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 =15; end % There are a total of 10 entries in each of the rate and state variable arrays. % There are a total of 38 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_STATES(:,1) = strpad('ATP_cyt in component ATP_cyt (micromolar)'); LEGEND_ALGEBRAIC(:,10) = strpad('J_hyd in component J_hyd (flux)'); LEGEND_ALGEBRAIC(:,2) = strpad('J_CKMM in component J_CKMM (flux)'); LEGEND_ALGEBRAIC(:,13) = strpad('J_diff_ATP in component J_diff_ATP (flux)'); LEGEND_CONSTANTS(:,1) = strpad('V_cyt in component fractional_volumes (dimensionless)'); LEGEND_STATES(:,2) = strpad('ADP_cyt in component ADP_cyt (micromolar)'); LEGEND_ALGEBRAIC(:,14) = strpad('J_diff_ADP in component J_diff_ADP (flux)'); LEGEND_STATES(:,3) = strpad('PCr_cyt in component PCr_cyt (micromolar)'); LEGEND_ALGEBRAIC(:,6) = strpad('J_diff_PCr in component J_diff_PCr (flux)'); LEGEND_STATES(:,4) = strpad('Cr_cyt in component Cr_cyt (micromolar)'); LEGEND_ALGEBRAIC(:,7) = strpad('J_diff_Cr in component J_diff_Cr (flux)'); LEGEND_STATES(:,5) = strpad('Pi_cyt in component Pi_cyt (micromolar)'); LEGEND_ALGEBRAIC(:,15) = strpad('J_diff_Pi in component J_diff_Pi (flux)'); LEGEND_STATES(:,6) = strpad('ATP_ims in component ATP_ims (micromolar)'); LEGEND_ALGEBRAIC(:,4) = strpad('J_CKMi in component J_CKMi (flux)'); LEGEND_ALGEBRAIC(:,12) = strpad('J_syn in component J_syn (flux)'); LEGEND_CONSTANTS(:,2) = strpad('V_ims in component fractional_volumes (dimensionless)'); LEGEND_STATES(:,7) = strpad('ADP_ims in component ADP_ims (micromolar)'); LEGEND_STATES(:,8) = strpad('PCr_ims in component PCr_ims (micromolar)'); LEGEND_STATES(:,9) = strpad('Cr_ims in component Cr_ims (micromolar)'); LEGEND_STATES(:,10) = strpad('Pi_ims in component Pi_ims (micromolar)'); LEGEND_ALGEBRAIC(:,1) = strpad('Den_MMCK in component J_CKMM (dimensionless)'); LEGEND_CONSTANTS(:,3) = strpad('Kia in component J_CKMM (micromolar)'); LEGEND_CONSTANTS(:,4) = strpad('Kb in component J_CKMM (micromolar)'); LEGEND_CONSTANTS(:,5) = strpad('Kib in component J_CKMM (micromolar)'); LEGEND_CONSTANTS(:,32) = strpad('KIb in component J_CKMM (micromolar)'); LEGEND_CONSTANTS(:,33) = strpad('Kc in component J_CKMM (micromolar)'); LEGEND_CONSTANTS(:,6) = strpad('Kic in component J_CKMM (micromolar)'); LEGEND_CONSTANTS(:,7) = strpad('Kd in component J_CKMM (micromolar)'); LEGEND_CONSTANTS(:,8) = strpad('Kid in component J_CKMM (micromolar)'); LEGEND_CONSTANTS(:,9) = strpad('Vmax_MM_f