Generated Code
The following is matlab code generated by the CellML API from this CellML file. (Back to language selection)
The raw code is available.
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 =9;
end
% There are a total of 7 entries in each of the rate and state variable arrays.
% There are a total of 35 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('IP3 in component IP3_dynamics (micromolar)');
LEGEND_ALGEBRAIC(:,1) = strpad('j_IP3 in component IP3_dynamics (micromolar_micrometre_per_second)');
LEGEND_CONSTANTS(:,1) = strpad('J_IP3 in component IP3_dynamics (micromolar_micrometre_per_second)');
LEGEND_CONSTANTS(:,2) = strpad('k_0 in component IP3_dynamics (first_order_rate_constant)');
LEGEND_CONSTANTS(:,3) = strpad('k_degr in component IP3_dynamics (first_order_rate_constant)');
LEGEND_CONSTANTS(:,4) = strpad('IP3_0 in component IP3_dynamics (micromolar)');
LEGEND_CONSTANTS(:,5) = strpad('Ca_ER in component ER (micromolar)');
LEGEND_STATES(:,2) = strpad('Ca in component Calcium_dynamics (micromolar)');
LEGEND_CONSTANTS(:,6) = strpad('alpha in component Calcium_dynamics (dimensionless)');
LEGEND_ALGEBRAIC(:,2) = strpad('J_channel in component Channel_kinetics (flux)');
LEGEND_ALGEBRAIC(:,8) = strpad('J_pump in component SERCA_pump_kinetics (flux)');
LEGEND_ALGEBRAIC(:,9) = strpad('J_leak in component Leak (flux)');
LEGEND_CONSTANTS(:,28) = strpad('R_buffering in component Calcium_buffering (flux)');
LEGEND_CONSTANTS(:,7) = strpad('J_max in component Channel_kinetics (flux)');
LEGEND_STATES(:,3) = strpad('h in component Channel_kinetics (dimensionless)');
LEGEND_CONSTANTS(:,8) = strpad('K_act in component Channel_kinetics (micromolar)');
LEGEND_CONSTANTS(:,9) = strpad('K_IP3 in component Channel_kinetics (micromolar)');
LEGEND_CONSTANTS(:,10) = strpad('K_inh in component Channel_kinetics (micromolar)');
LEGEND_CONSTANTS(:,11) = strpad('k_on in component Channel_kinetics (second_order_rate_constant)');
LEGEND_CONSTANTS(:,12) = strpad('V_max in component SERCA_pump_kinetics (flux)');
LEGEND_CONSTANTS(:,13) = strpad('K_p in component SERCA_pump_kinetics (micromolar)');
LEGEND_CONSTANTS(:,14) = strpad('L in component Leak (flux)');
LEGEND_CONSTANTS(:,15) = strpad('R1 in component Calcium_buffering (flux)');
LEGEND_CONSTANTS(:,16) = strpad('R2 in component Calcium_buffering (flux)');
LEGEND_STATES(:,4) = strpad('B1 in component Calcium_buffering (micromolar)');
LEGEND_STATES(:,5) = strpad('B2 in component Calcium_buffering (micromolar)');
LEGEND_STATES(:,6) = strpad('CaB1 in component Calcium_buffering (micromolar)');
LEGEND_STATES(:,7) = strpad('CaB2 in component Calcium_buffering (micromolar)');
LEGEND_ALGEBRAIC(:,3) = strpad('k1_on in component Calcium_buffering (second_order_rate_constant)');
