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 =19; end % There are a total of 7 entries in each of the rate and state variable arrays. % There are a total of 42 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 (s)'); LEGEND_STATES(:,1) = strpad('F6P in component F6P (mM)'); LEGEND_ALGEBRAIC(:,1) = strpad('V_hk in component V_hk (mM_per_s)'); LEGEND_ALGEBRAIC(:,13) = strpad('V_pfk in component V_pfk (mM_per_s)'); LEGEND_ALGEBRAIC(:,19) = strpad('V_pfk2 in component V_pfk2 (mM_per_s)'); LEGEND_STATES(:,2) = strpad('F26P in component F26P (mM)'); LEGEND_STATES(:,3) = strpad('GAP in component GAP (mM)'); LEGEND_ALGEBRAIC(:,11) = strpad('V_pk in component V_pk (mM_per_s)'); LEGEND_STATES(:,4) = strpad('PYR in component PYR (mM)'); LEGEND_ALGEBRAIC(:,2) = strpad('V_ldh in component V_ldh (mM_per_s)'); LEGEND_ALGEBRAIC(:,6) = strpad('V_op in component V_op (mM_per_s)'); LEGEND_STATES(:,5) = strpad('LAC in component LAC (mM)'); LEGEND_ALGEBRAIC(:,17) = strpad('V_lac in component V_lac (mM_per_s)'); LEGEND_STATES(:,6) = strpad('ATP in component ATP (mM)'); LEGEND_ALGEBRAIC(:,16) = strpad('V_ATPase in component V_ATPase (mM_per_s)'); LEGEND_ALGEBRAIC(:,7) = strpad('V_ck in component V_ck (mM_per_s)'); LEGEND_ALGEBRAIC(:,8) = strpad('dAMP_dATP in component dAMP_dATP (dimensionless)'); LEGEND_STATES(:,7) = strpad('PCr in component PCr (mM)'); LEGEND_CONSTANTS(:,1) = strpad('Vmax_hk in component V_hk (mM_per_s)'); LEGEND_CONSTANTS(:,2) = strpad('Km_ATP_hk in component V_hk (mM)'); LEGEND_CONSTANTS(:,3) = strpad('KI_F6P in component V_hk (mM)'); LEGEND_CONSTANTS(:,4) = strpad('Vmax_pfk in component V_pfk (mM_per_s)'); LEGEND_CONSTANTS(:,5) = strpad('Km_ATP_pfk in component V_pfk (mM)'); LEGEND_CONSTANTS(:,6) = strpad('Km_F6P_pfk in component V_pfk (mM)'); LEGEND_CONSTANTS(:,7) = strpad('Km_F26P_pfk in component V_pfk (mM)'); LEGEND_ALGEBRAIC(:,12) = strpad('AMP_act in component AMP_act (dimensionless)'); LEGEND_ALGEBRAIC(:,10) = strpad('ATP_inh in component ATP_inh (dimensionless)'); LEGEND_CONSTANTS(:,8) = strpad('Vmaxf_pfk2 in component V_pfk2 (mM_per_s)'); LEGEND_CONSTANTS(:,9) = strpad('Vmaxr_pfk2 in component V_pfk2 (mM_per_s)'); LEGEND_CONSTANTS(:,10) = strpad('Km_ATP_pfk2 in component V_pfk2 (mM)'); LEGEND_CONSTANTS(:,11) = strpad('Km_F6P_pfk2 in component V_pfk2 (mM)'); LEGEND_CONSTANTS(:,12) = strpad('Km_F26P_pfk2 in component V_pfk2 (mM)'); LEGEND_ALGEBRAIC(:,18) = strpad('AMP_pfk2 in component AMP_pfk2 (dimensionless)'); LEGEND_CONSTANTS(:,13) = strpad('Vmax_pk in component V_pk (mM_per_s)'); LEGEND_CONSTANTS(:,14) = strpad('Km_ADP_pk in component V_pk (mM)'); LEGEND_CONSTANTS(:,15) = strpad('Km_GAP_pk in component V_pk (mM)'); LEGEND_ALGEBRAIC(:,5) = strpad('ADP in component ADP (mM)'); LEGEND_CONSTANTS(:,16) = strpad('Vmax_op in component V_op (mM_per_s)'); LEGEND_CONSTANTS(:,17) = strpad('Km_ADP_op in component V_op (mM)'); LEGEND_CONSTANTS(:,18) = strpad('Km_PYR_op in component V_op (mM)'); LEGEND_CONSTANTS(:,19) = strpad('kf_ldh in component V_ldh (per_s)'); LEGEND_CONSTANTS(:,20) = strpad('kr_ldh in component V_ldh (per_s)'); LEGEND_CONSTANTS(:,21) = strpad('kf_ck in component V_ck (per_mM_s)'); LEGEND_CONSTANTS(:,22) = strpad('kr_ck in component V_ck (per_mM_s)'); LEGEND_ALGEBRAIC(:,3) = strpad('Cr in component Cr (mM)'); LEGEND_CONSTANTS(:,23) = strpad('PCrtot in component Cr (mM)'); LEGEND_CONSTANTS(:,24) = strpad('Vmax_ATPase in component V_ATPase (mM_per_s)'); LEGEND_CONSTANTS(:,25) = strpad('Km_ATP in component V_ATPase (mM)'); LEGEND_ALGEBRAIC(:,15) = strpad('v_stim in component v_stim (dimensionless)'); LEGEND_CONSTANTS(:,26) = strpad('Vlac_0 in component V_lac (mM_per_s)'); LEGEND_CONSTANTS(:,27) = strpad('K_LAC_eff in component V_lac (per_s)'); LEGEND_CONSTANTS(:,28) = strpad('K_LAC in component V_lac (dimensionless)'); LEGEND_ALGEBRAIC(:,4) = strpad('u in component ADP (dimensionless)'); LEGEND_CONSTANTS(:,29) = strpad('ANP in component model_parameters (mM)'); LEGEND_CONSTANTS(:,30) = strpad('Q_adk in component model_parameters (dimensionless)'); LEGEND_ALGEBRAIC(:,9) = strpad('AMP in component AMP (mM)'); LEGEND_CONSTANTS(:,31) = strpad('nATP in component ATP_inh (dimensionless)'); LEGEND_CONSTANTS(:,32) = strpad('KI_ATP in component ATP_inh (mM)'); LEGEND_CONSTANTS(:,33) = strpad('nAMP in component AMP_act (dimensionless)'); LEGEND_CONSTANTS(:,34) = strpad('Ka_AMP in component AMP_act (mM)'); LEGEND_ALGEBRAIC(:,14) = strpad('unitpulseSB in component v_stim (dimensionless)'); LEGEND_CONSTANTS(:,35) = strpad('stim in component v_stim (dimensionless)'); LEGEND_CONSTANTS(:,36) = strpad('to in component v_stim (s)'); LEGEND_CONSTANTS(:,37) = strpad('tend in component v_stim (s)'); LEGEND_CONSTANTS(:,38) = strpad('v1_n in component v_stim (dimensionless)'); LEGEND_CONSTANTS(:,39) = strpad('v2_n in component v_stim (dimensionless)'); LEGEND_CONSTANTS(:,40) = strpad('t_n_stim in component v_stim (s)'); LEGEND_CONSTANTS(:,41) = strpad('Kamp_pfk2 