =  CONSTANTS(:,1).*exp((ALGEBRAIC(:,11)+ALGEBRAIC(:,13))./( CONSTANTS(:,26).*CONSTANTS(:,27))) - exp(ALGEBRAIC(:,17)./( CONSTANTS(:,26).*CONSTANTS(:,27)));
ALGEBRAIC(:,1) = piecewise({VOI>0.100000&VOI<=1.00000, 0.380000 }, 1.00000e-16);
ALGEBRAIC(:,2) = STATES(:,9)+ALGEBRAIC(:,1);
ALGEBRAIC(:,9) =  CONSTANTS(:,26).*CONSTANTS(:,27).*log( CONSTANTS(:,9).*ALGEBRAIC(:,2));
ALGEBRAIC(:,7) = STATES(:,14)+STATES(:,5)+CONSTANTS(:,18);
ALGEBRAIC(:,19) =  CONSTANTS(:,26).*CONSTANTS(:,27).*log( CONSTANTS(:,14).*ALGEBRAIC(:,7));
ALGEBRAIC(:,23) =  CONSTANTS(:,2).*exp((ALGEBRAIC(:,17)+ALGEBRAIC(:,9))./( CONSTANTS(:,26).*CONSTANTS(:,27))) - exp(ALGEBRAIC(:,19)./( CONSTANTS(:,26).*CONSTANTS(:,27)));
RATES(:,13) = ALGEBRAIC(:,21) - ALGEBRAIC(:,23);
ALGEBRAIC(:,5) = STATES(:,12)+STATES(:,4)+CONSTANTS(:,19);
ALGEBRAIC(:,15) =  CONSTANTS(:,26).*CONSTANTS(:,27).*log( CONSTANTS(:,12).*ALGEBRAIC(:,5));
ALGEBRAIC(:,25) =  CONSTANTS(:,3).*exp((ALGEBRAIC(:,15)+ALGEBRAIC(:,13))./( CONSTANTS(:,26).*CONSTANTS(:,27))) - exp(ALGEBRAIC(:,19)./( CONSTANTS(:,26).*CONSTANTS(:,27)));
RATES(:,11) =  - ALGEBRAIC(:,21) - ALGEBRAIC(:,25);
RATES(:,14) = ALGEBRAIC(:,23)+ALGEBRAIC(:,25);
ALGEBRAIC(:,27) =  CONSTANTS(:,4).*exp((ALGEBRAIC(:,11)+ALGEBRAIC(:,9))./( CONSTANTS(:,26).*CONSTANTS(:,27))) - exp(ALGEBRAIC(:,15)./( CONSTANTS(:,26).*CONSTANTS(:,27)));
RATES(:,9) =  - ALGEBRAIC(:,23) - ALGEBRAIC(:,27);
RATES(:,10) =  - ALGEBRAIC(:,21) - ALGEBRAIC(:,27);
RATES(:,12) =  - ALGEBRAIC(:,25)+ALGEBRAIC(:,27);
ALGEBRAIC(:,14) =  CONSTANTS(:,26).*CONSTANTS(:,27).*log( CONSTANTS(:,10).*ALGEBRAIC(:,3));
ALGEBRAIC(:,18) =  CONSTANTS(:,26).*CONSTANTS(:,27).*log( CONSTANTS(:,13).*ALGEBRAIC(:,6));
ALGEBRAIC(:,8) = STATES(:,6)+CONSTANTS(:,23);
ALGEBRAIC(:,24) =  CONSTANTS(:,26).*CONSTANTS(:,27).*log( CONSTANTS(:,15).*ALGEBRAIC(:,8));
ALGEBRAIC(:,10) = STATES(:,7)+CONSTANTS(:,24);
ALGEBRAIC(:,26) =  CONSTANTS(:,26).*CONSTANTS(:,27).*log( CONSTANTS(:,16).*ALGEBRAIC(:,10));
ALGEBRAIC(:,29) =  CONSTANTS(:,5).*(exp(ALGEBRAIC(:,18)./( CONSTANTS(:,26).*CONSTANTS(:,27))) - exp((ALGEBRAIC(:,24)+ALGEBRAIC(:,26)+ALGEBRAIC(:,14))./( CONSTANTS(:,26).*CONSTANTS(:,27))));
RATES(:,1) = ALGEBRAIC(:,29);
RATES(:,3) =  - ALGEBRAIC(:,29);
ALGEBRAIC(:,20) =  CONSTANTS(:,26).*CONSTANTS(:,27).*log( CONSTANTS(:,12).*ALGEBRAIC(:,5));
ALGEBRAIC(:,22) =  CONSTANTS(:,26).*CONSTANTS(:,27).*log( CONSTANTS(:,14).*ALGEBRAIC(:,7));
