Fig 1.
Biochemical reactions originating from fluid phase activation of the alternative and classical pathways.
A complete explanation of the various steps, grouped in modules of initiation (fluid phase), amplification, termination, and regulation can be found below in Methods (Biochemical Model, Section 5.2). Initiation of the alternative pathway (blue) is induced through the tick-over reaction of C3, while classical pathway (yellow) is activated through the spontaneous intramolecular activation of complement complex C1. The tick-over of C3 in the alternative pathway forms the C3 convertase, C3(H2O)Bb, that cleaves C3 to generate nascent fluid phase C3b (nfC3b) and C3a, whereas activation of C1 cleaves C4 into nascent fluid phase C4b (nfC4b) and C4a. Subsequently, nfC3b and nfC4b can bind to host cells, form dimers such as C3bC4b (green), C3bC3b, and C4bC4b, or generate fluid phase C3b and C4b (fC3b and fC4b). Formation of fC3b and fC4b initiates a cascade of reactions that forms C3 and C5 convertases (fC3bBb and fC4bC2a). These enzymes (fC3bBb and fC4bC2a) further cleave plasma C3 to produce more nfC3b and C3a. Furthermore, fC3bBb and fC4bC2a can also cleave C5 to generate C5a and C5b. Continued propagation of complement through C5b leads to C5b-7 that can also attach to host cells and initiate a cascade of reactions to form MAC (C5b-9n). However, healthy host cells are shielded from complement attack due to fluid phase and surface bound complement regulators shown in red. Regulators FH, FHL-1, C4BP, C1-INH, CR1, and DAF provide early-phase checkpoints for complement activation and propagation, while late-step regulation of the terminal cascade is provided by fluid regulators Vn/Cn and surface bound regulator CD59. The nomenclature of complement system for selected proteins, fragments, and complexes is listed in Table 1.
Table 1.
Nomenclature of complement proteins, fragments, and complexes.
Fig 2.
Concentration-time profiles for C3 and C3a-desArg concentrations under four conditions: (i) normal state (blue), (ii) FH disorder state (red), (iii) FH disorder state with compstatin treatment (green), and (iv) FH disorder state with eculizumab treatment (cyan).
(A) Consumption of C3 under the four conditions. Plasma C3 is mostly consumed in the FH disorder state, while treatment with eculizumab had small effects on the consumption of C3. Treatment with compstatin leads to the formation of compstatin:C3 complexes, thus leaving small amounts of unbound C3 remain in plasma. (B) Production of C3a-desArg after cleavage of C3. Compstatin shows an over-restoration effect in the FH disorder state. Eculizumab has minor effects on C3 and C3a-desArg in the FH disorder state, with the effect on C3a-desArg being shown with more clarity in the zoomed-in inset of (B).
Fig 3.
Concentration-time profiles for C5 and C5a-desArg under four conditions: (i) normal state (blue), (ii) FH disorder state (red), (iii) FH disorder state with compstatin treatment (green), and (iv) FH disorder state with eculizumab treatment (cyan).
(A) Consumption of C5 under the four conditions. The inset is a zoom-in, showing that small amounts of C5 are consumed under the first three conditions (i–iii). Addition of eculizumab removed most of blood plasma C5 to form eculizumab:C5 complex (not shown). (B) Production of C5a-desArg after cleavage of C5. Treatment with eculizumab produced the lowest C5a-desArg levels, corresponding to about five orders of magnitude lower concentration compared with that of alternative pathway FH disorder.
Fig 4.
Concentration-time profiles for FB, Ba, and Bb under four conditions: (i) normal state (blue), (ii) FH disorder state (red), (iii) FH disorder state with compstatin treatment (green), and (iv) FH disorder state with eculizumab treatment (cyan).
(A) FB shows the highest level of consumption in the FH disorder state and FH disorder state with eculizumab, demonstrating the minor effects of eculizumab on FB. On the contrary, compstatin nearly restores the concentration-time profile of FB to that of normal. (B and C) Similar, but opposite in magnitude effects for FB cleavage fragments Ba (Panel B) and Bb (Panel C). The FH disorder results to overproduction of Ba and Bb (view of the red graph is obscured by the cyan graph, see insets for distinction). Compstatin has a strong over-restorative effect (compare green with red and blue graphs), whereas eculizumab has a small effect (compare cyan with red and blue graphs). Insets are zoomed-in portions of the parent Panels, showing that FB levels are tightly controlled in normal state and FH disorder state with compstatin treatment (A), whereas Ba and Bb reach the highest production levels in the FH disorder state and FH disorder state with eculizumab treatment (B and C, respectively).
