# Theoretical Explanation for the Rarity of Antibody-Dependent Enhancement of Infection (ADE) in COVID-19

^{1}

^{2}

^{3}

^{4}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Results

#### 2.1. Construction of Antibody Response Generation Module (Model Ab)

_{RNA}, which describes average number of antigens per viral RNA molecule; the parameter w

_{3}, which describes individual viral load; and the intrinsic parameters of the immune system (time delay for naive B-cell activation t

_{naive}; plasma cells death rate δ

_{pl}; and B-cell differentiation rate, π

_{pl}) (Table S6). A description of a typical individual patient’s antibody response [34] is given in Figure 1b. The kinetics of free viral epitopes for different β

_{RNA}and w

_{3}are shown in Figure S1 (mild cases) and Figure S2 (severe cases).

_{RNA}= 532.38, w

_{3}= 2.378 days, t

_{naive}= 10.5 days, δ

_{pl}= 0.166 days

^{−1}, and π

_{pl}= 10

^{−4}(APS∙days)

^{−1}. Typical dynamics of naive B-cells, plasma cells and memory B-cells are given in Figure 1c, Figure S1 and S2. Altogether, model Ab correctly describes antibody response, B-cell differentiation and immune system-mediated virus elimination in response to the given viral load. However, this model does not take into account variabilities in the types of antibodies and the possible infection of macrophages.

#### 2.2. The Infection Propagation Model (Model Cv) Suggests Possibilities of ADE Occurrence in COVID-19

_{inf}, the maximum virus–antibody complex formation constant α

_{c0}, the rate of viral degradation δ

_{v}and the initial viral load Virus

_{0}. After approximation of seven experiments, the following average parameter values were obtained: β

_{inf}= 4.72 × 10

^{−6}(days∙Virus)

^{−1}, α

_{c0}= 5.99 × 10

^{−4}days

^{−1}, δ

_{v}= 207.6 days

^{−1}and Virus

_{0}= 2.6 × 10

^{7}. Other parameters are given in Table S7. The dynamics of the viral load and the pneumocyte number for different ρ are given in Figure 1e,f.

^{−3}, the concentration of viral particles was the same as in the absence of macrophage infection, and no ADE was observed, while for ρ > 10

^{−3}, the probability of pneumocyte survival decreased and the times of viral clearance increased, allowing the occurrence of ADE. However, we could not investigate the impact of antibody parameters on ADE occurrence using only model Cv because the existing experimental data describe antibodies in terms of optical density and we needed module model Ab to obtain the absolute concentrations of antibodies.

#### 2.3. The Complete Model Is Capable of Describing Viral Load and Assessing the Influence of Pre-Existing Antibody Concentration on the Course of Disease

_{0}) impact on the viral load dynamics (Figure 2a) and on the percentage of infected pneumocytes (Figure 2b). The increase in the initial antigen concentration led to the earlier appearance of the viral load peak and a slight increase in its magnitude (Figure 2a). The amount of surviving pneumocytes at the end of the disease decreased with increasing initial viral load (Figure 2b).

_{0}≈ 10

^{13}particles) of antibodies could significantly change the course of disease; i.e., the number of surviving pneumocytes increased drastically (Figure 2d), while the viral load noticeably decreased (Figure 2c). As discussed above, the dissociation constant (K

_{d}) of the antigen–antibody complex could affect the course of the desease. To determine the extent of K

_{d}influence, we performed similar simulations for varied values of K

_{d}(Figure 2e–h). In the absence of pre-existing antibodies, Kd did not influence the viral load maximum, but larger Kd led to lower pneumocyte survival (Figure 2f) and prolonged virus elimination (Figure 2e). In the presence of pre-existing antibodies at the maximum concentration (A

_{0}≈ 10

^{13}particles), the viral load decreased with time, all pneumocytes survived for small Kd values (Kd < 10

^{−9}M) and up to 20% of the pneumocytes died for large Kd values (Kd > 10

^{−9}M). Therefore, the existance of low-affinity pre-existing antibodies could lead to ADE.

#### 2.4. Theoretical Conditions for ADE Occurrence in COVID-19

^{−3}. At ρ < 10

^{−3}, the concentration of viral particles was the same as in absence of macrophage infection. Upon an increase in the probability of macrophage infection, pneumocyte survival decreased and viral load clearance time increased.

^{−4}, ADE was not observed (the percentage of dead pneumocytes did not exceed levels 3% higher than with the course of disease without macrophage infection; this situation occurred with extremely high antibody concentrations 10

^{14}< Ab

_{old}< 10

^{15}). For ρ > 3 × 10

^{−4}, ADE occurred only if the concentration of pre-existing antibodis was high enough (Ab

_{old}> 10

^{10}).

^{−4}, the proportion of surviving pneumocytes increased upon a decrease in Kd. In this case, the maximal number of dead pneumocytes was no greater than their amount in the absence of antibodies and possible macrophage infection (Figure 5). For ρ > 3 × 10

^{−4}, the highest level of pneumocyte death was observed at the lowest Kd. In all these cases, the degree of Kd impact on pneumocyte survival depended on the pre-existing antibody concentration (Figure 5).

## 3. Discussion

## 4. Materials and Methods

#### 4.1. General Principles for the Construction of the Mathematical Models

#### 4.2. Model Ab—The Antibody Response

_{RNA}is the concentration of SARS-CoV-2 RNA, t is the model time and A

_{RNA}, x

_{0}, w

_{1}, w

_{2}and w

_{3}are parameters required to better fit the experimental data [34]. Numerical values of these parameters are represented in Table S1. It was assumed that the parameter w

_{3}was specific for individual patients. Individual parameter values are represented in Table S6.

_{f}). Subsequently, the number of free viral epitope could be described with the following formula:

_{RNA}is the constant of proportionality between the SARS-CoV-2 RNA number and the amount of free viral epitopes. It was assumed that this parameter implied the specificity of the viral kinetics in individual patients. Individual parameter values are represented in Table S2.

