Mathematics

Editorial

Jump to: Research

4 pages, 363 KiB

Open AccessEditorial

Mathematical and Computational Biology of Viruses at the Molecular or Cellular Levels

by Alexander Churkin and Danny Barash

Mathematics 2022, 10(23), 4446; https://doi.org/10.3390/math10234446 - 25 Nov 2022

Viewed by 1154

Abstract

Mathematical and computational biology of viruses at the molecular or cellular levels are more difficult to accurately address than at the population level [...] Full article

(This article belongs to the Special Issue Mathematical and Computational Biology of Viruses at the Molecular or Cellular Levels)

► Show Figures

Figure 1

Research

Jump to: Editorial

13 pages, 6421 KiB

Open AccessArticle

Modeling the Interplay between HDV and HBV in Chronic HDV/HBV Patients

by Adequate Mhlanga, Rami Zakh, Alexander Churkin, Vladimir Reinharz, Jeffrey S. Glenn, Ohad Etzion, Scott J. Cotler, Cihan Yurdaydin, Danny Barash and Harel Dahari

Mathematics 2022, 10(20), 3917; https://doi.org/10.3390/math10203917 - 21 Oct 2022

Cited by 4 | Viewed by 1843

Abstract

Hepatitis D virus is an infectious subviral agent that can only propagate in people infected with hepatitis B virus. In this study, we modified and further developed a recent model for early hepatitis D virus and hepatitis B virus kinetics to better reproduce [...] Read more.

Hepatitis D virus is an infectious subviral agent that can only propagate in people infected with hepatitis B virus. In this study, we modified and further developed a recent model for early hepatitis D virus and hepatitis B virus kinetics to better reproduce hepatitis D virus and hepatitis B virus kinetics measured in infected patients during anti-hepatitis D virus treatment. The analytical solutions were provided to highlight the new features of the modified model. The improved model offered significantly better prospects for modeling hepatitis D virus and hepatitis B virus interactions. Full article

(This article belongs to the Special Issue Mathematical and Computational Biology of Viruses at the Molecular or Cellular Levels)

► Show Figures

Figure 1

27 pages, 6233 KiB

Open AccessArticle

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

by Dmitry Grebennikov, Antonina Karsonova, Marina Loguinova, Valentina Casella, Andreas Meyerhans and Gennady Bocharov

Mathematics 2022, 10(17), 3154; https://doi.org/10.3390/math10173154 - 2 Sep 2022

Cited by 14 | Viewed by 2421

Abstract

A calibrated mathematical model of antiviral immune response to SARS-CoV-2 infection is developed. The model considers the innate and antigen-specific responses to SARS-CoV-2 infection. Recently published data sets from human challenge studies with SARS-CoV-2 were used for parameter evaluation. The calibration of the [...] Read more.

A calibrated mathematical model of antiviral immune response to SARS-CoV-2 infection is developed. The model considers the innate and antigen-specific responses to SARS-CoV-2 infection. Recently published data sets from human challenge studies with SARS-CoV-2 were used for parameter evaluation. 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. Understanding the regulation of multiple intertwined reaction components of the immune system is necessary for linking the kinetics of immune responses with the clinical phenotypes of COVID-19. Consideration of multiple immune reaction components in a single calibrated mathematical model allowed us to address some fundamental issues related to the pathogenesis of COVID-19, i.e., the sensitivity of the peak viral load to the parameters characterizing the antiviral specific response components, the kinetic coordination of the individual innate and adaptive immune responses, and the factors favoring a prolonged viral persistence. The model provides a tool for predicting the infectivity of patients, i.e., the amount of virus which is transmitted via droplets from the person infected with SARS-CoV-2, depending on the time of infection. The thresholds for variations of the innate and adaptive response parameters which lead to a prolonged persistence of SARS-CoV-2 due to the loss of a kinetic response synchrony/coordination between them were identified. Full article

(This article belongs to the Special Issue Mathematical and Computational Biology of Viruses at the Molecular or Cellular Levels)

► Show Figures

Figure 1

35 pages, 4056 KiB

Open AccessArticle

Parameter Estimation in the Age of Degeneracy and Unidentifiability

by Dylan Lederman, Raghav Patel, Omar Itani and Horacio G. Rotstein

Mathematics 2022, 10(2), 170; https://doi.org/10.3390/math10020170 - 6 Jan 2022

Cited by 3 | Viewed by 2925

Abstract

Parameter estimation from observable or experimental data is a crucial stage in any modeling study. Identifiability refers to one’s ability to uniquely estimate the model parameters from the available data. Structural unidentifiability in dynamic models, the opposite of identifiability, is associated with the [...] Read more.

