We propose a criterion for optimal parameter selection in coarse-grained models of proteins and develop a refined elastic network model (ENM) of bovine trypsinogen. The unimodal density-of-states distribution of the trypsinogen ENM disagrees with the bimodal distribution obtained from an all-atom model; however, the bimodal distribution is recovered by strengthening interactions between atoms that are backbone neighbors. We use the backbone-enhanced model to analyze allosteric mechanisms of trypsinogen and find relatively strong communication between the regulatory and active sites.