Figure 1.
Simplified schematic representation of the complement system and reaction network diagram of the mathematical model.
(A) The complement cascade is triggered when CRP or L-ficolin is recruited to the bacterial surface by binding to ligand PC (classical pathway) or GlcNAc (lectin pathway). Under inflammation condition, CRP and ficolin interact with each other and induce amplification pathways. The activated CRP and L-ficolin on the surface interacts with C1 and MASP-2 respectively and leads to the formation of the C3 convertase (C4bC2a), which cleaves C3 to C3b and C3a. Deposition of C3b initiates the opsonization, phagocytosis, and lysis. C4BP regulates the activation of complement pathways by: (a) binding to CRP, (b) accelerating the decay of the C4bC2a, (c) binding to C4b, and (d) preventing the assembly of C4bC2a (red bars). Solid arrows and dotted arrows indicate protein conversions and enzymatic reactions, respectively. (B) Complexes are denoted by the names of their components, separated by a “:”. Single-headed solid arrows characterize irreversible reactions and double-headed arrows characterize reversible reactions. Dotted arrows represent enzymatic reactions. The kinetic equations of individual reactions are presented in the supplementary material. The reactions with high global sensitivities are labeled in red.
Figure 2.
Model predictions and experimental validation.
(A–D) Experimental and simulated dynamics of the complement pathway. The time profiles of deposited C3, C4, MASP-2, CRP and C4BP under the following four conditions are simulated using estimated parameters and compared against the experimental data: (A) PC-initiated complement activation under inflammation condition, (B) PC-initiated complement activation under normal condition. (C) GlcNAc-initiated complement activation under inflammation condition; (D) GlcNAc-initiated complement activation under normal condition. Blue solid lines depict the simulation results and red dots indicate experimental data. (E–F) Model predictions and experimental validation of effects of the crosstalk. (E) Simulation results (black bar) of end-point bacterial killing rate in whole serum, CRP depleted serum (CRP-), ficolin-depleted serum (ficolin-), both CRP- and ficolin-depleted serum (CRP- & ficolin-) under normal and infection-inflammation conditions agree with the previous experimental observations (gray bar). (F) The simulated bacterial killing effect of high CRP level agrees with the experimental data.
Figure 3.
(A) Local sensitivities were calculated as the control coefficients of the initial protein concentrations for amplitude and integrated response of C3 deposition. (B) Global sensitivities were calculated according to the MPSA method. The most sensitive parameters are colored in light blue. kc2 refers to the association rate of C3b with the surface. kd01_1 refers to the association rate of CRP and ficolin. kd07_1 and kd_07_2 are the Michaelis-Menten constants governing the cleavage rate of C2. kd08_1 and kd_08_2 are the Michaelis-Menten constants governing the cleavage rate of C4. kt03_1 refers to the decay rate of C4bC2a. Those reactions are colored in red in Figure 1B.
Figure 4.
Simulation of antibacterial response with different pH and calcium level.
(A) The deposited C3 time profile at pH ranging from 5.5 to 7.4, in the presence of 2 mM calcium. (B) The deposited C3 time profile at pH ranging from 5.5 to 7.4, in the presence of 2.5 mM calcium. In the right panels of (A) and (B), dots denote the normalized binding affinities of CRP and L-ficolin reported previously [15]. Curves represent the estimated functions used for predicting. (C) The pH-antibacterial response curves of complement activation in the presence of 2 mM calcium (pink) or 2.5 mM calcium (blue).
Figure 5.
Model prediction and experimental verification of effects of C4BP under infection-inflammation condition.
(A–B) Simulation results. Predicted profiles of the deposited C3 after knocking down or over-expressing C4BP in the presence of PC (A) or GlcNAc (B). (C–D) Experimental data. Profiles of deposited C4BP (C) or C3 (D) across time points of 0–4 h under infection-inflammation condition via classical pathway (triggered by PC beads) or lectin pathway (triggered by GlcNAc beads) in untreated or treated sera with increased C4BP or decreased C4BP, were studied. The deposited protein was resolved in 12% reducing SDS PAGE and detected using polyclonal sheep anti-C4BP. Same amount of pure protein was loaded to each of the gels as the positive control (labeled as “C” in the image). The black triangles point to the peaks of the time serials data.
Figure 6.
Knockout simulations reveal the major role of C4BP.
(A) Simulation profiles of C3 deposition with or without reaction a. (B) Simulation profiles of C3 deposition with or without reaction b. (C) Simulation profiles of C3 deposition with or without reaction c. (D) Simulation profiles of C3 deposition with or without reaction d. Reactions (a–d) are labeled red in Figure 1A and explained in the caption: (a) C4BP binds to CRP, (b) C4BP binds to C4b, (c) C4BP prevents the assembly of C4bC2a, and (d) C4BP accelerates the decay of the C4bC2a,. (E) Experimental verification. Profiles of deposited cleaved/uncleaved C4 fragments across time points of 0–3.5 h under infection-inflammation condition occurring via classical pathway (triggered by PC beads) in untreated or treated sera with increased C4BP or decreased C4BP were studied. The black triangles point to the first appearance of inactive fragments.