_{lung}is the concentration of antibodies in the lungs; k

_{v}

_{1}and k

_{v}

_{−1}are the epitope–antibody association and dissociation rates, respectively; c

_{v}

_{1}is the maximal rate of clearance of viral protein–antibody complexes; and c

_{v}

_{2}is the half-decay constant.

_{lung}). Activation of APSs occurred in the lungs when viral epitopes interacted with antigen-presenting cells. B-cells could be activated in the lymphoid organs. Transition of activated antigen-presenting sites in the lung (APS

_{lung}) into activated antigen-presenting sites in lymphoid organs (APS

_{lo}) occurred in accordance with the law of mass action. In the absence of a pathogen, all sites were assumed to be in a neutral state, Ap, and they could not affect B-cell functioning. The dynamics of neutral APSs and activated APSs in lungs and lymphoid organs can be described by the following equations:

_{b}is the generation and degradation of neutral APSs in the absence of the virus (homeostasis rate of neutral APSs); Ap

_{0}and Ap are the initial and transient concentrations of neutral APSs; δ

_{ap}and δ

_{apm}are the rates of APS

_{lung}and APS

_{lo}deactivation, correspondingly; the terms β

_{apm}∗ Ap ∗ V

_{f}/(φ + V

_{f}) indicate the rate of APS

_{lung}activation, β

_{apm}is the maximal activation rate; and φ is the half-saturation constant for APS

_{lung}activation. φ was estimated from an existing model [49,50]. The terms k

_{s}

_{1}and k

_{s}

_{−1}denote rates of APS transition between two compartments: lungs and lymphoid organs. ν is the conversion coefficient reflecting the lymphoid organ:lung volume ratio.

_{lo}), naive B-cells (B) proliferated and differentiated into short-lived IgM-producing plasma cells, long-lived IgG-producing plasma cells (Pl) and memory B-cells (Bm) (Figure 5a). We focused on B-cells, which produce high-affinity class-switching IgG-antibodies. The possibility of B-cell differentiation into short-lived IgM-producing plasma cells was also included in the model. In the frame of the model, we assumed that B-cell proliferation and differentiation into short-lived plasma cells occurred after their contact with APSs, whereas differentiation into long-lived plasma cells and memory B-cells occurred after a time delay. The complete equation for the concentration of B-cells is the following:

_{0}and B are the initial and transient concentrations of B-cells; χ

_{b}is the B-cell generation and degradation in the absence of the virus (homeostasis rate of B-cells); π

_{b}is the naive B-cell proliferation rate (reflecting the increase in B-cell proliferation upon contact with APSs) [51]; the π parameters reflect probabilities of different B-cell fates upon contact with the APSs: π

_{pl}—into plasma cells, π

_{bm}—into memory cells and π

_{ps}—into short-lived Ig-M-producing plasma cells; τ

_{n}is used to introduce a time delay between the appearance of APSs and the initiation of naive B-cell differentiation into long-lived plasma cells and memory B-cells [48]; t

_{0}is the moment when APS

_{lo}becomes positive; and t

_{naive}is the lag-time required for B-cell differentiation.

_{pl}is the rate of plasma cell degradation and τ

_{mem}reflects the time lag (t

_{memory}) between the appearance of APSs (at t

_{0}) and the initiation of memory B-cells differentiation and proliferation [48].

_{bm}

_{1}and k

_{bm}

_{2}represent the B

_{m}growth rate and the lymphoid organ maximum capacity, respectively.

_{b}) could be described with the following equation:

_{pl}denotes the rate of IgG generation by long-living plasma cells [52] and δ

_{a}is the natural decay rate of antibodies (A

_{lo}and A

_{lung}) [38,51]. The terms k

_{a}

_{1}and k

_{a}

_{−1}denote rates of antibody transition between two compartments, the lungs and lymphoid organs.

_{lo}/Ig0+ω).

#### 4.3. Model Cv—Propagation of Infection

_{b}and μ

_{B}are the plasma cell production and degradation rates and α

_{B}is the rate of plasma cell proliferation upon contact with viral particles [36]. As antibodies are produced by plasma cells, in model Cv we assumed the concentration of antibodies to be proportional to the concentration of plasma cells and, in the following equations, Pl

_{mod}is used to indicate Ab concentration and Pl

_{mod}* Virus is used to indicate the concentration of virus–antibody complexes.

_{A}) and infected (M*). Healthy macrophages engulfed viral particles without changing their concentration or engulfed virus–antibody complexes and became infected. In the model, it was assumed that the infected macrophages could recover [36] and both healthy and infected macrophages could degrade. With the described assumption, the equations for M

_{A}and M* were the following:

_{M}is the macrophage generation and degradation in the absence of a virus (homeostasis rate of macrophages); δ

_{I}is the death rate of infected macrophages (δ

_{I}≥ χ

_{M}); σ is the rate of infected macrophage recovery; ρ denotes the probability of macrophages becoming infected; and α

_{c}is the rate for antibody–virus complex formation and subsequent engulfment, expressed as a step function:

_{c}

_{0}is the maximal constant rate, t is the model time and t

_{ser}is the day of seroconversion. The function of the rate for antibody–virus complex formation and the corresponding parameters were chosen to allow approximation of antibody kinetics with model Ab. We used ${t}_{ser}\ast 2$ to acquire a better approximation of the antibody kinetics.

_{n}) were assumed to be the main virus-producing cell. They could engulf the virus, become infected (P

_{i}) and, consequently, die [53]:

_{inf}is the rate of infection of pneumocytes and δ

_{p}is the death rate of infected pneumocytes.

_{v}is the rate of viral phagocytosis by the macrophages and δ

_{v}is the rate of macrophage-independent viral clearance.

