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 =16;
end
% There are a total of 3 entries in each of the rate and state variable arrays.
% There are a total of 34 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 interface (ms)');
LEGEND_STATES(:,1) = strpad('Vm in component interface (mV)');
LEGEND_STATES(:,2) = strpad('cMgADP in component interface (concentration)');
LEGEND_STATES(:,3) = strpad('cNa_i in component interface (concentration)');
LEGEND_ALGEBRAIC(:,16) = strpad('v_cyc in component NaK_pump (rate)');
LEGEND_ALGEBRAIC(:,10) = strpad('net_free_energy in component NaK_pump (energy)');
LEGEND_CONSTANTS(:,1) = strpad('body_temp in component NaK_pump (kelvin)');
LEGEND_CONSTANTS(:,2) = strpad('gas_const in component NaK_pump (gas_constant)');
LEGEND_CONSTANTS(:,3) = strpad('faraday_const in component NaK_pump (faraday_constant)');
LEGEND_CONSTANTS(:,4) = strpad('k1 in component NaK_pump (rate)');
LEGEND_CONSTANTS(:,5) = strpad('minus_k1 in component NaK_pump (minus_k1_rate)');
LEGEND_CONSTANTS(:,6) = strpad('k2 in component NaK_pump (rate)');
LEGEND_CONSTANTS(:,7) = strpad('minus_k2 in component NaK_pump (rate)');
LEGEND_CONSTANTS(:,8) = strpad('k3 in component NaK_pump (rate)');
LEGEND_CONSTANTS(:,9) = strpad('minus_k3 in component NaK_pump (minus_k3_rate)');
LEGEND_CONSTANTS(:,10) = strpad('k4 in component NaK_pump (rate)');
LEGEND_CONSTANTS(:,11) = strpad('minus_k4 in component NaK_pump (rate)');
LEGEND_CONSTANTS(:,12) = strpad('eq_Na_base_e in component NaK_pump (concentration)');
LEGEND_CONSTANTS(:,13) = strpad('eq_Na_base_i in component NaK_pump (concentration)');
LEGEND_CONSTANTS(:,14) = strpad('eq_K_e in component NaK_pump (concentration)');
LEGEND_CONSTANTS(:,15) = strpad('eq_K_i in component NaK_pump (concentration)');
LEGEND_CONSTANTS(:,16) = strpad('eq_MgATP in component NaK_pump (concentration)');
LEGEND_CONSTANTS(:,17) = strpad('eq_HPi in component NaK_pump (concentration)');
LEGEND_CONSTANTS(:,18) = strpad('eq_KPi in component NaK_pump (concentration)');
LEGEND_CONSTANTS(:,19) = strpad('eq_NaPi in component NaK_pump (concentration)');
LEGEND_ALGEBRAIC(:,4) = strpad('dimless_Na_e in component NaK_pump (dimensionless)');
LEGEND_ALGEBRAIC(:,2) = strpad('dimless_Na_i in component NaK_pump (dimensionless)');
LEGEND_CONSTANTS(:,28) = strpad('dimless_K_e in component NaK_pump (dimensionless)');
LEGEND_CONSTANTS(:,27) = strpad('dimless_K_i in component NaK_pump (dimensionless)');
LEGEND_CONSTANTS(:,29) = strpad('dimless_MgATP in component NaK_pump (dimensionless)');
LEGEND_ALGEBRAIC(:,6) = strpad('alpha1 in component NaK_pump (rate)');
LEGEND_CONSTANTS(:,30) = strpad('alpha2 in component NaK_pump (rate)');
LEGEND_ALGEBRAIC(:,8) = strpad('alpha3 in component NaK_pump (rate)');
LEGEND_CONSTANTS(:,31) = strpad('alpha4 in component NaK_pump (rate)');
