Mathematical Modeling of Complement Pathway Dynamics for Target Validation and Selection of Drug Modalities for Complement Therapies

Abstract

Motivation: The complement pathway plays a critical role in innate immune defense against infections. Dysregulation between activation and regulation of the complement pathway is widely known to contribute to several diseases. Nevertheless, very few drugs that target complement proteins have made it to the final regulatory approval because of factors such as high concentrations and dosing requirements for complement proteins and serious side effects from complement inhibition. Methods: A quantitative systems pharmacology (QSP) model of the complement pathway has been developed to evaluate potential drug targets to inhibit complement activation in autoimmune diseases. The model describes complement activation via the alternative and terminal pathways as well as the dynamics of several regulatory proteins. The QSP model has been used to evaluate the effect of inhibiting complement targets on reducing pathway activation caused by deficiency in factor H and CD59. The model also informed the feasibility of developing small-molecule or large-molecule antibody drugs by predicting the drug dosing and affinity requirements for potential complement targets. Results: Inhibition of several complement proteins was predicted to lead to a significant reduction in complement activation and cell lysis. The complement proteins that are present in very high concentrations or have high turnover rates (C3, factor B, factor D, and C6) were predicted to be challenging to engage with feasible doses of large-molecule antibody compounds (≤20 mg/kg). Alternatively, complement fragments that have a short half-life (C3b, C3bB, and C3bBb) were predicted to be challenging or infeasible to engage with small-molecule compounds because of high drug affinity requirements (>1 nM) for the inhibition of downstream processes. The drug affinity requirements for disease severity reduction were predicted to differ more than one to two orders of magnitude than affinities needed for the conventional 90% target engagement (TE) for several proteins. Thus, the QSP model analyses indicate the importance for accounting for TE requirements for achieving reduction in disease severity endpoints during the lead optimization stage.

Keywords: Quantitative Systems Pharmacology; complement pathway; dose prediction; drug modality selection; mathematical modeling; target validation.

FIGURE 1

Simplified overview of the processes in the complement pathway model for plasma and cell surface reactions. Key processes shown here: alternative pathway (AP) tickover, regulation by FH and FI in plasma and cell surface, AP surface amplification, terminal pathway, and surface regulators: sialic acid, DAF, and CD59. Dynamics for binding of complement proteins to Properdin are not included here for simplicity and represented separately in Figure 2. Other key processes included in the model but not shown here: dynamics of regulation by CR1, clusterin, and vitronectin.

FIGURE 2

Model implementation for Properdin dynamics in plasma and cell surface (expanded based on Figure 6 in Hourcade (2006)). (A) Cell surface: Properdin binds to surface bound C3b and C3-proconvertases, C- convertase, or iC3b, and provides two additional sites P* for the de novo assembly of the convertase. FPn binding to only surface-bound C3b is shown in the figure for simplicity. Similarly, in addition to C3b-P* binding, C3 proconvertase–C3bB, C3b-convertase, and iC3b can occupy P* sites. (B) Plasma: C3b or its complexes and cleavage products bind to three binding sites on FPn, leading to convertase assembly. Unlike on cell surface, P* does not contribute to amplification of the pathway through additional binding sites in plasma; however, complement activation in plasma is enhanced by Properdin due to increased binding between C3bP and FB, and stabilization of C3-convertase.

FIGURE 3

Representations of the complement model for validation with different datasets.

FIGURE 4

Comparison of the tickover complement model dynamics with in vitro data (Pangburn et al., 1981). (A) Model simulations match in vitro data for C3 hydrolysis alone (blue), with FB, FD added (green) and with FH, FI, FB, and FD added (red). (B) Zoomed in view of model simulations for decay in C3 hemolytic activity in the presence of FB, FD (green).

FIGURE 5

Comparison of model simulations with GSK in vitro assay data for alternative pathway. Model results are denoted by solid line, and the assay results are from two sets of independent, identical experiments, denoted as “Data 1” (o) and “Data 2” (*). (A) Model simulation and in vitro data for alternative pathway assay without Properdin (−) FP for C3a, Ba, iC3b. (B) Model simulation and in vitro data for alternative pathway assay with Properdin (+)FP for C3a, Ba, and iC3b.

FIGURE 6

Comparison of model simulations with in vitro assay data for terminal pathways. Model simulation results are denoted by solid blue line, and the terminal pathway assay results are from two sets of independent, identical experiments denoted as “Data 1” (o) and “Data 2” (*). Dose–response of cell lysis is shown for different concentrations of (A) C5b6 (μg/ml), (B) C7 (μg/ml), (C) C8 (μg/ml), and (D) C9 (μg/ml).

FIGURE 7

Effect of 99% reduction in cell surface regulators, CR1, DAF, and CD59, and 50% reduction in fluid phase regulator FH on complement fragments C3a, Ba, iC3b, and C5a.

FIGURE 8

Complement model predictions for (A) correlation between iC3b + iC3bP deposition on erythrocytes and levels of CR1, (B) surface MAC, (C) lysis of host erythrocytes due to 99% reduction in CR1, DAF, and CD59 and 50% reduction in fluid-phase regulator FH, and (D) consumption of complement proteins C3 and FB due to FH deficiency ranging from 0 to 99%.

FIGURE 9

Model predictions for the effect of 90 and 99% inhibition of complement proteins (C3, FB, FD, C5, C6, C7, C8, C9, FP, C3b, C3bB, C3-convertase (C3conv), and C5-convertase (C5conv)) on complement activation driven by CD59 deficiency or knockout such as in PNH disease.

FIGURE 10

Model predictions for the effect of 90 and 99% inhibition of complement proteins (C3, FB, FD, C5, C6, C7, C8, C9, FP, C3b, C3bB, C3-convertase (C3conv), and C5-convertase (C5conv)) on complement activation driven by 40% FH deficiency such as in aHUS.

FIGURE 11

Doses of SM/LM-Ab compounds needed for engaging complement proteins. Free complement protein levels are shown for different doses of SM (0, 1, 10, and 100 mg) and LM-Ab (0, 1, 10, and 20 mg/kg). Dashed lines: 50% inhibition (black), 90% inhibition (blue), 99% inhibition (pink) from baseline. Solid lines: % free target from the baseline at different dose levels. (A,D) Blocking of FD; (B,C) blocking of C5; (C,F) blocking of C3-convertases (C3bBb + C3bBbP).

FIGURE 12

Model predictions for dosing tractability of complement proteins for SM and LM-Ab drugs.

FIGURE 13

Fractional inhibition in (A) FD and (B) cell lysis at different affinities (K_D) and doses of a SM modality. Drug affinities required for 90% target inhibition versus 90% cell lysis inhibition for (C) small-molecule and (D) large-molecule Ab modalities. Plots (C) and (D): only the select targets that attain 90% TE and cell lysis are shown. The affinity ranges tested for SM modality—1 μM-0.1 nM and LM-Ab modality 1nM-0.1p.m. Affinity requirements predicted to be on the edges of the plots may be lower than the ranges tested.