key: cord-1013974-bc0oqzrb
authors: Yu, Zhenhua; Ellahi, R.; Nutini, Alessandro; Sohail, Ayesha; Sait, Sadiq M.
title: Modeling and simulations of CoViD-19 molecular mechanism induced by cytokines storm during SARS-CoV2 infection
date: 2020-11-28
journal: J Mol Liq
DOI: 10.1016/j.molliq.2020.114863
sha: dfee497f82c7a4060a80972e8d3481db52afe6c7
doc_id: 1013974
cord_uid: bc0oqzrb

It is highly desired to explore the interventions of COVID-19 for early treatment strategies. Such interventions are still under consideration. A model is benchmarked research and comprises target cells, virus infected cells, immune cells, pro-inflammatory cytokines, and, anti-inflammatory cytokine. The interaction of the drug with the inflammatory sub-system is analyzed with the aid of kinetic modeling. The impact of drug therapy on the immune cells is modelled and the computational framework is verified with the aid of numerical simulations. The work includes a significant hypothesis that quantifies the complex dynamics of the infection, by relating it to the effect of the inflammatory syndrome generated by IL-6. In this paper we use the cancer immunoediting process: a dynamic process initiated by cancer cells in response to immune surveillance of the immune system that it can be conceptualized by an alternating movement that balances immune protection with immune evasion. The mechanisms of resistance to immunotherapy seem to broadly overlap with those used by cancers as they undergo immunoediting to evade detection by the immune system. In this process the immune system can both constrain and promote tumour development, which proceeds through three phases termed: (i) Elimination, (ii) Equilibrium, and, (iii) Escape [1]. We can also apply these concepts to viral infection, which, although it is not exactly “immunoediting”, has many points in common and helps to understand how it expands into an “untreated” host and can help in understanding the SARS-CoV2 virus infection and treatment model.

Subsequent to infection, an inflammatory process is generated in the tissue affected by the infection itself; this process is characterized by the presence of leukocytes and plasma proteins. This inflammatory response occurs after elements of the immune system such as macrophages, dendritic cells and natural killer (NK) cells are activated, thanks to appropriate molecular signals: pathogen-associated molecular patterns (PAMPs) and damage-associated molecular patterns (DAMPs).

The proinflammatory cytokines, activated by the PAMP or DAMP signaling pathways, are central in the realization of the inflammatory process itself; these molecules are well represented by IL-1, IL-6, IL-8, IL-12, IFN-γ, IL-18 and TNF and their action is manifested in the control of inflammatory foci through specific responses. TNF also has the ability to activate a cascade of anti-inflammatory cytokines that block the ongoing inflammation process and, in most cases, this process is resolved. An overproduction of proinflammatory cytokines, however, can give rise to what is called a "cytokine storm" which can have a harmful effect on the body through the production of a syndrome called "SIRS" (Systemic Inflammatory Response Syndrome) which leads to hypotension , pulmonary thrombosis, J o u r n a l P r e -p r o o f Journal Pre-proof pulmonary edema and haemorrhage, and if not treated with appropriate therapy, it can lead to death.

The reproductive rate (R 0 ) for SARS-CoV2 is estimated to be 2.5 (with range 1.8-3.6) compared with 2.0-3.0 for SARS-CoV and the 1918 influenza pandemic, 0.9 for MERS-CoV, and 1.5 for the 2009 influenza pandemic [2] . The latter infected around 8,000 people in 2002 , causing 800 deaths, while SARS-CoV2 currently infected 47,362,304 people, causing 1,211,986 deaths (https://covid19.who.int/ access at october 05, 2020 11.50 am). SARS-CoV2 therefore shows a high diffusion capacity compared to SARS-CoV.

There are many similarities of SARS-CoV2 with the SARS-CoV virus; a model by Xu et al. [3] found that the S proteins of SARS-CoV2 and SARS-CoV have identical threedimensional structures in the receptor-binding domain (RBD) that maintains van der Waals forces. SARS-CoV S protein has a strong binding affinity to human ACE2, based studies and crystal structure analysis [4] . SARS-CoV-2 and SARS-CoV S proteins share 76.5% identity in aminoacid sequences and the SARS-CoV2 and SARS-CoV S proteins have a high degree of homology.

The S protein/ACE2 binding in SARS-CoV2 induces conformational changes in aminoacids that generate salt bridges, increase van der waals interactions and, by this action, facilitate binding with ACE2 with much greater affinity than SARS-CoV [5] .

