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Hailegiorgis A, Ishida Y, Collier N, Imamura M, Shi Z, Reinharz V, Tsuge M, Barash D, Hiraga N, Yokomichi H, Tateno C, Ozik J, Uprichard SL, Chayama K, Dahari H. Modeling suggests that virion production cycles within individual cells is key to understanding acute hepatitis B virus infection kinetics. PLoS Comput Biol 2023; 19:e1011309. [PMID: 37535676 PMCID: PMC10426918 DOI: 10.1371/journal.pcbi.1011309] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2022] [Revised: 08/15/2023] [Accepted: 06/26/2023] [Indexed: 08/05/2023] Open
Abstract
Hepatitis B virus (HBV) infection kinetics in immunodeficient mice reconstituted with humanized livers from inoculation to steady state is highly dynamic despite the absence of an adaptive immune response. To recapitulate the multiphasic viral kinetic patterns, we developed an agent-based model that includes intracellular virion production cycles reflecting the cyclic nature of each individual virus lifecycle. The model fits the data well predicting an increase in production cycles initially starting with a long production cycle of 1 virion per 20 hours that gradually reaches 1 virion per hour after approximately 3-4 days before virion production increases dramatically to reach to a steady state rate of 4 virions per hour per cell. Together, modeling suggests that it is the cyclic nature of the virus lifecycle combined with an initial slow but increasing rate of HBV production from each cell that plays a role in generating the observed multiphasic HBV kinetic patterns in humanized mice.
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Affiliation(s)
- Atesmachew Hailegiorgis
- The Program for Experimental & Theoretical Modeling, Division of Hepatology, Department of Medicine, Stritch School of Medicine, Loyola University Chicago, Maywood, Illinois, United States of America
| | - Yuji Ishida
- PhoenixBio Co., Ltd., Hiroshima, Japan
- Research Center for Hepatology and Gastroenterology, Graduate School of Biomedical and Health Sciences, Hiroshima University, Hiroshima, Japan
| | - Nicholson Collier
- Consortium for Advanced Science and Engineering, University of Chicago, Chicago, Illinois, United States of America
- Decision and Infrastructure Sciences, Argonne National Laboratory, Argonne, Illinois, United States of America
| | - Michio Imamura
- Research Center for Hepatology and Gastroenterology, Graduate School of Biomedical and Health Sciences, Hiroshima University, Hiroshima, Japan
| | - Zhenzhen Shi
- The Program for Experimental & Theoretical Modeling, Division of Hepatology, Department of Medicine, Stritch School of Medicine, Loyola University Chicago, Maywood, Illinois, United States of America
| | - Vladimir Reinharz
- Department of Computer Science, Université du Québec à Montréal, Montreal, Canada
| | - Masataka Tsuge
- The Program for Experimental & Theoretical Modeling, Division of Hepatology, Department of Medicine, Stritch School of Medicine, Loyola University Chicago, Maywood, Illinois, United States of America
- Research Center for Hepatology and Gastroenterology, Graduate School of Biomedical and Health Sciences, Hiroshima University, Hiroshima, Japan
- Department of Gastroenterology, Graduate School of Biomedical & Health Sciences, Hiroshima University, Hiroshima, Japan
| | - Danny Barash
- Department of Computer Science, Ben-Gurion University, Beer-Sheva, Israel
| | - Nobuhiko Hiraga
- Research Center for Hepatology and Gastroenterology, Graduate School of Biomedical and Health Sciences, Hiroshima University, Hiroshima, Japan
| | | | - Chise Tateno
- PhoenixBio Co., Ltd., Hiroshima, Japan
- Research Center for Hepatology and Gastroenterology, Graduate School of Biomedical and Health Sciences, Hiroshima University, Hiroshima, Japan
| | - Jonathan Ozik
- Consortium for Advanced Science and Engineering, University of Chicago, Chicago, Illinois, United States of America
- Decision and Infrastructure Sciences, Argonne National Laboratory, Argonne, Illinois, United States of America
| | - Susan L. Uprichard
- The Program for Experimental & Theoretical Modeling, Division of Hepatology, Department of Medicine, Stritch School of Medicine, Loyola University Chicago, Maywood, Illinois, United States of America