LEGEND_ALGEBRAIC(:,4) = strpad('k1_off in component Calcium_buffering (first_order_rate_constant)');
LEGEND_ALGEBRAIC(:,5) = strpad('k2_on in component Calcium_buffering (second_order_rate_constant)');
LEGEND_ALGEBRAIC(:,6) = strpad('k2_off in component Calcium_buffering (first_order_rate_constant)');
LEGEND_CONSTANTS(:,17) = strpad('K1 in component Calcium_buffering (micromolar)');
LEGEND_CONSTANTS(:,18) = strpad('K2 in component Calcium_buffering (micromolar)');
LEGEND_CONSTANTS(:,19) = strpad('soma_or_neurite in component Plasma_membrane_extrusion_mechanisms (dimensionless)');
LEGEND_ALGEBRAIC(:,7) = strpad('j_Ca in component Plasma_membrane_extrusion_mechanisms (micromolar_micrometre_per_second)');
LEGEND_CONSTANTS(:,20) = strpad('gamma_0 in component Plasma_membrane_extrusion_mechanisms (micrometre_per_second)');
LEGEND_CONSTANTS(:,31) = strpad('gamma in component Plasma_membrane_extrusion_mechanisms (micrometre_per_second)');
LEGEND_CONSTANTS(:,29) = strpad('gamma_s in component Plasma_membrane_extrusion_mechanisms (micrometre_per_second)');
LEGEND_CONSTANTS(:,30) = strpad('gamma_n in component Plasma_membrane_extrusion_mechanisms (micrometre_per_second)');
LEGEND_CONSTANTS(:,21) = strpad('delta in component Plasma_membrane_extrusion_mechanisms (dimensionless)');
LEGEND_CONSTANTS(:,22) = strpad('sigma in component Plasma_membrane_extrusion_mechanisms (per_micrometre)');
LEGEND_CONSTANTS(:,23) = strpad('w_n in component Plasma_membrane_extrusion_mechanisms (dimensionless)');
LEGEND_CONSTANTS(:,24) = strpad('w_s in component Plasma_membrane_extrusion_mechanisms (dimensionless)');
LEGEND_CONSTANTS(:,25) = strpad('sigma_soma_2D in component Plasma_membrane_extrusion_mechanisms (per_micrometre)');
LEGEND_CONSTANTS(:,26) = strpad('sigma_neurite_2D in component Plasma_membrane_extrusion_mechanisms (per_micrometre)');
LEGEND_CONSTANTS(:,27) = strpad('Ca_c in component Plasma_membrane_extrusion_mechanisms (micromolar)');
LEGEND_RATES(:,1) = strpad('d/dt IP3 in component IP3_dynamics (micromolar)');
LEGEND_RATES(:,2) = strpad('d/dt Ca in component Calcium_dynamics (micromolar)');
LEGEND_RATES(:,3) = strpad('d/dt h in component Channel_kinetics (dimensionless)');
LEGEND_RATES(:,4) = strpad('d/dt B1 in component Calcium_buffering (micromolar)');
LEGEND_RATES(:,6) = strpad('d/dt CaB1 in component Calcium_buffering (micromolar)');
LEGEND_RATES(:,5) = strpad('d/dt B2 in component Calcium_buffering (micromolar)');
LEGEND_RATES(:,7) = strpad('d/dt CaB2 in component Calcium_buffering (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) = 3.0;
CONSTANTS(:,1) = 20.86;
CONSTANTS(:,2) = 1.188;
CONSTANTS(:,3) = 0.14;
CONSTANTS(:,4) = 0.16;
CONSTANTS(:,5) = 400.0;
STATES(:,2) = 0.05;
CONSTANTS(:,6) = 0.0;
CONSTANTS(:,7) = 3500.0;
STATES(:,3) = 0.8;