Immune cells work as a sort of careful surveillance in a healthy body. In most viral infections, the immune system has the ability to oppose the viral particle, at certain times of the infection (before entering the cell or leaving it, after replication), and to infected cells (in the production of proteins or in that of the viral assembly).

The reason is the expression of antigens of the infection in the membrane, that activate the immune response. As the body gets infected, the infected cells secrete proinflammatory cytokines which in turn activate the immune cells to differentiate in Th17 cells from CD4+ naïve T lymphocytes differentiation of cytotoxic TCD8+ cells (CTL), differentiation in Th1 cells, resolution of the inflammatory state, repair of lung tissue, promotion of phagocytic activity of macrophages, prevents apoptosis induced by viral infection in lung epithelial cells, and regulates the expression of IgG isotypes [6] .

Therefore, during this research we focus on the concentration of immune cells and will develop an equation based on the interaction/responses of immune cells to virus and pro inflammatory cytokines.

In SARS-CoV2, the action of IL-6 and IL-1 cytokines is of central interest, since elevated interleukin-6 (IL-6) dose is strongly associated with the need for mechanical ventilation in CoViD-19 patients. Also, the risk of respiratory failure for patients with high IL-6 levels is higher compared to patients with lower IL-6 levels [7] . Another fact is that in case of CoViD-19, suppression of proinflammatory IL-1 family members showed some therapeutic effect [8] .

The anti-inflammatory cytokines do their job in both a healthy as well as in an infected body. When there is an onset of viral infection, these cytokines work in balance with proinflammatory cytokines. The action of the anti-inflammatory cytokines which tends to regulate the action of the inflammatory ones (in our case precisely of IL-6) is directed to the same cells that produce IL-6, which, through an inhibition mechanism, slow down (or J o u r n a l P r e -p r o o f Journal Pre-proof production ceases altogether). Evidently, in the case of the "IL-6 storm", the action of these anti-inflammatory cytokines is insufficient.

The blockade of IL-6R receptors through monoclonal antibody has proven to be optimal to manage complications and avoid potentially fatal situations. Hence, there are cells that overexpress IL-6 which in turn triggers a chronic inflammatory event that feeds on itself as cells such as macrophages and fibroblasts continue to secrete IL-6, without undergoing negative regulation processes by anti-inflammatory cytokines.

The drugs available to control the pro-inflammatory cytokines are listed as:

• Inhibitor of Janus kinases (i.e., Ruxolitinib )

• Monoclonal antibody (i.e., Tocilizumab )

In this research, we simulate the impact of Tocilizumab. Tocilizumab is a humanized anti-IL-6 monoclonal antibody that is used against rheumatoid arthritis, juvenile idiopathic Tocilizumab as it can exacerbate the symptoms related to CoViD-19 [11] . Cytokine storm syndrom Mehta et al. [12] has been identified in a group of CoViD-19 patients and data from 41 Wuhan patients in intensive care unit (ICU) indicated high levels of cytokines such as IL-2, IL-7, IL-10, GCSF and others while IL-6 was not detected in high concentration;

further data, however, indicates a high concentration of ferritin and a high presence of IL-6

as an indication of disease fatality. The China National Health Commission, in its revision to treatment for CoViD-19, seventh version (China's National Health Commission treatment guidelines 7th version, 2020), included Tocilizumab as therapy for SARS-CoV2 infected patients with serious lung damage and high levels of IL-6. There is still not much evidence on the effects of Tocilizumab in application to therapy for CoViD-19 and an evaluation of the concentration of cytokines present is recommended before administration of the drug [12] . In Table 1 below, a brief description of the evidence supporting Tocilizumab in the case of CoViD-19 is reported.

It was observed recently during a clinical study that when the drug was administered intermittently, the results were more convincing. We therefore propose that the use of tocilizumab of 8 mg/kg per day is recommended by Xu et al.

[13], therapeutic scheme: 20 mg/mL vials.

• Development of a model of IL-6 inflammatory syndrome in SARS-CoV2 and its quantification.

• Creation and application of a modelling computational framework for target cells (host), infected cells, immune cells, pro-inflammatory and anti-inflammatory cytokines.

• Analysis of cytokines related to viral load.

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• Creation of a mathematical inflammatory subsystem , where the role of antiinflammatory cytokines will not be considered.

