Directional Variant Tension (T v ): A Causal Framework for Quantifying Substitution Asymmetry

Amino acid substitutions are often directionally asymmetric due to underlying biophysical constraints and diverse evolutionary pressures. We introduce T v (variant tension), a kernel regression-based metric that quantifies this directional asymmetry directly from aligned multiple sequence alignments (MSAs). T v leverages empirical amino acid frequencies and a non-parametric Gaussian kernel to capture nonlinear substitution flows, providing a causality-inspired framework for understanding evolutionary dynamics. We also present a web-based application that implements the calculation, allowing users to input MSAs, adjust parameters (kernel bandwidth;, smoothing window size), and visualize results, including global tension scores and high-tension sites. Applying T_v to the human glutamate transporter (EAA1), we identify significant substitution asymmetries, localize high-tension sites, and reveal correlations between elevated T v and known pathogenic variants. This framework integrates statistical learning with protein evolution, offering a powerful tool for bridging protein design principles with evolutionary inference. Beyond variant prioritization, T v ; offers a scalable framework for simulating evolution under directional constraints, enabling predictive modeling of protein adaptation. The free web application is openly accsessible at https://www.karagolresearch.com/variantt