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 =29; end % There are a total of 7 entries in each of the rate and state variable arrays. % There are a total of 20 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('C_m in component environment (fF)'); LEGEND_STATES(:,1) = strpad('q_K_o in component environment (fmol)'); LEGEND_STATES(:,2) = strpad('q_K_i in component environment (fmol)'); LEGEND_STATES(:,3) = strpad('q_r0s0_TO in component environment (fmol)'); LEGEND_STATES(:,4) = strpad('q_r1s0_TO in component environment (fmol)'); LEGEND_STATES(:,5) = strpad('q_r0s1_TO in component environment (fmol)'); LEGEND_STATES(:,6) = strpad('q_r1s1_TO in component environment (fmol)'); LEGEND_STATES(:,7) = strpad('q_mem in component environment (fC)'); LEGEND_ALGEBRAIC(:,1) = strpad('Vmem in component environment (volt)'); LEGEND_CONSTANTS(:,2) = strpad('R in component environment (J_per_K_per_mol)'); LEGEND_CONSTANTS(:,3) = strpad('T in component environment (kelvin)'); LEGEND_CONSTANTS(:,4) = strpad('F in component environment (C_per_mol)'); LEGEND_ALGEBRAIC(:,21) = strpad('v_TO in component TO (fmol_per_sec)'); LEGEND_ALGEBRAIC(:,27) = strpad('I_mem_TO in component TO (fA)'); LEGEND_CONSTANTS(:,5) = strpad('kappa_TO in component TO_parameters (fmol_per_sec)'); LEGEND_CONSTANTS(:,6) = strpad('kappa_gTO_1 in component TO_parameters (fmol_per_sec)'); LEGEND_CONSTANTS(:,7) = strpad('kappa_gTO_2 in component TO_parameters (fmol_per_sec)'); LEGEND_CONSTANTS(:,8) = strpad('kappa_gTO_3 in component TO_parameters (fmol_per_sec)'); LEGEND_CONSTANTS(:,9) = strpad('kappa_gTO_4 in component TO_parameters (fmol_per_sec)'); LEGEND_CONSTANTS(:,10) = strpad('K_K_i in component TO_parameters (per_fmol)'); LEGEND_CONSTANTS(:,11) = strpad('K_K_o in component TO_parameters (per_fmol)'); LEGEND_CONSTANTS(:,12) = strpad('K_r0s0_TO in component TO_parameters (per_fmol)'); LEGEND_CONSTANTS(:,13) = strpad('K_r1s0_TO in component TO_parameters (per_fmol)'); LEGEND_CONSTANTS(:,14) = strpad('K_r0s1_TO in component TO_parameters (per_fmol)'); LEGEND_CONSTANTS(:,15) = strpad('K_r1s1_TO in component TO_parameters (per_fmol)'); LEGEND_CONSTANTS(:,16) = strpad('zK in component TO_parameters (dimensionless)'); LEGEND_CONSTANTS(:,17) = strpad('z_rTO_f in component TO_parameters (dimensionless)'); LEGEND_CONSTANTS(:,18) = strpad('z_sTO_f in component TO_parameters (dimensionless)'); LEGEND_CONSTANTS(:,19) = strpad('z_rTO_r in component TO_parameters (dimensionless)'); LEGEND_CONSTANTS(:,20) = strpad('z_sTO_r in component TO_parameters (dimensionless)'); LEGEND_ALGEBRAIC(:,2) = strpad('u_K_i in component TO (J_per_mol)'); LEGEND_ALGEBRAIC(:,3) = strpad('u_K_o in component TO (J_per_mol)'); LEGEND_ALGEBRAIC(:,4) = strpad('V_mem in component TO (J_per_C)'); LEGEND_ALGEBRAIC(:,5) = strpad('Am_TO in component TO (J_per_mol)'); LEGEND_ALGEBRAIC(:,19) = strpad('Af_TO in component TO (J_per_mol)'); LEGEND_ALGEBRAIC(:,20) = strpad('Ar_TO in component TO (J_per_mol)'); LEGEND_ALGEBRAIC(:,17) = strpad('v_r0s0_TO in component TO (fmol_per_sec)'); LEGEND_ALGEBRAIC(:,28) = strpad('v_r1s0_TO in component TO (fmol_per_sec)'); LEGEND_ALGEBRAIC(:,26) = strpad('v_r0s1_TO in component TO (fmol_per_sec)'); LEGEND_ALGEBRAIC(:,29) = strpad('v_r1s1_TO in component TO (fmol_per_sec)'); LEGEND_ALGEBRAIC(:,12) = strpad('v_gTO_1 in component TO (fmol_per_sec)'); LEGEND_ALGEBRAIC(:,16) = strpad('v_gTO_3 in component TO (fmol_per_sec)'); LEGEND_ALGEBRAIC(:,24) = strpad('v_gTO_2 in component TO (fmol_per_sec)'); LEGEND_ALGEBRAIC(:,25) = strpad('v_gTO_4 in component TO (fmol_per_sec)'); LEGEND_ALGEBRAIC(:,6) = strpad('mu_r0s0_TO in component TO (J_per_mol)'); LEGEND_ALGEBRAIC(:,9) = strpad('mu_r1s0_TO in component TO (J_per_mol)'); LEGEND_ALGEBRAIC(:,13) = strpad('mu_r0s1_TO in component TO (J_per_mol)'); LEGEND_ALGEBRAIC(:,18) = strpad('mu_r1s1_TO in component TO (J_per_mol)'); LEGEND_ALGEBRAIC(:,7) = strpad('Af_gTO_1 in component TO (J_per_mol)'); LEGEND_ALGEBRAIC(:,10) = strpad('Ar_gTO_1 in component TO (J_per_mol)'); LEGEND_ALGEBRAIC(:,8) = strpad('Af_gTO_3 in component TO (J_per_mol)'); LEGEND_ALGEBRAIC(:,14) = strpad('Ar_gTO_3 in component TO (J_per_mol)'); LEGEND_ALGEBRAIC(:,15) = strpad('Af_gTO_2 in component TO (J_per_mol)'); LEGEND_ALGEBRAIC(:,22) = strpad('Ar_gTO_2 in component TO (J_per_mol)'); LEGEND_ALGEBRAIC(:,11) = strpad('Af_gTO_4 in component TO (J_per_mol)'); LEGEND_ALGEBRAIC(:,23) = strpad('Ar_gTO_4 in component TO (J_per_mol)'); LEGEND_RATES(:,2) = strpad('d/dt q_K_i in component environment (fmol)'); LEGEND_RATES(:,1) = strpad('d/dt q_K_o in component environment (fmol)'); LEGEND_RATES(:,7) = strpad('d/dt q_mem in component environment (fC)'); LEGEND_RATES(:,3) = strpad('d/dt q_r0s0_TO in component environment (fmol)'); LEGEND_RATES(:,4) = strpad('d/dt