Modelling and analysis of the complement system signalling pathways: roles of C3, C5a and pro-inflammatory cytokines in SARS-CoV-2 infection

The complement system is an essential part of innate immunity. It is activated by invading pathogens causing inflammation, opsonization, and lysis via complement anaphylatoxins, complement opsonin’s and membrane attack complex (MAC), respectively. However, in SARS-CoV-2 infection overactivation of complement system is causing cytokine storm leading to multiple organs damage. In this study, the René Thomas kinetic logic approach was used for the development of biological regulatory network (BRN) to model SARS-CoV-2 mediated complement system signalling pathways. Betweenness centrality analysis in cytoscape was adopted for the selection of the most biologically plausible states in state graph. Among the model results, in strongly connected components (SCCs) pro-inflammatory cytokines (PICyts) oscillatory behaviour between recurrent generation and downregulation was found as the main feature of SARS-CoV-2 infection. Diversion of trajectories from the SCCs leading toward hyper-inflammatory response was found in agreement with in vivo studies that overactive innate immunity response caused PICyts storm during SARS-CoV-2 infection. The complex of negative regulators FI, CR1 and DAF in the inhibition of complement peptide (C5a) and PICyts was found desirable to increase immune responses. In modelling role of MAC and PICyts in lowering of SARS-CoV-2 titre was found coherent with experimental studies. Intervention in upregulation of C5a and PICyts by C3 was found helpful in back-and-forth variation of signalling pattern linked with the levels of PICyts. Moreover, intervention in upregulation of PICyts by C5a was found productive in downregulation of all activating factors in the normal SCCs. However, the computational model predictions require experimental studies to be validated by exploring the activation role of C3 and C5a which could change levels of PICyts at various phases of SARS-CoV-2 infection.

• SMBioNet input values: Minimum and maximum expression level provided as 0 and 1.
• SMBioNet output value and inference: The output value ′′ 0 ′′ infer that due to active inhibitory entities MAC and PICyts CoV2 would be inactive.
• Evidence: For some evidences with respect to active PICyts for the inhibation of CoV2 (see point-1).Additionally, active PICyts activate Inflammatory cells (ICs) which phagocytosis the virus directly in begin phase of innate response, clear the pathogen by promoting inflammation (Noris et al., 2020).PICyts activate ICs which further activate IFNα\β to inhibit the pathogen (Shemesh et al., 2021;Zhang et al., 2021;Yang et al., 2021).
• SMBioNet input values: Minimum and maximum expression level provided as 0 and 1.
• SMBioNet output value and inference: The output value ′′ 0 ′′ implies that CoV2 is inhibited due to the presence of PICyts.
• Evidence: Some evidences with respect to active MAC for inhibition of CoV2 are maintained in point-1.Moreover, active MAC suppresses CoV2 as It forms cytotoxic pores on the surface of pathogens.MAC punches a hole through the plasma membrane of the target cell, killing the pathogen and causes lysis of the pathogen.(Polycarpou et al., 2020;Shibabaw et al., 2020).
It plays a role in host defense processes through its ability to kill the virus and to promote inflammation by stimulating inflammatory cells (Xie et al., 2020).
• SMBioNet input values: Minimum and maximum expression level provided as 0 and 1.
• SMBioNet output value and inference: The output value ′′ 0 ′′ implies that CoV2 is inactivated due to active MAC.
• SMBioNet input values: Minimum and maximum expression level provided as 0 and 1.
• SMBioNet output value and inference: The output value ′′ 0 ′′ deduced that CoV2 would be inactivated in the absence of downregulators MAC and PICyts due to absence of upregulators.
• SMBioNet input values: Minimum and maximum expression level provided as 0 and 1.
• SMBioNet output value and inference: The value ′′ 0 ′′ as output infer that in the absence of CoV2 and PICyts as activators and presence of FI-CR1-DAF as inhibator C3 would be downregulated.
• SMBioNet output value and inference: The value ′′ 1 ′′ as output implies that due to loss of active negative regulatory complex FI-CR1-DAF and presence of CoV2 the C3 would be activated.
