# Multiscale Model of Antiviral Timing, Potency, and Heterogeneity Effects on an Epithelial Tissue Patch Infected by SARS-CoV-2

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## Abstract

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## 1. Introduction

_{50}), and the interval between doses.

## 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 $I{C}_{50}$ multiplier;
- Slow clearance: 120 h dose interval, 0.03 $I{C}_{50}$ multiplier;
- Partial containment: 96 h dose interval, 0.06 $I{C}_{50}$ multiplier;
- Widespread infection: 24 h dose interval, 0.1 $I{C}_{50}$ 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 ${C}_{max}$ | uM | 6.0 | 5.9 | 9.8 |

GS-443902 ${C}_{24hr}$ | uM | 3.7 | 3.3 | 6.9 |

GS-443902 ${t}_{1/2}$ | 1/h | 36 | 49 | |

GS-443902 $AU{C}_{24h}$ | h × uM | 157.4 | ||

GS-443902 $AU{C}_{inf}$ | h × uM | 297 | 394 | |

GS-443902 $AU{C}_{last}$ | h × uM | 272 | 340 |

**Figure A1.**Comparison of our simplified model to Gallo’s population simulation plot of predicted intracellular lung GS-443902 concentration. Gallo’s mean response is shown by the black line and the 95% interval is shaded. This data is from 5000 simulations in which the two key parameters in the Gallo model were sampled from distributions with 20% CV. See Gallo and their supplement Figure S5 for more information. Blue line is our simplified model’s output. The Gallo data used in this plot was digitized from the publication using https://automeris.io/WebPlotDigitizer/ (accessed on 3 November 2021).

#### Appendix A.1. COPASI Codes

#### Appendix A.1.1. COPASI Model File for Parameter Fitting

`GS-443902_PBMC_PK_v05_3data_plusEurope.cps does`the parameter estimation task based on the data of [7]. The data files are included in the GitHub repository. This COPASI file is set up to do both the parameter fitting task and a basic time course simulation. Load the file in COPASI and ensure that the following data files are in the same folder that contains the COPASI .cps file:

`Humeniuk_PK_data_Europe_Table_16.txt``Humeniuk_PK_data_Table_4_Cohort7.txt``Humeniuk_PK_data_Table_4_Cohort8.txt`

^{−11}. The model has now been updated with the results for the terminal clearance half life and the effective compartment volume, typically 30.2 h and 38.4 L, respectively. A time course can be run using these parameters by selecting “Tasks”, “Time Course” then “Run”. This COPASI model generate several graphs, some of which are for the fitting task and some for the time course task.

#### Appendix A.1.2. COPASI Model File for Calculating GS-443902 from Repetitive Remdesivir Doses

`GS-443902_PBMC_PK_v05_3data_repeatDose_Gallo.cps`simulates repetitive doses of 200, then 100 × 4 mg/day. This model is based on the parameter fitting model described above. The variable ${k}_{in}$ controls the infusion periods as well as the infusion dose since it can be thought of as a multiplier on the infusion dose (see Equation (A1)). During the initial infusion, ${k}_{in}$ is 1 and in subsequent infusion periods 0.5 to implement the initial 2× loading dose. This factor in combination with the remdesivir dose (Remdes_dose_mg) value gives the 200 mg then four times 100 mg dosing pattern. The infusion timing is shown in the “${k}_{in}$” plot generated by the COPASI code. Loading this model into COPASI, then “Task”, “Time Course”, “Run” produces output similar to what is shown in Figure A1. Note that the maximum units in COPASI on the Y-axis are mole/liter with values near ${10}^{-5}$ mol/L, which corresponds to the ∼10 μM values in Figure A1.

## Appendix B. Table of Parameters from Sego et al.

**Table A2.**Sego et al.’s conversion factors. We changed the simulation step time length from Sego’s simulation [24], going from 1200 s to 300 s. We have marked it with an asterix and included our value in parenthesis.

