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 =14; end % There are a total of 4 entries in each of the rate and state variable arrays. % There are a total of 25 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('C in component membrane (picoF)'); LEGEND_CONSTANTS(:,2) = strpad('i_app in component membrane (picoA)'); LEGEND_ALGEBRAIC(:,12) = strpad('i_NaP in component persistent_sodium_current (picoA)'); LEGEND_ALGEBRAIC(:,5) = strpad('i_Na in component fast_sodium_current (picoA)'); LEGEND_ALGEBRAIC(:,9) = strpad('i_K in component potassium_current (picoA)'); LEGEND_ALGEBRAIC(:,10) = strpad('i_KS in component slow_potassium_current (picoA)'); LEGEND_ALGEBRAIC(:,13) = strpad('i_L in component leakage_current (picoA)'); LEGEND_ALGEBRAIC(:,14) = strpad('i_tonic_e in component tonic_current (picoA)'); LEGEND_CONSTANTS(:,3) = strpad('E_Na in component fast_sodium_current (millivolt)'); LEGEND_CONSTANTS(:,4) = strpad('g_Na in component fast_sodium_current (nanoS)'); LEGEND_ALGEBRAIC(:,1) = strpad('m_infinity in component fast_sodium_current_m_gate (dimensionless)'); LEGEND_STATES(:,2) = strpad('n in component fast_sodium_current_n_gate (dimensionless)'); LEGEND_CONSTANTS(:,5) = strpad('theta_m in component fast_sodium_current_m_gate (millivolt)'); LEGEND_CONSTANTS(:,6) = strpad('sigma_m in component fast_sodium_current_m_gate (millivolt)'); LEGEND_ALGEBRAIC(:,2) = strpad('n_infinity in component fast_sodium_current_n_gate (dimensionless)'); LEGEND_ALGEBRAIC(:,6) = strpad('tau_n in component fast_sodium_current_n_gate (millisecond)'); LEGEND_CONSTANTS(:,7) = strpad('tau_n_max in component fast_sodium_current_n_gate (millisecond)'); LEGEND_CONSTANTS(:,8) = strpad('theta_n in component fast_sodium_current_n_gate (millivolt)'); LEGEND_CONSTANTS(:,9) = strpad('sigma_n in component fast_sodium_current_n_gate (millivolt)'); LEGEND_CONSTANTS(:,10) = strpad('E_K in component potassium_current (millivolt)'); LEGEND_CONSTANTS(:,11) = strpad('g_K in component potassium_current (nanoS)'); LEGEND_STATES(:,3) = strpad('n in component potassium_current_n_gate (dimensionless)'); LEGEND_ALGEBRAIC(:,3) = strpad('n_infinity in component potassium_current_n_gate (dimensionless)'); LEGEND_ALGEBRAIC(:,7) = strpad('tau_n in component potassium_current_n_gate (millisecond)'); LEGEND_CONSTANTS(:,12) = strpad('tau_n_max in component potassium_current_n_gate (millisecond)'); LEGEND_CONSTANTS(:,13) = strpad('theta_n in component potassium_current_n_gate (millivolt)'); LEGEND_CONSTANTS(:,14) = strpad('sigma_n in component potassium_current_n_gate (millivolt)'); LEGEND_CONSTANTS(:,15) = strpad('g_KS in component slow_potassium_current (nanoS)'); LEGEND_STATES(:,4) = strpad('k in component slow_potassium_current_k_gate (dimensionless)'); LEGEND_ALGEBRAIC(:,4) = strpad('k_infinity in component slow_potassium_current_k_gate (dimensionless)'); LEGEND_ALGEBRAIC(:,8) = strpad('tau_k in component slow_potassium_current_k_gate (millisecond)'); LEGEND_CONSTANTS(:,16) = strpad('tau_k_max in component slow_potassium_current_k_gate (millisecond)'); LEGEND_CONSTANTS(:,17) = strpad('theta_k in component slow_potassium_current_k_gate (millivolt)'); LEGEND_CONSTANTS(:,18) = strpad('sigma_k in component slow_potassium_current_k_gate (millivolt)'); LEGEND_CONSTANTS(:,19) = strpad('g_NaP in component persistent_sodium_current (nanoS)'); LEGEND_ALGEBRAIC(:,11) = strpad('m_infinity in component persistent_sodium_current_m_gate (dimensionless)'); LEGEND_CONSTANTS(:,20) = strpad('theta_m in component persistent_sodium_current_m_gate (millivolt)'); LEGEND_CONSTANTS(:,21) = strpad('sigma_m in component persistent_sodium_current_m_gate (millivolt)'); LEGEND_CONSTANTS(:,22) = strpad('g_L in component leakage_current (nanoS)'); LEGEND_CONSTANTS(:,23) = strpad('E_L in component leakage_current (millivolt)'); LEGEND_CONSTANTS(:,24) = strpad('g_tonic_e in component tonic_current (nanoS)'); LEGEND_CONSTANTS(:,25) = strpad('E_syn_e in component tonic_current (millivolt)'); LEGEND_RATES(:,1) = strpad('d/dt V in component membrane (millivolt)'); LEGEND_RATES(:,2) = strpad('d/dt n in component fast_sodium_current_n_gate (dimensionless)'); LEGEND_RATES(:,3) = strpad('d/dt n in component potassium_current_n_gate (dimensionless)'); LEGEND_RATES(:,4) = strpad('d/dt k in component slow_potassium_current_k_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) = -55.0; CONSTANTS(:,1) = 21.0; CONSTANTS(:,2) = 0.0; CONSTANTS(:,3) = 50.0; CONSTANTS(:,4) = 28.0; STATES(:,2) = 0.01; CONSTANTS(:,5) = -34.0; CONSTANTS(:,6) = -5.0; CONSTANTS(:,7) = 10.0; CONSTANTS(:,8) = -29.0; CONSTANTS(:,9) = -4.0; CONSTANTS(:,10) = -85.0; CONSTANTS(:,11) = 11.2; STATES(:,3) = 0.01; CONSTANTS(:,12) = 10.0; CONSTANTS(:,13) = -29.0; CONSTANTS(:,14) = -4.0; CONSTANTS(:,15) = 5.6; STATES(:,4) = 0.22; CONSTANTS(:,16) = 10000.0; CONSTANTS(:,17) = -38.0; CONSTANTS(:,18) = -6.0; CONSTANTS(:,19) = 2.8; CONSTANTS(:,20) = -40.0; CONSTANTS(:,21) = -6.0; CONSTANTS(:,22) = 2.8; CONSTANTS(:,23) = -50.0; CONSTANTS(:,24) = 0.0; CONSTANTS(:,25) = 0.0; 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) = 1.00000./(1.00000+exp((STATES(:,1) - CONSTANTS(:,8))./CONSTANTS(:,9))); ALGEBRAIC(:,6) = CONSTANTS(:,7)./cosh((STATES(:,1) - CONSTANTS(:,8))./( 2.00000.