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 =13; end % There are a total of 4 entries in each of the rate and state variable arrays. % There are a total of 14 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_ALGEBRAIC(:,5) = strpad('phi3_c1 in component phi (per_second)'); LEGEND_STATES(:,1) = strpad('h1 in component h1 (dimensionless)'); LEGEND_ALGEBRAIC(:,1) = strpad('phi1_c1 in component phi (second_order_rate)'); LEGEND_ALGEBRAIC(:,3) = strpad('phi2_c1 in component phi (per_second)'); LEGEND_CONSTANTS(:,1) = strpad('p in component model_parameters (micro_molar)'); LEGEND_ALGEBRAIC(:,2) = strpad('phi_1_c1 in component phi (per_second)'); LEGEND_ALGEBRAIC(:,9) = strpad('phi3_c2 in component phi (per_second)'); LEGEND_STATES(:,2) = strpad('h2 in component h2 (dimensionless)'); LEGEND_ALGEBRAIC(:,4) = strpad('phi1_c2 in component phi (second_order_rate)'); LEGEND_ALGEBRAIC(:,7) = strpad('phi2_c2 in component phi (per_second)'); LEGEND_ALGEBRAIC(:,6) = strpad('phi_1_c2 in component phi (per_second)'); LEGEND_CONSTANTS(:,2) = strpad('r2 in component model_parameters (second_order_rate)'); LEGEND_CONSTANTS(:,3) = strpad('R1 in component model_parameters (micro_molar)'); LEGEND_CONSTANTS(:,4) = strpad('k1 in component model_parameters (micro_molar_per_second)'); LEGEND_CONSTANTS(:,5) = strpad('R3 in component model_parameters (micro_molar)'); LEGEND_CONSTANTS(:,6) = strpad('k2 in component model_parameters (micro_molar_per_second)'); LEGEND_CONSTANTS(:,7) = strpad('r4 in component model_parameters (per_second)'); LEGEND_CONSTANTS(:,8) = strpad('k3 in component model_parameters (micro_molar_per_second)'); LEGEND_CONSTANTS(:,9) = strpad('R5 in component model_parameters (micro_molar)'); LEGEND_STATES(:,3) = strpad('c1 in component c1 (micro_molar)'); LEGEND_STATES(:,4) = strpad('c2 in component c2 (micro_molar)'); LEGEND_CONSTANTS(:,10) = strpad('Vp in component model_parameters (micro_molar_per_second)'); LEGEND_CONSTANTS(:,11) = strpad('Kp in component model_parameters (micro_molar)'); LEGEND_ALGEBRAIC(:,8) = strpad('j_pump_c1 in component j_pump (micro_molar_per_second)'); LEGEND_ALGEBRAIC(:,10) = strpad('j_pump_c2 in component j_pump (micro_molar_per_second)'); LEGEND_CONSTANTS(:,12) = strpad('kf in component model_parameters (micro_molar_per_second)'); LEGEND_ALGEBRAIC(:,11) = strpad('j_receptor_c1 in component j_receptor (micro_molar_per_second)'); LEGEND_ALGEBRAIC(:,12) = strpad('j_receptor_c2 in component j_receptor (micro_molar_per_second)'); LEGEND_ALGEBRAIC(:,13) = strpad('j_diffusion in component j_diffusion (micro_molar_per_second)'); LEGEND_CONSTANTS(:,13) = strpad('D in component model_parameters (per_second)'); LEGEND_CONSTANTS(:,14) = strpad('j_leak in component model_parameters (micro_molar_per_second)'); LEGEND_RATES(:,1) = strpad('d/dt h1 in component h1 (dimensionless)'); LEGEND_RATES(:,2) = strpad('d/dt h2 in component h2 (dimensionless)'); LEGEND_RATES(:,3) = strpad('d/dt c1 in component c1 (micro_molar)'); LEGEND_RATES(:,4) = strpad('d/dt c2 in component c2 (micro_molar)'); 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 = []; STATES(:,1) = 0.8; CONSTANTS(:,1) = 0.2778; STATES(:,2) = 0.1; CONSTANTS(:,2) = 100; CONSTANTS(:,3) = 6; CONSTANTS(:,4) = 44; CONSTANTS(:,5) = 50; CONSTANTS(:,6) = 26.5; CONSTANTS(:,7) = 20; CONSTANTS(:,8) = 1.6; CONSTANTS(:,9) = 1.6; STATES(:,3) = 0.3; STATES(:,4) = 0.1; CONSTANTS(:,10) = 1.2; CONSTANTS(:,11) = 0.18; CONSTANTS(:,12) = 28; CONSTANTS(:,13) = 0.01; CONSTANTS(:,14) = 0.2; 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(:,5) = CONSTANTS(:,8)./(CONSTANTS(:,9)+STATES(:,3)); ALGEBRAIC(:,1) = ( CONSTANTS(:,2).