Petri net modeling of high-order genetic systems using grammatical evolution

Abstract

Understanding how DNA sequence variations impact human health through a hierarchy of biochemical and physiological systems is expected to improve the diagnosis, prevention, and treatment of common, complex human diseases. We have previously developed a hierarchical dynamic systems approach based on Petri nets for generating biochemical network models that are consistent with genetic models of disease susceptibility. This modeling approach uses an evolutionary computation approach called grammatical evolution as a search strategy for optimal Petri net models. We have previously demonstrated that this approach routinely identifies biochemical network models that are consistent with a variety of genetic models in which disease susceptibility is determined by nonlinear interactions between two DNA sequence variations. In the present study, we evaluate whether the Petri net approach is capable of identifying biochemical networks that are consistent with disease susceptibility due to higher order nonlinear interactions between three DNA sequence variations. The results indicate that our model-building approach is capable of routinely identifying good, but not perfect, Petri net models. Ideas for improving the algorithm for this high-dimensional problem are presented.

Introduction

The field of human genetics is shifting its emphasis away from rare Mendelian diseases, such as cystic fibrosis, to common diseases that represent the vast majority of the public health burden. As this shift occurs, it is becoming increasingly clear that susceptibility to common human diseases, such as essential hypertension and sporadic breast cancer, is largely due to nonlinear interactions among multiple genes and multiple environmental factors (Ritchie et al., 2001, Moore and Williams, 2002, Moore, 2003). The idea that there will be a single gene with a large effect on disease susceptibility is not realistic. Thus, identification of genes that confer an increased susceptibility to a common disease will require a research strategy that embraces rather than ignores the complexity of these diseases. Further, if we are to successfully use genetic information at the public health level to improve the diagnosis, prevention, and treatment of common diseases, we will need to understand how DNA sequence information influences human health through hierarchical networks of biochemical and physiological systems. Making the connection between genes, biochemistry, and disease susceptibility using a discrete dynamic systems modeling approach is the focus of the present study.

We took the first step towards hierarchical systems modeling of disease susceptibility by addressing the following questions. First, is it possible to develop simple discrete dynamic systems models of biochemical networks that are consistent with nonlinear gene–gene interactions that are observed at the population level? Second, are these simple biochemical systems models biologically plausible? We used discrete dynamic systems models called Petri nets to develop two independent, biologically plausible, biochemical systems models of a well-known nonlinear gene–gene interaction model (unpublished results). This preliminary proof of principle study demonstrated the utility of Petri nets for modeling biochemical systems that are consistent with nonlinear gene–gene interactions in complex diseases. However, an important limitation of this modeling approach is that the Petri net models were developed by a human-based trial and error approach that is time consuming and difficult due to combinatorial complexities. In response to this limitation, Moore and Hahn (2003a) developed a machine intelligence strategy that uses an evolutionary computation approach called grammatical evolution for the automatic discovery of Petri net models. This approach routinely generates Petri net models that are consistent with a variety of genetic models in which disease susceptibility is dependent on nonlinear interactions between two DNA sequence variations (Moore and Hahn, 2003a, Moore and Hahn, 2003b).

The goal of the present study is to evaluate the ability of the grammatical evolution approach proposed by Moore and Hahn (2003a) to discover Petri net models of biochemical systems that are consistent with nonlinear interactions between three DNA sequence variations. The results indicate that our model-building approach is capable of routinely identifying good, but not perfect, Petri net models. Ideas for improving the algorithm for this high-dimensional problem are presented.