q_r1s0_TO in component environment (fmol)'); LEGEND_RATES(:,5) = strpad('d/dt q_r0s1_TO in component environment (fmol)'); LEGEND_RATES(:,6) = strpad('d/dt q_r1s1_TO in component environment (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) = 1.0e6; STATES(:,1) = 0.116325; STATES(:,2) = 3.65002; STATES(:,3) = 3.1966124E-07; STATES(:,4) = 3.1966124E-07; STATES(:,5) = 3.1966124E-07; STATES(:,6) = 3.1966124E-07; STATES(:,7) = -8.5e4; CONSTANTS(:,2) = 8.31; CONSTANTS(:,3) = 310; CONSTANTS(:,4) = 96500; CONSTANTS(:,5) = 1.91513; CONSTANTS(:,6) = 10.0063; CONSTANTS(:,7) = 0.053573; CONSTANTS(:,8) = 0.0622138; CONSTANTS(:,9) = 0.0155957; CONSTANTS(:,10) = 0.0402291; CONSTANTS(:,11) = 0.267055; CONSTANTS(:,12) = 0.00553253; CONSTANTS(:,13) = 0.0220702; CONSTANTS(:,14) = 1.03336; CONSTANTS(:,15) = 4.12222; CONSTANTS(:,16) = 1; CONSTANTS(:,17) = 2.28623234372134; CONSTANTS(:,18) = -1.51477720975217; CONSTANTS(:,19) = -0.131848324558065; CONSTANTS(:,20) = 1.75042355789096; 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(:,4) = STATES(:,7)./CONSTANTS(:,1); ALGEBRAIC(:,6) = CONSTANTS(:,2).*CONSTANTS(:,3).*log( CONSTANTS(:,12).*STATES(:,3)); ALGEBRAIC(:,7) = ALGEBRAIC(:,6)+ CONSTANTS(:,17).*CONSTANTS(:,4).*ALGEBRAIC(:,4); ALGEBRAIC(:,9) = CONSTANTS(:,2).*CONSTANTS(:,3).*log( CONSTANTS(:,13).*STATES(:,4)); ALGEBRAIC(:,10) = ALGEBRAIC(:,9)+ CONSTANTS(:,19).*CONSTANTS(:,4).*ALGEBRAIC(:,4); ALGEBRAIC(:,12) = CONSTANTS(:,6).*(exp(ALGEBRAIC(:,7)./( CONSTANTS(:,2).*CONSTANTS(:,3))) - exp(ALGEBRAIC(:,10)./( CONSTANTS(:,2).*CONSTANTS(:,3)))); ALGEBRAIC(:,8) = ALGEBRAIC(:,6)+ CONSTANTS(:,18).*CONSTANTS(:,4).*ALGEBRAIC(:,4); ALGEBRAIC(:,13) = CONSTANTS(:,2).*CONSTANTS(:,3).*log( CONSTANTS(:,14).*STATES(:,5)); ALGEBRAIC(:,14) = ALGEBRAIC(:,13)+ CONSTANTS(:,20).*CONSTANTS(:,4).*ALGEBRAIC(:,4); ALGEBRAIC(:,16) = CONSTANTS(:,8).*(exp(ALGEBRAIC(:,8)./( CONSTANTS(:,2).*CONSTANTS(:,3))) - exp(ALGEBRAIC(:,14)./( CONSTANTS(:,2).*CONSTANTS(:,3)))); ALGEBRAIC(:,17) = - ALGEBRAIC(:,12)+ALGEBRAIC(:,16); RATES(:,3) = ALGEBRAIC(:,17); ALGEBRAIC(:,5) = CONSTANTS(:,4).*ALGEBRAIC(:,4); ALGEBRAIC(:,2) = CONSTANTS(:,2).*CONSTANTS(:,3).*log( CONSTANTS(:,10).*STATES(:,2)); ALGEBRAIC(:,18) = CONSTANTS(:,2).*CONSTANTS(:,3).*log( CONSTANTS(:,15).*STATES(:,6)); ALGEBRAIC(:,19) = ALGEBRAIC(:,18)+ALGEBRAIC(:,2)+ALGEBRAIC(:,5); ALGEBRAIC(:,3) = CONSTANTS(:,2).*CONSTANTS(:,3).*log( CONSTANTS(:,11).