MAXWELL: Calibrating the probabilistic outputs of protein language models to the mutation-induced stability change landscape

Designing mutations that enhance protein stability is a central goal in protein engineering. However, experimentally screening large numbers of candidate mutations is costly and time-consuming, creating a strong need for computational methods that can identify potentially stabilizing mutations. Among these approaches, protein language models are particularly promising because they learn context-dependent amino acid preferences from large-scale sequence and structure datasets. Nevertheless, most existing stability prediction methods use these models primarily as feature extractors and do not fully exploit the amino acid probability distributions they encode. Here, we introduce MAXWELL (Matrix-wise Landscape Learning), a novel post-training method that calibrates the probabilistic outputs learned by protein language models during pretraining to generate mutational landscapes that quantify the effects of individual amino acid substitutions on protein stability. When applied to ProteinMPNN, MAXWELL yields a state-of-the-art predictor of the effects of protein mutations on stability, outperforming ThermoMPNN and other representative methods on a curated benchmark of experimentally measured stability changes. We next applied MAXWELL to the design of ten single-point mutations in the DhaA dehalogenase, seven of which (70%) increased thermal stability. Among them, G171W showed the largest improvement, with a measured Δ T _m of 4.91 °C. These experimental results establish MAXWELL as a novel post-training strategy for protein language models and a practical framework for designing stabilizing mutations.