Predicting the Kinetic Coordination of Immune Response Dynamics in SARS-CoV-2 Infection: Implications for Disease Pathogenesis

Round 1

Reviewer 1 Report

In this manuscript, the authors explore the coordination of the immune response in SARS-CoV-2 infection. These are my impression.

1. The research explores an important question. However, I think the abstract is quite misleading. It is true that the model is calibrated with SARS-CoV-2 data, but most of the parameters are guesses taken from a 1994 study by the senior author on Influenza A. The ranges of some parameters are taken from more recent studies by the authors specifically on SARS-CoV-2, but even then, the values used are guesses within those ranges. The authors also estimated several parameters using data from the human challenge study, but with so few data points, it is difficult to imagine the model is anywhere close to being identifiable. Due to the lack of information on the model parameters, the study should stay clearly in the abstract that this is a theoretical exploration type of study to not give the wrong impression that it is a completely validated mathematical model with actual data. 

2. Please include a section on the data. Since the human challenge data was published earlier this year, it is unlikely that it has become widely available. Thus, please include how the data was obtained.

3. The lack of confidence in the parameter values means that it is difficult to make use of the local sensitivity analysis. Perhaps examining the sensitivity in a global manner would help.

4. Due to the complexity of the model, I suggest whenever discussing the result, the authors explicitly restate the meaning of the parameters and the exact panel. This should apply to every discussion from figure 5 to 13. These figures are difficult to see, so if a panel is not important to the study, I suggest removing said panel to enlarge the figure. The complete figures can be put in the supplementary material.

5. What are the different curves in each figure? 

6. How is the final time T chosen in equation 20?

7. Please add more descriptions to Figure 1 regarding different model variables and transitions. 

8. The objective function (equation 18) is interesting. It is typical to fit not the viral load but the log viral load, which automatically balances out the high and low measurements. Is there a particular reason why the authors fit the viral load and not the log viral load? Additionally, how are data points below the limit of quantification or limit of detection treated in the fitting? In the fitting in Figure 2, I see uncertainty quantification bars on each data point. How are these utilized? If not, please remove them because the fitting figure is quite difficult to see clearly.

Overall, I appreciate the effort to model the coordination of immune responses in SARS-CoV-2 infection, as long as the authors emphasize the theoretical exploratory nature of the work.

Author Response

Response to Reviewer 1 comments

We thank the Reviewer for insightful comments and the thorough work on our manuscript.

Comments and Suggestions for Authors

In this manuscript, the authors explore the coordination of the immune response in SARS-CoV-2 infection. These are my impression.

Overall, I appreciate the effort to model the coordination of immune responses in SARS-CoV-2 infection, as long as the authors emphasize the theoretical exploratory nature of the work.

1. The research explores an important question. However, I think the abstract is quite misleading. It is true that the model is calibrated with SARS-CoV-2 data, but most of the parameters are guesses taken from a 1994 study by the senior author on Influenza A. The ranges of some parameters are taken from more recent studies by the authors specifically on SARS-CoV-2, but even then, the values used are guesses within those ranges. The authors also estimated several parameters using data from the human challenge study, but with so few data points, it is difficult to imagine the model is anywhere close to being identifiable. Due to the lack of information on the model parameters, the study should stay clearly in the abstract that this is a theoretical exploration type of study to not give the wrong impression that it is a completely validated mathematical model with actual data.

Our response:

Following the above suggestion, we have added the below statement about the category of our model to the Abstract and to the Discussion section.

„The calibration of the mathematical model of SARS-CoV-2 infection is based on combining the parameter guesses from our earlier study of influenza A virus infection, some recent quantitative models of SARS-CoV-2 infection and clinical data-based parameter estimation of a subset of the model parameters.  Hence, the calibrated mathematical model represents a theoretical exploration type of study, i.e. ‘in silico patient‘ with mild-to-moderate severity phenotype, rather than a completely validated quantitative model of COVID-19 with respect to all its state-space variables.“ 

 

2. Please include a section on the data. Since the human challenge data was published earlier this year, it is unlikely that it has become widely available. Thus, please include how the data was obtained.