Conversion Factors | Value |
---|---|

Simulation step $\Delta t$ | 1200.0 s * (300.0 s) |

Lattice width | 4.0 μm |

Scale factor for concentration | ${10}^{-14}$ mol |

Simulation Parameter Name | Value | Simulation Parameter Name | Value |
---|---|---|---|

Cell diameter | 12.0 μm | Viral decay rate ${\gamma}_{vir}$ | 7.71 × 10^{−6} s^{−1} |

Replication rate ${r}_{max}$ | (1/12)10^{−3} s^{−1} | Cytokine diffusion coefficient ${D}_{cyt}$ | 0.16 μm^{2} s^{−1} |

Translating rate ${r}_{t}$ | (1/18)10^{−3} s^{−1} | Cytokine diffusion length ${\lambda}_{cyt}$ | 100 μm |

Unpacking rate ${r}_{u}$ | (1/6)10^{−3} s^{−1} | Cytokine decay rate ${\gamma}_{cyt}$ | 1.32 × 10^{−5} s^{−1} |

Packaging rate ${r}_{p}$ | (1/6)10^{−3} s^{−1} | Maximum cytokine immune secretion rate ${\sigma}_{cyt}\left(immuneactivated\right)$ | 3.5 × 10^{−4} pMs^{−1} |

Release rate ${r}_{s}$ | (1/6)10^{−3} s^{−1} | Immune secretion midpoint ${V}_{cyt}\left(immuneactivated\right)$ | 1 pM |

Scale factor for number of mRNA per infected cell $mRN{A}_{avg}$ | 1000 cell^{−1} | Cytokine immune uptake rate ${\omega}_{cyt}\left(immuneactivated\right)$ | 3.5 × 10^{−4} pMs^{−1} |

Viral dissociation coefficient ${r}_{half}$ | 2000 | Maximum cytokine infected cell secretion rate ${\sigma}_{cyt}\left(infected\right)$ | 3.5 × 10^{−3} pMs^{−1} |

Viral diffusion coefficient ${D}_{vir}$ | 0.01 μm^{2} s^{−1} | Infected cell cytokine secretion mid-point ${V}_{cyt}\left(infected\right)$, ${V}_{cyt}(virus-releasing)$ | 0.1 |

Viral diffusion length ${\lambda}_{vir}$ | 36 μm | Cytokine secretion Hill coefficient ${h}_{cyt}$ | 2 |

Immune cell cytokine activation $E{C}_{50,cyt,ac}$ | 10 pM | Virally-induced apoptosis dissociation coefficient ${V}_{apo}$ | 100 |

Immune cell equilibrium bound cytokine $E{Q}_{ck}$ | 210 pM | Virally-induced apoptosis characteristic time constant ${\alpha}_{apo}$ | 20 min |

Immune cell bound cytokine memory ${\rho}_{cyt}$ | 0.99998 s^{−1} | Immune cell activation Hill coefficient ${h}_{act}$ | 2 |

Immune cell activated time | 10 h | Immune response add immune cell coefficient ${\beta}_{add}$ | 1/1200 s^{−1} |

Oxidation Agent diffusion coefficient ${D}_{oxi}$ | 0.64 μm^{2} s^{−1} | Immune response subtract immune cell coefficient ${\beta}_{sub}$ | 1/6000 cell^{−1} s^{−1} |

Oxidation Agent diffusion length ${\lambda}_{oxi}$ | 36 μm | Immune response delay coefficient ${\beta}_{delay}$ | 1.2 × 10^{6} s |

Oxidation Agent decay rate ${\gamma}_{oxi}$ | 1.32 × 10^{−5} s^{−1} | Immune response decay coefficient ${\beta}_{decay}$ | 1/12,000 s^{−1} |

Immune cell oxidation agent secretion rate ${\sigma}_{oxi}$ | 3.5 × 10^{−3} pMs^{−1} | Immune response cytokine transmission coefficient ${\alpha}_{sig}$ | 0.5 |

Immune cell ${C}_{cyt}$ threshold for Oxidation Agent release ${t}_{sec}$ | 10 $A.U.$ = 1.5625 pM | Immune response probability scaling coefficient ${\alpha}_{immune}$ | 0.01 |

