- Author:
- Shelley Fong <s.fong@auckland.ac.nz>
- Date:
- 2021-07-21 13:21:28+12:00
- Desc:
- Adding constraint of Gibbs free energy for PDE reaction
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/674/rawfile/807b1b4db76b95ba92b2cab7115970c165927585/saucerman_cAMP_exportedm.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 =1;
end
% There are a total of 2 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_VOI = strpad('time in component environment (second)');
LEGEND_CONSTANTS(:,1) = strpad('AC_tot in component cAMP_parameters (uM)');
LEGEND_CONSTANTS(:,2) = strpad('ATP in component cAMP_parameters (uM)');
LEGEND_CONSTANTS(:,3) = strpad('PDE_tot in component cAMP_parameters (uM)');
LEGEND_CONSTANTS(:,4) = strpad('IBMX_tot in component cAMP_parameters (uM)');
LEGEND_CONSTANTS(:,5) = strpad('Fsk_tot in component cAMP_parameters (uM)');
LEGEND_CONSTANTS(:,6) = strpad('k_ac_basal in component cAMP_parameters (per_sec)');
LEGEND_CONSTANTS(:,7) = strpad('k_ac_gsa in component cAMP_parameters (per_sec)');
LEGEND_CONSTANTS(:,8) = strpad('k_ac_fsk in component cAMP_parameters (per_sec)');
LEGEND_CONSTANTS(:,9) = strpad('k_pde in component cAMP_parameters (per_sec)');
LEGEND_CONSTANTS(:,10) = strpad('Km_basal in component cAMP_parameters (uM)');
LEGEND_CONSTANTS(:,11) = strpad('Km_gsa in component cAMP_parameters (uM)');
LEGEND_CONSTANTS(:,12) = strpad('Km_fsk in component cAMP_parameters (uM)');
LEGEND_CONSTANTS(:,13) = strpad('Km_pde in component cAMP_parameters (uM)');
LEGEND_CONSTANTS(:,14) = strpad('K_gsa in component cAMP_parameters (uM)');
LEGEND_CONSTANTS(:,15) = strpad('K_fsk in component cAMP_parameters (uM)');
LEGEND_CONSTANTS(:,16) = strpad('Ki_ibmx in component cAMP_parameters (uM)');
LEGEND_STATES(:,1) = strpad('cAMP in component cAMP_module (uM)');
LEGEND_STATES(:,2) = strpad('cAMP_no_PDE in component cAMP_module (uM)');
LEGEND_CONSTANTS(:,18) = strpad('Gsa_GTP in component cAMP_module (uM)');
LEGEND_CONSTANTS(:,26) = strpad('Fsk in component cAMP_module (uM)');
LEGEND_CONSTANTS(:,19) = strpad('AC in component cAMP_module (uM)');
LEGEND_CONSTANTS(:,21) = strpad('PDE in component cAMP_module (uM)');
LEGEND_CONSTANTS(:,22) = strpad('IBMX in component cAMP_module (uM)');
LEGEND_CONSTANTS(:,20) = strpad('Gsa_GTP_AC in component cAMP_module (uM)');
LEGEND_CONSTANTS(:,27) = strpad('Fsk_AC in component cAMP_module (uM)');
LEGEND_CONSTANTS(:,25) = strpad('AC_ACT_GSA in component cAMP_module (uM_per_sec)');
LEGEND_CONSTANTS(:,24) = strpad('AC_ACT_BASAL in component cAMP_module (uM_per_sec)');
LEGEND_CONSTANTS(:,28) = strpad('AC_ACT_FSK in component cAMP_module (uM_per_sec)');
LEGEND_ALGEBRAIC(:,1) = strpad('PDE_ACT in component cAMP_module (uM_per_sec)');
LEGEND_CONSTANTS(:,23) = strpad('PDE_IBMX in component cAMP_module (uM)');
LEGEND_CONSTANTS(:,17) = strpad('Gs_agtp_tot in component cAMP_module (uM)');
LEGEND_RATES(:,1) = strpad('d/dt cAMP in component cAMP_module (uM)');
LEGEND_RATES(:,2) = strpad('d/dt cAMP_no_PDE in component cAMP_module (uM)');
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) = 49.7e-3;
