A PDE multiscale model of hepatitis C virus infection can be transformed to a system of ODEs

Kitagawa, Kosaku; Nakaoka, Shinji; Asai, Yasufumi; Watashi, Koichi; Iwami, Shingo

doi:10.1016/j.jtbi.2018.04.006

Cited by 24 publications

(33 citation statements)

References 33 publications

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“…In this study, through a combined experimental-theoretical approach, we analyzed the dynamics of the HCV life cycle using two related HCV strains, JFH-1 and Jc1-n, employing different particle assembly/release strategies. We quantified the intra-and intercellular viral dynamics of these strains by applying an age-structured multiscale model to time-course experimental data from an HCV infection cell culture assay (Fig 2 and Table 1): as in [10,11], we transformed the multiscale model formulated by PDEs to an identical multiscale ODE model (i.e., Eqs 2-6), and we estimated parameters shared between the PDE and ODE models. It is technically challenging to obtain experimental measurements with age information, but thanks to the estimated values of these common parameters, we managed to reconstruct age information for intracellular viral RNA (S2 Fig).…”

Section: Discussionmentioning

confidence: 99%

Should a viral genome stay in the host cell or leave? A quantitative dynamics study of how hepatitis C virus deals with this dilemma

et al. 2020

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Virus proliferation involves gene replication inside infected cells and transmission to new target cells. Once positive-strand RNA virus has infected a cell, the viral genome serves as a template for copying ("stay-strategy") or is packaged into a progeny virion that will be released extracellularly ("leave-strategy"). The balance between genome replication and virion release determines virus production and transmission efficacy. The ensuing trade-off has not yet been well characterized. In this study, we use hepatitis C virus (HCV) as a model system to study the balance of the two strategies. Combining viral infection cell culture assays with mathematical modeling, we characterize the dynamics of two different HCV strains (JFH-1, a clinical isolate, and Jc1-n, a laboratory strain), which have different viral release characteristics. We found that 0.63% and 1.70% of JFH-1 and Jc1-n intracellular viral RNAs, respectively, are used for producing and releasing progeny virions. Analysis of the Malthusian parameter of the HCV genome (i.e., initial proliferation rate) and the number of de novo infections (i.e., initial transmissibility) suggests that the leave-strategy provides a higher level of initial transmission for Jc1-n, whereas, in contrast, the stay-strategy provides a higher initial proliferation rate for JFH-1. Thus, theoretical-experimental analysis of viral dynamics enables us to better understand the proliferation strategies of viruses, which contributes to the efficient control of virus transmission. Ours is the first study to analyze the stay-leave trade-off during the viral life cycle and the significance of the replication-release switching mechanism for viral proliferation.

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Section: Discussionmentioning

confidence: 99%

Should a viral genome stay in the host cell or leave? A quantitative dynamics study of how hepatitis C virus deals with this dilemma

et al. 2020

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“…1C ). In Supplementary Note 1 , we derived the following multiscale ordinary differential equation (ODE) model for HCV infection from the corresponding age-structured partial differential equation (PDE) model [10, 11]: …”

Section: Resultsmentioning

confidence: 99%

“…We quantified the intra- and inter-cellular viral dynamics of these strains by applying an age-structured multiscale model to time-course experimental data from an HCV infection cell culture assay ( Fig. 2A and Table 1 ): As in [10, 11], we transformed the multiscale model formulated by PDEs to an identical multiscale ODE model (i.e., Eqs. (2–6)), and estimated parameters shared between the PDE and ODE models.…”

Section: Discussionmentioning

confidence: 99%

Two strategies underlying the trade-off of hepatitis C virus proliferation: stay-at-home or leaving-home?