Tissue cell ${C}_{oxi}$ threshold for death ${t}_{death-oxi}$ | 1.5 $A.U.$ = 0.234375 pM | Number of immune cell seeding samples ${n}_{seeding}$ | 10 |

Simulation Parameter Name | Value | Simulation Parameter Name | Value |
---|---|---|---|

Initial density of unbound cell surface receptors ${R}_{o}$ | 200 cell^{−1} | Initial immune cell target volume | 64 μm^{3} |

Virus–receptor association affinity ${k}_{on}$ | 1.4 × 10^{4} M^{−1} s^{−1} | Immune cell lambda volume ${\lambda}_{volume}$ | 9 |

Virus–receptor dissociation affinity ${k}_{off}$ | 1.4 × 10^{4} s | Initial number of immune cells | 0 |

Infection threshold | 1 | Immune cells lambda chemotaxis ${\lambda}_{chemotaxis}$ | 1 |

Uptake Hill coefficient ${k}_{upt}$ | 2 | Intrinsic Random Motility ${H}^{M}$ | 10 |

Uptake characteristic time constant ${\alpha}_{upt}$ | 20 min | Contact coefficients J (all interfaces) | 10 |

Virally-induced apoptosis Hill coefficient ${h}_{apo}$ | 2 |

## Appendix C. Quantitative Metrics of Treatment Outcome

^{−4}$A.U.$ If the difference is close to zero, $|\Delta M|$ < 10

^{−4}$A.U.$, we classify the treatment as ineffective with a partial containment. If the difference is less than the negative of the threshold ($\Delta M$ < −10

^{−4}$A.U.$), we classify the treatment as effective and the clearance as slow. If the difference is above the positive threshold ($\Delta M>{10}^{-4}A.U.$), we classify the result as widespread infection.

^{−4}$A.U.$ for the classification.

## Appendix D. Instructions for Running the Multiscale CompuCell3D Simulations and for Analyzing the Results

#### Appendix D.1. CompuCell3D Simulations

`cellular-model/batch_run.py`, and (optionally) define the output directory in the script. For cluster execution, change the output directory in

`cellular-model/batch_exec.py`and run the script

`cellular-model/batch_exec.sh`. The script is set up for Slurm scheduling systems. In those files, you can define the output directory (variable

`sweep_output_folder`).

`cellular-model/ investigation_dictionaries.py`and are imported to

`batch_run.py`and

`batch_exec.py`. To change the investigated parameters, change the dictionary used as

`mult_dict`in one of those files, e.g.,

`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.

`num_rep`. The workflow will then run through all combinations of parameters in mult_dict, generating and running “

`num_rep`” simulations for each. All results will be stored in “

`sweep_output_folder`”. Each parameter combination is called a “set” and all results of a set are in their respective folder, e.g., for the following parameter dictionary the first set (

`set_0`) uses

`first_dose=0, dose_interval=1, ic50_multiplier=0.01`, and

`t_half_mult=1`. The results for it will be in

`sweep_output_folder/set_0`, each replica will be in

`sweep_output_folder/set_0/run_0, sweep_output_folder/ set_0/run_1`, [...],

`sweep_output_folder/set_0/run_num_rep`. The second set (

`set_1`) then uses

`dose_interval=1.5`and

`ic50_multiplier=0.01`; and so on.

#### Appendix D.2. Results Analysis

`cellular-model/grid_color_picker.py`does step one. You only need to set the variable base_path to your path to the “set” folders. Then step two is performed by

`cellular-model/PostMultiSet.py`, change

`base_path`in it to be the same as in step one.

