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 =24; end % There are a total of 5 entries in each of the rate and state variable arrays. % There are a total of 37 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 (millisecond)'); LEGEND_STATES(:,1) = strpad('V in component membrane (millivolt)'); LEGEND_CONSTANTS(:,1) = strpad('Cm in component membrane (femtoF)'); LEGEND_ALGEBRAIC(:,2) = strpad('i_K in component K_current (picoA)'); LEGEND_ALGEBRAIC(:,12) = strpad('i_K_Ca in component K_Ca_current (picoA)'); LEGEND_ALGEBRAIC(:,5) = strpad('i_K_ATP in component K_ATP_current (picoA)'); LEGEND_ALGEBRAIC(:,16) = strpad('i_CRAC in component CRAC_current (picoA)'); LEGEND_ALGEBRAIC(:,11) = strpad('i_Ca in component Ca_current_total (picoA)'); LEGEND_ALGEBRAIC(:,18) = strpad('i_leak in component leak_current (picoA)'); LEGEND_CONSTANTS(:,2) = strpad('V_K in component K_current (millivolt)'); LEGEND_CONSTANTS(:,3) = strpad('g_K in component K_current (picoS)'); LEGEND_STATES(:,2) = strpad('n in component K_channel_n_gate (dimensionless)'); LEGEND_ALGEBRAIC(:,1) = strpad('n_infinity in component K_channel_n_gate (dimensionless)'); LEGEND_ALGEBRAIC(:,4) = strpad('tau_n in component K_channel_n_gate (millisecond)'); LEGEND_CONSTANTS(:,4) = strpad('Vn in component K_channel_n_gate (millivolt)'); LEGEND_CONSTANTS(:,5) = strpad('Sn in component K_channel_n_gate (millivolt)'); LEGEND_CONSTANTS(:,6) = strpad('lambda_n in component K_channel_n_gate (dimensionless)'); LEGEND_CONSTANTS(:,7) = strpad('g_K_ATP in component K_ATP_current (picoS)'); LEGEND_ALGEBRAIC(:,8) = strpad('i_Ca_f in component fast_Ca_current (picoA)'); LEGEND_CONSTANTS(:,8) = strpad('V_Ca in component fast_Ca_current (millivolt)'); LEGEND_CONSTANTS(:,9) = strpad('g_Ca_f in component fast_Ca_current (picoS)'); LEGEND_ALGEBRAIC(:,7) = strpad('m_f_infinity in component fast_Ca_channel_m_gate (dimensionless)'); LEGEND_CONSTANTS(:,10) = strpad('Vm_f in component fast_Ca_channel_m_gate (millivolt)'); LEGEND_CONSTANTS(:,11) = strpad('Sm_f in component fast_Ca_channel_m_gate (millivolt)'); LEGEND_ALGEBRAIC(:,10) = strpad('i_Ca_s in component slow_Ca_current (picoA)'); LEGEND_CONSTANTS(:,12) = strpad('g_Ca_s in component slow_Ca_current (picoS)'); LEGEND_ALGEBRAIC(:,9) = strpad('m_s_infinity in component slow_Ca_channel_m_gate (dimensionless)'); LEGEND_STATES(:,3) = strpad('jm in component slow_Ca_channel_j_gate (dimensionless)'); LEGEND_CONSTANTS(:,13) = strpad('Vm_s in component slow_Ca_channel_m_gate (millivolt)'); LEGEND_CONSTANTS(:,14) = strpad('Sm_s in component slow_Ca_channel_m_gate (millivolt)'); LEGEND_ALGEBRAIC(:,3) = strpad('jm_infinity in component slow_Ca_channel_j_gate (dimensionless)'); LEGEND_CONSTANTS(:,15) = strpad('Vj in component slow_Ca_channel_j_gate (millivolt)'); LEGEND_ALGEBRAIC(:,6) = strpad('tau_j in component slow_Ca_channel_j_gate (millisecond)'); LEGEND_CONSTANTS(:,16) = strpad('Sj in component slow_Ca_channel_j_gate (millivolt)'); LEGEND_CONSTANTS(:,17) = strpad('g_K_Ca in component K_Ca_current (picoS)'); LEGEND_STATES(:,4) = strpad('Ca_i in component Ca_equations (micromolar)'); LEGEND_CONSTANTS(:,18) = strpad('kdkca in component K_Ca_current (micromolar)'); LEGEND_CONSTANTS(:,19) = strpad('g_CRAC in component CRAC_current (picoS)'); LEGEND_CONSTANTS(:,20) = strpad('V_CRAC in component CRAC_current (millivolt)'); LEGEND_STATES(:,5) = strpad('Ca_er in component Ca_equations (micromolar)'); LEGEND_ALGEBRAIC(:,14) = strpad('r_infinity in component CRAC_r_gate (dimensionless)'); LEGEND_CONSTANTS(:,21) = strpad('Ca_er_bar in component CRAC_r_gate (micromolar)'); LEGEND_CONSTANTS(:,22) = strpad('sloper in component CRAC_r_gate (micromolar)'); LEGEND_CONSTANTS(:,23) = strpad('g_leak in component leak_current (picoS)'); LEGEND_ALGEBRAIC(:,13) = strpad('J_er_p in component ER_parameters (micromolar_per_millisecond)'); LEGEND_CONSTANTS(:,24) = strpad('IP3 in component ER_parameters (micromolar)'); LEGEND_CONSTANTS(:,25) = strpad('kerp in component ER_parameters (micromolar)'); LEGEND_CONSTANTS(:,26) = strpad('verp in component ER_parameters (micromolar_per_millisecond)'); LEGEND_CONSTANTS(:,27) = strpad('dact in component ER_parameters (micromolar)'); LEGEND_CONSTANTS(:,28) = strpad('dinh in component ER_parameters (micromolar)'); LEGEND_CONSTANTS(:,29) = strpad('dip3 in component ER_parameters (micromolar)'); LEGEND_ALGEBRAIC(:,15) = strpad('a_infinity in component ER_parameters (dimensionless)'); LEGEND_CONSTANTS(:,37) = strpad('b_infinity in component ER_parameters (dimensionless)'); LEGEND_ALGEBRAIC(:,17) = strpad('h_infinity in component ER_parameters (dimensionless)'); LEGEND_ALGEBRAIC(:,19) = strpad('O in component ER_parameters (per_millisecond)'); LEGEND_ALGEBRAIC(:,22) = strpad('J_er_tot in component Ca_equations (micromolar_per_millisecond)'); LEGEND_ALGEBRAIC(:,21) = strpad('J_er_IP3 in component Ca_equations (micromolar_per_millisecond)'); LEGEND_ALGEBRAIC(:,20) = strpad('J_er_leak in component Ca_equations (micromolar_per_millisecond)'); LEGEND_ALGEBRAIC(:,24) = strpad('J_mem_tot in component Ca_membrane_flux (micromolar_per_millisecond)'); LEGEND_CONSTANTS(:,30) = strpad('perl in component Ca_equations (per_millisecond)'); LEGEND_CONSTANTS(:,31) = strpad('lambda_er in component Ca_equations (dimensionless)'); LEGEND_CONSTANTS(:,32) = strpad('sigma_er in component Ca_equations (dimensionless)'); LEGEND_CONSTANTS(:,33) = strpad('kmp in component Ca_membrane_flux (micromolar)'); LEGEND_CONSTANTS(:,34) = strpad('vmp in component Ca_membrane_flux (micromolar)'); LEGEND_CONSTANTS(:,35) = strpad('gamma in component Ca_membrane_flux (micromolar_per_picoA)'); LEGEND_ALGEBRAIC(:,23) = strpad('Jmp in component Ca_membrane_flux (micromolar)'); LEGEND_CONSTANTS(:,36) = strpad('f in component Ca_membrane_flux (per_millisecond)'); LEGEND_RATES(:,1) = strpad('d/dt V in component membrane (millivolt)'); LEGEND_RATES(:,2) = strpad('d/dt n in component K_channel_n_gate (dimensionless)'); LEGEND_RATES(:,3) = strpad('d/dt jm in component slow_Ca_channel_j_gate (dimensionless)'); LEGEND_RATES(:,5) = strpad('d/dt Ca_er in component Ca_equations (micromolar)'); LEGEND_RATES(:,4) = strpad('d/dt Ca_i in component Ca_equations (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) = -61; CONSTANTS(:,1) = 6158; CONSTANTS(:,2) = -70; CONSTANTS(:,3) = 3900; STATES(:,2) = 0.0005; CONSTANTS(:,4) = -15; CONSTANTS(:,5) = 6; CONSTANTS(:,6) = 1.85; CONSTANTS(:,7) = 150; CONSTANTS(:,8) = 100; CONSTANTS(:,9) = 810; CONSTANTS(:,10) = -20; CONSTANTS(:,11) = 7.5; CONSTANTS(:,12) = 510; STATES(:,3) = 0.12; CONSTANTS(:,13) = -16; CONSTANTS(:,14) = 10; CONSTANTS(:,15) = -53; CONSTANTS(:,16) = 2; CONSTANTS(:,17) = 1200; STATES(:,4) = 0.11; CONSTANTS(:,18) = 0.55; CONSTANTS(:,19) = 75; CONSTANTS(:,20) = 0; STATES(:,5) = 60; CONSTANTS(:,21) = 40; CONSTANTS(:,22) = 3; CONSTANTS(:,23) = 0; CONSTANTS(:,24) = 0; CONSTANTS(:,25) = 0.09; CONSTANTS(:,26) = 0.24; CONSTANTS(:,27) = 0.35; CONSTANTS(:,28) = 0.4; CONSTANTS(:,29) = 0.2; CONSTANTS(:,30) = 0.003; CONSTANTS(:,31) = 250; CONSTANTS(:,32) = 1; CONSTANTS(:,33) = 0.35; CONSTANTS(:,34) = 0.08; CONSTANTS(:,35) = 0.000003607; CONSTANTS(:,36) = 0.01; CONSTANTS(:,37) = CONSTANTS(:,24)./(CONSTANTS(:,24)+CONSTANTS(:,29)); 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./(1.00000+exp((CONSTANTS(:,4) - STATES(:,1))./CONSTANTS(:,5))); ALGEBRAIC(:,4) = 9.09000./(1.00000+exp((STATES(:,1) - CONSTANTS(:,4))./CONSTANTS(:,5))); RATES(:,2) = ( CONSTANTS(:,6).*(ALGEBRAIC(:,1) - STATES(:,2)))./ALGEBRAIC(:,4); ALGEBRAIC(:,3) = 1.00000 - 1.00000./(1.00000+exp((STATES(:,1) - CONSTANTS(:,15))./CONSTANTS(:,16))); ALGEBRAIC(:,6) = 50000.0./(exp((STATES(:,1) - CONSTANTS(:,15))./4.00000)+exp((CONSTANTS(:,15) - STATES(:,1))./4.00000))+1500.00; RATES(:,3) = (ALGEBRAIC(:,3) - STATES(:,3))./ALGEBRAIC(:,6); ALGEBRAIC(:,2) = CONSTANTS(:,3).*STATES(:,2).*(STATES(:,1) - CONSTANTS(:,2)); ALGEBRAIC(:,12) = (( CONSTANTS(:,17).*power(STATES(:,4), 5.00000))./(power(STATES(:,4), 5.00000)+power(CONSTANTS(:,18), 5.00000))).*(STATES(:,1) - CONSTANTS(:,2)); ALGEBRAIC(:,5) = CONSTANTS(:,7).*(STATES(:,1) - CONSTANTS(:,2)); ALGEBRAIC(:,14) = 1.00000./(1.00000+exp((STATES(:,5) - CONSTANTS(:,21))./CONSTANTS(:,22))); ALGEBRAIC(:,16) = CONSTANTS(:,19).*ALGEBRAIC(:,14).*(STATES(:,1) - CONSTANTS(:,20)); ALGEBRAIC(:,7) = 1.00000./(1.00000+exp((CONSTANTS(:,10) - STATES(:,1))./CONSTANTS(:,11))); ALGEBRAIC(:,8) = CONSTANTS(:,9).*ALGEBRAIC(:,7).*(STATES(:,1) - CONSTANTS(:,8)); ALGEBRAIC(:,9) = 1.00000./(1.00000+exp((CONSTANTS(:,13) - STATES(:,1))./CONSTANTS(:,14))); ALGEBRAIC(:,10) = CONSTANTS(:,12).*ALGEBRAIC(:,9).*(1.00000 - STATES(:,3)).*(STATES(:,1) - CONSTANTS(:,8)); ALGEBRAIC(:,11) = ALGEBRAIC(:,8)+ALGEBRAIC(:,10); ALGEBRAIC(:,18) = CONSTANTS(:,23).*(STATES(:,1) - CONSTANTS(:,20)); RATES(:,1) = - (ALGEBRAIC(:,11)+ALGEBRAIC(:,2)+ALGEBRAIC(:,5)+ALGEBRAIC(:,12)+ALGEBRAIC(:,16)+ALGEBRAIC(:,18))./CONSTANTS(:,1); ALGEBRAIC(:,13) = ( CONSTANTS(:,26).*power(STATES(:,4), 2.00000))./(power(STATES(:,4), 2.00000)+power(CONSTANTS(:,25), 2.00000)); ALGEBRAIC(:,15) = 1.00000./(1.00000+CONSTANTS(:,27)./STATES(:,4)); ALGEBRAIC(:,17) = 1.00000./(1.00000+STATES(:,4)./CONSTANTS(:,28)); ALGEBRAIC(:,19) = power(ALGEBRAIC(:,15), 3.00000).*power(CONSTANTS(:,37), 3.00000).*power(ALGEBRAIC(:,17), 3.00000).*1.00000; ALGEBRAIC(:,21) = ALGEBRAIC(:,19).*(STATES(:,5) - STATES(:,4)); ALGEBRAIC(:,20) = CONSTANTS(:,30).*(STATES(:,5) - STATES(:,4)); ALGEBRAIC(:,22) = (ALGEBRAIC(:,20)+ALGEBRAIC(:,21)) - ALGEBRAIC(:,13); RATES(:,5) = - ALGEBRAIC(:,22)./( CONSTANTS(:,31).*CONSTANTS(:,32)); ALGEBRAIC(:,23) = ( CONSTANTS(:,34).*power(STATES(:,4), 2.00000))./(power(STATES(:,4), 2.00000)+power(CONSTANTS(:,33), 2.00000)); ALGEBRAIC(:,24) = - CONSTANTS(:,36).*( CONSTANTS(:,35).*ALGEBRAIC(:,11)+ALGEBRAIC(:,23)); RATES(:,4) = ALGEBRAIC(:,22)./CONSTANTS(:,31)+ALGEBRAIC(:,24); 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) = 1.00000./(1.00000+exp((CONSTANTS(:,4) - STATES(:,1))./CONSTANTS(:,5))); ALGEBRAIC(:,4) = 9.09000./(1.00000+exp((STATES(:,1) - CONSTANTS(:,4))./CONSTANTS(:,5))); ALGEBRAIC(:,3) = 1.00000 - 1.00000./(1.00000+exp((STATES(:,1) - CONSTANTS(:,15))./CONSTANTS(:,16))); ALGEBRAIC(:,6) = 50000.0./(exp((STATES(:,1) - CONSTANTS(:,15))./4.00000)+exp((CONSTANTS(:,15) - STATES(:,1))./4.00000))+1500.00; ALGEBRAIC(:,2) = CONSTANTS(:,3).*STATES(:,2).*(STATES(:,1) - CONSTANTS(:,2)); ALGEBRAIC(:,12) = (( CONSTANTS(:,17).*power(STATES(:,4), 5.00000))./(power(STATES(:,4), 5.00000)+power(CONSTANTS(:,18), 5.00000))).*(STATES(:,1) - CONSTANTS(:,2)); ALGEBRAIC(:,5) = CONSTANTS(:,7).*(STATES(:,1) - CONSTANTS(:,2)); ALGEBRAIC(:,14) = 1.00000./(1.00000+exp((STATES(:,5) - CONSTANTS(:,21))./CONSTANTS(:,22))); ALGEBRAIC(:,16) = CONSTANTS(:,19).*ALGEBRAIC(:,14).*(STATES(:,1) - CONSTANTS(:,20)); ALGEBRAIC(:,7) = 1.00000./(1.00000+exp((CONSTANTS(:,10) - STATES(:,1))./CONSTANTS(:,11))); ALGEBRAIC(:,8) = CONSTANTS(:,9).*ALGEBRAIC(:,7).*(STATES(:,1) - CONSTANTS(:,8)); ALGEBRAIC(:,9) = 1.00000./(1.00000+exp((CONSTANTS(:,13) - STATES(:,1))./CONSTANTS(:,14))); ALGEBRAIC(:,10) = CONSTANTS(:,12).*ALGEBRAIC(:,9).*(1.00000 - STATES(:,3)).*(STATES(:,1) - CONSTANTS(:,8)); ALGEBRAIC(:,11) = ALGEBRAIC(:,8)+ALGEBRAIC(:,10); ALGEBRAIC(:,18) = CONSTANTS(:,23).*(STATES(:,1) - CONSTANTS(:,20)); ALGEBRAIC(:,13) = ( CONSTANTS(:,26).*power(STATES(:,4), 2.00000))./(power(STATES(:,4), 2.00000)+power(CONSTANTS(:,25), 2.00000)); ALGEBRAIC(:,15) = 1.00000./(1.00000+CONSTANTS(:,27)./STATES(:,4)); ALGEBRAIC(:,17) = 1.00000./(1.00000+STATES(:,4)./CONSTANTS(:,28)); ALGEBRAIC(:,19) = power(ALGEBRAIC(:,15), 3.00000).*power(CONSTANTS(:,37), 3.00000).*power(ALGEBRAIC(:,17), 3.00000).*1.00000; ALGEBRAIC(:,21) = ALGEBRAIC(:,19).*(STATES(:,5) - STATES(:,4)); ALGEBRAIC(:,20) = CONSTANTS(:,30).*(STATES(:,5) - STATES(:,4)); ALGEBRAIC(:,22) = (ALGEBRAIC(:,20)+ALGEBRAIC(:,21)) - ALGEBRAIC(:,13); ALGEBRAIC(:,23) = ( CONSTANTS(:,34).*power(STATES(:,4), 2.00000))./(power(STATES(:,4), 2.00000)+power(CONSTANTS(:,33), 2.00000)); ALGEBRAIC(:,24) = - CONSTANTS(:,36).*( CONSTANTS(:,35).*ALGEBRAIC(:,11)+ALGEBRAIC(:,23)); 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