In the frame of a Markov chain model for cooperative interactions in proteins, previously introduced by us, we deal here with estimation of unknown parameters from protein energy data. One of these parameters characterizes the cooperativity of a protein; we propose to measure it also by the so-called approximate entropy. By our computations the approximate entropy turns out to be a decreasing function of the cooperativity. We analyse both simulated data of the Markov chain, and protein energy data obtained by molecular dynamics simulation. Moreover, we compare two rubredoxin proteins at different temperatures, according to their degrees of cooperativity.