## Appendix E. Supplementary Results for the Untreated Simulations with Different Initial Conditions

**Figure A2.**Dead cell populations for 400 replicas of Sego et al.’s model performed by us [24]. In all the cases, the medians of simulation replicas are in black lines, the 0th to 100th quantiles are shaded as dark blue, 10th to 90th shaded in orange, and the 25th to 75th as light blue. (

**a**) Simulations start with 1 initially infected cell and 7 simulations result in failure to infect (1.75% of replicas), the 90th quantile includes the upper bound of the number of cells. (

**b**) Simulations start with 2 initially infected cells where 5 simulations result in failure to infect (1.25%), the 100th quantile includes the upper bound of the number of cells. (

**c**) Simulations start with 5 initially infected cells. (

**d**) Simulations start with 10 initially infected cells.

**Figure A3.**Extracellular viral load for 400 replicas of Sego et al.’s model [24], y-axis in log scale. In all the cases, the medians of simulation replicas are in black lines, the 0th to 100th quantiles are shaded as dark blue, 10th to 90th shaded in orange, and the 25th to 75th as light blue. (

**a**) Simulations start with 1 initially infected cell and 7 simulations result in failure to infect (1.75% of replicas), the 90th quantile includes the upper bound of the number of cells. (

**b**) Simulations start with 2 initially infected cells where 5 simulations result in failure to infect (1.25%), the 100th quantile includes the upper bound of the number of cells. (

**c**Simulations start with 5 initially infected cells. (

**d**) Simulations start with 10 initially infected cells.

**Figure A4.**Extracellular viral AUC for 400 replicas of Sego et al.’s model performed by us [24], y-axis in log scale. In all the cases, the medians of simulation replicas are in black lines, the 0th to 100th quantiles are shaded as dark blue, 10th to 90th shaded in orange, and the 25th to 75th as light blue. (

**a**) Simulations start with 1 initially infected cell and 7 simulations result in failure to infect (1.75% of replicas), the 90th quantile includes the upper bound of the number of cells. (

**b**) Simulations start with 2 initially infected cells where 5 simulations result in failure to infect (1.25%), the 100th quantile includes the upper bound of the number of cells. (

**c**) Simulations start with 5 initially infected cells. (

**d**) Simulations start with 10 initially infected cells.

## 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

**Figure A9.**Extracellular diffusive virus quantities (arbitrary units), Y axis in log scale, and exponent values as tick marks.

**Figure A10.**Total diffusive virus produced (AUC), Y axis in log scale, and exponent values as tick marks.

**Figure A12.**Amount of viral RNA in infected cells (arbitrary units), Y axis in log scale, and exponent values as tick marks.

**Figure A13.**Immune response state variable number. Positive values correspond to an inflammatory state, and negative to an anti-inflammatory state.

#### Appendix F.1.2. Treatment Initiation 12 h Post the Infection of Ten Epithelial Cells

**Figure A18.**Extracellular diffusive virus quantities (arbitrary units), Y axis in log scale, and exponent values as tick marks.

**Figure A20.**Immune response state variable number. Positive values correspond to an inflammatory state, and negative to an anti-inflammatory state.

#### Appendix F.1.3. Treatment Initiation One Day Post the Infection of Ten Epithelial Cells

**Figure A25.**Extracellular diffusive virus quantities (arbitrary units), Y axis in log scale, and exponent values as tick marks.

**Figure A26.**Total diffusive virus produced (AUC), Y axis in log scale, and exponent values as tick marks.

**Figure A28.**Amount of viral RNA in infected cells (arbitrary units), Y axis in log scale, and exponent values as tick marks.

**Figure A29.**Immune response state variable number. Positive values correspond to an inflammatory state, and negative to an anti-inflammatory state.

#### Appendix F.1.4. Treatment Initiation Three Days Post the Infection of Ten Epithelial Cells

**Figure A34.**Extracellular diffusive virus quantities (arbitrary units), Y axis in log scale, and exponent values as tick marks.

**Figure A35.**Total diffusive virus produced (AUC), Y axis in log scale, and exponent values as tick marks.

**Figure A37.**Amount of viral RNA in infected cells (arbitrary units), Y axis in log scale, and exponent values as tick marks.

**Figure A38.**Immune response state variable number. Positive values correspond to an inflammatory state, and negative to an anti-inflammatory state.

#### Appendix F.2. Homogeneous Metabolism, Halved GS-443902 Half-Life

#### Appendix F.2.1. Treatment Initiation with Infection of Ten Epithelial Cells

**Figure A43.**Extracellular diffusive virus quantities (arbitrary units), Y axis in log scale, and exponent values as tick marks.

