Fig 1.
The alternative pathway of the complement system.
The diagram shows the pathway as described in the model with its components (orange boxes), reactions (grey arrows), proactivators (green arrows), regulators (red arrows), convertases (yellow boxes), effectors (red boxes), and the positive regulator properdin (brown triangles). Association/dissociation reactions are displayed with a pointed arrowhead, enzymatic reactions with an oval. Degradation was implemented for all proteins and complexes. Proteins marked with a (*) are synthesized. The blue box indicates the reactions of the fluid phase in absence of erythrocytes. Activation of the AP begins with spontaneous hydrolysis (“tick-over”) of C3 producing C3(H2O), which in turn can form the initial convertase C3(H2O)Bb in presence of FB and factor D (FD). The initial convertase can generate more C3b through C3 cleavage. C3b may bind FB, leading to the formation of the fluid-phase convertase C3bBb, or attach to a nearby surface, such as a cell membrane. Surface-attached C3b can combine with FB to form the surface C3 convertase C3bBb, reacting with C3b to generate the C5 convertase, C3bBbC3b. Cleavage of C5 by the C5 convertase activates the terminal pathway. The anaphylatoxin C5a is released while C5b remains attached to the C5 convertase, followed by C6 and C7 binding. The complex C5b-7 is released into the fluid phase, from where it can reinsert into the cell membrane if not sequestered by the regulators vitronectin (Vn) or clusterin (Cn). Upon binding of membrane C5b-7 to C8 and up to 18 C9 molecules [42], the membrane attack complex (MAC) is formed. With sufficient terminal pathway activity, the cell is lysed as a result of the accumulation of MAC complexes, permitting free diffusion of molecules across its membrane. All negative regulators (FH, decay-accelerating factor (DAF), CD59, complement receptor type 1 (CR1), factor I (FI), Vn and Cn) are included in the model, as well as the only known positive regulator, properdin (P), which can stabilize the C3 and C5 convertase.
Fig 2.
Percent hemolysis displayed against the number of MACs per cell (module 3). Data (circles) of human complement-mediated lysis experiments on sheep erythrocytes were obtained from [48] (S3 Appendix). The data was fitted with the sigmoid model of Eq 1 (line), with γ = 1.60 and MAC50 = 1.15 MAC/cell.
Fig 3.
Fluid-phase alternative pathway activation.
Observed (symbols) and simulated (lines, module 1) complement factor levels in experiments of fluid-phase AP activation in in vitro samples. (A) Inactivation of C3 in absence or presence of FB, FD, FH, and FI. (B) Formation of C3b by preassembled C3 convertases. (C) Conversion of C3b to iC3b as a function of FH concentration (790 nM (a), 393 nM (b), 197 nM (c), 98.5 nM (d), 49.3 nM (e), 12.4 nM (f), 4.50 nM (g). Dashed lines: experimental data, solid lines: model simulation). (D-F) Formation of activation markers C3a (D), Bb (E), and C3dg (F) due to spontaneous activation of AP in human serum samples. Data was obtained from [10] (A), [62] (B), [61] (C), [38,64] (D), and [63] (E,F). C3a levels from [38,64] were baseline corrected. Bb and C3dg levels from [63] were converted to molar concentrations for comparison to model results, assuming a molecular weight of 63 kDa and 38 kDa, respectively.
Fig 4.
In vitro hemolytic experiments with rabbit erythrocytes.
Experimental data (symbols) and model simulations (lines module 1–3) in hemolytic assays with rabbit erythrocytes. (A) Time course of hemolysis at 400 ng/mL FD. (B-E) Dose-response curves for hemolysis of rabbit erythrocytes. (B,C) Hemolysis at different serum dilutions (B) or when using a mix of normal human serum and FD- (black) or C3-depleted (red) serum (C). (D) Hemolysis as a function of FD serum concentration at 5 (red) and 30 minutes (black). (E) Hemolysis at different concentrations of C5 (green), FB (blue) and FD (black). For titration of C5 and FD, data from two individual experiments are shown. (F) Dose-response curve for activation markers Bb and C5a as a function of FD concentration. Hemolysis was normalized to lysis in water (A-D) or to the activity of NHS assayed in parallel at the same dilution (E). The experimental data was obtained from [56] (A,C,D), [55] (B), and [60] (E,F).
Fig 5.
Hemolysis of human erythrocytes under partially disabled surface regulation.
(A) Observed versus predicted (module 1–3) hemolysis of human erythrocytes. Observations are from [59] (triangles), [57] (circles) and [58] (squares). Inhibited regulators are indicated. Suppression of FH regulation was assumed to be restricted to the surface. (B) Model predicted (module 1–3) hemolysis for pairwise suppressed regulators. Suppressed regulators are indicated on the axes (FH surf: abolished FH surface regulation, FH tot: complete absence of FH regulation). Predicted hemolysis is shown as heat map and with percent values.
Table 1.
Parameters optimized in the fitting procedure.
Fig 6.
In vitro and in vivo effects of eculizumab in PNH disease.
(A) Observed (symbols) and simulated (line, module 1–3) inhibition of PNH erythrocyte lysis in vitro as a function of eculizumab concentration. (B) Observed (symbols) and simulated (line, module 1–5) recovery of hemoglobin levels in PNH patients treated for 36 months with eculizumab. The experimental data was digitized from [77] (A) and [74] (B).
Table 2.
Hematological biomarkers in healthy and PNH population.