MM_ode2.m

function [f] = MM_ode2(t,x)
% FUNCTION MM_ode1 Full kinetic model of irreversible enzyme reaction with 
% inflow and outflow.
%
%   [f] = MM_ode2(t,x)
%
%  Inputs:  t - time (seconds)
%           x - vector of concentrations (a,b,c) (M)
%  Outputs: f - vector of time derivatives
%               {da/dt,db/dt,dc/dt}      

%State variables
a = x(1);   %substrate
b = x(2);   %product
c = x(3);   %enzyme complex

%Parameters
kp1 = 1000; %kp1 - forward rate constant (M^{-1} sec^{-1})
km1 = 1.0;  %km1 - reverse rate constant (sec^{-1})
kp2 = 0.1;  %kp2 - forward rate constant (sec^{-1})
E0  = 1e-4; %E0 - total enzyme concentration (M)
kp3 = 0.01;  %kp3 - rate constant product outflux (sec^{-1})

%Input
u = 1e-6;  %influx (M/sec)

%ODE's
f(1) = u + (km1 + kp1*a)*c - kp1*E0*a;
f(2) = kp2*c - kp3*b;
f(3) = kp1*a*(E0 - c) - (km1 + kp2)*c;

f = f(:);   %Output needs to be a column vector