**Figure A44.**Total diffusive virus produced (AUC), Y axis in log scale, and exponent values as tick marks.

**Figure A46.**Amount of viral RNA in infected cells (arbitrary units), Y axis in log scale, and exponent values as tick marks.

**Figure A47.**Immune response state variable number. Positive values correspond to an inflammatory state, and negative to an anti-inflammatory state.

#### Appendix F.2.2. Treatment Initiation One Day Post Infection of Ten Epithelial Cells

**Figure A52.**Extracellular diffusive virus quantities (arbitrary units), Y axis in log scale, and exponent values as tick marks.

**Figure A53.**Total diffusive virus produced (AUC), Y axis in log scale, and exponent values as tick marks.

**Figure A55.**Amount of viral RNA in infected cells (arbitrary units), Y axis in log scale, and exponent values as tick marks.

**Figure A56.**Immune response state variable number. Positive values correspond to an inflammatory state, and negative to an anti-inflammatory state.

#### Appendix F.2.3. Treatment Initiation Three Days Post Infection of Ten Epithelial Cells

**Figure A61.**Extracellular diffusive virus quantities (arbitrary units), Y axis in log scale, and exponent values as tick marks.

**Figure A62.**Total diffusive virus produced (AUC), Y axis in log scale, and exponent values as tick marks.

**Figure A64.**Amount of viral RNA in infected cells (arbitrary units), Y axis in log scale, and exponent values as tick marks.

**Figure A65.**Immune response state variable number. Positive values correspond to an inflammatory state, and negative to an anti-inflammatory state.

#### Appendix F.3. Homogeneous Metabolism, GS-443902 Half-Life Reduced by 75%

#### Treatment Initiation with Infection of Ten Epithelial Cells

**Figure A70.**Extracellular diffusive virus quantities (arbitrary units), Y axis in log scale, and exponent values as tick marks.

**Figure A71.**Total diffusive virus produced (AUC), Y axis in log scale, and exponent values as tick marks.

**Figure A73.**Amount of viral RNA in infected cells (arbitrary units), Y axis in log scale, and exponent values as tick marks.

**Figure A74.**Immune response state variable number. Positive values correspond to an inflammatory state, and negative to an anti-inflammatory state.

#### Appendix F.4. Heterogeneous Metabolism, Regular GS-443902 Half-Life

#### Appendix F.4.1. Treatment Initiation with Infection of Ten Epithelial Cells

**Figure A79.**Extracellular diffusive virus quantities (arbitrary units), Y axis in log scale, and exponent values as tick marks.

**Figure A80.**Total diffusive virus produced (AUC) for eight replicas of the treatment simulation, Y axis in log scale, and exponent values as tick marks.

**Figure A81.**Diffusive cytokine amount for eight replicas of the treatment simulation, Y axis in log scale, and exponent values as tick marks.

**Figure A82.**Amount of viral RNA in infected cells (arbitrary units), Y axis in log scale, and exponent values as tick marks.

**Figure A83.**Immune response state variable number. Positive values correspond to an inflammatory state, and negative to an anti-inflammatory state.

#### Appendix F.4.2. Treatment Initiation Twelve Hours Post the Infection of Ten Epithelial Cells

**Figure A88.**Extracellular diffusive virus quantities (arbitrary units), Y axis in log scale, and exponent values as tick marks.

**Figure A89.**Diffusive cytokine amount for eight replicas of the treatment simulation, Y axis in log scale, and exponent values as tick marks.

**Figure A90.**Immune response state variable number. Positive values correspond to an inflammatory state, and negative to an anti-inflammatory state.

#### Appendix F.4.3. Treatment Initiation One Day Post the Infection of Ten Epithelial Cells

**Figure A95.**Extracellular diffusive virus quantities (arbitrary units), Y axis in log scale, and exponent values as tick marks.

**Figure A96.**Total diffusive virus produced (AUC), Y axis in log scale, and exponent values as tick marks.

**Figure A97.**Diffusive cytokine amount for eight replicas of the treatment simulation, Y axis in log scale, and exponent values as tick marks.