#### 4.4. Complete Model—A Combination of Model Ab and Model Cv

_{A}and M*. Therefore, Equations (2), (3), (13) and (14) were modified as follows:

_{V}* and ρ* were recalculated from p and ρ by dividing them by the number of S proteins on the viral particle. Here, we did not include viral production by macrophages in Equation (18). In some studies, SARS-CoV-2 replication in immune cells has been shown to be abortive, as no viable virions were produced [25,26,27].

#### 4.5. Model Integration, Analysis and Parameter Estimation

_{memory}and t

_{naive}were calculated from known data on lymphocyte physiology [60,61] and experimental results [34] (see Text S1 for the calculation details).

_{V}* and δ

_{p}were estimated from the data on SARS-CoV-2 replication in human airway epithelial (HAE) cells [35]. The set of equations for HAE cell infection is represented in Text S3 in the Supplementary Materials. The parameters for the macrophage activity were calculated based on experimental data and published models [1,38,57], as described in Text S2 in the Supplementary Materials.

_{a}, A

_{b}, B, Lp, Bm at time 30 days for model Ab) and p

_{j}-s are the models parameters. The detailed results are represented in Table S5.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ACE 2 | Angiotensin-converting enzyme 2 |

ADE | Antibody-dependent enhancement |

APS | Antigen-presenting site |

Bm | Memory B-cell |

COVID-19 | Coronavirus disease (COVID-19) |

HIV | Human immunodeficiency viruses |

PCR | Polymerase chain reaction |

Pl | Plasma cell |

## References

- Wölfel, R.; Corman, V.M.; Guggemos, W.; Seilmaier, M.; Zange, S.; Müller, M.A.; Niemeyer, D.; Jones, T.C.; Vollmar, P.; Rothe, C.; et al. Virological Assessment of Hospitalized Patients with COVID-2019. Nature
**2020**, 581, 465–469. [Google Scholar] [CrossRef] [PubMed] - Ita, K. Coronavirus Disease (COVID-19): Current Status and Prospects for Drug and Vaccine Development. Arch. Med. Res.
**2021**, 52, 15–24. [Google Scholar] [CrossRef] [PubMed] - Grigorova, I. Overview of the Neutralizing Antibody and Memory B Cell Response Kinetics in SARS-CoV-2 Convalescent and/or MRNA Vaccinated Individuals. Syst. Biol. Physiol. Rep.
**2021**, 1, 1. [Google Scholar] [CrossRef] - Arvin, A.M.; Fink, K.; Schmid, M.A.; Cathcart, A.; Spreafico, R.; Havenar-Daughton, C.; Lanzavecchia, A.; Corti, D.; Virgin, H.W. A Perspective on Potential Antibody-Dependent Enhancement of SARS-CoV-2. Nature
**2020**, 584, 353–363. [Google Scholar] [CrossRef] - Tirado, S.M.C.; Yoon, K.-J. Antibody-Dependent Enhancement of Virus Infection and Disease. Viral. Immunol.
**2003**, 16, 69–86. [Google Scholar] [CrossRef] - Iwasaki, A.; Yang, Y. The Potential Danger of Suboptimal Antibody Responses in COVID-19. Nat. Rev. Immunol.
**2020**, 20, 339–341. [Google Scholar] [CrossRef] - Winarski, K.L.; Tang, J.; Klenow, L.; Lee, J.; Coyle, E.M.; Manischewitz, J.; Turner, H.L.; Takeda, K.; Ward, A.B.; Golding, H.; et al. Antibody-Dependent Enhancement of Influenza Disease Promoted by Increase in Hemagglutinin Stem Flexibility and Virus Fusion Kinetics. Proc. Natl. Acad. Sci. USA
**2019**, 116, 15194–15199. [Google Scholar] [CrossRef] - Takada, A.; Feldmann, H.; Ksiazek, T.G.; Kawaoka, Y. Antibody-Dependent Enhancement of Ebola Virus Infection. J. Virol.
**2003**, 77, 7539–7544. [Google Scholar] [CrossRef] - Dejnirattisai, W.; Jumnainsong, A.; Onsirisakul, N.; Fitton, P.; Vasanawathana, S.; Limpitikul, W.; Puttikhunt, C.; Edwards, C.; Duangchinda, T.; Supasa, S.; et al. Cross-Reacting Antibodies Enhance Dengue Virus Infection in Humans. Science
**2010**, 328, 745–748. [Google Scholar] [CrossRef] - Gorlani, A.; Forthal, D.N. Antibody-Dependent Enhancement and the Risk of HIV Infection. Curr. HIV Res.
**2013**, 11, 421–426. [Google Scholar] [CrossRef] - Kulkarni, R. Antibody-Dependent Enhancement of Viral Infections. In Dynamics of Immune Activation in Viral Diseases; Bramhachari, P., Ed.; Springer: Singapore, 2020; pp. 9–41. [Google Scholar] [CrossRef]
- Tay, M.Z.; Wiehe, K.; Pollara, J. Antibody-Dependent Cellular Phagocytosis in Antiviral Immune Responses. Front. Immunol.
