Equilibrium transitions between side-chain conformations in leucine and isoleucine

Despite recent improvements in computational methods for protein design, we still lack a quantitative, predictive understanding of the intrinsic probabilities for amino acids to adopt particular side-chain conformations. Surprisingly, this question has remained unsettled for many years, in part because of inconsistent results from different experimental approaches. To explicitly determine the relative populations of different side-chain dihedral angles, we performed all-atom hard-sphere Langevin Dynamics simulations of leucine (Leu) and isoleucine (Ile) dipeptide mimetics with stereo-chemical constraints and repulsive-only steric interactions between non-bonded atoms. We determine the relative populations of the different χ(1) and χ(2) dihedral angle combinations as a function of the backbone dihedral angles ϕ and ψ. We also propose, and test, a mechanism for inter-conversion between the different side-chain conformations. Specifically, we discover that some of the transitions between side-chain dihedral angle combinations are very frequent, whereas others are orders of magnitude less frequent, because they require rare coordinated motions to avoid steric clashes. For example, to transition between different values of χ(2), the Leu side-chain bond angles κ(1) and κ(2) must increase, whereas to transition in χ(1), the Ile bond angles λ(1) and λ(2) must increase. These results emphasize the importance of computational approaches in stimulating further experimental studies of the conformations of side-chains in proteins. Moreover, our studies emphasize the power of simple steric models to inform our understanding of protein structure, dynamics, and design.