**Figure A98.**Amount of viral RNA in infected cells (arbitrary units), Y axis in log scale, and exponent values as tick marks.

**Figure A99.**Immune response state variable number. Positive values correspond to an inflammatory state, and negative to an anti-inflammatory state.

#### Appendix F.4.4. Treatment Initiation Three Days Post the Infection of Ten Epithelial Cells

**Figure A104.**Extracellular diffusive virus quantities (arbitrary units), Y axis in log scale, and exponent values as tick marks.

**Figure A105.**Total diffusive virus produced (AUC), Y axis in log scale, and exponent values as tick marks.

**Figure A107.**Amount of viral RNA in infected cells (arbitrary units), Y axis in log scale, and exponent values as tick marks.

**Figure A108.**Immune response state variable number. Positive values correspond to an inflammatory state, and negative to an anti-inflammatory state.

#### Appendix F.5. Heterogeneous Metabolism Using Other Standard Deviations

#### Appendix F.5.1. Standard Deviation Set to 0.1

**Figure A113.**Extracellular diffusive virus quantities (arbitrary units), Y axis in log scale, and exponent values as tick marks.

**Figure A114.**Diffusive cytokine amount for eight replicas of the treatment simulation, Y axis in log scale, and exponent values as tick marks.

**Figure A115.**Immune response state variable number. Positive values correspond to an inflammatory state, and negative to an anti-inflammatory state.

#### Appendix F.5.2. Standard Deviation Set to 0.5

**Figure A120.**Extracellular diffusive virus quantities (arbitrary units), Y axis in log scale, and exponent values as tick marks.

**Figure A121.**Diffusive cytokine amount for eight replicas of the treatment simulation, Y axis in log scale, and exponent values as tick marks.

**Figure A122.**Immune response state variable number. Positive values correspond to an inflammatory state, and negative to an anti-inflammatory state.

#### Appendix F.5.3. How Heterogeneity Affects Intracellular Drug Levels

**Figure A123.**Mean antiviral drug levels in virus-releasing infected cells (solid lines) with standard deviation (shaded regions) versus time for individual simulation replicates under different simulation options. (

**a**) is treated with no metabolism heterogeneity, (

**b**) is treated with a metabolism standard deviation of 0.1, (

**c**) is treated with a metabolism standard deviation of 0.25, and (

**d**) is treated with a metabolism standard deviation of 0.25.

## Appendix G. Supplementary Results for Viral Production Metabolism Rate Correlation

**Figure A124.**Mean viral production of cells versus their metabolism rates normalized by the maximum mean production with rapid clearance parameters. (

**a**) Results for simulations varying only ${k}_{in}$. (

**b**) Results for simulations varying only ${k}_{out}$.

**Figure A125.**Mean viral production of cells versus their metabolism rates normalized by the maximum mean production with rapid clearance parameters. (

**a**) Results for simulations varying only ${k}_{in}$. (

**b**) Results for simulations varying only ${k}_{out}$.

**Figure A126.**Mean viral production of cells versus their metabolism rates normalized by the maximum mean production with slow clearance parameters. (

**a**) Results for simulations varying only ${k}_{in}$. (

**b**) Results for simulations varying only ${k}_{out}$.

**Figure A127.**Mean viral production of cells versus their metabolism rates normalized by the maximum mean production with widespread infection parameters. (

**a**) Results for simulations varying only ${k}_{in}$. (

**b**) Results for simulations varying only ${k}_{out}$.

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**Figure 1.**Schematic diagram of the minimalized PBPK model of remdesivir. PBMCs are a surrogate for lung alveolar epithelial cells for GS-443902.

