Systems pharmacology modelling of alternative pathway of complement activation
Suruchi Bakshi1, Jessica Neisen2, Sebastien Petit-Frere2, Marta Biedzka-Sarek2, Eva-Maria Nichols2, Stefano Zamuner3, Piet H. van der Graaf1,4
1Systems Pharmacology, LACDR, University of Leiden, 2 Cytokine, Chemokine & Complement DPU, Immunoinflammation TA unit, GSK, 3Clinical Pharmacology, Modelling and Simulation, GSK, 4 Certara QSP, Canterbury.
Objectives: The complement system can be activated by three pathways, namely classical, alternative and lectin. The Alternative pathway (AP) of complement activation is responsible for rapid amplification of signals from all three pathways. Its dysregulation leads to autoimmune diseases such as haemolytic uremic syndrome and age-related macular degeneration [1]. AP activation involves formation of several intermediate complexes (ICs). We aim to construct a systems model of AP activation to identify suitable ICs as drug targets and to study the amplification behaviour.
Methods: We have constructed differential equation-based models of AP, which are smaller in size in contrast to previous modelling efforts [2,3], thus allowing mathematical analysis. These models are analysed using techniques from dynamical systems and sensitivity analysis combined with fitting in vitro data. We are working with experimental biologists at GSK, with the results of mathematical analysis feeding into the experimental designs and vice versa.
Results: In a minimal model of AP, we selected potential drug targets from AP ICs with hypothetical drugs. We found that target suitability strongly depends upon certain reaction rates.
Steady-state analysis of the model predicted the equilibrium levels of ICs, which disagree with experimental data, suggesting hitherto unaccounted losses in the experimental system. Further experiments are underway to detect such losses.
Quasi-steady state analysis of the minimal model has provided insights into the timescales involved in the pathway. We extended this model by adding regulators of AP and re-evaluated target-suitability. Through sensitivity analysis and data fitting we have discovered crucial parameters.
Conclusions: Systems models of AP activation have allowed us to explore drug target-suitability of AP ICs and their dependence upon crucial parameters. Modelling and steady state analysis have been vital in uncovering and quantifying discrepancies with experimental data. In the future, we expect to gain further insight into the timescales and thresholds of amplification behaviour through mathematical analysis.
References:
[1] Zipfel PF, Heinen S, Jozsi, M and Skerka C. Complement and diseases: Defective alternative pathway control results in kidney and eye diseases. Mol Immunol (2006) 43: 97-106.
[2] Korotaevskiy AA, Hanin LG, Khanin MA. Non-linear dynamics of the complement system activation. Math Biosci (2009) 222:127-143.
[3] Zewde N, Gorham RD, Dorado A, Morikis D. Quantitative Modeling of the Alternative Pathway of the Complement System. PLOS One (2016) 11(3).