Multiscale Model of Antiviral Timing, Potency, and Heterogeneity Effects on an Epithelial Tissue Patch Infected by SARS-CoV-2
Abstract
:1. Introduction
2. Materials and Methods
2.1. Remdesivir Physiologically Based Pharmacokinetic Model
2.2. Sego et al.’s Agent-Based Model
2.3. Viral Life Cycle Model
2.4. Remdesivir Mode of Action (MOA) Model
2.5. Heterogeneous Cellular Metabolism of Remdesivir Modeling
2.6. Simulating Antiviral Treatment Regimens and Treatment Classification Metrics
3. Results
3.1. Remdesivir PK Model
3.2. Variability of Outcomes in Sego’s Model
3.3. Predictive Treatment Outcomes
3.3.1. Coarse-Parameter Variation
3.3.2. Fine Parameter Variation
3.3.3. Faster Clearing Drug Necessitates More Potent Antiviral in Order to Contain the Infection
3.3.4. Heterogeneous Cellular Metabolism of Remdesivir Results
3.3.5. Factors Responsible for Negative Treatment Outcomes in the Heterogeneous Metabolism Model
- Rapid clearance: 24 h dose interval, 0.01 multiplier;
- Slow clearance: 120 h dose interval, 0.03 multiplier;
- Partial containment: 96 h dose interval, 0.06 multiplier;
- Widespread infection: 24 h dose interval, 0.1 multiplier.
3.3.6. Effects of Variability in Cellular Drug Metabolism on Treatment Outcomes
4. Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
ABM | Agent-based model |
COPASI | Complex Pathway Simulator |
CPM | Cellular Potts model |
EBOV | Ebola virus |
GS-443902 | Remdesivir Triphosphate, CAS: 1355149-45-9, CHEBI:150869 |
MDPI | Multidisciplinary Digital Publishing Institute |
MOA | Mechanism of action |
ODE | Ordinary differential equation |
PBMC | Peripheral blood mononuclear cells |
PBPK | Physiological based pharmacokinetic model |
PD | Pharmacodynamic model |
PK | Pharmacokinetic model |
RdRP | RNA-dependent RNA polymerase |
SBML | Systems Biology Markup Language |
Appendix A. Simple PK Model for Remdesivir and GS-443902
Parameter | Unit | Humeniuk * Cohort 7 | Humeniuk * Cohort 8 | EU Compassionate Use ** |
---|---|---|---|---|
Remdesivir Dose | mg | 150 | 75 | 200 |
Infusion Duration | h | 2 | 0.5 | 1.0 *** |
GS-443902 | uM | 6.0 | 5.9 | 9.8 |
GS-443902 | uM | 3.7 | 3.3 | 6.9 |
GS-443902 | 1/h | 36 | 49 | |
GS-443902 | h × uM | 157.4 | ||
GS-443902 | h × uM | 297 | 394 | |
GS-443902 | h × uM | 272 | 340 |
Appendix A.1. COPASI Codes
Appendix A.1.1. COPASI Model File for Parameter Fitting
- Humeniuk_PK_data_Europe_Table_16.txt
- Humeniuk_PK_data_Table_4_Cohort7.txt
- Humeniuk_PK_data_Table_4_Cohort8.txt
Appendix A.1.2. COPASI Model File for Calculating GS-443902 from Repetitive Remdesivir Doses
Appendix B. Table of Parameters from Sego et al.