CONSTANTS(:,2) = 5e3;
CONSTANTS(:,3) = 39e-3;
CONSTANTS(:,4) = 1;
CONSTANTS(:,5) = 0;
CONSTANTS(:,6) = 0.2;
CONSTANTS(:,7) = 8.5;
CONSTANTS(:,8) = 0;
CONSTANTS(:,9) = 5;
CONSTANTS(:,10) = 1.03e3;
CONSTANTS(:,11) = 315;
CONSTANTS(:,12) = 860;
CONSTANTS(:,13) = 1.3;
CONSTANTS(:,14) = 0.4;
CONSTANTS(:,15) = 44;
CONSTANTS(:,16) = 30;
STATES(:,1) = 0.8453;
STATES(:,2) = 0.8453;
CONSTANTS(:,17) = 0.02505;
[CONSTANTS, STATES, ALGEBRAIC] = rootfind_0(VOI, CONSTANTS, STATES, ALGEBRAIC);
[CONSTANTS, STATES, ALGEBRAIC] = rootfind_1(VOI, CONSTANTS, STATES, ALGEBRAIC);
CONSTANTS(:,24) = ( CONSTANTS(:,6).*CONSTANTS(:,19).*CONSTANTS(:,2))./(CONSTANTS(:,10)+CONSTANTS(:,2));
CONSTANTS(:,25) = ( CONSTANTS(:,7).*CONSTANTS(:,20).*CONSTANTS(:,2))./(CONSTANTS(:,11)+CONSTANTS(:,2));
[CONSTANTS, STATES, ALGEBRAIC] = rootfind_2(VOI, CONSTANTS, STATES, ALGEBRAIC);
CONSTANTS(:,28) = ( CONSTANTS(:,8).*CONSTANTS(:,27).*CONSTANTS(:,2))./(CONSTANTS(:,12)+CONSTANTS(:,2));
CONSTANTS(:,28) = CONSTANTS(:,24)+CONSTANTS(:,25)+CONSTANTS(:,28);
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
RATES(:,2) = CONSTANTS(:,28);
ALGEBRAIC(:,1) = ( CONSTANTS(:,9).*CONSTANTS(:,21).*STATES(:,1))./(CONSTANTS(:,13)+STATES(:,1));
RATES(:,1) = ((CONSTANTS(:,24)+CONSTANTS(:,25)) - ALGEBRAIC(:,1))+CONSTANTS(:,28);
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(:,1) = ( CONSTANTS(:,9).*CONSTANTS(:,21).*STATES(:,1))./(CONSTANTS(:,13)+STATES(:,1));
end
% Functions required for solving differential algebraic equation
function [CONSTANTS, STATES, ALGEBRAIC] = rootfind_0(VOI, CONSTANTS_IN, STATES_IN, ALGEBRAIC_IN)
ALGEBRAIC = ALGEBRAIC_IN;
CONSTANTS = CONSTANTS_IN;
STATES = STATES_IN;
global initialGuess_0;
if (length(initialGuess_0) ~= 3), initialGuess_0 = [0.1,0.1,0.1];, end
options = optimset('Display', 'off', 'TolX', 1E-6);
if length(VOI) == 1
residualfn = @(algebraicCandidate)residualSN_0(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES);
soln = fsolve(residualfn, initialGuess_0, options);
initialGuess_0 = soln;
CONSTANTS(:,18) = soln(1);
CONSTANTS(:,19) = soln(2);
CONSTANTS(:,20) = soln(3);
else
SET_CONSTANTS(:,18) = logical(1);
SET_CONSTANTS(:,19) = logical(1);
SET_CONSTANTS(:,20) = logical(1);
for i=1:length(VOI)
residualfn = @(algebraicCandidate)residualSN_0(algebraicCandidate, ALGEBRAIC(i,:), VOI(i), CONSTANTS, STATES(i,:));
soln = fsolve(residualfn, initialGuess_0, options);
initialGuess_0 = soln;
TEMP_CONSTANTS(:,18) = soln(1);
TEMP_CONSTANTS(:,19) = soln(2);
TEMP_CONSTANTS(:,20) = soln(3);
ALGEBRAIC(i,SET_ALGEBRAIC) = TEMP_ALGEBRAIC(SET_ALGEBRAIC);
end
end
end
function resid = residualSN_0(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES)
CONSTANTS(:,18) = algebraicCandidate(1);
CONSTANTS(:,19) = algebraicCandidate(2);
CONSTANTS(:,20) = algebraicCandidate(3);
resid(1) = CONSTANTS(:,20) - ( CONSTANTS(:,18).*CONSTANTS(:,19))./CONSTANTS(:,14);
resid(2) = CONSTANTS(:,18) - (CONSTANTS(:,17) - CONSTANTS(:,20));
resid(3) = CONSTANTS(:,19) - (CONSTANTS(:,1) - CONSTANTS(:,20));
end
% Functions required for solving differential algebraic equation
