The strong and highly anisotropic influence of grain boundary (GB) character on the plasticity of crystalline materials motivates an overarching goal of developing a bicrystallography-sensitive GB model applicable across all misorientations, inclinations, and crystal systems. Here, we focus on the shear coupling factor of GBs, which quantifies the plastic shear associated with GB motion. Unlike symmetric tile GBs, molecular dynamics simulations of asymmetric tilt GBs demonstrate a substantial variance in their shear coupling factors. Interestingly, this variance is pronounced for certain inclination angles and negligible for others. We will explore to what extent the current disconnections model can quantify the shear coupling factors of ATGBs. Smith normal form bicrystallography, a framework developed to study crystalline interfaces, serves as a workhorse in our study.