- The Infectious Disease and Immunology Research Institute, Stritch School of Medicine, Loyola University Chicago, Maywood, Illinois, United States of America
| | - Kazuaki Chayama
- Research Center for Hepatology and Gastroenterology, Graduate School of Biomedical and Health Sciences, Hiroshima University, Hiroshima, Japan
- RIKEN Center for Integrative Medical Sciences, Yokohama, Japan
- Collaborative Research Laboratory of Medical Innovation, Graduate School of Biomedical and Health Sciences, Hiroshima University, Hiroshima, Japan
- Hiroshima Institute of Life Sciences, Hiroshima, Japan
| | - Harel Dahari
- The Program for Experimental & Theoretical Modeling, Division of Hepatology, Department of Medicine, Stritch School of Medicine, Loyola University Chicago, Maywood, Illinois, United States of America
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Advances in Parameter Estimation and Learning from Data for Mathematical Models of Hepatitis C Viral Kinetics. MATHEMATICS 2022; 10. [DOI: 10.3390/math10122136] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
Mathematical models, some of which incorporate both intracellular and extracellular hepatitis C viral kinetics, have been advanced in recent years for studying HCV–host dynamics, antivirals mode of action, and their efficacy. The standard ordinary differential equation (ODE) hepatitis C virus (HCV) kinetic model keeps track of uninfected cells, infected cells, and free virus. In multiscale models, a fourth partial differential equation (PDE) accounts for the intracellular viral RNA (vRNA) kinetics in an infected cell. The PDE multiscale model is substantially more difficult to solve compared to the standard ODE model, with governing differential equations that are stiff. In previous contributions, we developed and implemented stable and efficient numerical methods for the multiscale model for both the solution of the model equations and parameter estimation. In this contribution, we perform sensitivity analysis on model parameters to gain insight into important properties and to ensure our numerical methods can be safely used for HCV viral dynamic simulations. Furthermore, we generate in-silico patients using the multiscale models to perform machine learning from the data, which enables us to remove HCV measurements on certain days and still be able to estimate meaningful observations with a sufficiently small error.
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Lingas G, Rosenke K, Safronetz D, Guedj J. Lassa viral dynamics in non-human primates treated with favipiravir or ribavirin. PLoS Comput Biol 2021; 17:e1008535. [PMID: 33411731 PMCID: PMC7817048 DOI: 10.1371/journal.pcbi.1008535] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2020] [Revised: 01/20/2021] [Accepted: 11/13/2020] [Indexed: 02/07/2023] Open
Abstract
Lassa fever is an haemorrhagic fever caused by Lassa virus (LASV). There is no vaccine approved against LASV and the only recommended antiviral treatment relies on ribavirin, despite limited evidence of efficacy. Recently, the nucleotide analogue favipiravir showed a high antiviral efficacy, with 100% survival obtained in an otherwise fully lethal non-human primate (NHP) model of Lassa fever. However the mechanism of action of the drug is not known and the absence of pharmacokinetic data limits the translation of these results to the human setting. Here we aimed to better understand the antiviral effect of favipiravir by developping the first mathematical model recapitulating Lassa viral dynamics and treatment. We analyzed the viral dynamics in 24 NHPs left untreated or treated with ribavirin or favipiravir, and we put the results in perspective with those obtained with the same drugs in the context of Ebola infection. Our model estimates favipiravir EC50 in vivo to 2.89 μg.mL-1, which is much lower than what was found against Ebola virus. The main mechanism of action of favipiravir was to decrease virus infectivity, with an efficacy of 91% at the highest dose. Based on our knowledge acquired on the drug pharmacokinetics in humans, our model predicts that favipiravir doses larger than 1200 mg twice a day should have the capability to strongly reduce the production infectious virus and provide a milestone towards a future use in humans.
