A computational model for the evaluation of complement system regulation under homeostasis, disease, and drug intervention

Systems modeling of oncogenic G-protein and GPCR signaling reveals unexpected differences in downstream pathway activation

Mathematical models of biochemical reaction networks are an important and emerging tool for the study of cell signaling networks involved in disease processes. One promising potential application of such mathematical models is the study of how disease-causing mutations promote the signaling phenotype that contributes to the disease. It is commonly assumed that one must have a thorough characterization of the network readily available for mathematical modeling to be useful, but we hypothesized that mathematical modeling could be useful when there is incomplete knowledge and that it could be a tool for discovery that opens new areas for further exploration. In the present study, we first develop a mechanistic mathematical model of a G-protein coupled receptor signaling network that is mutated in almost all cases of uveal melanoma and use model-driven explorations to uncover and explore multiple new areas for investigating this disease. Modeling the two major, mutually-exclusive, oncogenic mutations (Gαq/11 and CysLT2R) revealed the potential for previously unknown qualitative differences between seemingly interchangeable disease-promoting mutations, and our experiments confirmed oncogenic CysLT2R was impaired at activating the FAK/YAP/TAZ pathway relative to Gαq/11. This led us to hypothesize that CYSLTR2 mutations in UM must co-occur with other mutations to activate FAK/YAP/TAZ signaling, and our bioinformatic analysis uncovers a role for co-occurring mutations involving the plexin/semaphorin pathway, which has been shown capable of activating this pathway. Overall, this work highlights the power of mechanism-based computational systems biology as a discovery tool that can leverage available information to open new research areas.

De-stabilizing innate immunity in COVID-19: effects of its own positive feedback and erratic viraemia on the alternative pathway of complement

Complement provides powerful, fast responses in the human circulation to SARS-CoV-2 (COVID-19 virus) infection of the lower respiratory tract. COVID-19 effects were investigated in a revised human in silico Mass Action model of complement's alternative pathway (AP) responses. Bursts of newly circulating virions increased the fission of Complement protein C3 into C3a and C3b via stimulation of the lectin pathway or inhibited complement factor H. Viral reproduction sub-models incorporated smoothly exponential or step-wise exponential growth. Starting complement protein concentrations were drawn randomly from published normal male or female ranges and each infection model run for 10 days. C3 and factor B (FB) syntheses driven by Lectin Pathway stimulation led to declining plasma C3 and increasing FB concentrations. The C3-convertase concentration, a driver of viral elimination, could match viral growth over three orders of magnitude but near-complete exhaustion of circulating C3 was more prevalent with step-wise than with 'smooth' increases in viral stimulation. C3 exhaustion could be prolonged. Type 2 Diabetes and hypertension led to greatly increased peak C3-convertase concentrations, as did short-term variability of COVID-19 viraemia, pulmonary capillary clotting and secondary acidosis. Positive feedback in the AP greatly extends its response range at the expense of stability.

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.

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

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.

Serum biomarker discovery related to pathogenesis in acute coronary syndrome by proteomic approach

Acute coronary syndrome (ACS) results from inadequate supply of blood flow from the coronary arteries to the heart or ischemia. ACS has an extremely high morbidity and mortality. The levels of biomarkers currently used for detection of ACS also increase in response to myocardial necrosis and other diseases and are not elevated immediately after symptoms appear, thus limiting their diagnostic capacity. Therefore, we aimed to discover new ACS diagnostic biomarkers with high sensitivity and specificity that are specifically related to ACS pathogenesis. Sera from 50 patients with ACS and healthy controls (discovery cohort) each were analyzed using mass spectrometry (MS) to identify differentially expressed proteins, and protein candidates were evaluated as ACS biomarkers in 120 people in each group (validation cohort). α-1-acid glycoprotein 1 (AGP1), complement C5 (C5), leucine-rich α-2-glycoprotein (LRG), and vitronectin (VN) were identified as biomarkers whose levels increase and gelsolin (GSN) as a biomarker whose levels decrease in patients with ACS. We concluded that these biomarkers are associated with the pathogenesis of ACS and can predict the onset of ACS prior to the appearance of necrotic biomarkers.