Our response:

The description of the reference data used to calibrate the model is provided in Section 2.2 and was extended to read as follows.

“In our study, we used recent data on viral kinetics during SARS-CoV-2 human challenge in young adults Killingley et al., Nature Medicine, 2022 (doi:10.1038/s41591-022-01780-9). Healthy adult volunteers without evidence of previous infection were challenged intranasally with 10 TCID₅₀ of a wild-type SARS-CoV-2. Viral load in twice-daily nose and throat swab samples was measured by qPCR. The original data from 18 infected individuals were expressed as mean ± sem copies per ml. . The data set on viral load kinetics to be used for model calibration was obtained using WebDigitizer from the Figure 2a of the published study. Mild-to-moderate symptoms defining the reference disease phenotype were observed in most (89%) of the participants starting from 2 to 4 days after inoculation. We did not consider the individual participant data as the summary statistics on the viral load consistently represents the infection kinetics of the above disease phenotype. The inter-patient variability of the viral load data is presented as pink shaded area in Figure 2. Additionally, the data on the scale of the interferon response (Cheermarla et al., 2021, JEM) and the serum levels of the infected patients of antigen-specific antibodies and CTLs (Tan et al. 2021, Cell Rep.) were taken into account during the model calibration. The data ranges from the above studies are plotted as green shaded areas in Figure 2.“

 

The Figure 2 legend was extended accordingly.

3. The lack of confidence in the parameter values means that it is difficult to make use of the local sensitivity analysis. Perhaps examining the sensitivity in a global manner would help.

Our response:

In response to the suggestion of the Reviewer, we have added the global sensitivity analysis using eFAST method. It is now described in Subsections 2.4 and 3.2 . In addition, the following comment was added to the Discussion section:

“The local sensitivity analysis allowed us to evaluate the effects of small parameter variations around the model parameters which were calibrated to describe the mild-to-moderate disease phenotype. For parameter sets corresponding to another clinical outcome, e.g., asymptomatic, severe or critical phenotype, the local sensitivity indices could change significantly. Therefore, in future studies the local sensitivity analysis should be performed and compared for various disease phenotypes. In addition, we performed the global sensitivity analysis for our model by applying the eFAST method (a variation of Sobol method utilizing the search in Fourier space). It is appropriate for general nonlinear models allowing the decomposition of the variance of the model solution uncertainty on the first- and total order components related to variations of individual parameters. Although the estimates for the admissible ranges on model parameters are specified in Table 1, a direct use of them as lower and upper bounds in sampling parameters might be inappropriate as these ranges characterize the uncertainty for each individual parameter without taking into account their possible interactions. To keep the parameter uncertainty within the range consistent with the mild-to-moderate disease phenotype, the respective scale of the parameter variance was identified to be around 20% of the basal values. The uniform distribution on the ranges was assumed for all model parameters.“

 

4. Due to the complexity of the model, I suggest whenever discussing the result, the authors explicitly restate the meaning of the parameters and the exact panel. This should apply to every discussion from figure 5 to 13. These figures are difficult to see, so if a panel is not important to the study, I suggest removing said panel to enlarge the figure. The complete figures can be put in the supplementary material.

Our response:

In response to the suggestion of the reviewer, we have provided the meaning of the parameters and the reference to the panels in the discussion of results in context of the above indicated figures range. We would prefer to keep all the model solution components in figures in order to make directly visible the cross-coordination and mutual dependence of the individual immune responses and the viral infection kinetics.  

5. What are the different curves in each figure?

Our response:

The meaning of the curves is given in Figure legends. Dashdot curves indicate the increase of a model parameter, dot curves indicate the decrease. The solid ones correspond to the baseline solution of the calibrated model as in Figure 2.

6. How is the final time T chosen in equation 20?

Our response:

The value for final time T = 25 days is specified in the text now. It refers to the time of the virus clearance according to the clinical data.

