Mathematical Model Predicting the Kinetics of Intracellular LCMV Replication

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Comment of mathematics-2663247

This paper studies the mathematical model predicting the kinetics of intracellular

LCMV replication Some comments are as follows:

1. The motivation need to be strengthened in the Introduction part.

2. The authors are encouraged to add some comparison results with the existing methods.

3. On page 1, the authors claim the prescribed-time convergence where settling time is arbitrarily chosen independently of the initial conditions and the system’s parameters. To illustrate this point, the authors should add a new numerical simulation in the example of Section V to demonstrate that the predetermined time stabilization can be achieved under different initial conditions and system’s parameters.

4. What are the advantages of the the mathematical model predicting the kinetics of intracellular LCMV replication given in this paper? Please give more discussion and comparison.

5. Please carefully read and check the language and typos throughout the manuscript.

Comments on the Quality of English Language

No

Author Response

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

Reviewer 1 stated that this paper studies the mathematical model predicting the kinetics of intracellular LCMV replication and the following comments were provided that we have taken into account in the revised manuscript as detailed below.

1. The motivation need to be strengthened in the Introduction part.

Response:
We have now extended the introduction to strengthen our motivation for this study. The added paragraph reads as follows:
Infectious diseases caused by viruses (e.g., HIV-1, HBV or SARS-CoV-2) present a serious problem to human health worldwide. To understand their pathogenesis, infections are studied experimentally and by mathematical modelling approaches. The current technologies including multiplex analyses, microscopic and mesoscopic visualization, "omics-" technologies and bioinformatic analyses now allow a multi-physics assessment of the processes regulating virus-host interactions at molecular-, cellular-, and systemic levels [1-3]. However, the adequate construction of mathematical models for studying the course and outcome of infectious diseases in terms of the description details to the level of understanding of its structure and functional components remains to be a great challenge. Indeed, models need to consider (1) virus replication at a single cell level, (2) spatial infection spreading across cell populations and (3) the systemic dynamics of disease characteristics. At present, mostly the population dynamics of antiviral immune responses has received substantial attention (e.g., [4-6]) while the development of integrative models is at its infancy. This latter requires models of intracellular virus life cycles as single infected cells are the initiating and fuelling events in systemic virus spreading and are the key targets for combination therapies.
[1]. Poon MML, Farber DL. The Whole Body as the System in Systems Immunology. iScience. 2020 Aug 28;23(9):101509. doi: 10.1016/j.isci.2020.101509. PMID: 32920485; PMCID: PMC7491152.
[2]. Germain RN, Radtke AJ, Thakur N, Schrom EC, Hor JL, Ichise H, Arroyo-Mejias AJ, Chu CJ, Grant S. Understanding immunity in a tissue-centric context: Combining novel imaging methods and mathematics to extract new insights into function and dysfunction. Immunol Rev. 2022 Mar;306(1):8-24. doi: 10.1111/imr.13052.
[3]. Hor JL, Germain RN. Intravital and high-content multiplex imaging of the immune system. Trends Cell Biol. 2022 May;32(5):406-420. doi: 10.1016/j.tcb.2021.11.007. [4]. Cardozo-Ojeda EF, Perelson AS. Modeling HIV-1 Within-Host Dynamics After Passive Infusion of the Broadly Neutralizing Antibody VRC01. Front Immunol. 2021 Aug 31;12:710012. doi: 10.3389/fimmu.2021.710012. [5]. Sanche S, Cassidy T, Chu P, Perelson AS, Ribeiro RM, Ke R. A simple model of COVID-19 explains disease severity and the effect of treatments. Sci Rep. 2022 Aug 20;12(1):14210. doi: 10.1038/s41598-022-18244-2.
2
[6.] Nikas A, Ahmed H, Moore MR, Zarnitsyna VI, Antia R. When does humoral memory enhance infection? PLoS Comput Biol. 2023 Aug 21;19(8):e1011377. doi: 10.1371/journal.pcbi.1011377

2. The authors are encouraged to add some comparison results with the existing methods.

Response:
Our manuscript describes the first model for the life cycle of LCMV. The existing models for other viruses including HIV-1, Influenza A virus and SARS-CoV-2 are referenced in the Discussion section and distinctive features between these are mentioned.
We have additionally stated this in the Conclusions section.

