# A universal kinetic framework for quantitative isothermal amplification governed by polymerase speed, amplicon size, and binding efficiency

## TL;DR

This paper introduces a new model to predict and optimize isothermal DNA amplification by linking enzyme speed, DNA size, and primer binding efficiency.

## Contribution

A universal kinetic framework for isothermal amplification that unifies diverse methods under a single predictive model.

## Key findings

- The model defines amplification efficiency using polymerase extension rate, amplicon size, and primer-template binding efficiency.
- LAMP's complex kinetics are shown to be structurally equivalent to simple exponential growth.
- The framework accurately predicts amplification outcomes under various conditions and enables robust viral quantification in wastewater.

## Abstract

The lack of a predictive, first-principles model has confined the development of isothermal exponential amplification (IEA) to empirical optimization for decades, hindering its quantitative potential. Here, we resolve this by establishing a universal kinetic framework that defines amplification efficiency through three fundamental physical parameters: the polymerase extension rate (Se), the amplicon size (Sa), and the primer-template binding efficiency (ξ). The model reveals the apparent doubling time as \documentclass[12pt]{minimal}
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$T = \frac{{{{S}_a}}}{{\xi \cdot {{S}_e}}}$\end{document}, providing a unified physical explanation for IEA efficiency across diverse mechanisms, including loop-mediated isothermal amplification (LAMP), strand displacement amplification (SDA), recombinase polymerase amplification (RPA), and helicase-dependent amplification (HDA). Crucially, we mathematically demonstrate that the complex kinetics of LAMP, a case study with extreme product heterogeneity, are structurally isomorphic to simple exponential growth. A Taylor expansion proves that LAMP product heterogeneity emerges as a Poisson process, a prediction we confirm experimentally. This framework accurately predicts quantification outcomes under varying conditions (enzyme, temperature, and inhibitors) and enables robust viral quantification in wastewater. By bridging fundamental enzymology with point-of-care applications, our work provides a general blueprint for optimizing IEA by engineering polymerase speed (Se), minimizing amplicon size (Sa), and fine-tuning primer-binding efficiency (ξ).

Graphical Abstract