Parameter estimation from observable or experimental data is a crucial stage in any modeling study. Identifiability refers to one’s ability to uniquely estimate the model parameters from the available data. Structural unidentifiability in dynamic models, the opposite of identifiability, is associated with the notion of degeneracy where multiple parameter sets produce the same pattern. Therefore, the inverse function of determining the model parameters from the data is not well defined. Degeneracy is not only a mathematical property of models, but it has also been reported in biological experiments. Classical studies on structural unidentifiability focused on the notion that one can at most identify combinations of unidentifiable model parameters. We have identified a different type of structural degeneracy/unidentifiability present in a family of models, which we refer to as the Lambda-Omega (

Λ

-

Ω

) models. These are an extension of the classical lambda-omega (

λ

-

ω

) models that have been used to model biological systems, and display a richer dynamic behavior and waveforms that range from sinusoidal to square wave to spike like. We show that the

Λ

-

Ω

models feature infinitely many parameter sets that produce identical stable oscillations, except possible for a phase shift (reflecting the initial phase). These degenerate parameters are not identifiable combinations of unidentifiable parameters as is the case in structural degeneracy. In fact, reducing the number of model parameters in the

Λ

-

Ω

models is minimal in the sense that each one controls a different aspect of the model dynamics and the dynamic complexity of the system would be reduced by reducing the number of parameters. We argue that the family of

Λ

-

Ω

models serves as a framework for the systematic investigation of degeneracy and identifiability in dynamic models and for the investigation of the interplay between structural and other forms of unidentifiability resulting on the lack of information from the experimental/observational data. Full article

(This article belongs to the Special Issue Mathematical and Computational Biology of Viruses at the Molecular or Cellular Levels)

► Show Figures

Figure 1

9 pages, 1399 KiB

Open AccessArticle

A Mathematical Model for Early HBV and -HDV Kinetics during Anti-HDV Treatment

by Rami Zakh, Alexander Churkin, William Bietsch, Menachem Lachiany, Scott J. Cotler, Alexander Ploss, Harel Dahari and Danny Barash

Mathematics 2021, 9(24), 3323; https://doi.org/10.3390/math9243323 - 20 Dec 2021

Cited by 3 | Viewed by 2577

Abstract

Hepatitis delta virus (HDV) is an infectious subviral agent that can only propagate in people infected with hepatitis B virus (HBV). HDV/HBV infection is considered to be the most severe form of chronic viral hepatitis. In this contribution, a mathematical model for the [...] Read more.

Hepatitis delta virus (HDV) is an infectious subviral agent that can only propagate in people infected with hepatitis B virus (HBV). HDV/HBV infection is considered to be the most severe form of chronic viral hepatitis. In this contribution, a mathematical model for the interplay between HDV and HBV under anti-HDV treatment is presented. Previous models were not designed to account for the observation that HBV rises when HDV declines with HDV-specific therapy. In the simple model presented here, HDV and HBV kinetics are coupled, giving rise to an improved viral kinetic model that simulates the early interplay of HDV and HBV during anti-HDV therapy. Full article

(This article belongs to the Special Issue Mathematical and Computational Biology of Viruses at the Molecular or Cellular Levels)

► Show Figures

Figure 1

16 pages, 1595 KiB

Open AccessArticle

A Mathematical Analysis of HDV Genotypes: From Molecules to Cells

by Rami Zakh, Alexander Churkin, Franziska Totzeck, Marina Parr, Tamir Tuller, Ohad Etzion, Harel Dahari, Michael Roggendorf, Dmitrij Frishman and Danny Barash

Mathematics 2021, 9(17), 2063; https://doi.org/10.3390/math9172063 - 26 Aug 2021

Cited by 4 | Viewed by 1994

Abstract

Hepatitis D virus (HDV) is classified according to eight genotypes. The various genotypes are included in the HDVdb database, where each HDV sequence is specified by its genotype. In this contribution, a mathematical analysis is performed on RNA sequences in HDVdb. The RNA [...] Read more.

