Quantifying Frustrations for Molecular Complexes with Noncovalent Interactions

Molecular systems bound together through noncovalent interactions are involved in a lot of life-essential processes such as molecular recognition, signal transduction, and allosteric regulation. While cooperation as an important effect discovered in these systems focuses on the behavior of system's entirety, we need also examine the behavior of individual parts. In this work, using the distortion energy as the descriptor, we quantify frustration as the energetic loss of individual parts due to the formation of nonadditive molecular complexes. The applicability of our approach has been illustrated by a few simple clusters. Our results show that the frustration effect is smaller than the cooperation effect, but same as cooperativity, it can be both positive and negative. The ultimate benefit of a system made of multiple parts is dictated by the balance between the cooperative behavior among parts and the sacrifice from its individuals. This conflicting yet complementary conceptual pair of cooperation and frustration provides us with a different perspective from the systems' viewpoint for molecular complexes. This new angle of appreciating molecular complexes can be applied in conformational changes, enzymatic catalysis, and many more.