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Open Access Highly Accessed Methodology article

Modeling miRNA-mRNA interactions: fitting chemical kinetics equations to microarray data

Zijun Luo12*, Robert Azencott1 and Yi Zhao2*

Author Affiliations

1 Department of Mathematics, University of Houston, 4800 Calhoun, Houston, TX, USA

2 School of Natural Sciences and Humanities, Harbin Institute of Technology, Shenzhen Graduate School, Shenzhen, Guangdong, China

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BMC Systems Biology 2014, 8:19  doi:10.1186/1752-0509-8-19

Published: 18 February 2014



The miRNAs are small non-coding RNAs of roughly 22 nucleotides in length, which can bind with and inhibit protein coding mRNAs through complementary base pairing. By degrading mRNAs and repressing proteins, miRNAs regulate the cell signaling and cell functions. This paper focuses on innovative mathematical techniques to model gene interactions by algorithmic analysis of microarray data. Our goal was to elucidate which mRNAs were actually degraded or had their translation inhibited by miRNAs belonging to a very large pool of potential miRNAs.


We proposed two chemical kinetics equations (CKEs) to model the interactions between miRNAs, mRNAs and the associated proteins. In order to reduce computational cost, we used a non linear profile clustering method named minimal net clustering and efficiently condensed the large set of expression profiles observed in our microarray data sets. We determined unknown parameters of the CKE models by minimizing the discrepancy between model prediction and data, using our own fast non linear optimization algorithm. We then retained only the CKE models for which the optimized fit to microarray data is of high quality and validated multiple miRNA-mRNA pairs.


The implementation of CKE modeling and minimal net clustering reduces drastically the potential set of miRNA-mRNA pairs, with a high gain for further experimental validations. The minimal net clustering also provides good miRNA candidates that have similar regulatory roles.

miRNA; Chemical kinetics modeling; Minimal net clustering