• SMBioNet input values: Minimum and maximum expression level provided as 0 and 1.
• SMBioNet output value and inference: The value ′′ 0 ′′ as output implies that due to unavailability of activating factors CoV2 and PICyts C3 would be inactivated.
• Evidence: Active PICyts can increase C3 expression and active FI-CR1-DAF inhibits C3 (Dos Santos et al., 2017).The C3 production is positive correlate with IL-6.IL-6 concentration level reported high in PICyts storm, at the same time C3 level reported high (Aljwaid et al., 2021).Moreover, the trajectory mediated PICyts and ICS denoting activation of C3 as shown in CS signalling pathways (Figure 1).
• SMBioNet input values: Minimum and maximum expression level provided as 0 and 1.
• SMBioNet input values: Minimum and maximum expression level provided as 0 and 1.
• SMBioNet output value and inference: The output value ′′ 1 ′′ implies that the availability of CoV2 would activate C3.
• SMBioNet input values: Minimum and maximum expression level provided as 0 and 1.
• SMBioNet output value and inference: The output value ′′ 1 ′′ infer that the positive regulator PICyts would activate C3.
• Evidence: Some references are followed from point-8 with respect to activation of C3 due to PICyts presence.Additionally, higher titres of SARS-CoV-2 and PICyts recruit more innate immune cells (eg.macrophages and neutrohils) and acquired immune cells (T-cells).The positive loop between the Cells and PICyts (Risitano et al., 2020) implies both entities are directly correlated.PICyts mediated ICS upregulate the C3.The CoV2 induced complement system pathways lead to production of C3 (Figure 1).
• SMBioNet input values: Minimum and maximum expression level provided as 0 and 1.
• SMBioNet output value and inference: The output value ′′ 1 ′′ infer that the C3 would be generated due to existence of activating factors CoV2 and PICyts and loss of active inhibator FI-CR1-DAF.
• Evidence: Some relevant references are to be followed from point-8 with respect to activation of C3 due to PICyts presence.Additionally, higher titres of SARS-CoV-2 and overexpressed PICyts have been recruited more innate immune cells (eg.macrophages and neutrohils) and acquired immune cells (T-cells).Positive loop between ICs and PICyts (Fan et al., 2021;Risitano et al., 2020) implies both entities are directly correlated.PICyts mediated ICS upregulate C3.
• SMBioNet output value and inference: The output value ′′ 1 ′′ implies that the C3 would be activated due to the presence of activators CoV2 and PICyts.
• SMBioNet input values: Minimum and maximum expression level provided as 0 and 1.
• SMBioNet output value and inference: The output value ′′ 0 ′′ infer that when FI-CR1-DAF be in activate state then C5a would be degenerated.
• Evidence: C3 is activated by CoV2 via C3-convertase, which is activated though C1 of classical pathway, MBL of lectin pathway and C3 of alternative pathways (Noris et al., 2020).
• SMBioNet output value and inference: The output value ′′ 1 ′′ implies that when C3 is in active state then C5a would be activated even in the presence of FI-CR1-DAF.

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• Evidence: It is necessary the presence of activating factors C3 and PIcyts for upregulation of C5a.
• SMBioNet output value and inference: The output value ′′ 0 ′′ implies that due to unavailability of activators, the C5a would remain suppressed.
• SMBioNet input values: Minimum and maximum expression level provided as 0 and 1.
• SMBioNet output value and inference: The output value ′′ 1 ′′ infer that when C3 is in active state then C5a would be activated.
• SMBioNet input values: Minimum and maximum expression level provided as 0 and 1.
• SMBioNet output value and inference: The output value ′′ 1 ′′ implies that C5a would be induced due to the presence of activator PICyts.
• SMBioNet input values: Minimum and maximum expression level provided as 0 and 1.
• SMBioNet output value and inference: The output value ′′ 1 ′′ deduced that C5a would be induced due to the presence of activators C3 and PICyts even the active FI-CR1-DAF not downregulate C5a.