in component J_CKMM (flux)'); LEGEND_CONSTANTS(:,10) = strpad('Vmax_MM_b in component J_CKMM (flux)'); LEGEND_ALGEBRAIC(:,3) = strpad('Den_MiCK in component J_CKMi (dimensionless)'); LEGEND_CONSTANTS(:,11) = strpad('Kia in component J_CKMi (micromolar)'); LEGEND_CONSTANTS(:,12) = strpad('Kb in component J_CKMi (micromolar)'); LEGEND_CONSTANTS(:,13) = strpad('Kib in component J_CKMi (micromolar)'); LEGEND_CONSTANTS(:,34) = strpad('KIb in component J_CKMi (micromolar)'); LEGEND_CONSTANTS(:,35) = strpad('Kc in component J_CKMi (micromolar)'); LEGEND_CONSTANTS(:,14) = strpad('Kic in component J_CKMi (micromolar)'); LEGEND_CONSTANTS(:,15) = strpad('Kd in component J_CKMi (micromolar)'); LEGEND_CONSTANTS(:,16) = strpad('Kid in component J_CKMi (micromolar)'); LEGEND_CONSTANTS(:,17) = strpad('Vmax_Mi_f in component J_CKMi (flux)'); LEGEND_CONSTANTS(:,18) = strpad('Vmax_Mi_b in component J_CKMi (flux)'); LEGEND_ALGEBRAIC(:,9) = strpad('H_ATPmax in component J_hyd (flux)'); LEGEND_CONSTANTS(:,19) = strpad('J_hyd_basis_1 in component J_hyd (flux)'); LEGEND_CONSTANTS(:,20) = strpad('J_hyd_basis_2 in component J_hyd (flux)'); LEGEND_CONSTANTS(:,21) = strpad('freq_1 in component J_hyd (dimensionless)'); LEGEND_CONSTANTS(:,22) = strpad('freq_2 in component J_hyd (dimensionless)'); LEGEND_CONSTANTS(:,36) = strpad('t_cycle_1 in component J_hyd (second)'); LEGEND_CONSTANTS(:,37) = strpad('t_cycle_2 in component J_hyd (second)'); LEGEND_ALGEBRAIC(:,8) = strpad('t_cycle in component J_hyd (second)'); LEGEND_CONSTANTS(:,23) = strpad('nb_of_cycles_1 in component J_hyd (dimensionless)'); LEGEND_CONSTANTS(:,38) = strpad('duration_1 in component J_hyd (second)'); LEGEND_ALGEBRAIC(:,5) = strpad('ltime in component J_hyd (second)'); LEGEND_ALGEBRAIC(:,11) = strpad('Den_syn in component J_syn (dimensionless)'); LEGEND_CONSTANTS(:,24) = strpad('KPi in component J_syn (micromolar)'); LEGEND_CONSTANTS(:,25) = strpad('KADP in component J_syn (micromolar)'); LEGEND_CONSTANTS(:,26) = strpad('V_max_syn in component J_syn (flux)'); LEGEND_CONSTANTS(:,27) = strpad('PS_tot_ATP in component J_diff_ATP (first_order_rate_constant)'); LEGEND_CONSTANTS(:,28) = strpad('PS_tot_ADP in component J_diff_ADP (first_order_rate_constant)'); LEGEND_CONSTANTS(:,29) = strpad('PS_tot_PCr in component J_diff_PCr (first_order_rate_constant)'); LEGEND_CONSTANTS(:,30) = strpad('PS_tot_Cr in component J_diff_Cr (first_order_rate_constant)'); LEGEND_CONSTANTS(:,31) = strpad('PS_tot_Pi