**2019**, 10, 332. [Google Scholar] [CrossRef] - Taylor, A.; Foo, S.-S.; Bruzzone, R.; Dinh, L.V.; King, N.J.C.; Mahalingam, S. Fc Receptors in Antibody-Dependent Enhancement of Viral Infections. Immunol. Rev.
**2015**, 268, 340–364. [Google Scholar] [CrossRef] - Coperchini, F.; Chiovato, L.; Croce, L.; Magri, F.; Rotondi, M. The Cytokine Storm in COVID-19: An Overview of the Involvement of the Chemokine/Chemokine-Receptor System. Cytokine Growth Factor Rev.
**2020**, 53, 25–32. [Google Scholar] [CrossRef] - Wang, S.; Wang, J.; Yu, X.; Jiang, W.; Chen, S.; Wang, R.; Wang, M.; Jiao, S.; Yang, Y.; Wang, W.; et al. Antibody-Dependent Enhancement (ADE) of SARS-CoV-2 Pseudoviral Infection Requires FcγRIIB and Virus-Antibody Complex with Bivalent Interaction. Commun. Biol.
**2022**, 5, 1–9. [Google Scholar] [CrossRef] - Bournazos, S.; Gupta, A.; Ravetch, J.V. The Role of IgG Fc Receptors in Antibody-Dependent Enhancement. Nat. Rev. Immunol.
**2020**, 20, 633–643. [Google Scholar] [CrossRef] - Jaume, M.; Yip, M.S.; Cheung, C.Y.; Leung, H.L.; Li, P.H.; Kien, F.; Dutry, I.; Callendret, B.; Escriou, N.; Altmeyer, R.; et al. Anti-Severe Acute Respiratory Syndrome Coronavirus Spike Antibodies Trigger Infection of Human Immune Cells via a PH- and Cysteine Protease-Independent FcγR Pathway. J. Virol.
**2011**, 85, 10582–10597. [Google Scholar] [CrossRef] - Kam, Y.W.; Kien, F.; Roberts, A.; Cheung, Y.C.; Lamirande, E.W.; Vogel, L.; Chu, S.L.; Tse, J.; Guarner, J.; Zaki, S.R.; et al. Antibodies against Trimeric S Glycoprotein Protect Hamsters against SARS-CoV Challenge despite Their Capacity to Mediate FcgammaRII-Dependent Entry into B Cells in Vitro. Vaccine
**2007**, 25, 729–740. [Google Scholar] [CrossRef] - Wan, Y.; Shang, J.; Sun, S.; Tai, W.; Chen, J.; Geng, Q.; He, L.; Chen, Y.; Wu, J.; Shi, Z.; et al. Molecular Mechanism for Antibody-Dependent Enhancement of Coronavirus Entry. J. Virol.
**2019**, 94, e02015-19. [Google Scholar] [CrossRef] - Eroshenko, N.; Gill, T.; Keaveney, M.K.; Church, G.M.; Trevejo, J.M.; Rajaniemi, H. Implications of Antibody-Dependent Enhancement of Infection for SARS-CoV-2 Countermeasures. Nat. Biotechnol.
**2020**, 38, 789–791. [Google Scholar] [CrossRef] - Lee, W.S.; Wheatley, A.K.; Kent, S.J.; DeKosky, B.J. Antibody-Dependent Enhancement and SARS-CoV-2 Vaccines and Therapies. Nat. Microbiol.
**2020**, 5, 1185–1191. [Google Scholar] [CrossRef] - Ricke, D.O. Two Different Antibody-Dependent Enhancement (ADE) Risks for SARS-CoV-2 Antibodies. Front. Immunol.
**2021**, 12, 443. [Google Scholar] [CrossRef] - Banerjee, A.; Nasir, J.A.; Budylowski, P.; Yip, L.; Aftanas, P.; Christie, N.; Ghalami, A.; Baid, K.; Raphenya, A.R.; Hirota, J.A.; et al. Isolation, Sequence, Infectivity, and Replication Kinetics of Severe Acute Respiratory Syndrome Coronavirus 2. Emerg. Infect. Dis.
**2020**, 26, 2054–2063. [Google Scholar] [CrossRef] - Abassi, Z.; Knaney, Y.; Karram, T.; Heyman, S.N. The Lung Macrophage in SARS-CoV-2 Infection: A Friend or a Foe? Front. Immunol.
**2020**, 11, 1312. [Google Scholar] [CrossRef] - Junqueira, C.; Crespo, Â.; Ranjbar, S.; de Lacerda, L.B.; Lewandrowski, M.; Ingber, J.; Parry, B.; Ravid, S.; Clark, S.; Schrimpf, M.R.; et al. FcγR-Mediated SARS-CoV-2 Infection of Monocytes Activates Inflammation. Nature
**2022**, 606, 576–584. [Google Scholar] [CrossRef] - Hui, K.P.Y.; Cheung, M.-C.; Perera, R.A.P.M.; Ng, K.-C.; Bui, C.H.T.; Ho, J.C.W.; Ng, M.M.T.; Kuok, D.I.T.; Shih, K.C.; Tsao, S.-W.; et al. Tropism, Replication Competence, and Innate Immune Responses of the Coronavirus SARS-CoV-2 in Human Respiratory Tract and Conjunctiva: An Analysis in Ex-Vivo and In-Vitro Cultures. Lancet Respir. Med.
**2020**, 8, 687–695. [Google Scholar] [CrossRef] - Zheng, J.; Wang, Y.; Li, K.; Meyerholz, D.K.; Allamargot, C.; Perlman, S. Severe Acute Respiratory Syndrome Coronavirus 2–Induced Immune Activation and Death of Monocyte-Derived Human Macrophages and Dendritic Cells. J. Infect. Dis.