LEGEND_ALGEBRAIC(:,11) = strpad('minus_alpha1 in component NaK_pump (rate)');
LEGEND_ALGEBRAIC(:,12) = strpad('minus_alpha2 in component NaK_pump (rate)');
LEGEND_ALGEBRAIC(:,13) = strpad('minus_alpha3 in component NaK_pump (rate)');
LEGEND_ALGEBRAIC(:,14) = strpad('minus_alpha4 in component NaK_pump (rate)');
LEGEND_CONSTANTS(:,20) = strpad('cNa_e in component NaK_pump (concentration)');
LEGEND_CONSTANTS(:,21) = strpad('cK_e in component NaK_pump (concentration)');
LEGEND_CONSTANTS(:,22) = strpad('cK_i in component NaK_pump (concentration)');
LEGEND_CONSTANTS(:,23) = strpad('cMgATP in component NaK_pump (concentration)');
LEGEND_CONSTANTS(:,24) = strpad('cPi_sum in component NaK_pump (concentration)');
LEGEND_ALGEBRAIC(:,1) = strpad('cPi in component NaK_pump (concentration)');
LEGEND_CONSTANTS(:,25) = strpad('cH in component NaK_pump (concentration)');
LEGEND_ALGEBRAIC(:,3) = strpad('dG_Na in component NaK_pump (energy)');
LEGEND_ALGEBRAIC(:,5) = strpad('dG_K in component NaK_pump (energy)');
LEGEND_ALGEBRAIC(:,7) = strpad('dG_pump in component NaK_pump (energy)');
LEGEND_ALGEBRAIC(:,9) = strpad('dG_ATP in component NaK_pump (energy)');
LEGEND_CONSTANTS(:,26) = strpad('partition_factor in component NaK_pump (dimensionless)');
LEGEND_ALGEBRAIC(:,15) = strpad('diagram_sum in component NaK_pump (rate_diagram_sum)');
LEGEND_RATES(:,1) = strpad('d/dt Vm in component interface (mV)');
LEGEND_RATES(:,2) = strpad('d/dt cMgADP in component interface (concentration)');
LEGEND_RATES(:,3) = strpad('d/dt cNa_i in component interface (concentration)');
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) = -150;
STATES(:,2) = 0.01;
STATES(:,3) = 50.;
CONSTANTS(:,1) = 310.;
CONSTANTS(:,2) = 8.314;
CONSTANTS(:,3) = 96485.;
CONSTANTS(:,4) = 1050.;
CONSTANTS(:,5) = 172.1;
CONSTANTS(:,6) = 481.;
CONSTANTS(:,7) = 40.1;
CONSTANTS(:,8) = 2000.;
CONSTANTS(:,9) = 79287.1;
CONSTANTS(:,10) = 320.;
CONSTANTS(:,11) = 40.1;
CONSTANTS(:,12) = 15.5;
CONSTANTS(:,13) = 2.49;
CONSTANTS(:,14) = 0.213;
CONSTANTS(:,15) = 0.5;
CONSTANTS(:,16) = 2.51;
CONSTANTS(:,17) = 0.000169;
CONSTANTS(:,18) = 292.;
CONSTANTS(:,19) = 224.;
CONSTANTS(:,20) = 150.;
CONSTANTS(:,21) = 5.4;
CONSTANTS(:,22) = 140.;
CONSTANTS(:,23) = 9.8;
CONSTANTS(:,24) = 4.2;
CONSTANTS(:,25) = 0.000081283;
CONSTANTS(:,26) = -0.031288692380984445;
CONSTANTS(:,27) = CONSTANTS(:,22)./CONSTANTS(:,15);
CONSTANTS(:,31) = 1.00000;
CONSTANTS(:,32) = 0.00000;
CONSTANTS(:,33) = 0.00000;
CONSTANTS(:,28) = CONSTANTS(:,21)./CONSTANTS(:,14);
CONSTANTS(:,29) = CONSTANTS(:,23)./CONSTANTS(:,16);
CONSTANTS(:,30) = CONSTANTS(:,6);
CONSTANTS(:,31) = ( CONSTANTS(:,10).*CONSTANTS(:,29))./(1.00000+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
RATES(:,1) = CONSTANTS(:,31);
RATES(:,2) = CONSTANTS(:,32);
RATES(:,3) = CONSTANTS(:,33);
