Exploring the Therapeutic Potential of Defective Interfering Particles in Reducing the Replication of SARS-CoV-2

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Review on the paper “Exploring the therapeutic potential of defective interfering particles in educing the replication of SARS-CoV-2” by M. Locke, D. Grebennikov, I. Sazonov, M. López-García, M. Loguinova, A. Meyerhans, G. Bocharov, and C. Molina-París.

 

 

Note that the paper concerns with very important part of applied mathematics. The authors deal with mathematical and computational modelling (good tools to study viral infection dynamics for predictive analysis). By means of the method suggested by Grebennikov in 2021 of SARS-CoV-2 intra-cellular replication dynamics the authors formulate a deterministic model that describes the replication of wild-type SARS-CoV-2 virus in the presence of defective interfering particles.

The analysis of parameters to several model outputs is employed to inform the reader on those parameters to be carefully calibrated from experimental data. The authors also study the effects of co-infection on wild-type replication and how defective interfering particles dose perturbs the release of wild-type viral particles.

Moreover, one can find in the paper a stochastic formulation of the model that is compared to the deterministic one. These models could be further developed into population-level models or used to guide the development and dose of therapeutic interfering particles.

 

According to my opinion, the results are new and interesting, but the author must specify in the introductory part, what is new in the paper and say about previous results in the comparison with new results.

 

After minor changes the paper can be published in the journal.

 

 

 

Comments.

Line 71. To be precise it is necessary to say something about the probability space.

Line 73. It is necessary to define the theta-star variable.

Formula (1). The author must have some citations (some references) or at least to comment this formula.

Linу 89. It is not clear, what is $\mathcal{M}$ and what is the dimension of this quantity.

Formulae (4)-(7). The authors must say about all unknowns and given functions. It is not clear, where is unknowns. It is also important to say about given coefficient, are they time – dependent functions or just constants?

Formulae (8)-(11). Same comment.

I wonder also if the authors consider Cauchy problems or boundary value problems for these systems of equations. If boundary value problem is considered, then the existence and uniqueness theorem must be proved. If it is a Cauchy problem, then it is important to pay attention to the smoothness of the coefficients.

Author Response

Response to Reviewer’s comments

 

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

 

Reviewer 1 stated that the paper concerns with very important part of applied mathematics. The authors deal with mathematical and computational modelling (good tools to study viral infection dynamics for predictive analysis). By means of the method suggested by Grebennikov in 2021 of SARS-CoV-2 intra-cellular replication dynamics the authors formulate a deterministic model that describes the replication of wild-type SARS-CoV-2 virus in the presence of defective interfering particles. The analysis of parameters to several model outputs is employed to inform the reader on those parameters to be carefully calibrated from experimental data. The authors also study the effects of co-infection on wild-type replication and how defective interfering particles dose perturbs the release of wild-type viral particles. Moreover, one can find in the paper a stochastic formulation of the model that is compared to the deterministic one. These models could be further developed into population-level models or used to guide the development and dose of therapeutic interfering particles. According to my opinion, the results are new and interesting, but the author must specify in the introductory part, what is new in the paper and say about previous results in the comparison with new results. After minor changes the paper can be published in the journal.

Comments.

 

All the concerns have been addressed in the revised manuscript as described below.

 

(1) … the author must specify in the introductory part, what is new in the paper and say about previous results in the comparison with new results

 

Response:

 

Thank you for this suggestion. We have added the following comments at the end of Introduction section.

 

“Overall, our study is the first one in which a detailed mathematical model (both in a deterministic and stochastic settings) of the reaction kinetics of SARS-CoV-2 life cycle in the presence of DIPs is formulated, calibrated and examined. The so far available mathematical models of SARS-CoV-2 infection dynamics considering the wild-type virus competition with the DIPs describe the within-host organism infection in upper and lower respiratory tract cells with only a single parameter characterising the intracellular biochemical reaction cascade [Chaturvedi et al., Identification of a therapeutic interfering particle—A single-dose SARS-CoV-2 antiviral intervention with a high barrier to resistance. Cell 2021, 184, 6022–6036]. The high-resolution model presented below allows us to explore in detail the determinants and limits of the efficacy of DIP-based treatment of COVID-19.”|       

 

(2) Line 71. To be precise it is necessary to say something about the probability space.

 

Response:

 

Thank you for this comment. In Subsection 2.1, we have now added extra explanation that every model parameter is considered to be a random variable with continuous uniform distribution defined on the associated support range specified by the upper and lower bounds it must lie between. Since Y is a function of these variables, it is also a random variable that takes values in Euclidean space with variance V(Y).