CONSTANTS(:,8) = 0.3;
CONSTANTS(:,9) = 0.8;
CONSTANTS(:,10) = 0.2;
CONSTANTS(:,11) = 2.7;
CONSTANTS(:,12) = 3.75;
CONSTANTS(:,13) = 0.27;
CONSTANTS(:,14) = 0.1;
CONSTANTS(:,15) = 0.1;
CONSTANTS(:,16) = 0.1;
STATES(:,4) = 450.0;
STATES(:,5) = 75.0;
STATES(:,6) = 0;
STATES(:,7) = 0;
CONSTANTS(:,17) = 10.0;
CONSTANTS(:,18) = 0.24;
CONSTANTS(:,19) = -1;
CONSTANTS(:,20) = 8.0;
CONSTANTS(:,21) = 1.45;
CONSTANTS(:,22) = 0.263;
CONSTANTS(:,23) = 0.377;
CONSTANTS(:,24) = 0.623;
CONSTANTS(:,25) = 0.132;
CONSTANTS(:,26) = 0.479;
CONSTANTS(:,27) = 0.2;
CONSTANTS(:,28) = CONSTANTS(:,15)+CONSTANTS(:,16);
CONSTANTS(:,29) = ( CONSTANTS(:,20).*CONSTANTS(:,22))./( CONSTANTS(:,21).*CONSTANTS(:,26).*CONSTANTS(:,23)+ CONSTANTS(:,25).*CONSTANTS(:,24));
CONSTANTS(:,31) = CONSTANTS(:,15);
CONSTANTS(:,32) = - CONSTANTS(:,15);
CONSTANTS(:,33) = CONSTANTS(:,16);
CONSTANTS(:,34) = - CONSTANTS(:,16);
CONSTANTS(:,30) = ( CONSTANTS(:,20).*CONSTANTS(:,22).*CONSTANTS(:,21))./( CONSTANTS(:,21).*CONSTANTS(:,26).*CONSTANTS(:,23)+ CONSTANTS(:,25).*CONSTANTS(:,24));
CONSTANTS(:,31) = piecewise({CONSTANTS(:,19)<=0.00000, CONSTANTS(:,29) }, CONSTANTS(:,30));
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
RATES(:,4) = CONSTANTS(:,31);
RATES(:,6) = CONSTANTS(:,32);
RATES(:,5) = CONSTANTS(:,33);
RATES(:,7) = CONSTANTS(:,34);
RATES(:,1) = - ( CONSTANTS(:,3).*(STATES(:,1) - CONSTANTS(:,4)));
RATES(:,3) = CONSTANTS(:,11).*(CONSTANTS(:,10) - STATES(:,3).*(STATES(:,2)+CONSTANTS(:,10)));
ALGEBRAIC(:,2) = CONSTANTS(:,7).*power( (STATES(:,1)./(STATES(:,1)+CONSTANTS(:,9))).*(STATES(:,2)./(STATES(:,2)+CONSTANTS(:,8))).*STATES(:,3), 3.00000).*(1.00000 - STATES(:,2)./CONSTANTS(:,5));
ALGEBRAIC(:,8) = CONSTANTS(:,12).*(power(STATES(:,2), 2.00000)./(power(STATES(:,2), 2.00000)+power(CONSTANTS(:,13), 2.00000)));
ALGEBRAIC(:,9) = CONSTANTS(:,14).*(1.00000 - STATES(:,2)./CONSTANTS(:,5));
RATES(:,2) = CONSTANTS(:,6).*(ALGEBRAIC(:,2)+ - ALGEBRAIC(:,8)+ALGEBRAIC(:,9))+CONSTANTS(:,28);
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) = CONSTANTS(:,7).*power( (STATES(:,1)./(STATES(:,1)+CONSTANTS(:,9))).*(STATES(:,2)./(STATES(:,2)+CONSTANTS(:,8))).*STATES(:,3), 3.00000).*(1.00000 - STATES(:,2)./CONSTANTS(:,5));
ALGEBRAIC(:,8) = CONSTANTS(:,12).*(power(STATES(:,2), 2.00000)./(power(STATES(:,2), 2.00000)+power(CONSTANTS(:,13), 2.00000)));
ALGEBRAIC(:,9) = CONSTANTS(:,14).*(1.00000 - STATES(:,2)./CONSTANTS(:,5));
ALGEBRAIC(:,1) = CONSTANTS(:,1).*exp( - CONSTANTS(:,2).*VOI);
[CONSTANTS, STATES, ALGEBRAIC] = rootfind_0(VOI, CONSTANTS, STATES, ALGEBRAIC);
[CONSTANTS, STATES, ALGEBRAIC] = rootfind_1(VOI, CONSTANTS, STATES, ALGEBRAIC);
ALGEBRAIC(:,7) = piecewise({STATES(:,2)>CONSTANTS(:,27), CONSTANTS(:,31).*(STATES(:,2) - CONSTANTS(:,27)) }, 0.00000);
end
% Functions required for solving differential algebraic equation
