The Mathematical Model and Numerical Method for Thermoelectric DNA Sequencing

Abstract

Thermoelectric DNA sequencing is a label-free sequencing-by-synthesis method that identifies incorporated nucleotides by measuring the minute heat released when DNA polymerase inserts a deoxyribonucleoside triphosphate into a growing DNA strand. The central mathematical challenge lies in accurately modelling the coupled chemical kinetics and heat transfer that occur within a confined microfluidic reaction zone: nucleotide incorporation proceeds through a stiff system of chemical rate equations, while the induced temperature field evolves as a two-dimensional transient process with steep local gradients. This work develops a two-dimensional continuum model that couples a stiff ordinary differential equation (ODE) system, describing nucleotide binding, catalysis, pyrophosphate release and hydrolysis, with a transient nonlinear energy equation governing the spatiotemporal temperature distribution. Gear’s backward differentiation formula (BDF) is used for the stiff chemical kinetics owing to its unconditional A-stability, while the Crank–Nicolson scheme is used for the parabolic heat equation for its unconditional stability and second-order accuracy. Numerical experiments confirm that the model captures the transient temperature rise and thermal relaxation associated with each nucleotide incorporation event, with peak increments on the order of nano- to microkelvins localised near the polymerase active site, consistent with reported experimental values. The resulting framework provides a rigorous computational basis for the design and optimisation of thermoelectric DNA sequencing platforms.