 

(3) Line 73. It is necessary to define the theta-star variable.

 

Response: 

 

Thank you for your feedback. In the explanation theta-star variable θ*_i   is intended to represent a known parameter value. The theta-star was used to denote the variance of Y over all possible values of model parameters except for an i-th parameter which is conditioned to a fixed value θ*_i. However, as stated later in the method theta-star is not known and that is why we instead average over conditional variance for different values of θ*_i from the support of the i-th parameter p.d.f. to estimate the expectation E(V(Y|θ_i)).

 

In subsection 2.1, we have now revised the description of the Sobol’s method of global sensitivity analysis to make the above aspect more clear and comprehensive.

 

(4) Formula (1). The author must have some citations (some references) or at least to comment this formula.

Response:

 

Thank you for mentioning this.

 

We now refer to the formula in equation (1) as to the law of total variance instead of the law of total probability as it was mistakenly referred before. This law is used in the book [1] and original papers [2,3] on the methods of global sensitivity analysis (see below), e.g., in equations (1.24), (1.44), (4.14), (4.15), (4.16). We have added the reference to this book, the Sobols 1993 paper on his method and the Saltelli et al. 2004s in the manuscript, Subsection 2.1.

 

[1] Saltelli, A.; Ratto, M.; Andres, T.; Campolongo, F.; Cariboni, J.; Gatelli, D.; Saisana, M.; Tarantola, S. Global Sensitivity Analysis. The Primer, 1 ed.; Wiley, 2007. https://doi.org/10.1002/9780470725184.

 

[2] Sobol, I.M. Sensitivity analysis for non-linear mathematical models. Mathematical modelling and computational experiment 1993, 1, 407–414.

 

[3] Saltelli, A.; Tarantola, S.; Campolongo, F.; Ratto, M.; et al. Sensitivity analysis in practice: a guide to assessing scientific models; Vol. 1, 511

Wiley Online Library, 2004.

(5) Linу 89. It is not clear, what is $\mathcal{M}$ and what is the dimension of this quantity.

Response:

 

Thank you for your comment. $\mathcal{M}$ is the model output that is to be compared to the experimental data $\boldmath{D}$. To make the presentation more clear, we have now changed the references to $\ boldmath{D}$ and $\mathcal{M}$ D on line 89 to the following ones:

“where T={24,48} hours is the set of time points within the experimental data set, D(t) is the observed progeny fold reduction under the treatment with DIPs at time t specified in Table 3, and M(θ*,t) is the respective progeny fold reduction predicted by the mathematical model. The dimensions of these two quantities will depend on how many experimental outputs one can compare against the mathematical model outputs.”

 

(6) Formulae (4)-(7). The authors must say about all unknowns and given functions. It is not clear, where is unknowns. It is also important to say about given coefficient, are they time – dependent functions or just constants?

Response:

 

Thank you for your comment. All unknown values are references in Table 4, while Table 3 references the parameters that have been previously estimated and used by Grebeenikov in 2021. These values are not time-dependent and are given as constants. We have added the following comment at the beginning of Section 3:

“The unknown functions [.] characterising the abundance of the constituents of the SARS-CoV-2 replication system are the time-dependent variables with their rates of change in time described by the system of the ordinary differential equations introduced below. The parameters (coefficients) appearing on the right-hand side of the equations are the rate constants of the processes specified in Tables 2,4.”

(7) Formulae (8)-(11). Same comment.

Response:

 

Thank you, please see previous response.

(8) I wonder also if the authors consider Cauchy problems or boundary value problems for these systems of equations. If boundary value problem is considered, then the existence and uniqueness theorem must be proved. If it is a Cauchy problem, then it is important to pay attention to the smoothness of the coefficients.

Response:

 

Thank you. In response to the above comment, we have now added the following clarification at the end of Subsection 3.4:

“The deterministic model specified by the set of equations (4)-(27) represents a bounded rate system. Modelling of SARS-CoV-2 replication dynamics amounts to solving an initial value problem which describes the system evolution with time for the given initial conditions of the system.”

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The paper investigates using defective interfering particles (DIPs) to reduce SARS-CoV-2 replication. Through mathematical and computational models, the researchers study how DIPs affect the virus's replication and explore the potential of DIPs as a therapeutic strategy.

In my opinion, the paper is well written and the presented results are correct.

I recommend the publication of the paper after the following corrections:

1- The captions of the figures should be corrected. All the details should be written in a separate paragraphs and the captions should be shorten.

2- Figure 2 should be mentioned before the inserted figure 2.

3- In line 63, write Figure 1 instead of Fig 1.

4- Each of Figures 6, 7, and 9 should be mentioned in the manuscript before its insertion.

