Quantitative Modeling of the Alternative Pathway of the Complement System.

The complement system is an integral part of innate immunity that detects and eliminates invading pathogens through a cascade of reactions. The destructive effects of the complement activation on host cells are inhibited through versatile regulators that are present in plasma and bound to membranes. Impairment in the capacity of these regulators to function in the proper manner results in autoimmune diseases. To better understand the delicate balance between complement activation and regulation, we have developed a comprehensive quantitative model of the alternative pathway. Our model incorporates a system of ordinary differential equations that describes the dynamics of the four steps of the alternative pathway under physiological conditions: (i) initiation (fluid phase), (ii) amplification (surfaces), (iii) termination (pathogen), and (iv) regulation (host cell and fluid phase). We have examined complement activation and regulation on different surfaces, using the cellular dimensions of a characteristic bacterium (E. coli) and host cell (human erythrocyte). In addition, we have incorporated neutrophil-secreted properdin into the model highlighting the cross talk of neutrophils with the alternative pathway in coordinating innate immunity. Our study yields a series of time-dependent response data for all alternative pathway proteins, fragments, and complexes. We demonstrate the robustness of alternative pathway on the surface of pathogens in which complement components were able to saturate the entire region in about 54 minutes, while occupying less than one percent on host cells at the same time period. Our model reveals that tight regulation of complement starts in fluid phase in which propagation of the alternative pathway was inhibited through the dismantlement of fluid phase convertases. Our model also depicts the intricate role that properdin released from neutrophils plays in initiating and propagating the alternative pathway during bacterial infection.