in component J_diff_Pi (first_order_rate_constant)'); LEGEND_RATES(:,1) = strpad('d/dt ATP_cyt in component ATP_cyt (micromolar)'); LEGEND_RATES(:,2) = strpad('d/dt ADP_cyt in component ADP_cyt (micromolar)'); LEGEND_RATES(:,3) = strpad('d/dt PCr_cyt in component PCr_cyt (micromolar)'); LEGEND_RATES(:,4) = strpad('d/dt Cr_cyt in component Cr_cyt (micromolar)'); LEGEND_RATES(:,5) = strpad('d/dt Pi_cyt in component Pi_cyt (micromolar)'); LEGEND_RATES(:,6) = strpad('d/dt ATP_ims in component ATP_ims (micromolar)'); LEGEND_RATES(:,7) = strpad('d/dt ADP_ims in component ADP_ims (micromolar)'); LEGEND_RATES(:,8) = strpad('d/dt PCr_ims in component PCr_ims (micromolar)'); LEGEND_RATES(:,9) = strpad('d/dt Cr_ims in component Cr_ims (micromolar)'); LEGEND_RATES(:,10) = strpad('d/dt Pi_ims in component Pi_ims (micromolar)'); 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) = 5912.77; CONSTANTS(:,1) = 0.75; STATES(:,2) = 64; STATES(:,3) = 5000; STATES(:,4) = 10500; STATES(:,5) = 913; STATES(:,6) = 5912.77; CONSTANTS(:,2) = 0.0625; STATES(:,7) = 39; STATES(:,8) = 5000; STATES(:,9) = 10500; STATES(:,10) = 910; CONSTANTS(:,3) = 9.0E2; CONSTANTS(:,4) = 1.55E4; CONSTANTS(:,5) = 3.49E4; CONSTANTS(:,6) = 2.224E2; CONSTANTS(:,7) = 1.67E3; CONSTANTS(:,8) = 4.73E3; CONSTANTS(:,9) = 1.144E4; CONSTANTS(:,10) = 4.804E4; CONSTANTS(:,11) = 7.5E2; CONSTANTS(:,12) = 5.2E3; CONSTANTS(:,13) = 2.88E4; CONSTANTS(:,14) = 2.048E2; CONSTANTS(:,15) = 5.0E2; CONSTANTS(:,16) = 1.6E3; CONSTANTS(:,17) = 8.82E2; CONSTANTS(:,18) = 3.704E3; CONSTANTS(:,19) = 4.865e2; CONSTANTS(:,20) = 6.276e2; CONSTANTS(:,21) = 135; CONSTANTS(:,22) = 220; CONSTANTS(:,23) = 5; CONSTANTS(:,24) = 8E2; CONSTANTS(:,25) = 25; CONSTANTS(:,26) = 1.504E4; CONSTANTS(:,27) = 13.3; CONSTANTS(:,28) = 13.3; CONSTANTS(:,29) = 155.0; CONSTANTS(:,30) = 155.0; CONSTANTS(:,31) = 194.0; CONSTANTS(:,32) = CONSTANTS(:,5); CONSTANTS(:,33) = ( CONSTANTS(:,6).*CONSTANTS(:,7))./CONSTANTS(:,8); CONSTANTS(:,34) = CONSTANTS(:,13); CONSTANTS(:,35) = ( CONSTANTS(:,14).*CONSTANTS(:,15))./CONSTANTS(:,16); CONSTANTS(:,36) = 60.0000./CONSTANTS(:,21); CONSTANTS(:,37) = 60.0000./CONSTANTS(:,22); CONSTANTS(:,38) = CONSTANTS(:,23).*CONSTANTS(:,36); 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(:,1) = 1.00000+STATES(:,4)./CONSTANTS(:,5)+STATES(:,3)./CONSTANTS(:,8)+ STATES(:,1).*(1.00000./CONSTANTS(:,3)+STATES(:,4)./( CONSTANTS(:,3).*CONSTANTS(:,4)))+ STATES(:,2).*(1.00000./CONSTANTS(:,6)+STATES(:,3)./( CONSTANTS(:,8).*CONSTANTS(:,33))+STATES(:,4)./( CONSTANTS(:,6).*CONSTANTS(:,32))); ALGEBRAIC(:,2) = ( CONSTANTS(:,9).*(( STATES(:,1).*STATES(:,4))./( CONSTANTS(:,3).*CONSTANTS(:,4))) - CONSTANTS(:,10).*(( STATES(:,2).*STATES(:,3))./( CONSTANTS(:,6).*CONSTANTS(:,7))))./ALGEBRAIC(:,1); ALGEBRAIC(:,6) = CONSTANTS(:,29).*(STATES(:,8) - STATES(:,3)); RATES(:,3) = (ALGEBRAIC(:,6)+ALGEBRAIC(:,2))./CONSTANTS(:,1); ALGEBRAIC(:,7) = CONSTANTS(:,30).*(STATES(:,9) - STATES(:,4)); RATES(:,4) = (ALGEBRAIC(:,7) - ALGEBRAIC(:,2))./CONSTANTS(:,1); ALGEBRAIC(:,3) = 1.00000+STATES(:,9)./CONSTANTS(:,13)+STATES(:,8)./CONSTANTS(:,16)+ STATES(:,6).*(1.00000./CONSTANTS(:,11)+STATES(:,9)./( CONSTANTS(:,11).*CONSTANTS(:,12)))+ STATES(:,7).*(1.00000./CONSTANTS(:,14)+STATES(:,8)./( CONSTANTS(:,16).*CONSTANTS(:,35))+STATES(:,9)./( CONSTANTS(:,14).*CONSTANTS(:,34))); ALGEBRAIC(:,4) = ( CONSTANTS(:,17).*(( STATES(:,6).*STATES(:,9))./( CONSTANTS(:,11).*CONSTANTS(:,12))) - CONSTANTS(:,18).*(( STATES(:,7).*STATES(:,8))./( CONSTANTS(:,14).*CONSTANTS(:,15))))./ALGEBRAIC(:,3); RATES(:,8) = (ALGEBRAIC(:,4) - ALGEBRAIC(:,6))./CONSTANTS(:,2); RATES(:,9) = - (ALGEBRAIC(:,4)+ALGEBRAIC(:,7))./CONSTANTS(:,2); ALGEBRAIC(:,9) = piecewise({VOI<=CONSTANTS(:,38), 6.00000.*CONSTANTS(:,19) }, 6.00000.*CONSTANTS(:,20)); ALGEBRAIC(:,8) = piecewise({VOI<=CONSTANTS(:,38), CONSTANTS(:,36) }, CONSTANTS(:,37)); ALGEBRAIC(:,5) = piecewise({VOI<=CONSTANTS(:,38), VOI - CONSTANTS(:,36).*floor(VOI./CONSTANTS(:,36)) }, (VOI - CONSTANTS(:,38)) - CONSTANTS(:,37).*floor((VOI - CONSTANTS(:,38))./CONSTANTS(:,37))); ALGEBRAIC(:,10) = piecewise({ALGEBRAIC(:,5)>=0.00000&ALGEBRAIC(:,5)< (1.00000./6.00000).*ALGEBRAIC(:,8), (( ALGEBRAIC(:,9).*ALGEBRAIC(:,5))./ALGEBRAIC(:,8)).*6.00000 , ALGEBRAIC(:,5)>= (1.00000./6.00000).*ALGEBRAIC(:,8)&ALGEBRAIC(:,5)< (1.00000./3.00000).*ALGEBRAIC(:,8), ALGEBRAIC(:,9).*(1.00000 - 6.00000.*(ALGEBRAIC(:,5)./ALGEBRAIC(:,8) - 1.00000./6.00000)) , ALGEBRAIC(:,5)>= (1.00000./3.00000).*ALGEBRAIC(:,8)&ALGEBRAIC(:,5)=0.00000&ALGEBRAIC(:,5)< (1.00000./6.00000).*ALGEBRAIC(:,8), (( ALGEBRAIC(:,9).*ALGEBRAIC(:,5))./ALGEBRAIC(:,8)).*6.00000 , ALGEBRAIC(:,5)>= (1.00000./6.00000).*ALGEBRAIC(:,8)&ALGEBRAIC(:,5)< (1.00000./3.00000).*ALGEBRAIC(:,8), ALGEBRAIC(:,9).*(1.00000 - 6.00000.*(ALGEBRAIC(:,5)./ALGEBRAIC(:,8) - 1.00000./6.00000)) , ALGEBRAIC(:,5)>= (1.00000./3.00000).*ALGEBRAIC(:,8)&ALGEBRAIC(:,5) req_length strout = strin(1:req_length); else strout = [strin, blanks(req_length - insize)]; end end