Coupled equilibrium model of hybridization error for the DNA microarray and tag-antitag systems

Area of Science:

• Biophysics
• Computational Biology
• Molecular Systems Engineering

Background:

• Microarray and toehold strand displacement (TAT) systems are crucial for molecular diagnostics and computation.
• Accurate prediction of hybridization error rates is essential for reliable system performance.
• Existing models often fail to capture the complex error dynamics in these systems.

Purpose of the Study:

• To develop and present a detailed coupled equilibrium model for predicting ensemble average hybridization error rates in microarray/TAT systems.
• To provide the first ensemble average method for estimating post-annealing error rates.
• To investigate the impact of temperature and input concentration on hybridization error response.

Main Methods:

• Development of a coupled equilibrium model based on a mismatched statistical zipper model of duplex formation.
• Implementation of the model using the "NucleicPark" software package.
• Simulation of error response for mean-energy and randomly encoded TAT systems under varying conditions.
• Analysis of model scaling behavior with system size and strand length.

Main Results:

• The model predicts a novel transition in hybridization error response: a logarithmically convex function of temperature for excess inputs (high error) and a monotonic, log-linear function for dilute inputs (low error).
• This behavior differs significantly from predictions of uncoupled equilibrium models.
• In silico evolution using the model resulted in a high-fidelity 100-strand TAT system with a nine standard deviation improvement in error response compared to mean random encoding.

Conclusions:

• The developed coupled equilibrium model accurately predicts hybridization error rates in microarray/TAT systems.
• The model reveals critical insights into error behavior transitions influenced by input concentration and temperature.
• The model serves as a valuable tool for designing more robust and high-fidelity molecular systems.