Insights into Gene Therapy for Urea Cycle Defects by Mathematical Modeling

Metabolic liver diseases are attractive gene therapy targets that necessitate reconstitution of enzymatic activity in functionally complex biochemical pathways. The levels of enzyme activity required in individual hepatocytes and the proportion of the hepatic cell mass that must be gene corrected for therapeutic benefit vary in a disease-dependent manner that is difficult to predict. While empirical evaluation is inevitably required, useful insights can nevertheless be gained from knowledge of disease pathophysiology and theoretical approaches such as mathematical modeling. Urea cycle defects provide an excellent example. Building on a previously described one-compartment model of the urea cycle, we have constructed a two-compartment model that can simulate liver-targeted gene therapy interventions using the computational program Mathematica. The model predicts that therapeutically effective reconstitution of ureagenesis will correlate most strongly with the proportion of the hepatic cell mass transduced rather than the level of enzyme-encoding transgene expression achieved in individual hepatocytes. Importantly, these predictions are supported by experimental data in mice and human genotype/phenotype correlations. The most notable example of the latter is ornithine transcarbamylase deficiency (X-linked) where impairment of ureagenesis in male and female patients is closely simulated by the one- and two-compartment models, respectively. Collectively, these observations support the practical value of mathematical modeling in evaluation of the disease-specific gene transfer challenges posed by complex metabolic phenotypes.