Machine Learning of Temperature-dependent Chemical Kinetics Using Parallel Droplet Microreactors

TL;DR

This work tackles the challenge of learning temperature-dependent chemical kinetics from high-throughput data. It introduces an end-to-end platform that couples parallel droplet microreactors with Neural ODEs, using a DNA-based fluorescent thermometer to obtain in situ temperature readouts and time-resolved product signals across thousands of droplets. Neural ODEs capture nonlinear temperature effects more faithfully than Arrhenius-based mechanistic models, demonstrated by $R^2$ values around $0.983$ versus $0.922$ for a model beta-glucosidase reaction, and extend to dynamic temperature gradients. The framework enables scalable, data-driven analysis of nonequilibrium kinetics under controlled thermal conditions, offering a pathway to rational design of temperature-sensitive biochemical processes and integration with physics-informed modeling.

Abstract

Temperature is a fundamental regulator of chemical and biochemical kinetics, yet capturing nonlinear thermal effects directly from experimental data remains a major challenge due to limited throughput and model flexibility. Recent advances in machine learning have enabled flexible modeling beyond conventional physical laws, but most existing strategies remain confined to surrogate models of end-point yields rather than full kinetic dynamics. Consequently, an end-to-end framework that unifies systematic kinetic data acquisition with machine learning based modeling has been lacking. In this paper, we present a unified framework that integrates droplet microfluidics with machine learning for the systematic analysis of temperature-dependent reaction kinetics. The platform is specifically designed to enable stable immobilization and long-term time-lapse imaging of thousands of droplets under dynamic thermal gradients. This configuration yields massively parallel time-resolved datasets across diverse temperature conditions that capture transient kinetics and provides particularly suitable inputs for training machine-learning models of reaction dynamics. Leveraging these datasets, we train Neural ODE models, which embed neural networks within differential equations to flexibly represent nonlinear temperature dependencies beyond conventional formulations. We demonstrate accurate prediction of enzymatic kinetics across diverse thermal environments, highlighting the robustness and versatility of the approach. Our framework bridges high-throughput experimental data acquisition with data-driven modeling, establishing a versatile foundation for enhanced predictive ability and rational analysis and design of temperature-sensitive biochemical processes.

Figures (4)

• Figure 1: End-to-end framework for data-driven modeling of temperature-dependent kinetics. A microfluidic device generates and immobilizes thousands of droplets under thermal gradients with droplet temperatures monitored by DNA thermometers. Automated microscopy and image analysis enable tracking of time-resolved fluorescence signals, capturing long-term kinetics across diverse thermal conditions. The resulting large-scale time-series datasets are used to train neural networks embedded in ordinary differential equations (Neural ODEs), which flexibly capture nonlinear temperature dependencies.
• Figure 2: Microfluidic platform for droplet immobilization and temperature readout. (A) Schematic of the two-layer microfluidic device integrating droplet generation and immobilization under thermal gradients. (B) Experimental validation showing stable confinement of droplets over extended periods without coalescence or displacement. Trajectory analysis of droplet centers over 180 min confirms that droplets remain immobilized with minimal displacement. (C) Fluorescence images of droplets encapsulating DNA thermometers under stationary temperature gradients. Calibration of fluorescence intensity to temperature. Scale bars represent 1 mm.
• Figure 3: Parallel measurements of temperature-dependent enzymatic kinetics and Neural ODE based modeling. (A) Fluorescence images of DNA thermometers in droplets under a constant temperature gradient. Left: fluorescence images over time. Center: fluorescence intensity profiles of droplets along the chamber position. Right: time-series of droplet temperatures obtained using the calibration curve in Fig. \ref{['fgr:fig2_verification']}C. (B) Fluorescence images of enzymatic reaction products under a constant temperature gradient. Left: fluorescence images of droplets over time. Center: fluorescence intensity profiles of droplets along the chamber position. Right: time-series of product fluorescence. (C) Workflow of Neural ODE modeling. Time-series data were split into 80% training, 10% validation, and 10% test sets. Hyperparameters were tuned using validation data, and the final model was evaluated using test data. (D) Time-series of product fluorescence (same as panel B, right) compared with prediction by Neural ODE model. (E) Predicted fluorescence obtained by Neural ODE plotted against experimental data. (F) Predicted fluorescence obtained by an ODE model with Arrhenius rate law plotted against experimental data, showing the advantage of the proposed framework in capturing nonlinear temperature dependencies. Scale bars represent 3 mm.
• Figure 4: Temperature-dependent kinetics under dynamic temperature gradients and Neural ODE based modeling. (A) Schematic of the experimental setup showing a dynamic temperature gradient with switching at $t=30$ and $t=60$ min. (B) Fluorescence images of DNA thermometers in droplets under a dynamic temperature gradient. (C) Fluorescence images of enzymatic reaction products in droplets under a dynamic temperature gradient. (D) Time-series of droplet temperatures obtained from DNA thermometer fluorescence (panel B). (E) Time-series of product fluorescence across diverse temperature range (panel C). (F) Time-series of product fluorescence compared with the prediction by Neural ODE model. The inset shows a scatter plot comparing Neural ODE predictions with experimental data, showing close agreement. Scale bars represent 3 mm.