*CONSTANTS(:,9))); RATES(:,2) = (ALGEBRAIC(:,2) - STATES(:,2))./ALGEBRAIC(:,6); ALGEBRAIC(:,3) = 1.00000./(1.00000+exp((STATES(:,1) - CONSTANTS(:,13))./CONSTANTS(:,14))); ALGEBRAIC(:,7) = CONSTANTS(:,12)./cosh((STATES(:,1) - CONSTANTS(:,13))./( 2.00000.*CONSTANTS(:,14))); RATES(:,3) = (ALGEBRAIC(:,3) - STATES(:,3))./ALGEBRAIC(:,7); ALGEBRAIC(:,4) = 1.00000./(1.00000+exp((STATES(:,1) - CONSTANTS(:,17))./CONSTANTS(:,18))); ALGEBRAIC(:,8) = CONSTANTS(:,16)./cosh((STATES(:,1) - CONSTANTS(:,17))./( 2.00000.*CONSTANTS(:,18))); RATES(:,4) = (ALGEBRAIC(:,4) - STATES(:,4))./ALGEBRAIC(:,8); ALGEBRAIC(:,11) = 1.00000./(1.00000+exp((STATES(:,1) - CONSTANTS(:,20))./CONSTANTS(:,21))); ALGEBRAIC(:,12) = CONSTANTS(:,19).*ALGEBRAIC(:,11).*(STATES(:,1) - CONSTANTS(:,3)); ALGEBRAIC(:,1) = 1.00000./(1.00000+exp((STATES(:,1) - CONSTANTS(:,5))./CONSTANTS(:,6))); ALGEBRAIC(:,5) = CONSTANTS(:,4).*power(ALGEBRAIC(:,1), 3.00000).*(1.00000 - STATES(:,2)).*(STATES(:,1) - CONSTANTS(:,3)); ALGEBRAIC(:,9) = CONSTANTS(:,11).*power(STATES(:,3), 4.00000).*(STATES(:,1) - CONSTANTS(:,10)); ALGEBRAIC(:,10) = CONSTANTS(:,15).*STATES(:,4).*(STATES(:,1) - CONSTANTS(:,10)); ALGEBRAIC(:,13) = CONSTANTS(:,22).*(STATES(:,1) - CONSTANTS(:,23)); ALGEBRAIC(:,14) = CONSTANTS(:,24).*(STATES(:,1) - CONSTANTS(:,25)); RATES(:,1) = ( - (ALGEBRAIC(:,12)+ALGEBRAIC(:,10)+ALGEBRAIC(:,5)+ALGEBRAIC(:,9)+ALGEBRAIC(:,13)+ALGEBRAIC(:,14))+CONSTANTS(:,2))./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) = 1.00000./(1.00000+exp((STATES(:,1) - CONSTANTS(:,8))./CONSTANTS(:,9))); ALGEBRAIC(:,6) = CONSTANTS(:,7)./cosh((STATES(:,1) - CONSTANTS(:,8))./( 2.00000.*CONSTANTS(:,9))); ALGEBRAIC(:,3) = 1.00000./(1.00000+exp((STATES(:,1) - CONSTANTS(:,13))./CONSTANTS(:,14))); ALGEBRAIC(:,7) = CONSTANTS(:,12)./cosh((STATES(:,1) - CONSTANTS(:,13))./( 2.00000.*CONSTANTS(:,14))); ALGEBRAIC(:,4) = 1.00000./(1.00000+exp((STATES(:,1) - CONSTANTS(:,17))./CONSTANTS(:,18))); ALGEBRAIC(:,8) = CONSTANTS(:,16)./cosh((STATES(:,1) - CONSTANTS(:,17))./( 2.00000.*CONSTANTS(:,18))); ALGEBRAIC(:,11) = 1.00000./(1.00000+exp((STATES(:,1) - CONSTANTS(:,20))./CONSTANTS(:,21))); ALGEBRAIC(:,12) = CONSTANTS(:,19).*ALGEBRAIC(:,11).*(STATES(:,1) - CONSTANTS(:,3)); ALGEBRAIC(:,1) = 1.00000./(1.00000+exp((STATES(:,1) - CONSTANTS(:,5))./CONSTANTS(:,6))); ALGEBRAIC(:,5) = CONSTANTS(:,4).*power(ALGEBRAIC(:,1), 3.00000).*(1.00000 - STATES(:,2)).*(STATES(:,1) - CONSTANTS(:,3)); ALGEBRAIC(:,9) = CONSTANTS(:,11).*power(STATES(:,3), 4.00000).*(STATES(:,1) - CONSTANTS(:,10)); ALGEBRAIC(:,10) = CONSTANTS(:,15).*STATES(:,4).*(STATES(:,1) - CONSTANTS(:,10)); ALGEBRAIC(:,13) = CONSTANTS(:,22).*(STATES(:,1) - CONSTANTS(:,23)); ALGEBRAIC(:,14) = CONSTANTS(:,24).*(STATES(:,1) - CONSTANTS(:,25)); 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