Predicting the Kinetic Coordination of Immune Response Dynamics in SARS-CoV-2 Infection: Implications for Disease Pathogenesis
Abstract
:1. Introduction
- 1.
- to develop a calibrated mathematical model of antiviral innate and adaptive immune responses to SARS-CoV-2 during mild-to-moderate symptoms infection;
- 2.
- to infer the sensitivity of the peak viral load to the kinetics of innate and adaptive responses;
- 3.
- to quantify the infectiousness of the COVID-19 patients from the onset to the recovery phase of the infection;
- 4.
- to examine the effect of the accelerated or decelerated components of the immune response on the viral load and prolonged viral persistence;
- 5.
- to evaluate the person’s infectiousness and effectiveness of testing procedures.
2. Materials and Methods
2.1. Mathematical Model of Antiviral Immune Response
2.1.1. Virus Spreading in Sensitive Tissue
2.1.2. Innate Immune Defence Reaction
2.1.3. Antigen-Specific Immune Response
2.1.4. Effects of Inflammation and Tissue Damage
2.1.5. Initial Conditions
2.2. Reference Data on SARS-CoV-2 Infection
2.3. Calibration of the Model
- First stage (incubation period, 0–3 days): .
- Second stage (activation of immune response and peak of viral load, 4–7 days) and third stage (recovery period, 8–13 days): .
- Forth stage (post-symptomatic period, 14–19 days): .
2.4. Sensitivity Analysis
3. Results
3.1. Local Sensitivity Analysis
3.2. Global Sensitivity Analysis
3.3. Induction of Antigen-Presenting Cells
3.4. Induction of Type I IFN Response
3.5. Disregulation of CTL and B-Cell Responses
3.6. Asymmetry of Th1 versus Th2 Responses
3.7. Kinetic Mechanisms of Long COVID-19 Pathogenesis
3.8. Individual’s Infectiousness
3.9. Day-by-Day Use of the Model
4. Discussion
Author Contributions
Funding
Conflicts of Interest
Abbreviations
SARS-CoV-2 | Severe acute respiratory syndrome coronavirus |
ODE | Ordinary differential equations |
COVID-19 | Infectious disease caused by SARS-CoV-2 |
IFN-I | Type I interferon |
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Parameter, Units | Range, Initial Guess | Estimate | |
---|---|---|---|
Concentration of APCs, cells/mL | |||
Concentration of IFN-producing APCs, cells/mL | |||
Concentration of SARS-CoV-2 specific Th1 cells, cells/mL | 600 | ||
Concentration of SARS-CoV-2 specific Th2 cells, cells/mL | 600 | ||
Concentration of SARS-CoV-2 specific CTLs, cells/mL | 600 | ||
Concentration of SARS-CoV-2 specific B cells, cells/mL | 600 | ||
Concentration of SARS-CoV-2 specific plasma cells, cells/mL | 10 | ||
Concentration of SARS-CoV-2 specific antibodies, molecules/mL | |||
Concentration of epithelial cells, cells/mL | |||
Rate of stimulated state loss for APCs, day−1 | |||
Rate of activated state loss for Th1 cells, day−1 | 1 | ||
Rate of activated state loss for Th2 cells, day−1 | 1 | ||
Rate of natural death for CTLs, day−1 | |||
Rate of natural death for B cells, day−1 | |||
Rate of natural death for plasma cells, day−1 | |||
Rate of natural death for antibodies, day−1 | |||
Duration of Th1 cell division cycle, days | |||
Duration of Th2 cell division cycle, days | |||
Duration of CTL division cycle, days | |||
Duration of B cell division cycle, days | |||
Duration of B cell differentiation into plasma cells, days | |||
Number of Th1 cells created during division cycle | 4 | ||
Number of Th2 cells created during division cycle | 4 | ||
