  Here we have systematically studied the cooperative binding of substrate
molecules on the active sites of a single oligomeric enzyme in a chemiostatic
condition. The average number of bound substrate and the net velocity of the
enzyme catalyzed reaction are studied by the formulation of stochastic master
equation for the cooperative binding classified here as spatial and temporal.
We have estimated the entropy production for the cooperative binding schemes
based on single trajectory analysis using a kinetic Monte Carlo technique. It
is found that the total as well as the medium entropy production show the same
generic diagnostic signature for detecting the cooperativity, usually
characterized in terms of the net velocity of the reaction. This feature is
also found to be valid for the total entropy production rate at the
nonequilibrium steady state. We have introduced an index of cooperativity, C,
defined in terms of the ratio of the surprisals or equivalently, the stochastic
system entropy associated with the fully bound state of the cooperative and
non-cooperative cases. The criteria of cooperativity in terms of C is compared
with that of the Hill coefficient and gives a microscopic insight on the
cooperative binding of substrate on a single oligomeric enzyme which is usually
characterized by macroscopic reaction rate.
