function dxdt = michaelis_menten(t,x)
% USAGE: dxdt = michaelis_menten(t,x)
global k1 km1 k2 e0

% initialize the time derivative for the model
dxdt = zeros(size(x));

% rename substrate (s) and product (p) for ease of reading
s = x(1);
p = x(2);

% define the mm constant from the rate constants in global memory
K = (km1+k2)/k1;

% the time derivatives of substrate (1) and product (2) are
% negatives of each other and defined by the mm model

dxdt(1) = -k2*e0*s/(K+s);
dxdt(2) =  k2*e0*s/(K+s);

% differential equation values computed. function completed.
return