Why Do We Need Graphical Models?
Mathematical modeling is an essential tool for understanding complex biological systems. Often biological parameters cannot be measured experimentally, either because of expense, ethical issues or technological limitations. However, we can use probability theory to bridge this gap in our knowledge in a informed manner. Ideally we want to represent the complexity of the system as compactly as possible and graph theory enables us to provide a simple visual representation for communicating the structure of complex data relationships, for example, by representing interacting genes by a series of interconnected nodes. Modeling of biological systems is expected to be an iterative process. The models provide the basis for hypotheses testing by experimentalists which in turn should lead to further refinement of the models. As such, collaboration between researchers spanning multiple disciplines is necessary including mathematicians, statisticians, physiologists, biochemists and geneticists.
Modeling of HDL Cholesterol Transport
It is well known that the risk of heart disease can be partially explained by the balance of High Density Lipoprotein (HDL) (good cholesterol) and low density lipoprotein (LDL) (bad cholesterol). Several drugs are available for lowering LDL cholesterol. However, there has been limited progress in a drug therapy for raising HDL levels. The identification of key genes associated with HDL is only the first step toward designing a drug target. The Churchill group is developing a genetically based Bayesian dynamic model of HDL metabolism for the purpose of performing system wide sensitivity studies of genetic perturbations in inbred mouse strains. Features of this methodology will be applied to predict how the metabolic pathways of different genetic populations function under variable conditions, e.g., environment, medicine, diet and disease. A model of this type can be applied to assess the system-wide effects of drug targets, and to validate and design future experiments.
Distinguishing Genetic Loci That Affect Adiposity From Those That Affect Overall Body Size
We have used structural equation modeling as a statistical method for the analysis of multilocus, multitrait genetic data that provides an intuitive and precise characterization of genetic architecture. We have shown that it is possible to infer the magnitude and direction of causal relationships among multiple correlated phenotypes and illustrated the technique using body composition and bone density data from mouse intercross populations. Using these techniques we were able to distinguish genetic loci that affect adiposity from those that affect overall body size and thus reveal a shortcoming of standardized measures such as body mass index that are widely used in obesity research. The identification of causal networks sheds light on the nature of genetic heterogeneity and pleiotropy in complex genetic systems.