Iwanami

Kitagawa

Asai

et al. 2019

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244/250) 2 Viruses proliferate through both genome replication inside infected cells and 3 transmission to new target cells or to new hosts. Each viral genome molecule in 4 infected cells is used either for amplifying the intracellular genome as a template 5 ("stay-at-home strategy") or for packaging into progeny virions to be released 6 extracellularly ("leaving-home strategy"). The balance between these strategies is 7 important for both initial growth and transmission of viruses. In this study, we used 8 hepatitis C virus (HCV) as a model system to study the functions of viral genomic 9 RNA in both RNA replication in cells and in progeny virus assembly and release.10 Using viral infection assays combined with mathematical modelling, we characterized 11 the dynamics of two different HCV strains (JFH-1, a clinical isolate, and Jc1-n, a 12 laboratory strain), which have different viral assembly and release characteristics. We 13 found that 1.27% and 3.28% of JFH-1 and Jc1-n intracellular viral RNAs, respectively, 14 are used for producing and releasing progeny virions. Analysis of the Malthusian 15 parameter of the HCV genome (i.e., initial growth rate) and the number of de novo 16 infections (i.e., initial transmissibility) suggests that the leaving-home strategy 17 provides a higher level of initial transmission for Jc1-n, while, in contrast, the 18 stay-at-home strategy provides a higher initial growth rate for JFH-1. Thus, 19 theoretical-experimental analysis of viral dynamics enables us to better understand 20 the proliferation strategies of viruses. Ours is the first study to analyze stay-leave 21 trade-offs during the viral life cycle and their significance for viral proliferation. 22 23 Keywords: 24 adaptation, trade-off, HCV, multi-scale model, viral proliferation strategy 25 3 26

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“…A more general and comprehensive approach to parameter fitting without relying on analytical approximations would be useful. In addition, although it was shown recently that it is possible to transform the PDE multiscale model to a system of ODEs [ 60 ], this transformation problematically introduces some of the boundary conditions, e.g., ζ , as new parameters inside the model equations. A numerical approach to parameter fitting of multiscale models was recently put forth and described in [ 50 ], by the use of the method of lines and canned methods that are available in Matlab.…”

Section: Methodsmentioning

confidence: 99%

“…The first strategy, employed in [ 48 ], utilizes an analytical solution named long-term approximation for solving the model equations along with calling the Levenberg–Marquardt [ 58 , 59 ] as a canned method for performing the fitting. The second strategy, employed in [ 60 ], transforms the multiscale model to a system of ODEs and, as such, simple parameter estimation methods can be used in the same manner as the biphasic model. The third strategy, employed in [ 50 ] that also deals with spatial models of intracellular virus replication, is based on the method of lines and utilizes canned methods for both the numerical solution of the resulting equations (Matlab’s ode45 ) and for performing the fitting (Matlab’s fmincon ).…”

Section: Introductionmentioning

confidence: 99%

Efficient Methods for Parameter Estimation of Ordinary and Partial Differential Equation Models of Viral Hepatitis Kinetics

et al. 2020

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Parameter estimation in mathematical models that are based on differential equations is known to be of fundamental importance. For sophisticated models such as age-structured models that simulate biological agents, parameter estimation that addresses all cases of data points available presents a formidable challenge and efficiency considerations need to be employed in order for the method to become practical. In the case of age-structured models of viral hepatitis dynamics under antiviral treatment that deal with partial differential equations, a fully numerical parameter estimation method was developed that does not require an analytical approximation of the solution to the multiscale model equations, avoiding the necessity to derive the long-term approximation for each model. However, the method is considerably slow because of precision problems in estimating derivatives with respect to the parameters near their boundary values, making it almost impractical for general use. In order to overcome this limitation, two steps have been taken that significantly reduce the running time by orders of magnitude and thereby lead to a practical method. First, constrained optimization is used, letting the user add constraints relating to the boundary values of each parameter before the method is executed. Second, optimization is performed by derivative-free methods, eliminating the need to evaluate expensive numerical derivative approximations. The newly efficient methods that were developed as a result of the above approach are described for hepatitis C virus kinetic models during antiviral therapy. Illustrations are provided using a user-friendly simulator that incorporates the efficient methods for both the ordinary and partial differential equation models.

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A PDE multiscale model of hepatitis C virus infection can be transformed to a system of ODEs

Cited by 24 publications

References 33 publications

Should a viral genome stay in the host cell or leave? A quantitative dynamics study of how hepatitis C virus deals with this dilemma

Should a viral genome stay in the host cell or leave? A quantitative dynamics study of how hepatitis C virus deals with this dilemma

Two strategies underlying the trade-off of hepatitis C virus proliferation: stay-at-home or leaving-home?

Efficient Methods for Parameter Estimation of Ordinary and Partial Differential Equation Models of Viral Hepatitis Kinetics

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