• Evidence: The active C3 leads to activation of C5a.C3 is activated by CoV2 via C3convertase, which is activated though C1 of classical pathway and MBL of lectin pathway (Noris et al., 2020).During SARS-CoV-2 infection, massive production of PICyts result in overstimulation of inflammatory cells, which leads to induction of C5a (Figure 1).
• SMBioNet output value and inference: The output value ′′ 1 ′′ infer that C5a would be induced due to the presence of activators C3 and PICyts.
• Evidence: MAC is unable to induce due to absence of activating entities.
• SMBioNet input values: Minimum and maximum expression level provided as 0 and 1.
• SMBioNet output value and inference: The output value ′′ 0 ′′ implied that due to unavailability of activators MAC remain inactive.
• Evidence: The presence of C3 is an initial factor for formation of terminal complement complex (TCC) MAC.Due to active C3 followed by triggering and cleaving mechanism of complement entities lead to the formation of MAC.The complete scenario of MAC induction shown in Figure 1.
• SMBioNet output value and inference: The output value ′′ 1 ′′ deduced that MAC would be generated due to the presence of upregulator C3.
• Evidence: Positive loop Risitano et al. (2020) exist between cytokine storm and overactivated inflammatory cells macrophages and neutrophils (Figure 1).PICyts stimulate ICs which activate C5 ultimately formation of active MAC.
• SMBioNet input values: Minimum and maximum expression level provided as 0 and 1.
• SMBioNet output value and inference: The output value ′′ 1 ′′ infer that MAC would be induced due to the presence of activator PICyts.
• SMBioNet output value and inference: The output value ′′ 1 ′′ implies that MAC would be produced due to the presence of activators C3 and PICyts.
• Evidence: FI-CR1-DAF remain inactive due to the absence of activator PICyts.
• SMBioNet input values: Minimum and maximum expression level provided as 0 and 1 • SMBioNet output value and inference: The output value ′′ 0 ′′ infer that FI-CR1-DAF would be inactivated due to unavailability of activating factor PICyts.
• Evidence: CR1 and DAF bind with C3b (Forneris et al., 2016), which are produced in a limited level due to normal stimulation of PICyts during SARS-CoV-2 infection.
• SMBioNet input values: Minimum and maximum expression level provided as 0 and 1.
• SMBioNet output value and inference: The output value ′′ 1 ′′ implies that due the presence of PICyts, FI-CR1-DAF would be activated.
• SMBioNet input values: Minimum and maximum expression level provided as 0 and 2.
• SMBioNet output value and inference: The output value ′′ 0 ′′ infer that due to availability of negative regulator FI-CR1-DAF, PICyts production would be suppressed.
• SMBioNet input values: Minimum and maximum expression level provided as 0 and 2.
• SMBioNet output value and inference: The output value ′′ 0 ′′ implies that due to presence of inhibator FI-CR1-DAF, PICyts would be inactivated even the activator C3 actively involved in the induction of PICyts.
• SMBioNet output value and inference: The output value as ′′ 2 ′′ deduced that due to the presence of activator C5a and even existence of inhibator FI-CR1-DAF, PICyts would be overactivated.
• Evidence: Presence of active C3 and C5a are necessary for the induction of PICyts Fan et al. (2021).
• SMBioNet input values: Minimum and maximum expression level provided as 0 and 2.
• SMBioNet output value and inference: The output value as ′′ 0 ′′ implies that due to absence of any activators C3 and C5a, PICyts would not be activated.
• SMBioNet output value and inference: The output value ′′ 2 ′′ infer that due to the availability of activators C3 and C5a, PICyts can reached to higher concentration level even the FI-CR1-DAF is actively evolved for downregulation of PICyts.
• SMBioNet input values: Minimum and maximum expression level provided as 0 and 2.
• SMBioNet output value and inference: The output value ′′ 2 ′′ infer that due to the availability of activator C5a, PICyts would be overactivated.
• SMBioNet input values: Minimum and maximum expression level provided as 0 and 2.
• SMBioNet output value and inference: The output value ′′ 1 ′′ implies that due to presence of C3, PICyts would be activated.
• SMBioNet output value and inference: The output value ′′ 2 ′′ implies that due to the presence of activators C3 and C5a, PICyts would reached to a higher expression level.