function [CONSTANTS, STATES, ALGEBRAIC] = rootfind_1(VOI, CONSTANTS_IN, STATES_IN, ALGEBRAIC_IN)
ALGEBRAIC = ALGEBRAIC_IN;
CONSTANTS = CONSTANTS_IN;
STATES = STATES_IN;
global initialGuess_1;
if (length(initialGuess_1) ~= 3), initialGuess_1 = [0.1,0.1,0.1];, end
options = optimset('Display', 'off', 'TolX', 1E-6);
if length(VOI) == 1
residualfn = @(algebraicCandidate)residualSN_1(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES);
soln = fsolve(residualfn, initialGuess_1, options);
initialGuess_1 = soln;
CONSTANTS(:,21) = soln(1);
CONSTANTS(:,22) = soln(2);
CONSTANTS(:,23) = soln(3);
else
SET_CONSTANTS(:,21) = logical(1);
SET_CONSTANTS(:,22) = logical(1);
SET_CONSTANTS(:,23) = logical(1);
for i=1:length(VOI)
residualfn = @(algebraicCandidate)residualSN_1(algebraicCandidate, ALGEBRAIC(i,:), VOI(i), CONSTANTS, STATES(i,:));
soln = fsolve(residualfn, initialGuess_1, options);
initialGuess_1 = soln;
TEMP_CONSTANTS(:,21) = soln(1);
TEMP_CONSTANTS(:,22) = soln(2);
TEMP_CONSTANTS(:,23) = soln(3);
ALGEBRAIC(i,SET_ALGEBRAIC) = TEMP_ALGEBRAIC(SET_ALGEBRAIC);
end
end
end
function resid = residualSN_1(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES)
CONSTANTS(:,21) = algebraicCandidate(1);
CONSTANTS(:,22) = algebraicCandidate(2);
CONSTANTS(:,23) = algebraicCandidate(3);
resid(1) = CONSTANTS(:,23) - ( CONSTANTS(:,21).*CONSTANTS(:,22))./CONSTANTS(:,16);
resid(2) = CONSTANTS(:,21) - (CONSTANTS(:,3) - CONSTANTS(:,23));
resid(3) = CONSTANTS(:,22) - (CONSTANTS(:,4) - CONSTANTS(:,23));
end
% Functions required for solving differential algebraic equation
function [CONSTANTS, STATES, ALGEBRAIC] = rootfind_2(VOI, CONSTANTS_IN, STATES_IN, ALGEBRAIC_IN)
ALGEBRAIC = ALGEBRAIC_IN;
CONSTANTS = CONSTANTS_IN;
STATES = STATES_IN;
global initialGuess_2;
if (length(initialGuess_2) ~= 2), initialGuess_2 = [0.1,0.1];, end
options = optimset('Display', 'off', 'TolX', 1E-6);
if length(VOI) == 1
residualfn = @(algebraicCandidate)residualSN_2(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES);
soln = fsolve(residualfn, initialGuess_2, options);
initialGuess_2 = soln;
CONSTANTS(:,26) = soln(1);
CONSTANTS(:,27) = soln(2);
else
SET_CONSTANTS(:,26) = logical(1);
SET_CONSTANTS(:,27) = logical(1);
for i=1:length(VOI)
residualfn = @(algebraicCandidate)residualSN_2(algebraicCandidate, ALGEBRAIC(i,:), VOI(i), CONSTANTS, STATES(i,:));
soln = fsolve(residualfn, initialGuess_2, options);
initialGuess_2 = soln;
TEMP_CONSTANTS(:,26) = soln(1);
TEMP_CONSTANTS(:,27) = soln(2);
ALGEBRAIC(i,SET_ALGEBRAIC) = TEMP_ALGEBRAIC(SET_ALGEBRAIC);
end
end
end
function resid = residualSN_2(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES)
CONSTANTS(:,26) = algebraicCandidate(1);
CONSTANTS(:,27) = algebraicCandidate(2);
resid(1) = CONSTANTS(:,27) - ( CONSTANTS(:,26).*CONSTANTS(:,19))./CONSTANTS(:,15);
resid(2) = CONSTANTS(:,26) - (CONSTANTS(:,5) - CONSTANTS(:,27));
end
% Pad out or shorten strings to a set length
function strout = strpad(strin)
req_length = 160;
insize = size(strin,2);
if insize > req_length
strout = strin(1:req_length);
else
strout = [strin, blanks(req_length - insize)];
end
end
