Before revision:  Challenges and implications inspired by these observations are discussed .
After revision:  Further analysis revealed that the direct cause of non-linear contributions are heterogeneous, and in extreme cases canceling, linear correlations associated with different torsional states of participating torsions. Therefore, torsional state transitions of participating torsions for a correlated BTP are only necessary but not sufficient condition for significant non-linear contributions. These findings implicate a general search strategy for novel allosteric modulation of protein activities. Meanwhile, it was suggested that ensemble averaged correlation calculation and static contact network analysis, while insightful, are not sufficient to elucidate mechanisms underlying allosteric signal transmission in general, dynamical and time scale resolved analysis are essential .