Complement is an important pathway in innate immunity, inflammation, and many disease processes. However, despite its importance, there are few validated mathematical models of complement activation. In this study, we developed an ensemble of experimentally validated reduced order complement models. We combined ordinary differential equations with logical rules to produce a compact yet predictive model of complement activation. The model, which described the lectin and alternative pathways, was an order of magnitude smaller than comparable models in the literature. We estimated an ensemble of model parameters from in vitro dynamic measurements of the C3a and C5a complement proteins. Subsequently, we validated the model on unseen C3a and C5a measurements not used for model training. Despite its small size, the model was surprisingly predictive. Global sensitivity and robustness analysis suggested complement was robust to any single therapeutic intervention. Only the simultaneous knockdown of both C3 and C5 consistently reduced C3a and C5a formation from all pathways. Taken together, we developed a validated mathematical model of complement activation that was computationally inexpensive, and could easily be incorporated into pre-existing or new pharmacokinetic models of immune system function. The model described experimental data, and predicted the need for multiple points of therapeutic intervention to fully disrupt complement activation.
Complement is an important pathway in innate immunity, inflammation, and many disease processes. However, despite its importance, there are few validated mathematical models of complement activation. In this study, we developed an ensemble of experimentally validated reduced order complement models. We combined ordinary differential equations with logical rules to produce a compact yet predictive model of complement activation. The model, which described the lectin and alternative pathways, was an order of magnitude smaller than comparable models in the literature. We estimated an ensemble of model parameters from in vitro dynamic measurements of the C3a and C5a complement proteins. Subsequently, we validated the model on unseen C3a and C5a measurements not used for model training. Despite its small size, the model was surprisingly predictive. Global sensitivity and robustness analysis suggested complement was robust to any single therapeutic intervention. Only the simultaneous knockdown of both C3 and C5 consistently reduced C3a and C5a formation from all pathways. Taken together, we developed a validated mathematical model of complement activation that was computationally inexpensive, and could easily be incorporated into pre-existing or new pharmacokinetic models of immune system function. The model described experimental data, and predicted the need for multiple points of therapeutic intervention to fully disrupt complement activation.
Mathematical models of biochemical networks are useful tools to understand and ultimately predict how cells utilize nutrients to produce valuable products. Hybrid cybernetic models in combination with elementary modes (HCM) is a tool to model cellular metabolism. However, HCM is limited to reduced metabolic networks because of the computational burden of calculating elementary modes. In this study, we developed the hybrid cybernetic modeling with flux balance analysis or HCM-FBA technique which uses flux balance solutions instead of elementary modes to dynamically model metabolism. We show HCM-FBA has comparable performance to HCM for a proof of concept metabolic network and for a reduced anaerobic E. coli network. Next, HCM-FBA was applied to a larger metabolic network of aerobic E. coli metabolism which was infeasible for HCM (29 FBA modes versus more than 153,000 elementary modes). Global sensitivity analysis further reduced the number of FBA modes required to describe the aerobic E. coli data, while maintaining model fit. Thus, HCM-FBA is a promising alternative to HCM for large networks where the generation of elementary modes is infeasible.
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