Conversion Factors | Value |
---|---|
Simulation step | 1200.0 s * (300.0 s) |
Lattice width | 4.0 μm |
Scale factor for concentration | mol |
Simulation Parameter Name | Value | Simulation Parameter Name | Value |
---|---|---|---|
Cell diameter | 12.0 μm | Viral decay rate | 7.71 × 10−6 s−1 |
Replication rate | (1/12)10−3 s−1 | Cytokine diffusion coefficient | 0.16 μm2 s−1 |
Translating rate | (1/18)10−3 s−1 | Cytokine diffusion length | 100 μm |
Unpacking rate | (1/6)10−3 s−1 | Cytokine decay rate | 1.32 × 10−5 s−1 |
Packaging rate | (1/6)10−3 s−1 | Maximum cytokine immune secretion rate | 3.5 × 10−4 pMs−1 |
Release rate | (1/6)10−3 s−1 | Immune secretion midpoint | 1 pM |
Scale factor for number of mRNA per infected cell | 1000 cell−1 | Cytokine immune uptake rate | 3.5 × 10−4 pMs−1 |
Viral dissociation coefficient | 2000 | Maximum cytokine infected cell secretion rate | 3.5 × 10−3 pMs−1 |
Viral diffusion coefficient | 0.01 μm2 s−1 | Infected cell cytokine secretion mid-point , | 0.1 |
Viral diffusion length | 36 μm | Cytokine secretion Hill coefficient | 2 |
Immune cell cytokine activation | 10 pM | Virally-induced apoptosis dissociation coefficient | 100 |
Immune cell equilibrium bound cytokine | 210 pM | Virally-induced apoptosis characteristic time constant | 20 min |
Immune cell bound cytokine memory | 0.99998 s−1 | Immune cell activation Hill coefficient | 2 |
Immune cell activated time | 10 h | Immune response add immune cell coefficient | 1/1200 s−1 |
Oxidation Agent diffusion coefficient | 0.64 μm2 s−1 | Immune response subtract immune cell coefficient | 1/6000 cell−1 s−1 |
Oxidation Agent diffusion length | 36 μm | Immune response delay coefficient | 1.2 × 106 s |
Oxidation Agent decay rate | 1.32 × 10−5 s−1 | Immune response decay coefficient | 1/12,000 s−1 |
Immune cell oxidation agent secretion rate | 3.5 × 10−3 pMs−1 | Immune response cytokine transmission coefficient | 0.5 |
Immune cell threshold for Oxidation Agent release | 10 = 1.5625 pM | Immune response probability scaling coefficient | 0.01 |
Tissue cell threshold for death | 1.5 = 0.234375 pM | Number of immune cell seeding samples | 10 |
Simulation Parameter Name | Value | Simulation Parameter Name | Value |
---|---|---|---|
Initial density of unbound cell surface receptors | 200 cell−1 | Initial immune cell target volume | 64 μm3 |
Virus–receptor association affinity | 1.4 × 104 M−1 s−1 | Immune cell lambda volume | 9 |
Virus–receptor dissociation affinity | 1.4 × 104 s | Initial number of immune cells | 0 |
Infection threshold | 1 | Immune cells lambda chemotaxis | 1 |
Uptake Hill coefficient | 2 | Intrinsic Random Motility | 10 |
Uptake characteristic time constant | 20 min | Contact coefficients J (all interfaces) | 10 |
Virally-induced apoptosis Hill coefficient | 2 |
Appendix C. Quantitative Metrics of Treatment Outcome
Appendix D. Instructions for Running the Multiscale CompuCell3D Simulations and for Analyzing the Results
Appendix D.1. CompuCell3D Simulations
- mult_dict = treatment_starts_0, parameters varied in the fine investigation with treatment starting with the infection of 10 epithelial cells;
- mult_dict = treatment_starts_3_halved_half_life, parameters varied in the fine investigation with treatment starting3 days post the infection of 10 epithelial cells and with the half life of GS-443902 halved.