**2020**, 223, 785–795. [Google Scholar] [CrossRef] [PubMed] - Rodrigues, T.S.; de Sá, K.S.G.; Ishimoto, A.Y.; Becerra, A.; Oliveira, S.; Almeida, L.; Gonçalves, A.V.; Perucello, D.B.; Andrade, W.A.; Castro, R.; et al. Inflammasomes Are Activated in Response to SARS-CoV-2 Infection and Are Associated with COVID-19 Severity in Patients. J. Exp. Med.
**2021**, 218, e20201707. [Google Scholar] [CrossRef] - Szekely, L.; Bozoky, B.; Bendek, M.; Ostad, M.; Lavignasse, P.; Haag, L.; Wu, J.; Jing, X.; Gupta, S.; Saccon, E.; et al. Pulmonary Stromal Expansion and Intra-Alveolar Coagulation Are Primary Causes of COVID-19 Death. Heliyon
**2021**, 7, e07134. [Google Scholar] [CrossRef] - Desforges, M.; Miletti, T.C.; Gagnon, M.; Talbot, P.J. Activation of Human Monocytes after Infection by Human Coronavirus 229E. Virus Res.
**2007**, 130, 228–240. [Google Scholar] [CrossRef] - Gómez-Rial, J.; Rivero-Calle, I.; Salas, A.; Martinón-Torres, F. Role of Monocytes/Macrophages in Covid-19 Pathogenesis: Implications for Therapy. Infect. Drug Resist.
**2020**, 13, 2485–2493. [Google Scholar] [CrossRef] - Beeraka, N.M.; Tulimilli, S.V.; Karnik, M.; Sadhu, S.P.; Pragada, R.R.; Aliev, G.; Madhunapantula, S.V. The Current Status and Challenges in the Development of Vaccines and Drugs against Severe Acute Respiratory Syndrome-Corona Virus-2 (SARS-CoV-2). Biomed. Res. Int.
**2021**, 2021, 8160860. [Google Scholar] [CrossRef] [PubMed] - Wu, F.; Yan, R.; Liu, M.; Liu, Z.; Wang, Y.; Luan, D.; Wu, K.; Song, Z.; Sun, T.; Ma, Y.; et al. Antibody-Dependent Enhancement (ADE) of SARS-CoV-2 Infection in Recovered COVID-19 Patients: Studies Based on Cellular and Structural Biology Analysis. medRxiv
**2020**. [Google Scholar] [CrossRef] - To, K.K.-W.; Tsang, O.T.-Y.; Leung, W.-S.; Tam, A.R.; Wu, T.-C.; Lung, D.C.; Yip, C.C.-Y.; Cai, J.-P.; Chan, J.M.-C.; Chik, T.S.-H.; et al. Temporal profiles of viral load in posterior oropharyngeal saliva samples and serum antibody responses during infection by SARS-CoV-2: An observational cohort study. Lancet Infect. Dis.
**2020**, 20, 565–574. [Google Scholar] [CrossRef] - Zhu, N.; Wang, W.; Liu, Z.; Liang, C.; Wang, W.; Ye, F.; Huang, B.; Zhao, L.; Wang, H.; Zhou, W.; et al. Morphogenesis and Cytopathic Effect of SARS-CoV-2 Infection in Human Airway Epithelial Cells. Nat. Commun.
**2020**, 11, 3910. [Google Scholar] [CrossRef] - Cerón Gómez, M.; Yang, H.M. A Simple Mathematical Model to Describe Antibody-Dependent Enhancement in Heterologous Secondary Infection in Dengue. Math. Med. Biol.
**2019**, 36, 411–438. [Google Scholar] [CrossRef] - Fain, B.; Dobrovolny, H.M. Initial Inoculum and the Severity of COVID-19: A Mathematical Modeling Study of the Dose-Response of SARS-CoV-2 Infections. Epidemiologia
**2020**, 1, 5–15. [Google Scholar] [CrossRef] - Lee, H.Y.; Topham, D.J.; Park, S.Y.; Hollenbaugh, J.; Treanor, J.; Mosmann, T.R.; Jin, X.; Ward, B.M.; Miao, H.; Holden-Wiltse, J.; et al. Simulation and Prediction of the Adaptive Immune Response to Influenza a Virus Infection. J. Virol.
**2009**, 83, 7151–7165. [Google Scholar] [CrossRef] - Danchin, A.; Pagani-Azizi, O.; Turinici, G.; Yahiaoui, G. COVID-19 Adaptive Humoral Immunity Models: Weakly Neutralizing Versus Antibody-Disease Enhancement Scenarios. Acta Biotheor.
**2022**, 70, 23. [Google Scholar] [CrossRef] - Schieffelin, J.S.; Costin, J.M.; Nicholson, C.O.; Orgeron, N.M.; Fontaine, K.A.; Isern, S.; Michael, S.F.; Robinson, J.E. Neutralizing and Non-Neutralizing Monoclonal Antibodies against Dengue Virus E Protein Derived from a Naturally Infected Patient. Virol. J.
**2010**, 7, 28. [Google Scholar] [CrossRef] [Green Version] - Hegazy, A.N.; Krönke, J.; Angermair, S.; Schwartz, S.; Weidinger, C.; Keller, U.; Treskatsch, S.; Siegmund, B.; Schneider, T. Anti-SARS-CoV2 Antibody-Mediated Cytokine Release Syndrome in a Patient with Acute Promyelocytic Leukemia. BMC Infect. Dis.
**2022**, 22, 537. [Google Scholar] [CrossRef] - Nechipurenko, Y.D.; Anashkina, A.A.; Matveeva, O.V. Change of Antigenic Determinants of SARS-CoV-2 Virus S-Protein as a Possible Cause of Antibody-Dependent Enhancement of Virus Infection and Cytokine Storm. Biophysics
**2020**, 65, 703–709. [Google Scholar] [CrossRef] - Zaichuk, T.A.; Nechipurenko, Y.D.; Adzhubey, A.A.; Onikienko, S.B.; Chereshnev, V.A.; Zainutdinov, S.S.; Kochneva, G.V.; Netesov, S.V.; Matveeva, O.V. The Challenges of Vaccine Development against Betacoronaviruses: Antibody Dependent Enhancement and Sendai Virus as a Possible Vaccine Vector. Mol. Biol.
