From Molecular Cleavage to Clinical Effect: A Probabilistic Field Model of Botulinum Toxin Action.

Botulinum toxin (BoNT) is a highly specific molecular enzyme whose therapeutic action is based on the proteolytic cleavage of SNARE proteins, most notably SNAP-25. Despite the deterministic nature of this molecular mechanism, the clinical effects of BoNT exhibit substantial variability in efficacy, spatial extent, and duration that cannot be fully explained by dose-response relationships or diffusion-based models. In this work, we propose the Molecular Probability Field (MPF-BoNT) as a conceptual framework that bridges discrete molecular events and emergent functional outcomes. The MPF is defined as the spatial-temporal distribution of the probability that presynaptic terminals reach a functional silencing state (operationalized via SNAP-25 cleavage exceeding a threshold), shaped by exposure, uptake, target density, and temporal dynamics following toxin exposure. Within this framework, clinical effects arise from the integration of probabilistic molecular events across space and time, rather than from toxin presence or concentration alone. The MPF-BoNT framework accounts for key features of botulinum toxin action, including spread, nonlinearity of dose effects, variability in duration, and differences between technical and biological non-response. By explicitly incorporating molecular variables such as local concentration, exposure time, terminal density, internalization probability, and functional silencing thresholds, the framework provides an integrative interpretation of tissue-level behavior grounded in molecular biology. The MPF-BoNT offers a formal language to describe how established enzymatic events generate observable spatial, temporal, and functional patterns. As a generative framework grounded in explicit testable structure, it establishes a foundation for future experimental and clinical research.