7. Please add more descriptions to Figure 1 regarding different model variables and transitions.

Our response:

We have extended the figure legend by adding the following description:

„Biological scheme of the mathematical model of the immune response in SARS-CoV-2 infection depicting three levels of the virus interactions with the host organism. The first level is the virus (V) spreading in a sensitive epithelial tissue that consists of the known concentration of epithelial cells (C^*). Some of them, are infected (C_V) and produce new viruses. The infected cells die (D) either due the cytophatic effect of the virus or the CTL-mediated killing. At the second level of the virus-host interaction, the viral population is recognized by cells of the innate immune system, i.e. the type I IFN-producing cells (APC_I) and the antigen presenting cells (APC_V). The produced type I IFN makes some of the target cells protected from the viral infection (C_R). Free viruses are eliminated by specific antibodies (IgG). Professional antigen-presenting cells activate the two subsets of CD4 T cells (Th1 and Th2) participating in the regulation of the cellular (CTL) and humoral immune reactions comprising the third level of the virus-host interaction. B cells (B) differentiate into plasma cells (P) which secret virus-specific antibodies (IgG) via multiple interactions. The damage of the target organs induces suppression of the immune responses via a negative feedback. The inflammation-related enhancement of the functional effect of CTLs and antibodies on elimination of infected cells and free viruses, respectively, is parameterized in the model via the relative abundance of virus-infected cells. All viral-, humoral- or cellular components in the model either die or degrade, however the respective processes are not shown for clarity of the figure.“

8. The objective function (equation 18) is interesting. It is typical to fit not the viral load but the log viral load, which automatically balances out the high and low measurements. Is there a particular reason why the authors fit the viral load and not the log viral load? Additionally, how are data points below the limit of quantification or limit of detection treated in the fitting? In the fitting in Figure 2, I see uncertainty quantification bars on each data point. How are these utilized? If not, please remove them because the fitting figure is quite difficult to see clearly.

Our response:

The objective function which we used should indeed provide similar results as the sum of squares of the differences between the model and experimental log viral load. Both of them are based on the relative rather than absolute distances between model predictions and observations. In using it for data fitting, we considered the following arguments concerning the equal sensitivity of the mismatch functional to the same relative deviation  (1) of the model solution and empirical data regardless their magnitude, and (2) the symmetry with respect to deviation of the data and solution. We refer in the text to example of its successful use for data fitting (subsection 2.3).

 

The horizontal dotted line in Figure 2 refers to the median level of viral load on the day of symptoms onset accroding to Kim et al., A quantitative model used to compare within-host SARS-CoV-2, MERS-CoV, and SARS-CoV dynamics provides insights into the pathogenesis and treatment of SARS-CoV-2. PLoS Biol. 2021 Mar 22;19(3):e3001128. doi: 10.1371/journal.pbio.3001128) rather than  to the detection limit. We have added the respective explanation to the figure legend.

 

The uncertainty quantification bars indicate the standard errors of the mean values of the viral load. They were not used in the data fitting.  In response to the suggestion, they have now been removed from Figure2. However, to make the figure more clear and still characterzie the variablity of the viral load we show only the variance envelope of the individual viral load time series as pink shaded areas.

 

 

Author Response File: Author Response.pdf

Reviewer 2 Report

This article is very interesting as it explains how immunological response can be predicted from SARS-Covid 19 infection

1. Figure 1 needs little more explanation since this would help readers in terms of understanding the prediction clearly.

2. The author has mentioned about looking at 10-fold in viral increase in viral infection. It would be great if the author explains why this 10-fold factor was chosen.

3. Which part of the respiratory tract was considered in this study since immune cells vary in different places of the respiratory tract.

Author Response

Response to Reviewer 2 comments

We thank the Reviewer for insightful comments and the thorough work on our manuscript.

Comments and Suggestions for Authors

This article is very interesting as it explains how immunological response can be predicted from SARS-Covid 19 infection

1. Figure 1 needs little more explanation since this would help readers in terms of understanding the prediction clearly.