**2020**, 54, 812–826. [Google Scholar] [CrossRef] - Yang, X.; Zhang, X.; Zhao, X.; Yuan, M.; Zhang, K.; Dai, J.; Guan, X.; Qiu, H.-J.; Li, Y. Antibody-Dependent Enhancement: ″Evil″ Antibodies Favorable for Viral Infections. Viruses
**2022**, 14, 1739. [Google Scholar] [CrossRef] - Okuya, K.; Hattori, T.; Saito, T.; Takadate, Y.; Sasaki, M.; Furuyama, W.; Marzi, A.; Ohiro, Y.; Konno, S.; Hattori, T.; et al. Multiple Routes of Antibody-Dependent Enhancement of SARS-CoV-2 Infection. Microbiol. Spectr.
**2022**, 10, e01553-21. [Google Scholar] [CrossRef] - Clark, N.M.; Janaka, S.K.; Hartman, W.; Stramer, S.; Goodhue, E.; Weiss, J.; Evans, D.T.; Connor, J.P. Anti-SARS-CoV-2 IgG and IgA Antibodies in COVID-19 Convalescent Plasma Do Not Enhance Viral Infection. PLoS ONE
**2022**, 17, e0257930. [Google Scholar] [CrossRef] - Dassarma, B.; Tripathy, S.; Matsabisa, M. Emergence of Ancient Convalescent Plasma (CP) Therapy: To Manage COVID-19 Pandemic. Transfus. Clin. Et Biol.
**2021**, 28, 123–127. [Google Scholar] [CrossRef] - Turner, J.S.; Benet, Z.L.; Grigorova, I.L. Signals 1, 2 and B Cell Fate or: Where, When and for How Long? Immunol. Rev.
**2020**, 296, 9–23. [Google Scholar] [CrossRef] - Reis, R.F.; Pigozzo, A.B.; Bonin, C.R.B.; de Melo Quintela, B.; Pompei, L.T.; Vieira, A.C.; de Lima e Silva, L.; Xavier, M.P.; Weber dos Santos, R.; Lobosco, M. A Validated Mathematical Model of the Cytokine Release Syndrome in Severe COVID-19. Front. Mol. Biosci.
**2021**, 8, 680. [Google Scholar] [CrossRef] - Goutelle, S.; Maurin, M.; Rougier, F.; Barbaut, X.; Bourguignon, L.; Ducher, M.; Maire, P. The Hill Equation: A Review of Its Capabilities in Pharmacological Modelling. Fundam. Clin. Pharmacol.
**2008**, 22, 633–648. [Google Scholar] [CrossRef] - Bonin, C.R.B.; Fernandes, G.C.; dos Santos, R.W.; Lobosco, M. A Qualitatively Validated Mathematical-Computational Model of the Immune Response to the Yellow Fever Vaccine. BMC Immunol.
**2018**, 19, 15. [Google Scholar] [CrossRef] - Nguyen, D.C.; Joyner, C.J.; Sanz, I.; Lee, F.E.-H. Factors Affecting Early Antibody Secreting Cell Maturation into Long-Lived Plasma Cells. Front. Immunol.
**2019**, 10, 2138. [Google Scholar] [CrossRef] - Wang, S.; Pan, Y.; Wang, Q.; Miao, H.; Brown, A.N.; Rong, L. Modeling the Viral Dynamics of SARS-CoV-2 Infection. Math. Biosci.
**2020**, 328, 108438. [Google Scholar] [CrossRef] [PubMed] - Ajmeriya, S.; Kumar, A.; Karmakar, S.; Rana, S.; Singh, H. Neutralizing Antibodies and Antibody-Dependent Enhancement in COVID-19: A Perspective. J. Indian Inst. Sci.
**2022**, 102, 1–17. [Google Scholar] [CrossRef] - Bergmann, F.T.; Hoops, S.; Klahn, B.; Kummer, U.; Mendes, P.; Pahle, J.; Sahle, S. COPASI and Its Applications in Biotechnology. J. Biotechnol.
**2017**, 261, 215–220. [Google Scholar] [CrossRef] - Petzold, L. Automatic Selection of Methods for Solving Stiff and Nonstiff Systems of Ordinary Differential Equations. SIAM J. Sci. Stat. Comput.
**1983**, 4, 136–148. [Google Scholar] [CrossRef] - Kapellos, T.S.; Taylor, L.; Lee, H.; Cowley, S.A.; James, W.S.; Iqbal, A.J.; Greaves, D.R. A Novel Real Time Imaging Platform to Quantify Macrophage Phagocytosis. Biochem. Pharmacol.
**2016**, 116, 107–119. [Google Scholar] [CrossRef] - Bromage, E.; Stephens, R.; Hassoun, L. The Third Dimension of ELISPOTs: Quantifying Antibody Secretion from Individual Plasma Cells. J. Immunol. Methods
**2009**, 346, 75–79. [Google Scholar] [CrossRef] - Seydoux, E.; Homad, L.J.; MacCamy, A.J.; Parks, K.R.; Hurlburt, N.K.; Jennewein, M.F.; Akins, N.R.; Stuart, A.B.; Wan, Y.-H.; Feng, J.; et al. Characterization of Neutralizing Antibodies from a SARS-CoV-2 Infected Individual. bioRxiv, 2020; preprint. [Google Scholar] [CrossRef]
- Itoua Maïga, R.; Bonnaure, G.; Tremblay Rochette, J.; Néron, S. Human CD38hiCD138+ Plasma Cells Can Be Generated In Vitro from CD40-Activated Switched-Memory B Lymphocytes. J. Immunol. Res.