ALGEBRAIC(:,30) =  CONSTANTS(:,6).*(exp(ALGEBRAIC(:,22)./( CONSTANTS(:,26).*CONSTANTS(:,27))) - exp((ALGEBRAIC(:,24)+ALGEBRAIC(:,26)+ALGEBRAIC(:,20))./( CONSTANTS(:,26).*CONSTANTS(:,27))));
RATES(:,4) = ALGEBRAIC(:,30);
RATES(:,5) =  - ALGEBRAIC(:,30);
ALGEBRAIC(:,12) = STATES(:,8)+CONSTANTS(:,25);
ALGEBRAIC(:,28) =  CONSTANTS(:,26).*CONSTANTS(:,27).*log( CONSTANTS(:,17).*ALGEBRAIC(:,12));
ALGEBRAIC(:,31) =  CONSTANTS(:,7).*(exp(ALGEBRAIC(:,24)./( CONSTANTS(:,26).*CONSTANTS(:,27))) - exp(ALGEBRAIC(:,28)./( CONSTANTS(:,26).*CONSTANTS(:,27))));
RATES(:,6) = (ALGEBRAIC(:,29)+ALGEBRAIC(:,30)) - ALGEBRAIC(:,31);
ALGEBRAIC(:,16) =  CONSTANTS(:,26).*CONSTANTS(:,27).*log( CONSTANTS(:,11).*ALGEBRAIC(:,4));
ALGEBRAIC(:,32) =  CONSTANTS(:,8).*(exp((ALGEBRAIC(:,28)+ALGEBRAIC(:,26))./( CONSTANTS(:,26).*CONSTANTS(:,27))) - exp(ALGEBRAIC(:,16)./( CONSTANTS(:,26).*CONSTANTS(:,27))));
RATES(:,2) = ALGEBRAIC(:,32);
RATES(:,7) = (ALGEBRAIC(:,29)+ALGEBRAIC(:,30)) - ALGEBRAIC(:,32);
RATES(:,8) = ALGEBRAIC(:,31) - ALGEBRAIC(:,32);
RATES = RATES';
end

% Calculate algebraic variables
function ALGEBRAIC = computeAlgebraic(ALGEBRAIC, CONSTANTS, STATES, VOI)
statesSize = size(STATES);
statesColumnCount = statesSize(2);
if ( statesColumnCount == 1)
STATES = STATES';
utilOnes = 1;
else
statesRowCount = statesSize(1);
utilOnes = ones(statesRowCount, 1);
end
ALGEBRAIC(:,3) = STATES(:,10)+STATES(:,1)+CONSTANTS(:,20);
ALGEBRAIC(:,11) =  CONSTANTS(:,26).*CONSTANTS(:,27).*log( CONSTANTS(:,10).*ALGEBRAIC(:,3));
ALGEBRAIC(:,4) = STATES(:,11)+STATES(:,2)+CONSTANTS(:,21);
ALGEBRAIC(:,13) =  CONSTANTS(:,26).*CONSTANTS(:,27).*log( CONSTANTS(:,11).*ALGEBRAIC(:,4));
ALGEBRAIC(:,6) = STATES(:,13)+STATES(:,3)+CONSTANTS(:,22);
ALGEBRAIC(:,17) =  CONSTANTS(:,26).*CONSTANTS(:,27).*log( CONSTANTS(:,13).*ALGEBRAIC(:,6));
ALGEBRAIC(:,21) =  CONSTANTS(:,1).*exp((ALGEBRAIC(:,11)+ALGEBRAIC(:,13))./( CONSTANTS(:,26).*CONSTANTS(:,27))) - exp(ALGEBRAIC(:,17)./( CONSTANTS(:,26).*CONSTANTS(:,27)));
ALGEBRAIC(:,1) = piecewise({VOI>0.100000&VOI<=1.00000, 0.380000 }, 1.00000e-16);
ALGEBRAIC(:,2) = STATES(:,9)+ALGEBRAIC(:,1);
ALGEBRAIC(:,9) =  CONSTANTS(:,26).*CONSTANTS(:,27).*log( CONSTANTS(:,9).*ALGEBRAIC(:,2));
ALGEBRAIC(:,7) = STATES(:,14)+STATES(:,5)+CONSTANTS(:,18);
ALGEBRAIC(:,19) =  CONSTANTS(:,26).*CONSTANTS(:,27).*log( CONSTANTS(:,14).*ALGEBRAIC(:,7));
ALGEBRAIC(:,23) =  CONSTANTS(:,2).*exp((ALGEBRAIC(:,17)+ALGEBRAIC(:,9))./( CONSTANTS(:,26).*CONSTANTS(:,27))) - exp(ALGEBRAIC(:,19)./( CONSTANTS(:,26).*CONSTANTS(:,27)));
ALGEBRAIC(:,5) = STATES(:,12)+STATES(:,4)+CONSTANTS(:,19);