in component AMP_pfk2 (mM)'); LEGEND_CONSTANTS(:,42) = strpad('nh_amp in component AMP_pfk2 (dimensionless)'); LEGEND_RATES(:,1) = strpad('d/dt F6P in component F6P (mM)'); LEGEND_RATES(:,2) = strpad('d/dt F26P in component F26P (mM)'); LEGEND_RATES(:,3) = strpad('d/dt GAP in component GAP (mM)'); LEGEND_RATES(:,4) = strpad('d/dt PYR in component PYR (mM)'); LEGEND_RATES(:,5) = strpad('d/dt LAC in component LAC (mM)'); LEGEND_RATES(:,6) = strpad('d/dt ATP in component ATP (mM)'); LEGEND_RATES(:,7) = strpad('d/dt PCr in component PCr (mM)'); 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) = 0.2; STATES(:,2) = 0.001; STATES(:,3) = 0.0405; STATES(:,4) = 0.1; STATES(:,5) = 0.5; STATES(:,6) = 2.402; STATES(:,7) = 18.14; CONSTANTS(:,1) = 2.5; CONSTANTS(:,2) = 0.5; CONSTANTS(:,3) = 0.068; CONSTANTS(:,4) = 3.85; CONSTANTS(:,5) = 0.05; CONSTANTS(:,6) = 0.18; CONSTANTS(:,7) = 0.01; CONSTANTS(:,8) = 0; CONSTANTS(:,9) = 0; CONSTANTS(:,10) = 0.05; CONSTANTS(:,11) = 0.01; CONSTANTS(:,12) = 0.0001; CONSTANTS(:,13) = 5.0; CONSTANTS(:,14) = 0.005; CONSTANTS(:,15) = 0.4; CONSTANTS(:,16) = 1.0; CONSTANTS(:,17) = 0.005; CONSTANTS(:,18) = 0.5; CONSTANTS(:,19) = 0; CONSTANTS(:,20) = 0; CONSTANTS(:,21) = 0; CONSTANTS(:,22) = 0; CONSTANTS(:,23) = 20.0; CONSTANTS(:,24) = 0.9355; CONSTANTS(:,25) = 0.5; CONSTANTS(:,26) = 0.355; CONSTANTS(:,27) = 0.71; CONSTANTS(:,28) = 0.641; CONSTANTS(:,29) = 2.51; CONSTANTS(:,30) = 0.92; CONSTANTS(:,31) = 0.4; CONSTANTS(:,32) = 1.0; CONSTANTS(:,33) = 0.5; CONSTANTS(:,34) = 0.05; CONSTANTS(:,35) = 1; CONSTANTS(:,36) = 50; CONSTANTS(:,37) = 200; CONSTANTS(:,38) = 0.5; CONSTANTS(:,39) = 0.0; CONSTANTS(:,40) = 2; CONSTANTS(:,41) = 0.005; CONSTANTS(:,42) = 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(:,4) = power(CONSTANTS(:,30), 2.00000)+ 4.00000.*CONSTANTS(:,30).*(CONSTANTS(:,29)./STATES(:,6) - 1.00000); ALGEBRAIC(:,5) = (STATES(:,6)./2.00000).*( - CONSTANTS(:,30)+power(ALGEBRAIC(:,4), 1.0 ./ 2)); ALGEBRAIC(:,3) = CONSTANTS(:,23) - STATES(:,7); ALGEBRAIC(:,7) = CONSTANTS(:,21).*STATES(:,7).*ALGEBRAIC(:,5) - CONSTANTS(:,22).*ALGEBRAIC(:,3).*STATES(:,6); RATES(:,7) = - ALGEBRAIC(:,7); ALGEBRAIC(:,10) = power((1.00000+ CONSTANTS(:,31).*(STATES(:,6)./CONSTANTS(:,32)))./(1.00000+STATES(:,6)./CONSTANTS(:,32)), 4.00000); ALGEBRAIC(:,11) = CONSTANTS(:,13).*(STATES(:,3)./(STATES(:,3)+CONSTANTS(:,15))).*(ALGEBRAIC(:,5)./(ALGEBRAIC(:,5)+CONSTANTS(:,14))).*ALGEBRAIC(:,10); ALGEBRAIC(:,2) = CONSTANTS(:,19).