Number of CTLs created during division cycle | 2 | ||
Number of B cells in clone created by series of 1 or 2 divisions | 3 | ||
Number of plasma cells in clone created by series of 1 or 2 divisions | 1 | ||
Rate of IgG production per plasma cell, molecules/cell/day | |||
Rate of Th1 cells stimulation, (cells/mL)−1day−1 | , | ||
Rate of Th2 cells stimulation, (cells/mL)−1day−1 | , | ||
Rate of CTL stimulation, (cells/mL)−2day−1 | , | ||
Rate of B cell stimulation, (cells/mL)−2day−1 | , | ||
Rate of plasma cell stimulation, (cells/mL)−2day−1 | , | ||
Rate of Th1 cells suppression, (cells/mL)−2day−1 | |||
Rate of Th2 cells suppression, (cells/mL)−2day−1 | |||
Rate of APC stimulation, (cells/mL)−1day−1 | , | ||
Rate of IgG binding to SARS-CoV-2, (virions/mL)−1day−1 | , | ||
Rate of epithelial cell infection with SARS-CoV-2, (cells/mL)−1day−1 | , | ||
Rate of infected epithelial cell damage by CTLs, (virions/mL)−1day−1 | , | ||
Rate of CTL death due to lytic interactions with infected cells, (cells/mL)−1day−1 | |||
Rate of infected cell damage due to SARS-CoV-2 cytopathicity, day−1 | |||
Rate of epithelial cell regeneration, day−1 | 4 | ||
Rate of SARS-CoV-2 virions secretion per infected epithelial cell, day−1 | , 130 | 144 | |
Rate of SARS-CoV-2 absorption by epithelial cell, (cells/mL)−1day−1 | , | ||
Rate of nonspecific SARS-CoV-2 elimination, day−1 | , | 4 | |
Rate of SARS-CoV-2 neutralization by specific IgG, (virions/mL)−1day−1 | , | ||
Parameter for inflammation-based enhancement of IgG effect | , 1000 | 2628 | |
Parameter for inflammation-based enhancement of CTL effect | , 1000 | 1407 | |
Rate of induction of IFN-producing state in APCs, (cells/mL)−1day−1 | , | ||
Rate of IFN-producing state loss by APCs, day−1 | |||
Rate of IFN production per IFN-producing cells, molecules/cell/day | 6000 | ||
Type I IFN clearance rate, day−1 | 24 | ||
Rate of IFN binding with epithelial cells, (cells/mL)−1day−1 | , | ||
Rate of virus-resistant state induction in epithelial cells, (cells/mL)−1day−1 | , | ||
Rate of virus-resistant state loss in epithelial cells, day−1 | 1 |
Parameter | ||||||||||
Variation | − | − |
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Grebennikov, D.; Karsonova, A.; Loguinova, M.; Casella, V.; Meyerhans, A.; Bocharov, G. Predicting the Kinetic Coordination of Immune Response Dynamics in SARS-CoV-2 Infection: Implications for Disease Pathogenesis. Mathematics 2022, 10, 3154. https://doi.org/10.3390/math10173154
Grebennikov D, Karsonova A, Loguinova M, Casella V, Meyerhans A, Bocharov G. Predicting the Kinetic Coordination of Immune Response Dynamics in SARS-CoV-2 Infection: Implications for Disease Pathogenesis. Mathematics. 2022; 10(17):3154. https://doi.org/10.3390/math10173154
Chicago/Turabian StyleGrebennikov, Dmitry, Antonina Karsonova, Marina Loguinova, Valentina Casella, Andreas Meyerhans, and Gennady Bocharov. 2022. "Predicting the Kinetic Coordination of Immune Response Dynamics in SARS-CoV-2 Infection: Implications for Disease Pathogenesis" Mathematics 10, no. 17: 3154. https://doi.org/10.3390/math10173154
APA StyleGrebennikov, D., Karsonova, A., Loguinova, M., Casella, V., Meyerhans, A., & Bocharov, G. (2022). Predicting the Kinetic Coordination of Immune Response Dynamics in SARS-CoV-2 Infection: Implications for Disease Pathogenesis. Mathematics, 10(17), 3154. https://doi.org/10.3390/math10173154