*STATES(:,1)); ALGEBRAIC(:,20) = ALGEBRAIC(:,18)+ALGEBRAIC(:,3); ALGEBRAIC(:,21) = piecewise({ALGEBRAIC(:,5)==0.00000, 1.00000.*CONSTANTS(:,5).*(exp(ALGEBRAIC(:,19)./( CONSTANTS(:,2).*CONSTANTS(:,3))) - exp(ALGEBRAIC(:,20)./( CONSTANTS(:,2).*CONSTANTS(:,3)))) }, ((( 1.00000.*CONSTANTS(:,5).*ALGEBRAIC(:,5))./( CONSTANTS(:,2).*CONSTANTS(:,3)))./(exp(ALGEBRAIC(:,5)./( CONSTANTS(:,2).*CONSTANTS(:,3))) - 1.00000)).*(exp(ALGEBRAIC(:,19)./( CONSTANTS(:,2).*CONSTANTS(:,3))) - exp(ALGEBRAIC(:,20)./( CONSTANTS(:,2).*CONSTANTS(:,3))))); RATES(:,2) = - ALGEBRAIC(:,21); RATES(:,1) = ALGEBRAIC(:,21); ALGEBRAIC(:,15) = ALGEBRAIC(:,13)+ CONSTANTS(:,17).*CONSTANTS(:,4).*ALGEBRAIC(:,4); ALGEBRAIC(:,22) = ALGEBRAIC(:,18)+ CONSTANTS(:,19).*CONSTANTS(:,4).*ALGEBRAIC(:,4); ALGEBRAIC(:,24) = CONSTANTS(:,7).*(exp(ALGEBRAIC(:,15)./( CONSTANTS(:,2).*CONSTANTS(:,3))) - exp(ALGEBRAIC(:,22)./( CONSTANTS(:,2).*CONSTANTS(:,3)))); ALGEBRAIC(:,26) = - ALGEBRAIC(:,24)+ALGEBRAIC(:,16); RATES(:,5) = ALGEBRAIC(:,26); ALGEBRAIC(:,11) = ALGEBRAIC(:,9)+ CONSTANTS(:,18).*CONSTANTS(:,4).*ALGEBRAIC(:,4); ALGEBRAIC(:,23) = ALGEBRAIC(:,18)+ CONSTANTS(:,20).*CONSTANTS(:,4).*ALGEBRAIC(:,4); ALGEBRAIC(:,25) = CONSTANTS(:,9).*(exp(ALGEBRAIC(:,11)./( CONSTANTS(:,2).*CONSTANTS(:,3))) - exp(ALGEBRAIC(:,23)./( CONSTANTS(:,2).*CONSTANTS(:,3)))); ALGEBRAIC(:,27) = CONSTANTS(:,4).*( - CONSTANTS(:,16).*ALGEBRAIC(:,21)+ (ALGEBRAIC(:,12)+ALGEBRAIC(:,24)).*(CONSTANTS(:,19) - CONSTANTS(:,17))+ (ALGEBRAIC(:,16)+ALGEBRAIC(:,25)).*(CONSTANTS(:,20) - CONSTANTS(:,18))); RATES(:,7) = ALGEBRAIC(:,27); ALGEBRAIC(:,28) = ALGEBRAIC(:,12) - ALGEBRAIC(:,25); RATES(:,4) = ALGEBRAIC(:,28); ALGEBRAIC(:,29) = ALGEBRAIC(:,24)+ALGEBRAIC(:,25); RATES(:,6) = ALGEBRAIC(:,29); 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(:,4) = STATES(:,7)./CONSTANTS(:,1); ALGEBRAIC(:,6) = CONSTANTS(:,2).*CONSTANTS(:,3).*log( CONSTANTS(:,12).*STATES(:,3)); ALGEBRAIC(:,7) = ALGEBRAIC(:,6)+ CONSTANTS(:,17).*CONSTANTS(:,4).*ALGEBRAIC(:,4); ALGEBRAIC(:,9) = CONSTANTS(:,2).*CONSTANTS(:,3).*log( CONSTANTS(:,13).*STATES(:,4)); ALGEBRAIC(:,10) = ALGEBRAIC(:,9)+ CONSTANTS(:,19).*CONSTANTS(:,4).*ALGEBRAIC(:,4); ALGEBRAIC(:,12) = CONSTANTS(:,6).*(exp(ALGEBRAIC(:,7)./( CONSTANTS(:,2).*CONSTANTS(:,3))) - exp(ALGEBRAIC(:,10)./( CONSTANTS(:,2).*CONSTANTS(:,3)))); ALGEBRAIC(:,8) = ALGEBRAIC(:,6)+ CONSTANTS(:,18).*CONSTANTS(:,4).*ALGEBRAIC(:,4); ALGEBRAIC(:,13) = CONSTANTS(:,2).