IntroductionKnowledge-based statistical energy functions are widely used in protein structure modeling and prediction 1 . They are usually constructed based on statistical analysis of predefined interacting units from a set of selected high-resolution structures. The interacting units can be either coarse-grained structural components, such as Cα atoms for representing a whole residue, or atomistic structural components as in all-atom representation. The energy function is potential of mean force, or free energy cost, required for generating the observed distribution of the interacting units in the real structures from a zero-interaction reference state. Thus, the choices of interacting units are crucial for the effectiveness of the energy functions. One of the key issues is the orientation dependence in the interaction between the units. This is because the chemical bond connectivity is often ignored in constructing statistical energy functions leading to mis-or under-representation of anisotropic orientation preference in molecular interactions.In the literature, substantial efforts have been made to model anisotropic orientation preference [2][3][4][5][6][7][8][9] . An early attempt employed a side-chain-specific local reference frame to construct distance-and orientation-dependent residue-based statistical potentials for proteins 10 . In a subsequent work 4 , it was shown that contacts between side-chains and main-chains are important, and a Cα-SC-Pep model was introduced to represent orientation dependence. In a more recent highly coarse-grained potential, called OPUS-Ca 8 , orientation preference was introduced into a distance-dependent pairwise potential. In that case, the orientation dependence between two side-chains was described by the relative orientation between two Cα-Cβ vectors. It was found that inclusion of this effect improved the potential's ability to recognize the native state and to improve Z-scores in decoy set tests. Orientation dependence for homodimeric 11 and heterodimeric 12 interactions among seven hydrophobic residues in water has also been included in an analytical modeling of potentials of mean force.Although a certain degree of success in describing orientation dependence was achieved in the aforementioned work, there is still much room for improvement. Recently, a new type of potential, called OPUS-PSP, was developed to maximally capture the orientation dependence in side-chain interactions 13 . OPUS-PSP is an orientation-dependent statistical all-atom potential derived from side-chain packing. §JM: To whom the correspondence should be addressed. Here, we first briefly outline the general framework of OPUS-PSP, followed by the results of its performance on decoy set tests. Then, we will discuss a major application of OPUS-PSP on side-chain conformation modeling via a method called OPUS-Rota 14 . Most importantly, based on the lessons learned from our own work and others, we will discuss issues and insights in the modeling of orientation dependence in molecular interactions.
Theo...