Invariance under Structure Translation as the Origin of Host Immune Capacity Conservation from Noether's Theorem

TL;DR

This paper introduces a physics-inspired theoretical framework for understanding immune capacity as a conserved quantity arising from symmetry principles, linking immunological phenomena to a physical conservation law.

Contribution

It applies Lagrangian mechanics and Noether's theorem to model immune recognition, proposing a quantifiable conserved measure of host immunity.

Findings

Identifies a conserved quantity $I$ as the physical basis of immunity.

Unifies phenomena like vaccination, memory, and tolerance under a single conservation law.

Aligns the model with clinical observations and experimental data.

Abstract

The capacity to resist pathogens is recognized as a fundamental property of the immune system, yet the capacity itself remains a phenomenological concept and lacks a defined physical basis. Its fundamental entity, definition, and quantification are thus unresolved. Here, we address these questions by introducing a theoretical framework based on Lagrangian analytical mechanics, which recasts immune recognition as a dynamical system in an immunological state space. Generalized coordinates are used to describe the conformational states of immune receptors, and their evolution is governed by Euler-Lagrange equations constructed from the antigen-receptor interaction. Central to our theory is the identification of a continuous symmetry: the action remains invariant under specific translations within the antigenic structure space or time. From this symmetry, Noether's theorem dictates a conserved quantity, $I$. We propose that $I$ is the physical embodiment of host immunity, a quantifiable measure that integrates the system's protective sensitivity (with dimensions of action) and response intensity (with dimensions of energy). Furthermore, this framework unifies key immunological phenomena as dynamical consequences of the same underlying conservation law, including vaccination, immune memory, tolerance, original antigenic sin, and T cell exhaustion. The consistency of this model with established clinical observations (e.g., conserved symptom profiles across distinct influenza strains) and published experimental data provides its initial validation. By transforming immune capacity from a phenomenological concept into a quantifiable physical entity defined by a conservation law, this work establishes a foundational framework for a unified, predictive immunology.