**Figure 2.**Simulated epithelial cell layers colored by the change in ${k}_{in}$ (

**a**), ${k}_{out}$ (

**b**). The values displayed are relative to the base ${k}_{in}$ and ${k}_{out}$, a cell colored blue in (

**b**) has, e.g., ${k}_{out}^{\prime}\left(\sigma \right)=0.3\times {k}_{out}$.

**Figure 3.**(

**a**) Concentration of GS-443902 (remdesivir’s active metabolite) for a 14 day treatment with a 200 mg loading dose and 100 mg subsequent daily doses (IV infusion) is obtained by solving Equations (1a) and (1b). Concentration peaks (red) and troughs (blue) are pointed out, and their mid-point (dashed line) is our base $I{C}_{50}$. (

**b**) Concentrations of the active metabolite, GS-443902, in PK simulations for the different dosing regimens of remdesivir, with the doses rescaled to keep the total average amount of remdesivir given over 24 h constant. (

**c**) Some selected PK profiles from (

**b**).

**Figure 4.**Uninfected cell populations for 400 replicas of Sego et al.’s model [24] performed by us are shown using Sego’s default parameters [24]. In all the cases, the medians of simulation replicas are in black lines, the 0th to 100th quantiles are shaded as dark blue, 10th to 90th shaded in orange, and the 25th to 75th as light blue. (

**a**) Simulations start with 1 initially infected cell and 63 simulations result in “failure to infect” (15.75% of replicas), the 90th quantile includes the upper bound of the number of cells. (

**b**) Simulations start with 2 initially infected cells where 5 simulations result in “failure to infect” (1.25%), and the 100th quantile includes the upper bound of the number of cells. (

**c**) Simulations start with 5 initially infected cells. (

**d**) Simulations start with 10 initially infected cells.

**Figure 5.**Extracellular viral load curve for untreated simulations with five initially infected cells in the tissue patch.

**Figure 6.**Coarse-parameter investigation (10 replicas of the treatment simulation). Treatment starts with 10 infected cells. For all subfigures, the median measurement of simulation replicas is the black line, the 0th to 100th quantiles are shaded as dark blue, 10th to 90th shaded in orange, and 25th to 75th as light blue. Treatments with an $I{C}_{50}$ multiplier <0.055 contain the infection, while treatments with $I{C}_{50}$ multiplier ≥0.05 do not. The top two rows show a reduction in viral load due to treatment, while in the lower two rows the decrease is due to all cells being dead. (

**a**) Uninfected cell population. (

**b**) Extracellular diffusive virus; y-axis in log scale, and exponent values as tick marks.

**Figure 7.**Treatment starts with the infection of 10 epithelial cells. For all subfigures, the median measurement of simulation replicas is the black line, the 0th to 100th quantiles are shaded as dark blue, 10th to 90th shaded in orange, and 25th to 75th as light blue. Rapid clearance plot axis in green, slow clearance plot axis in blue, partial containment in black, and widespread infection in red. (

**a**) Uninfected cell population. (

**b**) Extracellular diffusive virus; y axis in log scale, and exponent values as tick marks.

**Figure 8.**Treatment starts three days post the infection of 10 epithelial cells. For all subfigures, the median measurement of simulation replicas is the black line, the 0th to 100th quantiles are shaded as dark blue, 10th to 90th shaded in orange, and 25th to 75th as light blue. Rapid clearance plot axis in green, slow clearance plot axis in blue, partial containment in black, and widespread infection in red. (

**a**) Uninfected cell population. (

**b**) Extracellular diffusive virus; y-axis in log scale, and exponent values as tick marks.

**Figure 9.**Replica snapshots of the tissue patch are shown for different treatment classifications. In all the cases, the top row is the epithelial layer (blue uninfected cells, green infected cells in eclipse phase, red infected cells releasing virus, black dead cells), the middle row is the extracellular virus concentrations (high concentration in red, low concentration in blue), and the third row is the immune cell layer (immune cells in red, extracellular environment in black). (

**A**) Fast clearance (36 h dosing period, 0.01 $I{C}_{50}$ multiplier), (

**B**) slow clearance (84 h dosing period, 0.05 $I{C}_{50}$ multiplier), (

**C**) partial containment (84 h dosing period, 0.06 $I{C}_{50}$ multiplier), and (

**D**) widespread infection (108 h dosing period, 0.07 $I{C}_{50}$ multiplier). In all the cases, snapshots are shown at the start of the simulation (day 0), at the start of treatment (3 days post infection of 10 cells), after 14 days of treatment, and at the end of the simulation (Day 28).

