Statistical Model for Biochemical Network Inference

Abstract

We describe a statistical method for predicting most likely reactions in a biochemical reaction network from the longitudinal data on species concentrations. Such data is relatively easily available in biochemical laboratories, for instance, via the popular RT-PCR technology. Under the assumed kinetics of the law of mass action, we also propose the data-based algorithms for estimating the prediction errors and for network dimension reduction. The second algorithm allows in particular for the application of the original algebraic inferential procedure described in Craciun et al. (2009) without the unnecessary restrictions on the dimension of the network stoichiometric space. Simulated examples of biochemical networks are analyzed, in order to assess the proposed methods' performance.

Keywords:

• Algebraic statistical model
• Biochemical reaction network
• Dimension reduction
• Law of mass action
• Polyhedral geometry

2000 Mathematics Subject Classification:

• 92C40
• 92C45
• 52B70
• 62F

Acknowledgments

This research was partially sponsored by the “Focused Research Group” grants NSF–DMS 0840695 (Rempala) and NSF–DMS 0553687 (Craciun) as well as by NIH grant R01DE019243 (Rempala, Kim), NIH grant R01GM086881 (Craciun, Pantea), and NSF-DMS grant 1106485 (Rempala). The authors are grateful to the anonymous referee for useful comments and for pointing out several important references.

Notes

In general, it may be beneficial to consider various measures vol(·) that are absolutely continuous with respect to the usual volume (Lebesgue) measure. For instance, in our numerical examples in the next section, we define this measure via gamma densities.

The extension to non-equidistant time grid is straightforward but, for simplicity, not pursued here.