Systems Biology Modeling of the Complement System Under Immune Susceptible Pathogens

The complement system is assembled from a network of proteins that function to bring about the first line of defense of the body against invading pathogens. However, complement deficiencies or invasive pathogens can hijack complement to subsequently increase susceptibility of the body to infections. Moreover, invasive pathogens are increasingly becoming resistant to the currently available therapies. Hence, it is important to gain insights into the highly dynamic interaction between complement and invading microbes in the frontlines of immunity. Here, we developed a mathematical model of the complement system composed of 670 ordinary differential equations with 328 kinetic parameters, which describes all three complement pathways (alternative, classical, and lectin) and includes description of mannose-binding lectin, collectins, ficolins, factor H-related proteins, immunoglobulin M, and pentraxins. Additionally, we incorporate two pathogens: (type 1) complement susceptible pathogen and (type 2) Neisseria meningitidis located in either nasopharynx or bloodstream. In both cases, we generate time profiles of the pathogen surface occupied by complement components and the membrane attack complex (MAC). Our model shows both pathogen types in bloodstream are saturated by complement proteins, whereas MACs occupy <<1.0% of the pathogen surface. Conversely, the MAC production in nasopharynx occupies about 1.5-10% of the total N. meningitidis surface, thus making nasal MAC levels at least about eight orders of magnitude higher. Altogether, we predict complement-imbalance, favoring overactivation, is associated with nasopharynx homeostasis. Conversely, orientating toward complement-balance may cause disruption to the nasopharynx homeostasis. Thus, for sporadic meningococcal disease, our model predicts rising nasal levels of complement regulators as early infection biomarkers.

Soluble Membrane Attack Complex: Biochemistry and Immunobiology

The soluble membrane attack complex (sMAC, a.k.a., sC5b-9 or TCC) is generated on activation of complement and contains the complement proteins C5b, C6, C7, C8, C9 together with the regulatory proteins clusterin and/or vitronectin. sMAC is a member of the MACPF/cholesterol-dependent-cytolysin superfamily of pore-forming molecules that insert into lipid bilayers and disrupt cellular integrity and function. sMAC is a unique complement activation macromolecule as it is comprised of several different subunits. To date no complement-mediated function has been identified for sMAC. sMAC is present in blood and other body fluids under homeostatic conditions and there is abundant evidence documenting changes in sMAC levels during infection, autoimmune disease and trauma. Despite decades of scientific interest in sMAC, the mechanisms regulating its formation in healthy individuals and its biological functions in both health and disease remain poorly understood. Here, we review the structural differences between sMAC and its membrane counterpart, MAC, and examine sMAC immunobiology with respect to its presence in body fluids in health and disease. Finally, we discuss the diagnostic potential of sMAC for diagnostic and prognostic applications and potential utility as a companion diagnostic.

Modeling the activation of the alternative complement pathway and its effects on hemolysis in health and disease

The complement system is a powerful mechanism of innate immunity poised to eliminate foreign cells and pathogens. It is an intricate network of >35 proteins, which, once activated, leads to the tagging of the surface to be eliminated, produces potent chemoattractants to recruit immune cells, and inserts cytotoxic pores into nearby lipid surfaces. Although it can be triggered via different pathways, its net output is largely based on the direct or indirect activation of the alternative pathway. Complement dysregulation or deficiencies may cause severe pathologies, such as paroxysmal nocturnal hemoglobinuria (PNH), where a lack of complement control proteins leads to hemolysis and life-threatening anemia. The complexity of the system poses a challenge for the interpretation of experimental data and the design of effective pharmacological therapies. To address this issue, we developed a mathematical model of the alternative complement pathway building on previous modelling efforts. The model links complement activation to the hemolytic activity of the terminal alternative pathway, providing an accurate description of pathway activity as observed in vitro and in vivo, in health and disease. Through adjustment of the parameters describing experimental conditions, the model was capable of reproducing the results of an array of standard assays used in complement research. To demonstrate its clinical applicability, we compared model predictions with clinical observations of the recovery of hematological biomarkers in PNH patients treated with the complement inhibiting anti-C5 antibody eculizumab. In conclusion, the model can enhance the understanding of complement biology and its role in disease pathogenesis, help identifying promising targets for pharmacological intervention, and predict the outcome of complement-targeting pharmacological interventions.

Quantification of Factor H Mediated Self vs. Non-self Discrimination by Mathematical Modeling