5- The authors could discuss and cite different approaches of other viruses and diseases recently studied such as:

https://doi.org/10.1016/j.aej.2023.08.063
https://doi.org/10.1038/s41598-023-48405-w
https://doi.org/10.1016/j.imu.2024.101467

6- A separate conclusion section with a future direction could be added at the end of the manuscript.

 

 

Best regards

Author Response

Response to Reviewer’s comments

 

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

 

Reviewer 2 stated that the paper investigates using defective interfering particles (DIPs) to reduce SARS-CoV-2 replication. Through mathematical and computational models, the researchers study how DIPs affect the virus's replication and explore the potential of DIPs as a therapeutic strategy.

In my opinion, the paper is well written and the presented results are correct. I recommend the publication of the paper after the following corrections…

 

All the concerns have been addressed in the revised manuscript as described below.

 1- The captions of the figures should be corrected. All the details should be written in a separate paragraphs and the captions should be shorten.

Response: 

 

Thank you for your comment. We have amended all figures in the main text so that they have a shorter explanatory title and shorter caption. However, we tried to keep the captions informative enough so that figures could be able to be interpreted without reading the full text. These final figure captions allow this and ensure readers can skim read the paper without first reading the entire text.

2- Figure 2 should be mentioned before the inserted figure 2.

Response: 

 

Thank you. This is a formatting issue, and we have now referenced this figure before use by moving the respective paragraph.

3- In line 63, write Figure 1 instead of Fig 1.

Response: 

 

Thank you for your comment. This has been addressed.

4- Each of Figures 6, 7, and 9 should be mentioned in the manuscript before its insertion.

Response: 

 

Thank you for your feedback. This formatting issue has been addressed, and we have now placed the respective paragraphs before the corresponding figures.

5- The authors could discuss and cite different approaches of other viruses and diseases recently studied such as:

https://doi.org/10.1016/j.aej.2023.08.063

https://doi.org/10.1038/s41598-023-48405-w

https://doi.org/10.1016/j.imu.2024.101467

 

Response: 

 

Thank you. In the context of our study, we added discussion of other viruses (please, see the reply to the next comment) and consistently refer to the first two models from above publications. The text added to the Discussion section reads as follows:

“In our study, we have analysed the possibility of utilizing the competitive interactions between viruses for the benefit of the infected host. Whether a similar phenomenon could be examined for other pathogens of major public concern, e.g.  bacterial infections with Salmonella typhi, Leptospira, using available mathematical models deserves a systematic multidisciplinary investigation (Fawaz et al., Analysis of Leptospirosis transmission dynamics with environmental effects and bifurcation using fractional-order derivative, Alexandria Engineering Journal, 80: 372-382 (2023); Dayan et al. Numerical investigation of a typhoid disease model in fuzzy environment. Sci Rep 13, 21993 (2023).”

6- A separate conclusion section with a future direction could be added at the end of the manuscript.

Response: 

 

Thank you for the suggestion. We have added the following paragraph:

 

“Studies of other virus infections such as dengue virus, Zika virus, yellow fever virus respiratory syncytial virus, influenza A virus showed that DIP-treatment of human target cells inhibited virus production via activation of cellular innate immunity which included interferon-dependent antiviral responses.  Future direction of DIP-integrating mathematical modeling should incorporate a broad spectrum of virus-host interaction processes in order to robustly quantify and predict the function which the DIPs could have in vaccines, modulation of viral disease, innate immune responses, virus persistence and virus evolution [1,2]. Although the DIPs offer a novel approach to antiviral therapy, the efforts to translate the in vitro studies to in vivo models are still limited. Recently, the Syrian hamster model of lethal Nipah virus (NiV) disease was used to examine the potential of DIPs to improve clinical outcomes. The results strongly support further research on the development and optimization of DIP-mediated treatment against high-consequence pathogens [3], which requires calibrated mathematical models as a powerful analytical tool.”

 

[1] Lin et al., Defective Interfering Particles with Broad-Acting Antiviral Activity for Dengue, Zika, Yellow Fever, Respiratory Syncytial and SARS-CoV-2 Virus Infection. Microbiol Spectr. 2022;10(6):e0394922.

[2] Wu  et al., Defective Interfering Particles of Influenza Virus and Their Characteristics, Impacts, and Use in Vaccines and Antiviral Strategies: A Systematic Review. Viruses. 2022;14(12):2773.

[3] Welch et al., Defective Interfering Viral Particle Treatment Reduces Clinical Signs and Protects Hamsters from Lethal Nipah Virus Disease. mBio. 2022 13(2):e0329421.

 

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The results are very good .