**Figure 10.**Extracellular diffusive virus populations for eight replicas of the treatment simulation. Treatment starts with the infection of 10 cells, the half-life of GS-443902 was halved (to 15.2 h). For all subfigures, the median measurement of simulation replicas is the black line, the 0th to 100th quantiles are shaded as dark blue, 10th to 90th shaded in orange, and 25th to 75th as light blue. Rapid clearance plot axis in green, slow clearance plot axis in blue, partial containment in black, and widespread infection in red.

**Figure 11.**Extracellular diffusive virus populations for eight replicas of the treatment simulation. Epithelial cells’ metabolism and clearance varies from cell to cell. For all subfigures, the median measurement of simulation replicas is the black line, the 0th to 100th quantiles are shaded as dark blue, 10th to 90th shaded in orange, and 25th to 75th as light blue. Rapid clearance plot axis in green, slow clearance plot axis in blue, partial containment in black, and widespread infection in red. (

**a**) Treatment starts with the infection of 10 cells. (

**b**) Treatment starts three days post the infection of 10 cells.

**Figure 12.**Mean viral production of cells versus their relative metabolic rates normalized by the maximum mean production with partial containment parameters. (

**a**) Results for simulations varying only ${k}_{in}$, uses the partial containment parameter set. (

**b**) Results for simulations varying only ${k}_{out}$, uses the widespread infection parameter set.

**Figure 13.**Extracellular diffusive virus populations for eight replicas of the treatment simulation. Epithelial cells’ metabolism and clearance varies from cell to cell. For all subfigures, the median measurement of simulation replicas is the black line, the 0th to 100th quantiles are shaded as dark blue, 10th to 90th shaded in orange, and 25th to 75th as light blue. Rapid clearance plot axis in green, slow clearance plot axis in blue, partial containment in black, and widespread infection in red. (

**a**) Cells’ metabolism standard deviation set to 0.1. (

**b**) Cells’ metabolism standard deviation set to 0.5.

**Figure 14.**Ineffective–effective treatment transition border for different levels of metabolic variability. In blue is the homogeneous metabolism case, in black the heterogeneous metabolism case applying a modulation by a Gaussian random number with standard deviation (S.D.) set to 0.1 for ${k}_{in}$ and ${k}_{out}$, in red the heterogeneous case with the Gaussian random number S.D. set to 0.25, in green with the S.D. set to 0.5.

**Figure 15.**Mean RNA levels in virus-releasing infected cells (solid lines) with standard deviation (shaded regions) versus time for individual simulation replicates under different simulation options: (

**a**) is untreated, (

**b**) is treated with no metabolic heterogeneity, (

**c**) is treated with a metabolism standard deviation of 0.1, (

**d**) is treated with a metabolism standard deviation of 0.25, and (

**e**) is treated with a metabolism standard deviation of 0.5. Please note that the y-range in (

**a**,

**b**) differs from the others.

Parameter | Value | Source |
---|---|---|

${k}_{in}$ (unit-less) | 0 or 1 | Fit to [7] |

GS-443902 observed Half-life, ${t}_{1/2}$ (h) | 30.2 | [7] |

${k}_{out}$, GS-443902’s decay rate (1/h) | $ln\left(2\right)/{t}_{1/2}$ | |

${D}_{rmd}$ (mg/day) | 100 (200 for loading dose) | Doses used in clinical situations |

$vol$ (L) | 38.4 | Fit to [7,39] |

${\tau}_{\mathrm{I}}$ (h) | 1 |

**Table 2.**List of parameters for the ABM and PD models as well as parameters varied for the treatment effectiveness investigation.

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 $I{C}_{50}$ (μmol/L) | 7.897 |

Viral replication rate reduction (Equation (11)) Hill coefficient | 2 |

$I{C}_{50}$ 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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**MDPI and ACS Style**

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

**AMA Style**

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 Style**

Ferrari 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