function [CONSTANTS, STATES, ALGEBRAIC] = rootfind_0(VOI, CONSTANTS_IN, STATES_IN, ALGEBRAIC_IN)
ALGEBRAIC = ALGEBRAIC_IN;
CONSTANTS = CONSTANTS_IN;
STATES = STATES_IN;
global initialGuess_0;
if (length(initialGuess_0) ~= 2), initialGuess_0 = [0.1,0.1];, end
options = optimset('Display', 'off', 'TolX', 1E-6);
if length(VOI) == 1
residualfn = @(algebraicCandidate)residualSN_0(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES);
soln = fsolve(residualfn, initialGuess_0, options);
initialGuess_0 = soln;
ALGEBRAIC(:,3) = soln(1);
ALGEBRAIC(:,4) = soln(2);
else
SET_ALGEBRAIC(:,3) = logical(1);
SET_ALGEBRAIC(:,4) = logical(1);
for i=1:length(VOI)
residualfn = @(algebraicCandidate)residualSN_0(algebraicCandidate, ALGEBRAIC(i,:), VOI(i), CONSTANTS, STATES(i,:));
soln = fsolve(residualfn, initialGuess_0, options);
initialGuess_0 = soln;
TEMP_ALGEBRAIC(:,3) = soln(1);
TEMP_ALGEBRAIC(:,4) = soln(2);
ALGEBRAIC(i,SET_ALGEBRAIC) = TEMP_ALGEBRAIC(SET_ALGEBRAIC);
end
end
end
function resid = residualSN_0(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES)
ALGEBRAIC(:,3) = algebraicCandidate(1);
ALGEBRAIC(:,4) = algebraicCandidate(2);
resid(1) = CONSTANTS(:,15) - ( - ( ALGEBRAIC(:,3).*STATES(:,2).*STATES(:,4))+ ALGEBRAIC(:,4).*STATES(:,6));
resid(2) = CONSTANTS(:,17) - ALGEBRAIC(:,4)./ALGEBRAIC(:,3);
end
% Functions required for solving differential algebraic equation
function [CONSTANTS, STATES, ALGEBRAIC] = rootfind_1(VOI, CONSTANTS_IN, STATES_IN, ALGEBRAIC_IN)
ALGEBRAIC = ALGEBRAIC_IN;
CONSTANTS = CONSTANTS_IN;
STATES = STATES_IN;
global initialGuess_1;
if (length(initialGuess_1) ~= 2), initialGuess_1 = [0.1,0.1];, end
options = optimset('Display', 'off', 'TolX', 1E-6);
if length(VOI) == 1
residualfn = @(algebraicCandidate)residualSN_1(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES);
soln = fsolve(residualfn, initialGuess_1, options);
initialGuess_1 = soln;
ALGEBRAIC(:,5) = soln(1);
ALGEBRAIC(:,6) = soln(2);
else
SET_ALGEBRAIC(:,5) = logical(1);
SET_ALGEBRAIC(:,6) = logical(1);
for i=1:length(VOI)
residualfn = @(algebraicCandidate)residualSN_1(algebraicCandidate, ALGEBRAIC(i,:), VOI(i), CONSTANTS, STATES(i,:));
soln = fsolve(residualfn, initialGuess_1, options);
initialGuess_1 = soln;
TEMP_ALGEBRAIC(:,5) = soln(1);
TEMP_ALGEBRAIC(:,6) = soln(2);
ALGEBRAIC(i,SET_ALGEBRAIC) = TEMP_ALGEBRAIC(SET_ALGEBRAIC);
end
end
end
function resid = residualSN_1(algebraicCandidate, ALGEBRAIC, VOI, CONSTANTS, STATES)
ALGEBRAIC(:,5) = algebraicCandidate(1);
ALGEBRAIC(:,6) = algebraicCandidate(2);
resid(1) = CONSTANTS(:,16) - ( - ( ALGEBRAIC(:,5).*STATES(:,2).*STATES(:,5))+ ALGEBRAIC(:,6).*STATES(:,7));
resid(2) = CONSTANTS(:,18) - ALGEBRAIC(:,6)./ALGEBRAIC(:,5);
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