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) = CONSTANTS(:,24)./(1.00000+CONSTANTS(:,22)./CONSTANTS(:,18)+CONSTANTS(:,25)./CONSTANTS(:,17)+STATES(:,3)./CONSTANTS(:,19));
ALGEBRAIC(:,2) = STATES(:,3)./( CONSTANTS(:,13).*exp(( CONSTANTS(:,26).*CONSTANTS(:,3).*0.00100000.*STATES(:,1))./( 3.00000.*CONSTANTS(:,2).*CONSTANTS(:,1))));
ALGEBRAIC(:,3) = CONSTANTS(:,2).*CONSTANTS(:,1).*log(CONSTANTS(:,20)./STATES(:,3)) - CONSTANTS(:,3).*0.00100000.*STATES(:,1);
ALGEBRAIC(:,4) = CONSTANTS(:,20)./( CONSTANTS(:,12).*exp(( (1.00000+CONSTANTS(:,26)).*CONSTANTS(:,3).*0.00100000.*STATES(:,1))./( 3.00000.*CONSTANTS(:,2).*CONSTANTS(:,1))));
ALGEBRAIC(:,5) = CONSTANTS(:,2).*CONSTANTS(:,1).*log(CONSTANTS(:,22)./CONSTANTS(:,21))+ CONSTANTS(:,3).*0.00100000.*STATES(:,1);
ALGEBRAIC(:,6) = ( CONSTANTS(:,4).*power(ALGEBRAIC(:,2), 3.00000))./((power(1.00000+ALGEBRAIC(:,2), 3.00000)+power(1.00000+CONSTANTS(:,27), 2.00000)) - 1.00000);
ALGEBRAIC(:,7) = 2.00000.*ALGEBRAIC(:,5)+ 3.00000.*ALGEBRAIC(:,3);
ALGEBRAIC(:,8) = ( CONSTANTS(:,8).*power(CONSTANTS(:,28), 2.00000))./((power(1.00000+ALGEBRAIC(:,4), 3.00000)+power(1.00000+CONSTANTS(:,28), 2.00000)) - 1.00000);
ALGEBRAIC(:,9) = -29600.0 - CONSTANTS(:,2).*CONSTANTS(:,1).*log(CONSTANTS(:,23)./( 0.00100000.*STATES(:,2).*ALGEBRAIC(:,1)));
ALGEBRAIC(:,10) = ALGEBRAIC(:,9)+ALGEBRAIC(:,7);
ALGEBRAIC(:,11) = CONSTANTS(:,5).*STATES(:,2);
ALGEBRAIC(:,12) = ( CONSTANTS(:,7).*power(ALGEBRAIC(:,4), 3.00000))./((power(1.00000+ALGEBRAIC(:,4), 3.00000)+power(1.00000+CONSTANTS(:,28), 2.00000)) - 1.00000);
ALGEBRAIC(:,13) = ( CONSTANTS(:,9).*ALGEBRAIC(:,1).*CONSTANTS(:,25))./(1.00000+CONSTANTS(:,29));
ALGEBRAIC(:,14) = ( CONSTANTS(:,11).*power(CONSTANTS(:,27), 2.00000))./((power(1.00000+ALGEBRAIC(:,2), 3.00000)+power(1.00000+CONSTANTS(:,27), 2.00000)) - 1.00000);
ALGEBRAIC(:,15) = ALGEBRAIC(:,13).*ALGEBRAIC(:,12).*ALGEBRAIC(:,11)+ CONSTANTS(:,31).*ALGEBRAIC(:,12).*ALGEBRAIC(:,11)+ CONSTANTS(:,31).*CONSTANTS(:,30).*ALGEBRAIC(:,8)+ CONSTANTS(:,31).*ALGEBRAIC(:,11).*ALGEBRAIC(:,8)+ ALGEBRAIC(:,13).*ALGEBRAIC(:,12).*ALGEBRAIC(:,6)+ CONSTANTS(:,31).*ALGEBRAIC(:,12).*ALGEBRAIC(:,6)+ CONSTANTS(:,31).*ALGEBRAIC(:,6).*ALGEBRAIC(:,8)+ ALGEBRAIC(:,13).*ALGEBRAIC(:,6).*CONSTANTS(:,30)+ CONSTANTS(:,31).*ALGEBRAIC(:,6).*CONSTANTS(:,30)+ ALGEBRAIC(:,6).*CONSTANTS(:,30).*ALGEBRAIC(:,8)+ ALGEBRAIC(:,14).*ALGEBRAIC(:,13).*ALGEBRAIC(:,11)+ ALGEBRAIC(:,14).*ALGEBRAIC(:,13).*CONSTANTS(:,30)+ ALGEBRAIC(:,14).*ALGEBRAIC(:,13).*ALGEBRAIC(:,12)+ ALGEBRAIC(:,14).*ALGEBRAIC(:,11).*ALGEBRAIC(:,12)+ ALGEBRAIC(:,14).*CONSTANTS(:,30).*ALGEBRAIC(:,8)+ ALGEBRAIC(:,14).*ALGEBRAIC(:,11).*ALGEBRAIC(:,8);
ALGEBRAIC(:,16) = ( ALGEBRAIC(:,6).*CONSTANTS(:,30).*ALGEBRAIC(:,8).*CONSTANTS(:,31) - ALGEBRAIC(:,11).*ALGEBRAIC(:,12).*ALGEBRAIC(:,13).*ALGEBRAIC(:,14))./ALGEBRAIC(:,15);
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