Fig 5.
Concentration-time profiles for fC5b-9 under four conditions: (i) normal state (blue), (ii) FH disorder state (red), (iii) FH disorder state with compstatin treatment (green), and (iv) FH disorder state with eculizumab treatment (cyan).
Highest concentration of fC5b-9 is produced in FH disorder state, with compstatin showing a restorative trend, but incomplete restoration, and eculizumab showing an over-restorative effect. Production of fC5b-9 under FH disorder is about one order of magnitude higher than normal. Compstatin treatment generates lower levels of fC5b-9 than FH disorder state, but fC5b-9 levels are still higher compared to normal state. Finally, eculizumab treatment shows production of fC5b-9 to be about three orders of magnitude lower than normal.
Fig 6.
Multi-parametric sensitivity analysis was performed to identify parameters that affect central substrates C3 and C5 under normal conditions. Both substrates are sensitive to the activation and propagation of the classical pathway. (A) Regulation of C1* through the action of C1-INH is the most sensitivity parameter that mediates C3 levels. (B) C5 levels are predominantly affected by regulation of C4b through C4BP. This step inhibits formation of C3/C5 convertases. In addition, both C3 and C5 are affected by the alternative pathway regulation step that inactivates C3b through the actions of FH in conjunction with FI (Panels A and B).
Fig 7.
Concentration-time profiles for C3a-desArg under four conditions: (i) normal state (blue), (ii) FH disorder state (red), (iii) FH disorder state with compstatin treatment (green), and (iv) FH disorder state with eculizumab treatment (cyan).
Concentrations of compstatin used: 7.1×10-6M (one-to-one with C3; A), and 1.4×10-6M (5-fold lower than that of C3; B). Concentrations of eculizumab used: 3.7×10-7M (one-to-one with C5; A), and 7.4×10-8M (5-fold lower concentration than that of C5; B). A dose-dependent response is observed for C3a-desArg under different concentrations of compstatin. Low levels of C3a-desArg are produced under the higher compstatin concentration of 7.1×10-6M (A), whereas high levels of C3a-desArg are produced under the lowest compstatin concentration of 1.4×10-6M (B). Restorative effects of compstatin are compromised at a dose of 5-fold lower concentration than the concentration of target protein C3. Conversely, varying concentrations of eculizumab had minor effects on the levels of C3a-desArg, as shown in the insets of Panels (A and B).
Fig 8.
Concentration-time profiles for fC5b-9 under four conditions (i) normal state (blue), (ii) FH disorder state (red), (iii) FH disorder state with compstatin treatment (green), and (iv) FH disorder state with eculizumab treatment (cyan).
Concentrations of compstatin used: 7.1×10-6M (one-to-one with C3; A), and 1.4×10-6M (5-fold lower than that of C3; B). Concentrations for eculizumab used: 3.7×10-7M (one-to-one with C5; A), and 7.4×10-8M (5-fold lower than C5; B). Treatment with different doses of compstatin showed small effects on fC5b-9 levels. In contrast, treatment with varying concentrations of eculizumab generated a dose-dependent response for fC5b-9. Lowest fC5b-9 levels are produced under the highest eculizumab dosage, and vice versa. Similar to the insufficient dose of compstatin in restoring C3a-desArg, eculizumab also loses restorative effects if the used dose is 5-fold lower than the concentration of the target protein C5.
Fig 9.
Concentration-time profiles for C3a-desArg and fC5b-9 concentrations under five conditions: (i) normal state (blue), (ii) FH disorder state (red), (iii) FH disorder state with compstatin treatment (green), (iv) FH disorder state with eculizumab treatment (cyan), and (v) FH disorder state with compstatin and eculizumab treatment (magenta).
Compstatin and eculizumab are at concentrations 20-fold higher than the concentrations of their respective targets, C3 and C5. (A) Production of C3a-desArg. Dual treatment with compstatin and eculizumab and treatment with compstatin-alone over-restore the level of C3a-desArg to the same extent (overlapping concentration-time profiles), as opposed to treatment with eculizumab-alone that has little effect (overlapping time profile with that of the FH disorder state). (B) Production of fC5b-9. Dual treatment with eculizumab and compstatin and treatment with eculizumab-alone over-restore the level of fC5b-9, but treatment with eculizumab-alone over-restores to a lesser extent than dual treatment. On the other hand, treatment with compstatin-alone is not as effective, regulating towards normal state, but not restoring or over-restoring the level of fC5b-9.