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

## TL;DR

This paper introduces a new framework to explain how botulinum toxin's molecular effects translate into variable clinical outcomes by considering probabilistic events across tissue.

## Contribution

The novel contribution is the Molecular Probability Field (MPF-BoNT) framework, which links molecular events to spatial and temporal clinical effects probabilistically.

## Key findings

- The MPF-BoNT framework explains variability in botulinum toxin effects through probabilistic functional silencing of nerve terminals.
- The framework integrates molecular variables like exposure, uptake, and silencing thresholds to describe tissue-level outcomes.
- It provides a formal language to connect enzymatic events with observable clinical patterns.

## Abstract

Botulinum toxin is widely used in medicine and aesthetics to reduce muscle activity, yet its clinical effects often vary even when the same dose is administered. Traditionally, these variations have been explained mainly in terms of how the drug spreads or how much is injected. However, this approach does not fully account for why similar doses can produce different spatial patterns of effect. In this study, we propose a new conceptual framework that describes treatment effects as a probability field across tissue. Instead of focusing only on drug concentration, the framework considers the likelihood that individual nerve endings become functionally silenced after exposure. This probability depends on several biological factors, including local exposure, cellular uptake, molecular activity inside the cell, and the threshold required to impair nerve signaling. The framework does not introduce new biological mechanisms but provides a structured way to connect molecular events to observable clinical outcomes across space and time. By clarifying how spatial patterns of response emerge, this approach may help guide future experimental research and improve the interpretation of variability in therapeutic and aesthetic applications.

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.