Understanding the hierarchical relationships among biochemical, metabolic, and physiological systems in the mapping between genotype and phenotype is expected to improve the diagnosis, prevention, and treatment of common, complex human diseases. We previously developed a systems biology approach based on Petri nets for carrying out thought experiments for the generation of hypotheses about biological network models that are consistent with genetic models of disease susceptibility. Our systems biology strategy uses grammatical evolution for symbolic manipulation and optimization of Petri net models. We previously demonstrated that this approach routinely identifies biological systems models that are consistent with a variety of complex genetic models in which disease susceptibility is determined by nonlinear interactions between two DNA sequence variations. However, the modeling strategy was generally not successful when extended to modeling nonlinear interactions between three DNA sequence variations. In the present study, we develop a new grammar that uniformly generates Petri net models across the entire search space. The results indicate that choice of grammar plays an important role in the success of grammatical evolution searches in this bioinformatics modeling domain.