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 =7; end % There are a total of 2 entries in each of the rate and state variable arrays. % There are a total of 2 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_ALGEBRAIC(:,1) = strpad('V in component environment (millivolt)'); LEGEND_VOI = strpad('t in component environment (millisec)'); LEGEND_STATES(:,1) = strpad('m in component sodium_channel_m_gate (dimensionless)'); LEGEND_STATES(:,2) = strpad('h in component sodium_channel_h_gate (dimensionless)'); LEGEND_CONSTANTS(:,1) = strpad('g_Na in component sodium_channel (milliS_per_cm2)'); LEGEND_CONSTANTS(:,2) = strpad('E_Na in component sodium_channel (millivolt)'); LEGEND_ALGEBRAIC(:,2) = strpad('Na_conductance in component sodium_channel (milliS_per_cm2)'); LEGEND_ALGEBRAIC(:,5) = strpad('i_Na in component sodium_channel (microA_per_cm2)'); LEGEND_ALGEBRAIC(:,3) = strpad('alpha_m in component sodium_channel_m_gate (per_millisec)'); LEGEND_ALGEBRAIC(:,6) = strpad('beta_m in component sodium_channel_m_gate (per_millisec)'); LEGEND_ALGEBRAIC(:,4) = strpad('alpha_h in component sodium_channel_h_gate (per_millisec)'); LEGEND_ALGEBRAIC(:,7) = strpad('beta_h in component sodium_channel_h_gate (per_millisec)'); LEGEND_RATES(:,1) = strpad('d/dt m in component sodium_channel_m_gate (dimensionless)'); LEGEND_RATES(:,2) = strpad('d/dt h in component sodium_channel_h_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) = 0.05; STATES(:,2) = 0.6; CONSTANTS(:,1) = 120; CONSTANTS(:,2) = 35; 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) = piecewise({VOI>5.00000&VOI<15.0000, 0.00000 }, - 85.0000); ALGEBRAIC(:,3) = ( - 0.100000.*(ALGEBRAIC(:,1)+50.0000))./(exp( - (ALGEBRAIC(:,1)+50.0000)./10.0000) - 1.00000); ALGEBRAIC(:,6) = 4.00000.*exp( - (ALGEBRAIC(:,1)+75.0000)./18.0000); RATES(:,1) = ALGEBRAIC(:,3).*(1.00000 - STATES(:,1)) - ALGEBRAIC(:,6).*STATES(:,1); ALGEBRAIC(:,4) = 0.0700000.*exp( - (ALGEBRAIC(:,1)+75.0000)./20.0000); ALGEBRAIC(:,7) = 1.00000./(exp( - (ALGEBRAIC(:,1)+45.0000)./10.0000)+1.00000); RATES(:,2) = ALGEBRAIC(:,4).*(1.00000 - STATES(:,2)) - ALGEBRAIC(:,7).*STATES(:,2); 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) = piecewise({VOI>5.00000&VOI<15.0000, 0.00000 }, - 85.0000); ALGEBRAIC(:,3) = ( - 0.100000.*(ALGEBRAIC(:,1)+50.0000))./(exp( - (ALGEBRAIC(:,1)+50.0000)./10.0000) - 1.00000); ALGEBRAIC(:,6) = 4.00000.*exp( - (ALGEBRAIC(:,1)+75.0000)./18.0000); ALGEBRAIC(:,4) = 0.0700000.*exp( - (ALGEBRAIC(:,1)+75.0000)./20.0000); ALGEBRAIC(:,7) = 1.00000./(exp( - (ALGEBRAIC(:,1)+45.0000)./10.0000)+1.00000); ALGEBRAIC(:,2) = CONSTANTS(:,1).*power(STATES(:,1), 3.00000).*STATES(:,2); ALGEBRAIC(:,5) = ALGEBRAIC(:,2).*(ALGEBRAIC(:,1) - CONSTANTS(:,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