The complement system is part of the innate immune system and plays an important role in the host defense against infectious pathogens. One of the main effects is the opsonization of foreign invaders and subsequent uptake by phagocytosis. Due to the continuous default basal level of active complement molecules, a tight regulation is required to protect the body's own cells (self cells) from opsonization and from complement damage. A major complement regulator is Factor H, which is recruited from the fluid phase and attaches to cell surfaces where it effectively controls complement activation. Besides self cells, pathogens also have the ability to bind Factor H; they can thus escape opsonization and phagocytosis causing severe infections. In order to advance our understanding of the opsonization process at a quantitative level, we developed a mathematical model for the dynamics of the complement system-termed DynaCoSys model-that is based on ordinary differential equations for cell surface-bound molecules and on partial differential equations for concentration profiles of the fluid phase molecules in the environment of cells. This hybrid differential equation approach allows to model the complement cascade focusing on the role of active C3b in the fluid phase and on the cell surface as well as on its inactivation on the cell surface. The DynaCoSys model enables us to quantitatively predict the conditions under which Factor H mediated complement evasion occurs. Furthermore, investigating the quantitative impact of model parameters by a sensitivity analysis, we identify the driving processes of complement activation and regulation in both the self and non-self regime. The two regimes are defined by a critical Factor H concentration on the cell surface and we use the model to investigate the differential impact of complement model parameters on this threshold value. The dynamic modeling on the surface of pathogens are further relevant to understand pathophysiological situations where Factor H mutants and defective Factor H binding to target surfaces results in pathophysiology such as renal and retinal disease. In the future, this DynaCoSys model will be extended to also enable evaluating treatment strategies of complement-related diseases.

Development of a Sensitive Assay to Screen Nanoparticles in vitro for Complement Activation

Nanomedicines are often recognized by the innate immune system as a threat, leading to unwanted clearance due to complement activation. This adverse reaction not only alters the bioavailability of the therapeutic but can also cause cardiopulmonary complications and death in a portion of the population. There is a need for tools for assessing complement response in the early stage of development of nanomedicines. Currently, quantifying complement-mediated response in vitro is limited due to differences between in vitro and in vivo responses for the same precursors, differences in the complement systems in different species, and lack of highly sensitive tools for quantifying the changes. Hence, we have worked on developing complement assay conditions and sample preparation techniques that can be highly sensitive in assessing the complement-mediated response in vitro mimicking the in vivo activity. We are screening the impact of incubation time, nanoparticle dosage, anticoagulants, and species of the donor in both blood and blood components. We have validated the optimal assay conditions by replicating the impact of zeta potential seen in vivo on complement activation in vitro. As observed in our previous in vivo studies, where nanoparticles with neutral zeta-potential were able to suppress complement response, the change in the complement biomarker was least for the neutral nanoparticles as well through our developed guidelines. These assay conditions provide a vital tool for assessing the safety of intravenously administered nanomedicines.

Mathematical Modelling of Alternative Pathway of Complement System

The complement system (CS) is an integral part of innate immunity and can be activated via three different pathways. The alternative pathway (AP) has a central role in the function of the CS. The AP of complement system is implicated in several human disease pathologies. In the absence of triggers, the AP exists in a time-invariant resting state (physiological steady state). It is capable of rapid, potent and transient activation response upon challenge with a trigger. Previous models of AP have focused on the activation response. In order to understand the molecular machinery necessary for AP activation and regulation of a physiological steady state, we built parsimonious AP models using experimentally supported kinetic parameters. The models further allowed us to test quantitative roles played by negative and positive regulators of the pathway in order to test hypotheses regarding their mechanisms of action, thus providing more insight into the complex regulation of AP.

Surface loops of trypsin-like serine proteases as determinants of function

Trypsin and chymotrypsin-like serine proteases from family S1 (clan PA) constitute the largest protease group in humans and more generally in vertebrates. The prototypes chymotrypsin, trypsin and elastase represent simple digestive proteases in the gut, where they cleave nearly any protein. Multidomain trypsin-like proteases are key players in the tightly controlled blood coagulation and complement systems, as well as related proteases that are secreted from diverse immune cells. Some serine proteases are expressed in nearly all tissues and fluids of the human body, such as the human kallikreins and kallikrein-related peptidases with specialization for often unique substrates and accurate timing of activity. HtrA and membrane-anchored serine proteases fulfill important physiological tasks with emerging roles in cancer. The high diversity of all family members, which share the tandem β-barrel architecture of the chymotrypsin-fold in the catalytic domain, is conferred by the large differences of eight surface loops, surrounding the active site. The length of these loops alters with insertions and deletions, resulting in remarkably different three-dimensional arrangements. In addition, metal binding sites for Na+, Ca2+ and Zn2+ serve as regulatory elements, as do N-glycosylation sites. Depending on the individual tasks of the protease, the surface loops determine substrate specificity, control the turnover and allow regulation of activation, activity and degradation by other proteins, which are often serine proteases themselves. Most intriguingly, in some serine proteases, the surface loops interact as allosteric network, partially tuned by protein co-factors. Knowledge of these subtle and complicated molecular motions may allow nowadays for new and specific pharmaceutical or medical approaches.