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

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 $T = \frac{{{{S}_a}}}{{\xi \cdot {{S}_e}}}$, 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).