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Affiliation(s)
| | - Kyle Rosenke
- Laboratory of Virology, National Institute of Allergy and Infectious Diseases, National Institutes of Health, Rocky Mountain Laboratories, Hamilton, Montana, USA
| | - David Safronetz
- Department of Medical Microbiology, University of Manitoba, Winnipeg, Manitoba, Canada.,Zoonotic Diseases and Special Pathogens, Public Health Agency of Canada, Winnipeg, Manitoba, Canada
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Nath BJ, Dehingia K, Mishra VN, Chu YM, Sarmah HK. Mathematical analysis of a within-host model of SARS-CoV-2. ADVANCES IN DIFFERENCE EQUATIONS 2021; 2021:113. [PMID: 33619433 PMCID: PMC7888694 DOI: 10.1186/s13662-021-03276-1] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2020] [Accepted: 02/04/2021] [Indexed: 05/08/2023]
Abstract
In this paper, we have mathematically analyzed a within-host model of SARS-CoV-2 which is used by Li et al. in the paper "The within-host viral kinetics of SARS-CoV-2" published in (Math. Biosci. Eng. 17(4):2853-2861, 2020). Important properties of the model, like nonnegativity of solutions and their boundedness, are established. Also, we have calculated the basic reproduction number which is an important parameter in the infection models. From stability analysis of the model, it is found that stability of the biologically feasible steady states are determined by the basic reproduction number ( χ 0 ) . Numerical simulations are done in order to substantiate analytical results. A biological implication from this study is that a COVID-19 patient with less than one basic reproduction ratio can automatically recover from the infection.
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Affiliation(s)
- Bhagya Jyoti Nath
- Department of Mathematics, Barnagar College, Sorbhog, 781317 Barpeta, Assam India
| | - Kaushik Dehingia
- Department of Mathematics, Gauhati University, Guwahati, 781014 Assam India
| | - Vishnu Narayan Mishra
- Department of Mathematics, Indira Gandhi National Tribal University, Amarkantak, 484 887 Madhya Pradesh India
| | - Yu-Ming Chu
- Department of Mathematics, Huzhou University, Huzhou, 313000 P.R. China
- Hunan Provincial Key Labortory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha, 410114 P.R. China
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Liao LE, Carruthers J, Smither SJ, Weller SA, Williamson D, Laws TR, García-Dorival I, Hiscox J, Holder BP, Beauchemin CAA, Perelson AS, López-García M, Lythe G, Barr JN, Molina-París C. Quantification of Ebola virus replication kinetics in vitro. PLoS Comput Biol 2020; 16:e1008375. [PMID: 33137116 PMCID: PMC7660928 DOI: 10.1371/journal.pcbi.1008375] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2020] [Revised: 11/12/2020] [Accepted: 09/23/2020] [Indexed: 12/17/2022] Open
Abstract
Mathematical modelling has successfully been used to provide quantitative descriptions of many viral infections, but for the Ebola virus, which requires biosafety level 4 facilities for experimentation, modelling can play a crucial role. Ebola virus modelling efforts have primarily focused on in vivo virus kinetics, e.g., in animal models, to aid the development of antivirals and vaccines. But, thus far, these studies have not yielded a detailed specification of the infection cycle, which could provide a foundational description of the virus kinetics and thus a deeper understanding of their clinical manifestation. Here, we obtain a diverse experimental data set of the Ebola virus infection in vitro, and then make use of Bayesian inference methods to fully identify parameters in a mathematical model of the infection. Our results provide insights into the distribution of time an infected cell spends in the eclipse phase (the period between infection and the start of virus production), as well as the rate at which infectious virions lose infectivity. We suggest how these results can be used in future models to describe co-infection with defective interfering particles, which are an emerging alternative therapeutic.
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Affiliation(s)
- Laura E. Liao
- Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos, NM, USA 87545
| | - Jonathan Carruthers
- Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK
| | | | | | - Simon A. Weller
- Defence Science and Technology Laboratory, Salisbury SP4 0JQ, UK
| | - Diane Williamson
- Defence Science and Technology Laboratory, Salisbury SP4 0JQ, UK
| | - Thomas R. Laws
- Defence Science and Technology Laboratory, Salisbury SP4 0JQ, UK
| | - Isabel García-Dorival
- Institute of Infection and Global Health, University of Liverpool, Liverpool, L69 7BE, UK
| | - Julian Hiscox
- Institute of Infection and Global Health, University of Liverpool, Liverpool, L69 7BE, UK
| | - Benjamin P. Holder
- Department of Physics, Grand Valley State University, Allendale, MI, USA 49401
| | - Catherine A. A. Beauchemin
- Department of Physics, Ryerson University, Toronto, ON, Canada M5B 2K3
- Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS) Research Program at RIKEN, Wako, Saitama, Japan, 351-0198
| | - Alan S. Perelson
- Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos, NM, USA 87545
| | - Martín López-García
- Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK
| | - Grant Lythe
- Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK
| | - John N. Barr
- School of Molecular and Cellular Biology, University of Leeds, Leeds LS2 9JT, UK
| | - Carmen Molina-París
- Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK
- * E-mail:
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