Appendix D.2. Results Analysis
Appendix E. Supplementary Results for the Untreated Simulations with Different Initial Conditions
Appendix F. Supplementary Results from Treatment Initiation Delay, Antiviral Potency, and GS-443902 Half-Life Variation
Appendix F.1. Homogeneous Metabolism, Regular GS-443902 Half-Life
Appendix F.1.1. Treatment Initiation with Infection of Ten Epithelial Cells
Appendix F.1.2. Treatment Initiation 12 h Post the Infection of Ten Epithelial Cells
Appendix F.1.3. Treatment Initiation One Day Post the Infection of Ten Epithelial Cells
Appendix F.1.4. Treatment Initiation Three Days Post the Infection of Ten Epithelial Cells
Appendix F.2. Homogeneous Metabolism, Halved GS-443902 Half-Life
Appendix F.2.1. Treatment Initiation with Infection of Ten Epithelial Cells
Appendix F.2.2. Treatment Initiation One Day Post Infection of Ten Epithelial Cells
Appendix F.2.3. Treatment Initiation Three Days Post Infection of Ten Epithelial Cells
Appendix F.3. Homogeneous Metabolism, GS-443902 Half-Life Reduced by 75%
Treatment Initiation with Infection of Ten Epithelial Cells
Appendix F.4. Heterogeneous Metabolism, Regular GS-443902 Half-Life
Appendix F.4.1. Treatment Initiation with Infection of Ten Epithelial Cells
Appendix F.4.2. Treatment Initiation Twelve Hours Post the Infection of Ten Epithelial Cells
Appendix F.4.3. Treatment Initiation One Day Post the Infection of Ten Epithelial Cells
Appendix F.4.4. Treatment Initiation Three Days Post the Infection of Ten Epithelial Cells
Appendix F.5. Heterogeneous Metabolism Using Other Standard Deviations
Appendix F.5.1. Standard Deviation Set to 0.1
Appendix F.5.2. Standard Deviation Set to 0.5
Appendix F.5.3. How Heterogeneity Affects Intracellular Drug Levels
Appendix G. Supplementary Results for Viral Production Metabolism Rate Correlation
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Parameter | Value | Source |
---|---|---|
(unit-less) | 0 or 1 | Fit to [7] |
GS-443902 observed Half-life, (h) | 30.2 | [7] |
, GS-443902’s decay rate (1/h) | ||
(mg/day) | 100 (200 for loading dose) | Doses used in clinical situations |
(L) | 38.4 | Fit to [7,39] |
(h) | 1 |
Parameter | Values Used |
---|---|
Total epithelial population | 900 |
Number of initially infected cells | 5 |
Treatment initiation delay (day) | 0, 1, 3 |
Time between antiviral doses | 8, 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144 |
Remdesivir doses (rescaled to match the schedules) (mg) | 25, 50, 100, 150, 200, 250, 300, 350, 400, 450, 500, 550, 600 |
Base (μmol/L) | 7.897 |
Viral replication rate reduction (Equation (11)) Hill coefficient | 2 |
multipliers | 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1, 0.5, 1, 5, 10 |
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Ferrari Gianlupi, J.; Mapder, T.; Sego, T.J.; Sluka, J.P.; Quinney, S.K.; Craig, M.; Stratford, R.E., Jr.; Glazier, J.A. Multiscale Model of Antiviral Timing, Potency, and Heterogeneity Effects on an Epithelial Tissue Patch Infected by SARS-CoV-2. Viruses 2022, 14, 605. https://doi.org/10.3390/v14030605
Ferrari Gianlupi J, Mapder T, Sego TJ, Sluka JP, Quinney SK, Craig M, Stratford RE Jr., Glazier JA. Multiscale Model of Antiviral Timing, Potency, and Heterogeneity Effects on an Epithelial Tissue Patch Infected by SARS-CoV-2. Viruses. 2022; 14(3):605. https://doi.org/10.3390/v14030605
Chicago/Turabian StyleFerrari Gianlupi, Juliano, Tarunendu Mapder, T. J. Sego, James P. Sluka, Sara K. Quinney, Morgan Craig, Robert E. Stratford, Jr., and James A. Glazier. 2022. "Multiscale Model of Antiviral Timing, Potency, and Heterogeneity Effects on an Epithelial Tissue Patch Infected by SARS-CoV-2" Viruses 14, no. 3: 605. https://doi.org/10.3390/v14030605