*STATES(:,4) - CONSTANTS(:,20).*STATES(:,5); ALGEBRAIC(:,6) = CONSTANTS(:,16).*(STATES(:,4)./(STATES(:,4)+CONSTANTS(:,18))).*(ALGEBRAIC(:,5)./(ALGEBRAIC(:,5)+CONSTANTS(:,17))).*(1.00000./(1.00000+ 0.100000.*24.0000)); RATES(:,4) = ALGEBRAIC(:,11) - (ALGEBRAIC(:,6)+ALGEBRAIC(:,2)); ALGEBRAIC(:,9) = CONSTANTS(:,29) - (STATES(:,6)+ALGEBRAIC(:,5)); ALGEBRAIC(:,12) = power((1.00000+ALGEBRAIC(:,9)./CONSTANTS(:,34))./(1.00000+ CONSTANTS(:,33).*(ALGEBRAIC(:,9)./CONSTANTS(:,34))), 4.00000); ALGEBRAIC(:,13) = CONSTANTS(:,4).*(STATES(:,1)./(STATES(:,1)+CONSTANTS(:,6))).*(STATES(:,6)./(STATES(:,6)+CONSTANTS(:,5))).*(STATES(:,2)./(STATES(:,2)+CONSTANTS(:,7))).*ALGEBRAIC(:,10).*ALGEBRAIC(:,12); RATES(:,3) = 2.00000.*ALGEBRAIC(:,13) - ALGEBRAIC(:,11); ALGEBRAIC(:,14) = piecewise({VOI>=CONSTANTS(:,36)&VOI<=CONSTANTS(:,36)+CONSTANTS(:,37), 1.00000 }, 0.00000); ALGEBRAIC(:,15) = CONSTANTS(:,35).*(CONSTANTS(:,38)+ CONSTANTS(:,39).*((VOI - CONSTANTS(:,36))./CONSTANTS(:,40)).*exp( - ( (VOI - CONSTANTS(:,36)).*(ALGEBRAIC(:,14)./CONSTANTS(:,40))))).*ALGEBRAIC(:,14); ALGEBRAIC(:,17) = CONSTANTS(:,26).*(1.00000+ ALGEBRAIC(:,15).*CONSTANTS(:,28)) - CONSTANTS(:,27).*STATES(:,5); RATES(:,5) = 2.25000.*ALGEBRAIC(:,2)+ALGEBRAIC(:,17); ALGEBRAIC(:,1) = CONSTANTS(:,1).*(STATES(:,6)./(STATES(:,6)+CONSTANTS(:,2))).*power(1.00000+power(STATES(:,1)./CONSTANTS(:,3), 4.00000), -1.00000); ALGEBRAIC(:,18) = power(ALGEBRAIC(:,9)./CONSTANTS(:,41), CONSTANTS(:,42))./(1.00000+power(ALGEBRAIC(:,9)./CONSTANTS(:,41), CONSTANTS(:,42))); ALGEBRAIC(:,19) = CONSTANTS(:,8).*(STATES(:,6)./(STATES(:,6)+CONSTANTS(:,10))).*(STATES(:,1)./(STATES(:,1)+CONSTANTS(:,11))).*ALGEBRAIC(:,18) - CONSTANTS(:,9).*(STATES(:,2)./(STATES(:,2)+CONSTANTS(:,12))); RATES(:,1) = ALGEBRAIC(:,1) - (ALGEBRAIC(:,13) - ALGEBRAIC(:,19)); RATES(:,2) = ALGEBRAIC(:,19); ALGEBRAIC(:,16) = CONSTANTS(:,24).*(STATES(:,6)./(STATES(:,6)+CONSTANTS(:,25))).*(1.00000+ALGEBRAIC(:,15)); ALGEBRAIC(:,8) = - 1.00000+CONSTANTS(:,30)./2.00000+ - ( 0.500000.*power(ALGEBRAIC(:,4), 1.0 ./ 2))+ CONSTANTS(:,30).*(CONSTANTS(:,29)./( STATES(:,6).*power(ALGEBRAIC(:,4), 1.0 ./ 2))); RATES(:,6) = (( 2.00000.*ALGEBRAIC(:,11)+ 15.0000.*ALGEBRAIC(:,6)+ALGEBRAIC(:,7)) - (ALGEBRAIC(:,1)+ALGEBRAIC(:,13)+ALGEBRAIC(:,19)+ALGEBRAIC(:,16))).*power(1.00000 - ALGEBRAIC(:,8), -1.00000); 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) = power(CONSTANTS(:,30), 2.00000)+ 4.00000.*CONSTANTS(:,30).