**2014**, 2014, 635108. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Amanna, I.J.; Slifka, M.K. Mechanisms That Determine Plasma Cell Lifespan and the Duration of Humoral Immunity. Immunol. Rev.
**2010**, 236, 125–138. [Google Scholar] [CrossRef] - Marino, S.; Hogue, I.B.; Ray, C.J.; Kirschner, D.E. A Methodology for Performing Global Uncertainty and Sensitivity Analysis in Systems Biology. J. Theor. Biol.
**2008**, 254, 178–196. [Google Scholar] [CrossRef] [PubMed] - Saltelli, A.; Ratto, M.; Tarantola, S.; Campolongo, F. Sensitivity Analysis for Chemical Models. Chem. Rev.
**2005**, 105, 2811–2828. [Google Scholar] [CrossRef] [PubMed] - Sender, R.; Bar-On, Y.M.; Gleizer, S.; Bernshtein, B.; Flamholz, A.; Phillips, R.; Milo, R. The total number and mass of SARS-CoV-2 virions. Proc. Natl. Acad. Sci. USA
**2021**, 118, e2024815118. [Google Scholar] [CrossRef] [PubMed] - Chi, X.; Liu, X.; Wang, C.; Zhang, X.; Li, X.; Hou, J.; Ren, L.; Jin, Q.; Wang, J.; Yang, W. Humanized single domain antibodies neutralize SARS-CoV-2 by targeting the spike receptor binding domain. Nat. Commun.
**2020**, 11, 4528. [Google Scholar] [CrossRef] - Kamath, A.T.; Henri, S.; Battye, F.; Tough, D.F.; Shortman, K. Developmental kinetics and lifespan of dendritic cells in mouse lymphoid organs. Blood
**2002**, 100, 1734–1741. [Google Scholar] [CrossRef] - Sathe, P.; Shortman, K. The steady-state development of splenic dendritic cells. Mucosal Immunol.
**2008**, 1, 425–431. [Google Scholar] [CrossRef] - Liu, K.; Waskow, C.; Liu, X.; Yao, K.; Hoh, J.; Nussenzweig, M. Origin of dendritic cells in peripheral lymphoid organs of mice. Nat. Immunol.
**2007**, 8, 578–583. [Google Scholar] [CrossRef] - Hartley, G.E.; Edwards, E.S.; Aui, P.M.; Varese, N.; Stojanovic, S.; McMahon, J.; Peleg, A.Y.; Boo, I.; Drummer, H.E.; Hogarth, P.M.; et al. Rapid generation of durable B cell memory to SARS-CoV-2 spike and nucleocapsid proteins in COVID-19 and convalescence. Sci. Immunol.
**2020**, 5, eabf8891. [Google Scholar] [CrossRef] - Mamani-Matsuda, M.; Cosma, A.; Weller, S.; Faili, A.; Staib, C.; Garçon, L.; Hermine, O.; Beyne-Rauzy, O.; Fieschi, C.; Pers, J.O.; et al. The human spleen is a major reservoir for long-lived vaccinia virus–specific memory B cells. Blood
**2008**, 111, 4653–4659. [Google Scholar] [CrossRef] [Green Version] - Bujoreanu, I.; Gupta, V. Anatomy, Lymph Nodes. In StatPearls; StatPearls Publishing: Treasure Island, FL, USA, 2022. Available online: http://www.ncbi.nlm.nih.gov/books/NBK557717/ (accessed on 18 July 2022).
- Alberts, B.; Johnson, A.; Lewis, J.; Raff, M.; Roberts, K.; Walter, P. B Cells and Antibodies. In Molecular Biology of the Cell, 4th ed.; Garland Science: New Yoek, NY, USA, 2002. Available online: https://www.ncbi.nlm.nih.gov/books/NBK26884/ (accessed on 19 July 2022).
- Hibi, T.; Dosch, H.M. Limiting dilution analysis of the B cell compartment in human bone marrow. Eur. J. Immunol.
**1986**, 16, 139–145. [Google Scholar] [CrossRef] - Arvola, M.; Gustafsson, E.; Svensson, L.; Jansson, L.; Holmdahl, R.; Heyman, B.; Okabe, M.; Mattsson, R. Immunoglobulin-Secreting Cells of Maternal Origin Can Be Detected in B Cell-Deficient Mice1. Biol. Reprod.
**2000**, 63, 1817–1824. [Google Scholar] [CrossRef] - Pawelek, K.A.; Huynh, G.T.; Quinlivan, M.; Cullinane, A.; Rong, L.; Perelson, A.S. Modeling Within-Host Dynamics of Influenza Virus Infection Including Immune Responses. PLoS Comput. Biol.
**2012**, 8, e1002588. [Google Scholar] [CrossRef] - Yap, T.F.; Liu, Z.; Shveda, R.A.; Preston, D.J. A predictive model of the temperature-dependent inactivation of coronaviruses. Appl. Phys. Lett.
**2020**, 117, 060601. [Google Scholar] [CrossRef] - Laidlaw, B.J.; Cyster, J.G. Transcriptional regulation of memory B cell differentiation. Nat. Rev. Immunol.
**2021**, 21, 209–220. [Google Scholar] [CrossRef] - Ke, Z.; Oton, J.; Qu, K.; Cortese, M.; Zila, V.; McKeane, M.; Nakane, T.; Zivanov, J.; Neufeldt, C.J.; Cerikan, B.; et al. Structures and distributions of SARS-CoV-2 spike proteins on intact virions. Nature
**2020**, 588, 498–502. [Google Scholar] [CrossRef]