Hepatitis D virus (HDV) is classified according to eight genotypes. The various genotypes are included in the HDVdb database, where each HDV sequence is specified by its genotype. In this contribution, a mathematical analysis is performed on RNA sequences in HDVdb. The RNA folding predicted structures of the Genbank HDV genome sequences in HDVdb are classified according to their coarse-grain tree-graph representation. The analysis allows discarding in a simple and efficient way the vast majority of the sequences that exhibit a rod-like structure, which is important for the virus replication, to attempt to discover other biological functions by structure consideration. After the filtering, there remain only a small number of sequences that can be checked for their additional stem-loops besides the main one that is known to be responsible for virus replication. It is found that a few sequences contain an additional stem-loop that is responsible for RNA editing or other possible functions. These few sequences are grouped into two main classes, one that is well-known experimentally belonging to genotype 3 for patients from South America associated with RNA editing, and the other that is not known at present belonging to genotype 7 for patients from Cameroon. The possibility that another function besides virus replication reminiscent of the editing mechanism in HDV genotype 3 exists in HDV genotype 7 has not been explored before and is predicted by eigenvalue analysis. Finally, when comparing native and shuffled sequences, it is shown that HDV sequences belonging to all genotypes are accentuated in their mutational robustness and thermodynamic stability as compared to other viruses that were subjected to such an analysis. Full article

(This article belongs to the Special Issue Mathematical and Computational Biology of Viruses at the Molecular or Cellular Levels)

► Show Figures

Figure 1

19 pages, 4114 KiB

Open AccessEditor’s ChoiceArticle

Markov Chain-Based Stochastic Modelling of HIV-1 Life Cycle in a CD4 T Cell

by Igor Sazonov, Dmitry Grebennikov, Andreas Meyerhans and Gennady Bocharov

Mathematics 2021, 9(17), 2025; https://doi.org/10.3390/math9172025 - 24 Aug 2021

Cited by 13 | Viewed by 3283

Abstract

Replication of Human Immunodeficiency Virus type 1 (HIV) in infected CD4

^{+}

T cells represents a key driver of HIV infection. The HIV life cycle is characterised by the heterogeneity of infected cells with respect to multiplicity of infection and the variability in [...] Read more.

Replication of Human Immunodeficiency Virus type 1 (HIV) in infected CD4

^{+}

T cells represents a key driver of HIV infection. The HIV life cycle is characterised by the heterogeneity of infected cells with respect to multiplicity of infection and the variability in viral progeny. This heterogeneity can result from the phenotypic diversity of infected cells as well as from random effects and fluctuations in the kinetics of biochemical reactions underlying the virus replication cycle. To quantify the contribution of stochastic effects to the variability of HIV life cycle kinetics, we propose a high-resolution mathematical model formulated as a Markov chain jump process. The model is applied to generate the statistical characteristics of the (i) cell infection multiplicity, (ii) cooperative nature of viral replication, and (iii) variability in virus secretion by phenotypically identical cells. We show that the infection with a fixed number of viruses per CD4

^{+}

T cell leads to some heterogeneity of infected cells with respect to the number of integrated proviral genomes. The bottleneck factors in the virus production are identified, including the Gag-Pol proteins. Sensitivity analysis enables ranking of the model parameters with respect to the strength of their impact on the size of viral progeny. The first three globally influential parameters are the transport of genomic mRNA to membrane, the tolerance of transcription activation to Tat-mediated regulation, and the degradation of free and mature virions. These can be considered as potential therapeutical targets. Full article

(This article belongs to the Special Issue Mathematical and Computational Biology of Viruses at the Molecular or Cellular Levels)

► Show Figures

Figure 1

13 pages, 2593 KiB

Open AccessArticle

A Mathematical Analysis of RNA Structural Motifs in Viruses

by Alexander Churkin, Franziska Totzeck, Rami Zakh, Marina Parr, Tamir Tuller, Dmitrij Frishman and Danny Barash

Mathematics 2021, 9(6), 585; https://doi.org/10.3390/math9060585 - 10 Mar 2021

Cited by 4 | Viewed by 2332

Abstract

RNA stem-loop structures play an important role in almost every step of the viral replication cycle. In this contribution, a mathematical analysis is performed on a large dataset of RNA secondary structure elements in the coding regions of viruses by using topological indices [...] Read more.

RNA stem-loop structures play an important role in almost every step of the viral replication cycle. In this contribution, a mathematical analysis is performed on a large dataset of RNA secondary structure elements in the coding regions of viruses by using topological indices that capture the Laplacian eigenvalues of the associated RNA graph representations and thereby enable structural classification, supplemented by folding energy and mutational robustness. The application of such an analysis for viral RNA structural motifs is described, being able to extract structural categories such as stem-loop structures of different sizes according to the tree-graph representation of the RNA structure, in our attempt to find novel functional motifs. While the analysis is carried on a large dataset of viral RNA structures, it can be applied more generally to other data that involve RNA secondary structures in biological agents. Full article

(This article belongs to the Special Issue Mathematical and Computational Biology of Viruses at the Molecular or Cellular Levels)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Mathematical and Computational Biology of Viruses at the Molecular or Cellular Levels

Share This Special Issue

Special Issue Editors

Special Issue Information

Keywords

Benefits of Publishing in a Special Issue

Published Papers (8 papers)

Editorial

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI