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 =12; end % There are a total of 4 entries in each of the rate and state variable arrays. % There are a total of 5 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('V in component membrane (millivolt)'); LEGEND_CONSTANTS(:,1) = strpad('Cm in component membrane (microF)'); LEGEND_ALGEBRAIC(:,5) = strpad('i_Na in component sodium_channel (nanoA)'); LEGEND_ALGEBRAIC(:,11) = strpad('i_K in component potassium_channel (nanoA)'); LEGEND_ALGEBRAIC(:,12) = strpad('i_Leak in component leakage_current (nanoA)'); LEGEND_CONSTANTS(:,2) = strpad('g_Na_max in component sodium_channel (microS)'); LEGEND_ALGEBRAIC(:,1) = strpad('g_Na in component sodium_channel (microS)'); LEGEND_CONSTANTS(:,3) = strpad('E_Na in component sodium_channel (millivolt)'); LEGEND_STATES(:,2) = strpad('m in component sodium_channel_m_gate (dimensionless)'); LEGEND_STATES(:,3) = strpad('h in component sodium_channel_h_gate (dimensionless)'); LEGEND_ALGEBRAIC(:,2) = strpad('alpha_m in component sodium_channel_m_gate (per_second)'); LEGEND_ALGEBRAIC(:,6) = strpad('beta_m in component sodium_channel_m_gate (per_second)'); LEGEND_ALGEBRAIC(:,3) = strpad('alpha_h in component sodium_channel_h_gate (per_second)'); LEGEND_ALGEBRAIC(:,7) = strpad('beta_h in component sodium_channel_h_gate (per_second)'); LEGEND_ALGEBRAIC(:,9) = strpad('g_K1 in component potassium_channel (microS)'); LEGEND_ALGEBRAIC(:,10) = strpad('g_K2 in component potassium_channel (microS)'); LEGEND_STATES(:,4) = strpad('n in component potassium_channel_n_gate (dimensionless)'); LEGEND_ALGEBRAIC(:,4) = strpad('alpha_n in component potassium_channel_n_gate (per_second)'); LEGEND_ALGEBRAIC(:,8) = strpad('beta_n in component potassium_channel_n_gate (per_second)'); LEGEND_CONSTANTS(:,4) = strpad('g_L in component leakage_current (microS)'); LEGEND_CONSTANTS(:,5) = strpad('E_L in component leakage_current (millivolt)'); LEGEND_RATES(:,1) = strpad('d/dt V in component membrane (millivolt)'); LEGEND_RATES(:,2) = strpad('d/dt m in component sodium_channel_m_gate (dimensionless)'); LEGEND_RATES(:,3) = strpad('d/dt h in component sodium_channel_h_gate (dimensionless)'); LEGEND_RATES(:,4) = strpad('d/dt n in component potassium_channel_n_gate (dimensionless)'); 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) = -87; CONSTANTS(:,1) = 12; CONSTANTS(:,2) = 400000; CONSTANTS(:,3) = 40; STATES(:,2) = 0.01; STATES(:,3) = 0.8; STATES(:,4) = 0.01; CONSTANTS(:,4) = 75; CONSTANTS(:,5) = -60; 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(:,2) = ( 100.000.*( - STATES(:,1) - 48.0000))./(exp(( - STATES(:,1) - 48.0000)./15.0000) - 1.00000); ALGEBRAIC(:,6) = ( 120.000.*(STATES(:,1)+8.00000))./(exp((STATES(:,1)+8.00000)./5.00000) - 1.00000); RATES(:,2) = ALGEBRAIC(:,2).*(1.00000 - STATES(:,2)) - ALGEBRAIC(:,6).*STATES(:,2); ALGEBRAIC(:,3) = 170.000.*exp(( - STATES(:,1) - 90.0000)./20.0000); ALGEBRAIC(:,7) = 1000.00./(1.00000+exp(( - STATES(:,1) - 42.0000)./10.0000)); RATES(:,3) = ALGEBRAIC(:,3).*(1.00000 - STATES(:,3)) - ALGEBRAIC(:,7).*STATES(:,3); ALGEBRAIC(:,4) = ( 0.100000.*( - STATES(:,1) - 50.0000))./(exp(( - STATES(:,1) - 50.0000)./10.0000) - 1.00000); ALGEBRAIC(:,8) = 2.00000.*exp(( - STATES(:,1) - 90.0000)./80.0000); RATES(:,4) = ALGEBRAIC(:,4).*(1.00000 - STATES(:,4)) - ALGEBRAIC(:,8).*STATES(:,4); ALGEBRAIC(:,1) = power(STATES(:,2), 3.00000).*STATES(:,3).*CONSTANTS(:,2); ALGEBRAIC(:,5) = (ALGEBRAIC(:,1)+140.000).*(STATES(:,1) - CONSTANTS(:,3)); ALGEBRAIC(:,9) = 1200.00.*exp(( - STATES(:,1) - 90.0000)./50.0000)+ 15.0000.*exp((STATES(:,1)+90.0000)./60.0000); ALGEBRAIC(:,10) = 1200.00.*power(STATES(:,4), 4.00000); ALGEBRAIC(:,11) = (ALGEBRAIC(:,9)+ALGEBRAIC(:,10)).*(STATES(:,1)+100.000); ALGEBRAIC(:,12) = CONSTANTS(:,4).*(STATES(:,1) - CONSTANTS(:,5)); RATES(:,1) = - (ALGEBRAIC(:,5)+ALGEBRAIC(:,11)+ALGEBRAIC(:,12))./CONSTANTS(:,1); 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(:,2) = ( 100.000.*( - STATES(:,1) - 48.0000))./(exp(( - STATES(:,1) - 48.0000)./15.0000) - 1.00000); ALGEBRAIC(:,6) = ( 120.000.*(STATES(:,1)+8.00000))./(exp((STATES(:,1)+8.00000)./5.00000) - 1.00000); ALGEBRAIC(:,3) = 170.000.*exp(( - STATES(:,1) - 90.0000)./20.0000); ALGEBRAIC(:,7) = 1000.00./(1.00000+exp(( - STATES(:,1) - 42.0000)./10.0000)); ALGEBRAIC(:,4) = ( 0.100000.*( - STATES(:,1) - 50.0000))./(exp(( - STATES(:,1) - 50.0000)./10.0000) - 1.00000); ALGEBRAIC(:,8) = 2.00000.*exp(( - STATES(:,1) - 90.0000)./80.0000); ALGEBRAIC(:,1) = power(STATES(:,2), 3.00000).*STATES(:,3).*CONSTANTS(:,2); ALGEBRAIC(:,5) = (ALGEBRAIC(:,1)+140.000).*(STATES(:,1) - CONSTANTS(:,3)); ALGEBRAIC(:,9) = 1200.00.*exp(( - STATES(:,1) - 90.0000)./50.0000)+ 15.0000.*exp((STATES(:,1)+90.0000)./60.0000); ALGEBRAIC(:,10) = 1200.00.*power(STATES(:,4), 4.00000); ALGEBRAIC(:,11) = (ALGEBRAIC(:,9)+ALGEBRAIC(:,10)).*(STATES(:,1)+100.000); ALGEBRAIC(:,12) = CONSTANTS(:,4).*(STATES(:,1) - CONSTANTS(:,5)); 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