**Figure 1.**Antibody-response generation (model Ab) and infection propagation (model Cv) outputs. (

**a**–

**c**) model Ab: (

**a**) approximation of experimental data for viral load dynamics [34]. The following parameter values were chosen (Equation (1)): A

_{RNA}= 798,292 RNA numbers, x

_{0}= 2.998 days, w

_{1}= w

_{2}= 2.069 days

^{−1}, w

_{3}= 2.38 days. (

**b**) Changes in relative numbers of antibodies and dynamic of viral epitopes for an individual patient [34]. (

**c**) Kinetics of naive B-cells, plasma cells and memory B-cells for the same patient. The following donor-specific parameters were used: δ

_{pl}= 0.004 days

^{−1}, π

_{pl}= 3 × 10

^{−5}(APS∙days)

^{−1}, β

_{RNA}= 264, w

_{3}= 2.62 days, t

_{naive}= 12.8 days, w = 1.04. (

**d**–

**f**) model Cv (

**d**) A typical fit to the experimental data (black dots) on viral load in COVID-19 patients [1]. The day of seroconversion is marked with the grey dotted line and assumed to happen on day 6. The following donor-specific parameters were used: β

_{inf}= 2.21 × 10

^{−6}(Virus∙days)

^{−1}, δ

_{v}= 255 days

^{−1}, ac

_{0}= 2.17 × 10

^{−10}(cells∙cells∙days)

^{−1}, Virus

_{0}= 1.32 × 10

^{7}particles; (

**e**) The dependence of the viral response dynamics for different values of the probability on macrophage infection probability ρ. (

**f**) The dependence of the pneumocytes dynamics for different values on the probability of macrophage infection ρ.

**Figure 2.**Influence of initial viral load, pre-existing antibody concentration and dissociation constant of the antigen–antibody complex (Kd) on the free viral epitope and pneumocyte dynamics in the complete model. (

**a**,

**b**) Dynamics of free viral epitope (

**a**) and pneumocytes (

**b**) at various initial viral loads. (

**c**,

**d**) Dynamics of free viral epitope (

**c**) and pneumocytes (

**d**) at different concentrations of pre-existing antibodies. Label Ab

_{0}denotes the concentration of pre-existing antibodies in lymphoid organs at the onset of disease. (

**e**,

**f**) Dynamics of free viral epitope (

**e**) and pneumocytes (

**f**) at various dissociation constants for the antigen–antibody complex for primary antibodies. (

**g**,

**h**) Dynamics of free viral epitope (

**g**) and pneumocytes (

**h**) at various dissociation constants for the antigen-antibody complex for pre-existing antibodies. The initial concentration of pre-existing antibodies equaled 10

^{13}particles (Ab

_{lo}= 10

^{13}).

**Figure 3.**Influence of macrophage infection probability ρ on the course of disease. (

**a**) The dependence of the viral response dynamics for different probabilities of macrophage infection ρ. (

**b**) The dependence of the pneumocyte dynamics for different probabilities of macrophage infection ρ. (

**c**,

**d**) The dependence of the macrophage dynamics for different probabilities of macrophage infection ρ.

**Figure 4.**Influence of pre-existing antibodies with different macrophage infection probabilities on possible ADE occurrence. (

**a**–

**c**) Viral load dynamics (

**a**), pneumocyte number (

**b**) and macrophage kinetics (

**c**) with different macrophage infection probabilities (Ab

_{old}= 10

^{9}). (

**d**–

**f**) Viral load dynamics (

**d**), pneumocyte number (

**e**) and macrophage kinetics (

**f**) with different macrophage infection probabilities (Ab

_{old}= 10

^{11}). (

**g**–

**i**) Viral load dynamics (

**g**), pneumocyte number (

**h**) and macrophage kinetics (

**i**) with different macrophage infection probabilities (Ab

_{old}= 10

^{13}). (

**j**–

**l**) Viral load dynamics (

**j**), pneumocyte number (

**k**) and macrophage kinetics (

**l**) with different macrophage infection probabilities (Ab

_{old}= 10

^{15}).

**Figure 5.**Influence of antigen–pre-existing antibody complex dissociation constant (Kd

_{old}) on possible ADE occurrence. (

**a**–

**c**) Viral load dynamics (

**a**), pneumocyte number (

**b**) and macrophage kinetics (

**c**) with different Kd

_{old}(Ab

_{old}= 10

^{9}). (

**d**–

**f**) Viral load dynamics (

**d**), pneumocyte number (

**e**) and macrophage kinetics (

**f**) with different Kd

_{old}(Ab

_{old}= 10

^{11}). (

**g**–

**i**) Viral load dynamics (

**g**), pneumocyte number (

**h**) and macrophage kinetics (

**i**) with different Kd

_{old}(Ab

_{old}= 10

^{13}). (

**j**–

**l**) Viral load dynamics (

**j**), pneumocyte number (

**k**) and macrophage kinetics (

**l**) with different Kd

_{old}(Ab

_{old}= 10

^{15}).

**Figure 6.**Schematic representations of the models. (

**a**) The scheme of model Ab—antibody generation. The model describes the stimulation of the antibody-producing system after an interaction with a pathogen. Activation of B-cells by some antigen-presenting sites (APSs) and their differentiation into antibody-secreting plasma cells and memory B-cells occur in lymphoid organs. The APSs occur in response to the infection. In the absence of pathogens, APSs are in the inactivated state (yellow cycle), and they change the activated state (orange cycle) after infection of the body. (

**b**) The scheme of model Cv—viral infection of the alveolus. The model describes the processes of pneumocyte and macrophage viral infection and virus degradation through the immune system and thermal degradation. (

**c**) The scheme of the complete model, which is the combination of model Ab and model Cv. Black solid arrows denote transitions between different states and grey dashed arrows denote indirect interactions.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Boldova, A.E.; Korobkin, J.D.; Nechipurenko, Y.D.; Sveshnikova, A.N.
Theoretical Explanation for the Rarity of Antibody-Dependent Enhancement of Infection (ADE) in COVID-19. *Int. J. Mol. Sci.* **2022**, *23*, 11364.
https://doi.org/10.3390/ijms231911364

**AMA Style**

Boldova AE, Korobkin JD, Nechipurenko YD, Sveshnikova AN.
Theoretical Explanation for the Rarity of Antibody-Dependent Enhancement of Infection (ADE) in COVID-19. *International Journal of Molecular Sciences*. 2022; 23(19):11364.
https://doi.org/10.3390/ijms231911364

**Chicago/Turabian Style**

Boldova, Anna E., Julia D. Korobkin, Yury D. Nechipurenko, and Anastasia N. Sveshnikova.
2022. "Theoretical Explanation for the Rarity of Antibody-Dependent Enhancement of Infection (ADE) in COVID-19" *International Journal of Molecular Sciences* 23, no. 19: 11364.
https://doi.org/10.3390/ijms231911364