We study the asymptotic properties of Maximum likelihood estimator for a parameter of the law of the environment in the model of one-dimensional RWRE and explain how this model is used by biophysicists to describe the DNA unzipping experiment. When the walk is transient (ballistic and sub-ballistic), we show that the underlying process of left steps, which exhibits a structure of branching process in random environment, is recurrent. This process permits to find out the MLE's asymptotic in this case. When the RWRE is recurrent, this last process of left steps explodes and became useless. We propose instead to use the localization of the RWRE in its main valley.