*(CONSTANTS(:,29)./STATES(:,6) - 1.00000); ALGEBRAIC(:,5) = (STATES(:,6)./2.00000).*( - CONSTANTS(:,30)+power(ALGEBRAIC(:,4), 1.0 ./ 2)); ALGEBRAIC(:,3) = CONSTANTS(:,23) - STATES(:,7); ALGEBRAIC(:,7) = CONSTANTS(:,21).*STATES(:,7).*ALGEBRAIC(:,5) - CONSTANTS(:,22).*ALGEBRAIC(:,3).*STATES(:,6); ALGEBRAIC(:,10) = power((1.00000+ CONSTANTS(:,31).*(STATES(:,6)./CONSTANTS(:,32)))./(1.00000+STATES(:,6)./CONSTANTS(:,32)), 4.00000); ALGEBRAIC(:,11) = CONSTANTS(:,13).*(STATES(:,3)./(STATES(:,3)+CONSTANTS(:,15))).*(ALGEBRAIC(:,5)./(ALGEBRAIC(:,5)+CONSTANTS(:,14))).*ALGEBRAIC(:,10); ALGEBRAIC(:,2) = CONSTANTS(:,19).*STATES(:,4) - CONSTANTS(:,20).*STATES(:,5); ALGEBRAIC(:,6) = CONSTANTS(:,16).*(STATES(:,4)./(STATES(:,4)+CONSTANTS(:,18))).*(ALGEBRAIC(:,5)./(ALGEBRAIC(:,5)+CONSTANTS(:,17))).*(1.00000./(1.00000+ 0.100000.*24.0000)); ALGEBRAIC(:,9) = CONSTANTS(:,29) - (STATES(:,6)+ALGEBRAIC(:,5)); ALGEBRAIC(:,12) = power((1.00000+ALGEBRAIC(:,9)./CONSTANTS(:,34))./(1.00000+ CONSTANTS(:,33).*(ALGEBRAIC(:,9)./CONSTANTS(:,34))), 4.00000); ALGEBRAIC(:,13) = CONSTANTS(:,4).*(STATES(:,1)./(STATES(:,1)+CONSTANTS(:,6))).*(STATES(:,6)./(STATES(:,6)+CONSTANTS(:,5))).*(STATES(:,2)./(STATES(:,2)+CONSTANTS(:,7))).*ALGEBRAIC(:,10).*ALGEBRAIC(:,12); ALGEBRAIC(:,14) = piecewise({VOI>=CONSTANTS(:,36)&VOI<=CONSTANTS(:,36)+CONSTANTS(:,37), 1.00000 }, 0.00000); ALGEBRAIC(:,15) = CONSTANTS(:,35).*(CONSTANTS(:,38)+ CONSTANTS(:,39).*((VOI - CONSTANTS(:,36))./CONSTANTS(:,40)).*exp( - ( (VOI - CONSTANTS(:,36)).*(ALGEBRAIC(:,14)./CONSTANTS(:,40))))).*ALGEBRAIC(:,14); ALGEBRAIC(:,17) = CONSTANTS(:,26).*(1.00000+ ALGEBRAIC(:,15).*CONSTANTS(:,28)) - CONSTANTS(:,27).*STATES(:,5); ALGEBRAIC(:,1) = CONSTANTS(:,1).*(STATES(:,6)./(STATES(:,6)+CONSTANTS(:,2))).*power(1.00000+power(STATES(:,1)./CONSTANTS(:,3), 4.00000), -1.00000); ALGEBRAIC(:,18) = power(ALGEBRAIC(:,9)./CONSTANTS(:,41), CONSTANTS(:,42))./(1.00000+power(ALGEBRAIC(:,9)./CONSTANTS(:,41), CONSTANTS(:,42))); ALGEBRAIC(:,19) = CONSTANTS(:,8).*(STATES(:,6)./(STATES(:,6)+CONSTANTS(:,10))).*(STATES(:,1)./(STATES(:,1)+CONSTANTS(:,11))).*ALGEBRAIC(:,18) - CONSTANTS(:,9).*(STATES(:,2)./(STATES(:,2)+CONSTANTS(:,12))); ALGEBRAIC(:,16) = CONSTANTS(:,24).*(STATES(:,6)./(STATES(:,6)+CONSTANTS(:,25))).*(1.00000+ALGEBRAIC(:,15)); ALGEBRAIC(:,8) = - 1.00000+CONSTANTS(:,30)./2.00000+ - ( 0.500000.*power(ALGEBRAIC(:,4), 1.0 ./ 2))+ CONSTANTS(:,30).*(CONSTANTS(:,29)./( STATES(:,6).*power(ALGEBRAIC(:,4), 1.0 ./ 2))); 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