Systems mapping of metabolic genes through control theory

The formation of any complex phenotype involves a web of metabolic pathways in which one chemical is transformed through the catalysis of enzymes into another. Traditional approaches for mapping quantitative trait loci (QTLs) are based on a direct association analysis between DNA marker genotypes and end-point phenotypes, neglecting the mechanistic processes of how a phenotype is formed biochemically. Here, we propose a new dynamic framework for mapping metabolic QTLs (mQTLs) responsible for phenotypic formation. By treating metabolic pathways as a biological system, robust differential equations have proven to be a powerful means of studying and predicting the dynamic behavior of biochemical reactions that cause a high-order phenotype. The new framework integrates these differential equations into a statistical mixture model for QTL mapping. Since the mathematical parameters that define the emergent properties of the metabolic system can be estimated and tested for different mQTL genotypes, the framework allows the dynamic pattern of genetic effects to be quantified on metabolic capacity and efficacy across a time-space scale. Based on a recent study of glycolysis in Saccharomyces cerevisiae, we design and perform a series of simulation studies to investigate the statistical properties of the framework and validate its usefulness and utilization in practice. This framework can be generalized to mapping QTLs for any other dynamic systems and may stimulate pharmacogenetic research toward personalized drug and treatment intervention.