• Creation of a "connection model" with the therapeutic use of a monoclonal antibody (tocilizumab) and analysis of the hypothesis of intermittent therapy as the best therapeutic value: the drug controlled the disease onset by delaying the cycle and changing its period.

• Analysis of the parallelism of the computational development of the "three Es" hypothesis in the development of cancer also applied to viral infection: quantitative analysis of the system and verification of the cells population.

Different computational models based on the molecular mechanism of the said problems, are available in the literature [14] [15] [16] [17] . During this research, we developed a model comprising target cells (X), virus infected cells (Y), immune cells (Z), pro-inflammatory cytokines C, and, anti-inflammatory cytokine A.

where ( ) is the logistic growth, is the infection rate and inhibition by immune response, r is the growth factor and K is the carrying capacity.

J o u r n a l P r e -p r o o f Journal Pre-proof where is infected cells proliferation, is inhibition by immune response and is the death rate.

( ) ( ) ( )

( )

The equation for drug is:

In Eq. 2, the term ρYZ represents the loss of infected cells caused by the immune cells. The fraction is the proliferation of infected cells through interactions with targeted cells.

In Eq. 3, the term represents the increase in immune cells due to pro-inflammatory cytokines. Tocilizumab is inhibiting pro-inflammatory cytokines to increase immune cells rapidly [18, 19] .

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In Eq. 4, the term represents the release of pro-inflammatory cytokines C, when a cell (a particular line of cells) interacts with infected cells, there is a release of cytokines.

Anti-inflammatory cytokines ( ) interact with pro-inflammatory cytokines ( ) and inhibit them in a two-variable model for the interactions between pro-inflammatory and anti-inflammatory cytokines, following a model that illustrates a range of possible behaviors, such as bistability and oscillations [20] . The term ( ) captures the effect of the drug on pro-inflammatory cytokines [21] .

In Eq. 5, the anti-inflammatory cytokines act on modulating immune response and create a negative regulation circuits to the cascade of inflammatory cytokines that act locally or systemically; they are produced by monocyte-macrophages. They inhibit the immune inflammatory response.

In Eq. 6, we have used a single compartment model to calculate the concentration of drug in plasma. Administration of drug through intravenous infusion and its concentration in plasma can be easily calculated with exponential function [22, 23] . In this equation, h 2 represents the absorption rate of the drug while h 3 is representing the clearance rate. The drug inhibits pro-inflammatory cytokines to activate immune cells rapidly. This action is modelled as and the effect of drug on pro-inflammatory cytokines is modeled as ( ). Here, l 2 represents maximum drug interaction with pro-inflammatory cytokines while K is quasi-steady-state constant [ 21] .

Now, we will nondimensionalize the system in a manner similar to [24] , furthermore, we will reduce the system to inflammatory subsystem, where the role of anti-inflammatory J o u r n a l P r e -p r o o f Journal Pre-proof cytokines will not be considered [25] . Here x, y, z, c and u are the dimensionless variables presenting the concentration of target cells, infected cells (viral load), immune cells, and, pro-inflammatory cytokines, with time scaled as well by r (details of nondimensionalization are provided in [26] . The equation for target cells is given as:

equation for viral load is given as:

equation for immune cells is given as:

equation for pro-inflammatory cytokines is given as: ̂ ̂ equation for drug is given as:

To describe dimensionless parameter, we use hat on it, however, in the rest of paper we do not use hat for convenience.

Sensitivity analysis is a tool that helps build confidence in the model by studying uncertainty of the parameters. Here, we perform sensitivity analysis in order to check

Journal Pre-proof influence of parameters on the designed model. The parameters selected for sensitivity analysis are given in Table 1 .

If there is no viral load (i.e, y=0) and no treatment term, then the above subsystem can be reduced to:

For equilibrium point, we put . Now from Eqs. (12) and (13) Thus is an equilibrium point.

If and , then the equilibrium point is locally asymptotically stable. The proof of this theorem is straightforward by defining Jacobian matrix at and using Lyapunov stability criterion. To analyze the regions, where the system will give convergent results, we have obtained the nulclines.

The aim of this section is to delibtrate the role of associatede key parameters arising in the model configuration as shown in in Figure 1 .

These results are obtained from the analysis of nondimensional inflammatory subsystem (Eq-7-11). We can see that the parameter k c i.e., the cytokine sensitivity parameter, plays an important role. From Figure 2 , we can see that without drug, when the cytokine sensitivty J o u r n a l P r e -p r o o f Journal Pre-proof parameter was increased, the infection load increased. For the dynamics with the infusion of drug, we can see that the infection load was much controlled.