*CONSTANTS(:,3).*log( CONSTANTS(:,14).*STATES(:,5)); ALGEBRAIC(:,14) = ALGEBRAIC(:,13)+ CONSTANTS(:,20).*CONSTANTS(:,4).*ALGEBRAIC(:,4); ALGEBRAIC(:,16) = CONSTANTS(:,8).*(exp(ALGEBRAIC(:,8)./( CONSTANTS(:,2).*CONSTANTS(:,3))) - exp(ALGEBRAIC(:,14)./( CONSTANTS(:,2).*CONSTANTS(:,3)))); ALGEBRAIC(:,17) = - ALGEBRAIC(:,12)+ALGEBRAIC(:,16); ALGEBRAIC(:,5) = CONSTANTS(:,4).*ALGEBRAIC(:,4); ALGEBRAIC(:,2) = CONSTANTS(:,2).*CONSTANTS(:,3).*log( CONSTANTS(:,10).*STATES(:,2)); ALGEBRAIC(:,18) = CONSTANTS(:,2).*CONSTANTS(:,3).*log( CONSTANTS(:,15).*STATES(:,6)); ALGEBRAIC(:,19) = ALGEBRAIC(:,18)+ALGEBRAIC(:,2)+ALGEBRAIC(:,5); ALGEBRAIC(:,3) = CONSTANTS(:,2).*CONSTANTS(:,3).*log( CONSTANTS(:,11).*STATES(:,1)); ALGEBRAIC(:,20) = ALGEBRAIC(:,18)+ALGEBRAIC(:,3); ALGEBRAIC(:,21) = piecewise({ALGEBRAIC(:,5)==0.00000, 1.00000.*CONSTANTS(:,5).*(exp(ALGEBRAIC(:,19)./( CONSTANTS(:,2).*CONSTANTS(:,3))) - exp(ALGEBRAIC(:,20)./( CONSTANTS(:,2).*CONSTANTS(:,3)))) }, ((( 1.00000.*CONSTANTS(:,5).*ALGEBRAIC(:,5))./( CONSTANTS(:,2).*CONSTANTS(:,3)))./(exp(ALGEBRAIC(:,5)./( CONSTANTS(:,2).*CONSTANTS(:,3))) - 1.00000)).*(exp(ALGEBRAIC(:,19)./( CONSTANTS(:,2).*CONSTANTS(:,3))) - exp(ALGEBRAIC(:,20)./( CONSTANTS(:,2).*CONSTANTS(:,3))))); ALGEBRAIC(:,15) = ALGEBRAIC(:,13)+ CONSTANTS(:,17).*CONSTANTS(:,4).*ALGEBRAIC(:,4); ALGEBRAIC(:,22) = ALGEBRAIC(:,18)+ CONSTANTS(:,19).*CONSTANTS(:,4).*ALGEBRAIC(:,4); ALGEBRAIC(:,24) = CONSTANTS(:,7).*(exp(ALGEBRAIC(:,15)./( CONSTANTS(:,2).*CONSTANTS(:,3))) - exp(ALGEBRAIC(:,22)./( CONSTANTS(:,2).*CONSTANTS(:,3)))); ALGEBRAIC(:,26) = - ALGEBRAIC(:,24)+ALGEBRAIC(:,16); ALGEBRAIC(:,11) = ALGEBRAIC(:,9)+ CONSTANTS(:,18).*CONSTANTS(:,4).*ALGEBRAIC(:,4); ALGEBRAIC(:,23) = ALGEBRAIC(:,18)+ CONSTANTS(:,20).*CONSTANTS(:,4).*ALGEBRAIC(:,4); ALGEBRAIC(:,25) = CONSTANTS(:,9).*(exp(ALGEBRAIC(:,11)./( CONSTANTS(:,2).*CONSTANTS(:,3))) - exp(ALGEBRAIC(:,23)./( CONSTANTS(:,2).*CONSTANTS(:,3)))); ALGEBRAIC(:,27) = CONSTANTS(:,4).*( - CONSTANTS(:,16).*ALGEBRAIC(:,21)+ (ALGEBRAIC(:,12)+ALGEBRAIC(:,24)).*(CONSTANTS(:,19) - CONSTANTS(:,17))+ (ALGEBRAIC(:,16)+ALGEBRAIC(:,25)).*(CONSTANTS(:,20) - CONSTANTS(:,18))); ALGEBRAIC(:,28) = ALGEBRAIC(:,12) - ALGEBRAIC(:,25); ALGEBRAIC(:,29) = ALGEBRAIC(:,24)+ALGEBRAIC(:,25); ALGEBRAIC(:,1) = STATES(:,7)./CONSTANTS(:,1); 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 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