Our response:

We have extended the figure legend by adding the following description:

„Biological scheme of the mathematical model of the immune response in SARS-CoV-2 infection depicting three levels of the virus interactions with the host organism. The first level is the virus (V) spreading in a sensitive epithelial tissue that consists of the known concentration of epithelial cells (C^*). Some of them, are infected (C_V) and produce new viruses. The infected cells die (D) either due the cytophatic effect of the virus or the CTL-mediated killing. At the second level of the virus-host interaction, the viral population is recognized by cells of the innate immune system, i.e. the type I IFN-producing cells (APC_I) and the antigen presenting cells (APC_V). The produced type I IFN makes some of the target cells protected from the viral infection (C_R). Free viruses are eliminated by specific antibodies (IgG). Professional antigen-presenting cells activate the two subsets of CD4 T cells (Th1 and Th2) participating in the regulation of the cellular (CTL) and humoral immune reactions comprising the third level of the virus-host interaction. B cells (B) differentiate into plasma cells (P) which secret virus-specific antibodies (IgG) via multiple interactions. The damage of the target organs induces suppression of the immune responses via a negative feedback. The inflammation-related enhancement of the functional effect of CTLs and antibodies on elimination of infected cells and free viruses, respectively, is parameterized in the model via the relative abundance of virus-infected cells. All viral-, humoral- or cellular components in the model either die or degrade, however the respective processes are not shown for clarity of the figure.“

2. The author has mentioned about looking at 10-fold in viral increase in viral infection. It would be great if the author explains why this 10-fold factor was chosen.

Our response:

In response to the above remark, we have added the following explanation:

„The sensitivity of the dynamics of viral load to the activation rates of the immune system components is examined at two scales, i.e., a fine-resolution scale and globally. The first one allowed us to identify the exact biases in the activation rates that lead to a prolonged persistence of SARS-CoV-2. To check whether this phenomenon is robust, we also considered a large-scale variation of the activation rates, e.g., the 10-fold change of he respective parameters.“ 

3. Which part of the respiratory tract was considered in this study since immune cells vary in different places of the respiratory tract.

Our response:

In response to the above suggestion, we have added the following details to the Discussion section:

„The data we used for model calibration characterize the kinetics of viral load in the upper respiratory tract (the nose compartment) from Killengly et al., 2022, Nature Medicine. The data on the scale of the interferon response (Cheermarla et al., 2021, JEM), the antigen-specific antibodies and CTLs (Tan et al. 2021, Cell Rep.) refer to their respective levels in serum of the infected patients.“

 

Author Response File: Author Response.pdf

Reviewer 3 Report

The paper, although of interest due to the global health emergency, should be improved in order to give some clear points on how this study can be reflected in the real-world. below some concerns that should be addressed in the revised version:

-the main concern is related on how this model can be applied and used day-by-day. In fact, in my opinion the proposed approach lack of a rigorous validation. In fact, the authors wrote "Finally, the model can be used to predict the intensity of airborne infection spreading by infected individuals, e.g. the amount of virus which is transmitted via droplets from a SARS-CoV-2 infected person, depending on the time of infection and the immune
response parameters. This type of estimates provide a direct information that may be included into the epidemiological models of virus spreading in the human population". It will be interesting to evaluate in a prospective validation the power of the model. I strongly recommend to perform this step to justify the generation and the usage of the developed model

-the limitation of the study and how can be overcome in the future should be reported

-A conclusion section summarizing the work is in my opinion strongly necessary also reporting a future outlook regrading the mathematical modelling on covid19

-english grammar check is necessary

Author Response

Response to Reviewer 3 comments

We thank the Reviewer for insightful comments and the thorough work on our manuscript.

Comments and Suggestions for Authors

The paper, although of interest due to the global health emergency, should be improved in order to give some clear points on how this study can be reflected in the real-world. below some concerns that should be addressed in the revised version:

1.-the main concern is related on how this model can be applied and used day-by-day. In fact, in my opinion the proposed approach lack of a rigorous validation. In fact, the authors wrote "Finally, the model can be used to predict the intensity of airborne infection spreading by infected individuals, e.g. the amount of virus which is transmitted via droplets from a SARS-CoV-2 infected person, depending on the time of infection and the immune response parameters. This type of estimates provide a direct information that may be included into the epidemiological models of virus spreading in the human population". It will be interesting to evaluate in a prospective validation the power of the model. I strongly recommend to perform this step to justify the generation and the usage of the developed model

Our response:

Mathematical models provide a theoretical tool to describe, explain and predict the features of SARS-CoV-2 interaction with the human organism. The developed model of infection with SARS-CoV-2 describes the available patients’ data. It proposes a novel hypothesis on the effect of kinetic coordination of innate and adaptive immune reaction in the establishment of prolonged viral persistence. A rigorous validation of this conceptually new regulatory mechanism requires substantial well controlled experimental and clinical studies and thus, goes beyond the scope of our research. To illustrate the power of the model in addressing existing controversial issues concerning the pathogenesis and treatment of SARS-CoV-2 infection, we added the analysis of the effect of passive immunotherapy with virus-specific antibodies on the duration of the infectiousness and symptoms for COVID-19 patents. The existing treatments with immunoglobulins include the use of convalescent plasma therapy, intravenous immunoglobulins, and monoclonal antibody therapy (Farhangnia et al., 2022). The regimens used are highly variable (Xiang et al., 2021, Deere et al., 2021).  As a proof-of-concept we simulated a daily introduction of virus-specific IgG at doses ranging from 0.4d10 to 1d11 molecules/ml starting from day 2 post establishment of symptoms during 5 days treatment period. The model predicts that 25-times increase of the dose of administered IgG results in shortening of the period of viral load above the infectiousness threshold from 7 days to 3 days for the considered set of model parameters. Further translation of the predicted dynamics of viral load into infectiousness of the patients requires more rigorous definition of the viral load-based threshold for disease symptoms onset and application of the probabilistic model linking the viral load to the infectiousness as elaborated recently in Ke et al. 2022. The duration of the symptomatic period of COVID-19 reduced from 8 to 3.6 days. The simulations also showed that that smaller amounts (below some threshold) of IgG can favour a prolonged viral persistence resembling the experimental observation that convalescent plasma, administered to medium titers, has limited efficacy, even when given very early after infection (Deere et al., 2021). Overall, these model-generated predictions corroborate empirical findings that the use of high doses of virus-specific immunolglobulins in treatment of COVID-10 is effective but not without potential adverse consequences (Nguyen et al., 2020), Deere et al., 2021, Salehi et al., 2022).

In response to the concern of the reviewer, the above description has been added to the manuscript as Subsection 3.8.

2. -the limitation of the study and how can be overcome in the future should be reported

Our response:

Calibration of the developed model of SARS-CoV-2 infection is based on a limited set of empirical data. However, for all processes considered in the model various parameterizations could be used. To proceed with the identification of optimal descriptions of the immune responses to SARS-CoV-2, quantitative definitions of COVID-19 dynamics- and outcome phenotypes are needed. These should define the regulation levels, processes, tissues and organs to be considered in the models and enable a rationale implementation of the reductionist approach to model refinement. A final objective would be the application of the minimum description length-based methodology for a parsimonious mapping (using the model equations) of the virus and immune system parameters to the observed spectrum of COVID-19.  

In response to the suggestion of the reviewer, the above consideration was added to the Discussion section.

3. -A conclusion section summarizing the work is in my opinion strongly necessary also reporting a future outlook regrading the mathematical modelling on covid19

Our response:

Mathematical models of infectious disease can be formulated as descriptive, explanatory or predictive ‘in silico‘ tools. Although the SARS-CoV-2 infection of humans is a multifactorial systemic phenomenon and induces a broad spectrum of disease kinetics and severity, the mathematical models of COVID-19 do not need necessarily be high-dimensional or notorously complex. The available mathematical models serve as reductionist-type representations of the real SARS-CoV-2 - human organism interactions. The maturation of the models functionality from a mere descriptive tool to a predictive exploratory method requires a genuine collaboration of the modelers with clinical immunologists and virologists in order to implement a question-driven data-based mechanistic approach. The availability of mathematically well-posed and statistically calibrated models of specfic processes would be a key step in developing the spectrum of toolkits for addressing practically relevant issues of COVID-19 pathogenesis and treatment.

 In response to the suggestion of the reviewer, the above consideration was added to the Discussion section.

4. -english grammar check is necessary

Our response:

We have checked the grammar as proposed.

 

 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

I appreciate the revised version. 

Reviewer 3 Report

-