We have conducted numerical experiments for three increasing values of β, these results are presented in Figure 3 . Figure 4 presents the dynamics for k 1 (immune cells activation rate) fixed to be 0.1. Without drug, the cytokine IL-6 release was higher, with increasing values of β, whereas with drug, it was controlled. On the other hand, when similar numerical experiments were repeated for k 1 =0.05 (immune cells activation rate), we can see different results. The infection is more periodic and there is damping relative to time.

The 3Es of immunoediting are defined as:

We have known for some time that the immune system and malignant cells often coexist in a dynamic equilibrium, and the complex interaction between growing tumor and immune system can determine the course of the disease. Tumors must develop the ability to evade the immune system to proliferate and metastasize. Immune surveillance theory suggests that the immune system is proactively able to eliminate abnormal cells and prevent cancer formation in the body. Studies have shown that patients with impaired or suppressed immune function are exposed to an increased risk of developing cancer. In addition, although controversial, the use of immunosuppressive agents has been associated with an 

We can also apply these concepts to viral infection, which, although it is not exactly "immunoediting", has many points in common and helps to understand how it expands into an "untreated" host. Immunoediting in untreated viral infections involves the equilibrium to the examination of a sort of viral "reservoir" which, through its expression/latency, affects CTL functionality.

There's a role of intrinsic immunoediting in the viral reservoir persistence [27] that passes through a balance between the persistence of the viral load and adaptation to the response of the CTL cells up to an increasingly ineffective response of the latter. This event leads to strengthening of the viral infectious capacity and due to the lack of immune response produces a deficiency of infection control. In the case of SARS-CoV2, all this passes through a strong induction of an inflammatory regimen operated by cytokines such as IL-6

and IL-1, which lead to an inflammatory syndrome that contributes to a lack of control of the infection. Furthermore it leads to the viral escape , relative to a high viral reservoir, due to the strong infectious capacity of this virus [27] .

We therefore propose an analysis based on the three immunoediting phases.

During this research, based on the results provided in the literature, the graphical interpretation of equilibrium, escape, and, elimination of the infection are presented in Figures 5, 6 and 7 respectively. The analysis was based on the key parameters listed in Table 1 . 

The pandemic generated by the SARS-CoV2 virus is currently causing several problems including many deaths and difficulties in health systems around the world. The creation of a vaccine is certainly desirable at the moment [28] , but the need to understand both the SARS-CoV2 infection system and a possible therapy that can reduce the symptoms imposed by CoViD-19 is fundamental to reduce the heavy pathological damage and the load that every health system must bear, although containment measures such as "lockdowns" have managed to contain the spread of the infection and the various epidemiological conditions have entailed different choices, country by country, and often not uniformly (targeted lockdowns), reporting a reduction in infections [29] .

The computation analysis carried out in this paper focuses on the inflammatory syndrome triggered by SARS-CoV2 infection and analyzes, through a sensitivity analysis, the J o u r n a l P r e -p r o o f Journal Pre-proof parameters that trigger the CoViD-19 symptomatology and, thanks to an analogy conducted with the immunoediting related to cancer, quantitatively and qualitatively illustrates the interactions between the signal molecules of the immune system (cytokines) and the infectious characteristics, indicating the efficiency of a possible therapy that includes the use of monoclonal antibodies such as tocilizumab. Based on the results obtained from the nonlinear model, we conclude the following:

• The cytokines are sensitive to the viral load. The parameters controlling the cytokine sensitivity was helpful to drive this conclusion. The concentration of cytokine expression was affected by two important factors, k c and drug dose. With drug infusion, the function was inhibited.

• The interaction rate matters a lot in the disease onset. The time delay is visible during the numerical analysis for different values of interaction rates.

• The drug controlled the disease onset by delaying the cycle and changing its period.

• TCZ does not overactive the immune cells except to induce, initially and temporarily, an increase in the level of IL-6 only to then begin to act by lowering the levels of IL-6 itself and this is integrated into the proinflammatory cytokines equation of the model.

In fact, if the therapy is  abruptly stopped in the initial phase, there is a sort of "disease flare" according to a theory called "bathtube theory". TCZ has a very low antigenicity which also entails little propensity to an autoimmune reactions therefore, also in this sense it does not activate (or very poorly active) the cells of the immune system.

• For reduced value of k 2 , we achieved the escape dynamics. 

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