3. On page 1, the authors claim the prescribed-time convergence where settling time is arbitrarily chosen independently of the initial conditions and the system’s parameters. To illustrate this point, the authors should add a new numerical simulation in the example of Section V to demonstrate that the predetermined time stabilization can be achieved under different initial conditions and system’s parameters.

Response:
This comment does not seem to apply to our study as the time-convergence is not an issue and section 5 refers do the discussion.

4. What are the advantages of the the mathematical model predicting the kinetics of intracellular LCMV replication given in this paper? Please give more discussion and comparison.

Response:
In addition to the already mentioned advantages of the mathematical model predictions, we have now added the following statement to the Discussion section: “This enables an informed screening for antiviral drugs and may reduce the underlying experimental work.”

5. Please carefully read and check the language and typos throughout the manuscript.

Response:
We have additionally checked the manuscript for spelling and grammatical mistakes.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript by Sergeeva et al. presents a mathematical model predicting the kinetics of biochemical processes including the transcription, the translation, and the degradation of molecular components of the lymphocytic choriomeningitis virus (LMCV) underlying its replication in infected cells. The model is the first quantitative mathematical model of intracellular LCMV growth. It is a stochastic model that enables to predict the variability of the replication process, the probability of productive infection, and the production of LCMV virions deficient in protein content. It provides a building module for developing multi-scale mathematical models of LCMV in mice. The method is formulated, calibrated, analyzed and solved. Finally, a realistic strategy for experimental validation is suggested.

The manuscript is well written, highly detailed, and the model approach is comprehensive. It provides an important contribution in modeling LCMV.

Besides some very small things like the need to add a minus sign for "-0.1" in the y-axis of Figure 13 left/bottom, for example, and "second member explains" -> "second term explains", which the authors will self-check in the final stage, I could not find any additional points that need to be addressed in this fine contribution.

Author Response

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

Reviewer 2 stated that the manuscript by Sergeeva et al. presents a mathematical model predicting the kinetics of biochemical processes including the transcription, the translation, and the degradation of molecular components of the lymphocytic choriomeningitis virus (LMCV) underlying its replication in infected cells. The model is the first quantitative mathematical model of intracellular LCMV growth. It is a stochastic model that enables to predict the variability of the replication process, the probability of productive infection, and the production of LCMV virions deficient in protein content. It provides a building module for developing multi-scale mathematical models of LCMV in mice. The method is formulated, calibrated, analyzed and solved. Finally, a realistic strategy for experimental validation is suggested. The manuscript is well written, highly detailed, and the model approach is comprehensive. It provides an important contribution in modeling LCMV.

The following remarks were provided that we have taken into account in the revised manuscript as explained below.

1. Besides some very small things like the need to add a minus sign for "-0.1" in the y-axis of Figure 13 left/bottom, for example, and "second member explains" -> "second term explains", which the authors will self-check in the final stage, I could not find any additional points that need to be addressed in this fine contribution.

Response:

We have checked the manuscript for the spelling and grammar mistakes including the mentioned points.

Please note that there should not be a minus sign in the y-axis of Figure 13 left/bottom. The plot illustrates two different densities (for complete and incomplete virions) both with positive values that are just placed above and below the horizontal line y=0.

We have corrected "second member explains" to "second term explains".

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Report on “Mathematical model predicting the kinetics of intracellular LCMV replication.”

Ref: Mathematics-2663247

Title: Mathematical model predicting the kinetics of intracellular LCMV replication.

Journal: Mathematics (MDPI)

In this work, the authors formulated a dynamical system modeling the kinetics of biochemical processes covering the transcription, translation, degradation of molecular components of LCMV and its conversion into infected cells. The model was calibrated to empirical data and the parameters of the model were quantified and supported by some numerical simulations. The authors also studied the sensitivity of virus growth providing a clear ranking of intracellular virus replication processes with respect to their contribution to net viral production. The stochastic formulation of the model enables the quantification of the variability characteristics in viral production, the probability of productive infection and the secretion of protein-deficient viral particles. As it is recognized that antiviral therapeutic options in human LCMV infection are currently limited, the results suggest potential targets for antiviral therapies. The model provides a currently missing building module for developing multi-scale mathematical models of LCMV infection in mice.