ALGEBRAIC(:,15) =  CONSTANTS(:,26).*CONSTANTS(:,27).*log( CONSTANTS(:,12).*ALGEBRAIC(:,5));
ALGEBRAIC(:,25) =  CONSTANTS(:,3).*exp((ALGEBRAIC(:,15)+ALGEBRAIC(:,13))./( CONSTANTS(:,26).*CONSTANTS(:,27))) - exp(ALGEBRAIC(:,19)./( CONSTANTS(:,26).*CONSTANTS(:,27)));
ALGEBRAIC(:,27) =  CONSTANTS(:,4).*exp((ALGEBRAIC(:,11)+ALGEBRAIC(:,9))./( CONSTANTS(:,26).*CONSTANTS(:,27))) - exp(ALGEBRAIC(:,15)./( CONSTANTS(:,26).*CONSTANTS(:,27)));
ALGEBRAIC(:,14) =  CONSTANTS(:,26).*CONSTANTS(:,27).*log( CONSTANTS(:,10).*ALGEBRAIC(:,3));
ALGEBRAIC(:,18) =  CONSTANTS(:,26).*CONSTANTS(:,27).*log( CONSTANTS(:,13).*ALGEBRAIC(:,6));
ALGEBRAIC(:,8) = STATES(:,6)+CONSTANTS(:,23);
ALGEBRAIC(:,24) =  CONSTANTS(:,26).*CONSTANTS(:,27).*log( CONSTANTS(:,15).*ALGEBRAIC(:,8));
ALGEBRAIC(:,10) = STATES(:,7)+CONSTANTS(:,24);
ALGEBRAIC(:,26) =  CONSTANTS(:,26).*CONSTANTS(:,27).*log( CONSTANTS(:,16).*ALGEBRAIC(:,10));
ALGEBRAIC(:,29) =  CONSTANTS(:,5).*(exp(ALGEBRAIC(:,18)./( CONSTANTS(:,26).*CONSTANTS(:,27))) - exp((ALGEBRAIC(:,24)+ALGEBRAIC(:,26)+ALGEBRAIC(:,14))./( CONSTANTS(:,26).*CONSTANTS(:,27))));
ALGEBRAIC(:,20) =  CONSTANTS(:,26).*CONSTANTS(:,27).*log( CONSTANTS(:,12).*ALGEBRAIC(:,5));
ALGEBRAIC(:,22) =  CONSTANTS(:,26).*CONSTANTS(:,27).*log( CONSTANTS(:,14).*ALGEBRAIC(:,7));
ALGEBRAIC(:,30) =  CONSTANTS(:,6).*(exp(ALGEBRAIC(:,22)./( CONSTANTS(:,26).*CONSTANTS(:,27))) - exp((ALGEBRAIC(:,24)+ALGEBRAIC(:,26)+ALGEBRAIC(:,20))./( CONSTANTS(:,26).*CONSTANTS(:,27))));
ALGEBRAIC(:,12) = STATES(:,8)+CONSTANTS(:,25);
ALGEBRAIC(:,28) =  CONSTANTS(:,26).*CONSTANTS(:,27).*log( CONSTANTS(:,17).*ALGEBRAIC(:,12));
ALGEBRAIC(:,31) =  CONSTANTS(:,7).*(exp(ALGEBRAIC(:,24)./( CONSTANTS(:,26).*CONSTANTS(:,27))) - exp(ALGEBRAIC(:,28)./( CONSTANTS(:,26).*CONSTANTS(:,27))));
ALGEBRAIC(:,16) =  CONSTANTS(:,26).*CONSTANTS(:,27).*log( CONSTANTS(:,11).*ALGEBRAIC(:,4));
ALGEBRAIC(:,32) =  CONSTANTS(:,8).*(exp((ALGEBRAIC(:,28)+ALGEBRAIC(:,26))./( CONSTANTS(:,26).*CONSTANTS(:,27))) - exp(ALGEBRAIC(:,16)./( CONSTANTS(:,26).*CONSTANTS(:,27))));
end

% Compute result of a piecewise function
function x = piecewise(cases, default)
set = [0];
for i = 1:2:length(cases)
if (length(cases{i+1}) == 1)
x(cases{i} & ~set,:) = cases{i+1};
else
x(cases{i} & ~set,:) = cases{i+1}(cases{i} & ~set);
end
set = set | cases{i};
if(set), break, end
end
if (length(default) == 1)
x(~set,:) = default;
else
x(~set,:) = default(~set);
end
end

% Pad out or shorten strings to a set length