*STATES(:,3))./(CONSTANTS(:,3)+STATES(:,3)); ALGEBRAIC(:,3) = (CONSTANTS(:,6)+ CONSTANTS(:,7).*STATES(:,3))./(CONSTANTS(:,5)+STATES(:,3)); ALGEBRAIC(:,2) = CONSTANTS(:,4)./(CONSTANTS(:,5)+STATES(:,3)); RATES(:,1) = ALGEBRAIC(:,5).*(1.00000 - STATES(:,1)) - ( ALGEBRAIC(:,1).*ALGEBRAIC(:,3).*STATES(:,1).*CONSTANTS(:,1))./( ALGEBRAIC(:,1).*CONSTANTS(:,1)+ALGEBRAIC(:,2)); ALGEBRAIC(:,9) = CONSTANTS(:,8)./(CONSTANTS(:,9)+STATES(:,4)); ALGEBRAIC(:,4) = ( CONSTANTS(:,2).*STATES(:,4))./(CONSTANTS(:,3)+STATES(:,4)); ALGEBRAIC(:,7) = (CONSTANTS(:,6)+ CONSTANTS(:,7).*STATES(:,4))./(CONSTANTS(:,5)+STATES(:,4)); ALGEBRAIC(:,6) = CONSTANTS(:,4)./(CONSTANTS(:,5)+STATES(:,4)); RATES(:,2) = ALGEBRAIC(:,9).*(1.00000 - STATES(:,2)) - ( ALGEBRAIC(:,4).*ALGEBRAIC(:,7).*STATES(:,2).*CONSTANTS(:,1))./( ALGEBRAIC(:,4).*CONSTANTS(:,1)+ALGEBRAIC(:,6)); ALGEBRAIC(:,8) = ( CONSTANTS(:,10).*power(STATES(:,3), 2.00000))./(power(CONSTANTS(:,11), 2.00000)+power(STATES(:,3), 2.00000)); ALGEBRAIC(:,11) = CONSTANTS(:,12).*power(( CONSTANTS(:,1).*STATES(:,1).*ALGEBRAIC(:,1))./( ALGEBRAIC(:,1).*CONSTANTS(:,1)+ALGEBRAIC(:,2)), 4.00000); ALGEBRAIC(:,13) = CONSTANTS(:,13).*(STATES(:,4) - STATES(:,3)); RATES(:,3) = (ALGEBRAIC(:,11) - ALGEBRAIC(:,8))+CONSTANTS(:,14)+ALGEBRAIC(:,13); ALGEBRAIC(:,10) = ( CONSTANTS(:,10).*power(STATES(:,4), 2.00000))./(power(CONSTANTS(:,11), 2.00000)+power(STATES(:,4), 2.00000)); ALGEBRAIC(:,12) = CONSTANTS(:,12).*power(( CONSTANTS(:,1).*STATES(:,2).*ALGEBRAIC(:,4))./( ALGEBRAIC(:,4).*CONSTANTS(:,1)+ALGEBRAIC(:,6)), 4.00000); RATES(:,4) = (ALGEBRAIC(:,12) - ALGEBRAIC(:,10))+CONSTANTS(:,14)+ALGEBRAIC(:,13); 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(:,5) = CONSTANTS(:,8)./(CONSTANTS(:,9)+STATES(:,3)); ALGEBRAIC(:,1) = ( CONSTANTS(:,2).*STATES(:,3))./(CONSTANTS(:,3)+STATES(:,3)); ALGEBRAIC(:,3) = (CONSTANTS(:,6)+ CONSTANTS(:,7).*STATES(:,3))./(CONSTANTS(:,5)+STATES(:,3)); ALGEBRAIC(:,2) = CONSTANTS(:,4)./(CONSTANTS(:,5)+STATES(:,3)); ALGEBRAIC(:,9) = CONSTANTS(:,8)./(CONSTANTS(:,9)+STATES(:,4)); ALGEBRAIC(:,4) = ( CONSTANTS(:,2).*STATES(:,4))./(CONSTANTS(:,3)+STATES(:,4)); ALGEBRAIC(:,7) = (CONSTANTS(:,6)+ CONSTANTS(:,7).*STATES(:,4))./(CONSTANTS(:,5)+STATES(:,4)); ALGEBRAIC(:,6) = CONSTANTS(:,4)./(CONSTANTS(:,5)+STATES(:,4)); ALGEBRAIC(:,8) = ( CONSTANTS(:,10).*power(STATES(:,3), 2.00000))./(power(CONSTANTS(:,11), 2.00000)+power(STATES(:,3), 2.00000)); ALGEBRAIC(:,11) = CONSTANTS(:,12).*power(( CONSTANTS(:,1).*STATES(:,1).*ALGEBRAIC(:,1))./( ALGEBRAIC(:,1).*CONSTANTS(:,1)+ALGEBRAIC(:,2)), 4.00000); ALGEBRAIC(:,13) = CONSTANTS(:,13).*(STATES(:,4) - STATES(:,3)); ALGEBRAIC(:,10) = ( CONSTANTS(:,10).*power(STATES(:,4), 2.00000))./(power(CONSTANTS(:,11), 2.00000)+power(STATES(:,4), 2.00000)); ALGEBRAIC(:,12) = CONSTANTS(:,12).*power(( CONSTANTS(:,1).*STATES(:,2).*ALGEBRAIC(:,4))./( ALGEBRAIC(:,4).*CONSTANTS(:,1)+ALGEBRAIC(:,6)), 4.00000); 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