The numerical simulations, sensitivity, calibration, and statistical analysis should be appreciated by a non-mathematically oriented reader biologist. In my opinion, the results presented in this paper are interesting and I suggest that the paper be accepted for publication in Mathematics (MDPI).

Hereafter some remarks.

1.      Did free and bound virions have the same degradation rate? Please give an explanation.

2.      The authors should give some details on the mathematical method used to calibrate the model to empirical data. Maybe be Least-square method? Which ranges were chosen for each of the parameters.

Author Response

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

Reviewer 3 stated that in this work, the authors formulated a dynamical system modeling the kinetics of biochemical processes covering the transcription, translation, degradation of molecular components of LCMV and its conversion into infected cells. The model was calibrated to empirical data and the parameters of the model were quantified and supported by some numerical simulations. The authors also studied the sensitivity of virus growth providing a clear ranking of intracellular virus replication processes with respect to their contribution to net viral production. The stochastic formulation of the model enables the quantification of the variability characteristics in viral production, the probability of productive infection and the secretion of protein-deficient viral particles. As it is recognized that antiviral therapeutic options in human LCMV infection are currently limited, the results suggest potential targets for antiviral therapies. The model provides a currently missing building module for developing multi-scale mathematical models of LCMV infection in mice. The numerical simulations, sensitivity, calibration, and statistical analysis should be appreciated by a non-mathematically oriented reader biologist. In my opinion, the results presented in this paper are interesting and I suggest that the paper be accepted for publication in Mathematics (MDPI).

The following remarks were provided that we have taken into account in the revised manuscript as explained below.

1. Did free and bound virions have the same degradation rate? Please give an explanation.

Response:

There are no experimental data for the degradation kinetics of LCMV virions in free, bound and endosomal states. We have therefore used the simplifying assumption that the degradation rates of free and bound virions are the same, and similar to those estimated for SARS-CoV-2 as described in reference (Grebennikov, D., Kholodareva, E., Sazonov, I., Karsonova, A., Meyerhans, A., & Bocharov, G. Intracellular life cycle kinetics of SARS-CoV-2 predicted using mathematical modelling. Viruses. 2021, 13(9), 1735. doi: 10.3390/v13091735). This assumed rate then matches the description for Influenza viruses for which around 50% of virions fail to release the virus genome upon cell entry. We now added an explanatory comment to subsection “3.7 Calibration of LCMV replication model”, and added the reference to the Influenza virus study. (Heldt, F. S., Kupke, S. Y., Dorl, S., Reichl, U., & Frensing, T. Single-cell analysis and stochastic modelling unveil large cell-to-cell variability in influenza A virus infection. Nat. Commun. 2015, 6(1), 8938. doi: 10.1038/ncomms9938)

2. The authors should give some details on the mathematical method used to calibrate the model to empirical data. Maybe be Least-square method? Which ranges were chosen for each of the parameters.

Response:

The calibration of our model was done by manual adjustment of parameter values to match the generalized kinetics of LCMV production illustrated in Figure 3 and described in Sections 2.1-2.2. This was necessary because detailed single-cell experimental data are lacking and thus we could not apply a maximum likelihood approach. Moreover, some aspects of the LCMV replication cycle kinetics have not been empirically observed which resulted in a calibration uncertainty as estimated in Section 4.

As a starting point for model calibration, the parameter estimates from the previously developed mathematical models of IAV, HIV-1 and SARS-CoV-2 life cycles have been used, as well as the functional dependences for the nonlinear regulation processes. As viruses are very simple biological entities, they share many common biochemical reaction steps in their life cycles including viral genome replication, transcription, translation, virus particle assembly and virus release from the cell. However, they differ in genome length and arrangement, protein composition and structure. Parameter values of the calibrated model therefore are a mix of some LCMV-specific parameters like protein composition, genome structure, replication stages and more general parameters that also characterise other viruses.

To make the calibration of the model more transparent to the reader, we have now extended the discussion of this issue in the second paragraph of the Discussion section.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I have no further comment.