PDE Models of Virus Replication Coupling 2D Manifold and 3D Volume Effects Evaluated at Realistic Reconstructed Cell Geometries

Knodel, Markus M.; Nägel, Arne; Herrmann, Eva; Wittum, Gabriel

doi:10.1007/978-3-031-40864-9_26

Cited by 4 publications

(16 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Surface diffusivity of NSPs on the ER is an important material parameter that is needed to arrive at quantitative predictions of the rates of the biochemical reaction kinetics of processes located on the ER [ 53 , 55 , 56 , 65 , 66 ]. For instance, we recently adopted the NSP surface diffusion constant derived in the present study in a coupled surface–volume PDE model [ 50 , 51 ]. This allowed us to perform biophysical simulations for the dynamics of the major components of an intracellular virus genome replication cycle which are in quantitative agreement with experimental data [ 49 ].…”

Section: Discussionmentioning

confidence: 99%

“…HCV belongs to the family of plus-stranded RNA (ss(+)RNA) viruses [ 27 , 48 ], such as Dengue and yellow fever viruses (DNFV and YFV) [ 27 , 32 ], and Coronaviridiae such as SARS-CoV-1 and SARS-CoV-2 [ 24 ]. The aim of this project is to develop an “in silico microscope” for direct comparisons between experiments and simulations of biophysical models of intracellular virus replication [ 49 , 50 , 51 ]. The present approach augments this method by estimates of material parameters derived directly from the experimental data.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Efficient Estimates of Surface Diffusion Parameters for Spatio-Temporally Resolved Virus Replication Dynamics

Knodel,

Wittum,

Vollmer

2024

IJMS

View full text Add to dashboard Cite

Advanced methods of treatment are needed to fight the threats of virus-transmitted diseases and pandemics. Often, they are based on an improved biophysical understanding of virus replication strategies and processes in their host cells. For instance, an essential component of the replication of the hepatitis C virus (HCV) proceeds under the influence of nonstructural HCV proteins (NSPs) that are anchored to the endoplasmatic reticulum (ER), such as the NS5A protein. The diffusion of NSPs has been studied by in vitro fluorescence recovery after photobleaching (FRAP) experiments. The diffusive evolution of the concentration field of NSPs on the ER can be described by means of surface partial differential equations (sufPDEs). Previous work estimated the diffusion coefficient of the NS5A protein by minimizing the discrepancy between an extended set of sufPDE simulations and experimental FRAP time-series data. Here, we provide a scaling analysis of the sufPDEs that describe the diffusive evolution of the concentration field of NSPs on the ER. This analysis provides an estimate of the diffusion coefficient that is based only on the ratio of the membrane surface area in the FRAP region to its contour length. The quality of this estimate is explored by a comparison to numerical solutions of the sufPDE for a flat geometry and for ten different 3D embedded 2D ER grids that are derived from fluorescence z-stack data of the ER. Finally, we apply the new data analysis to the experimental FRAP time-series data analyzed in our previous paper, and we discuss the opportunities of the new approach.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Efficient Estimates of Surface Diffusion Parameters for Spatio-Temporally Resolved Virus Replication Dynamics

Knodel,

Wittum,

Vollmer

2024

IJMS

View full text Add to dashboard Cite

show abstract

“…Surface diffusivity of NSPs on the ER is an important material parameter that is needed to arrive at quantitative predictions of the rates of the biochemical reaction kinetics of processes located on the ER [53,55,56,65,66]. For instance, we recently adopted the NSP surface diffusion constant derived in the present study in a coupled surface-volume PDE model [50,51]. This allowed us to perform biophysical simulations for the dynamics of the major components of an intracellular virus genome replication cycle which are in quantitative agreement with experimental data [49].…”

Section: Discussionmentioning

confidence: 99%

“…HCV belongs to the family of plus-stranded RNA (ss(+)RNA) viruses [27,48], such as Dengue and yellow fever viruses (DNFV and YFV) [27,32], and Coronaviridiae such as SARS-CoV-1 and SARS-CoV-2 [24]. The aim of this project is to develop an "in silico microscope" for direct comparisons between experiments and simulations of biophysical models of intracellular virus replication [49][50][51]. The present approach augments this method by estimates of material parameters derived directly from the experimental data.…”

Section: Introductionmentioning

confidence: 99%

Efficient Estimates of Surface Diffusion Parameters for Spatio-Temporal Resolved Virus Replication Dynamics

Knodel,

Wittum,

Vollmer

2024

Preprint

View full text Add to dashboard Cite

Advanced methods of treatment are needed to fight the threats of virus-transmitted deseases and pandemics. Often they are based on an improved biophysical understanding of virus replication strategies and processes in their host cells. For instance, an essential component of the replication of the Hepatitis C virus (HCV) proceeds under the influence of non-structural HCV proteins (NSPs) that are anchored to the endoplasmatic reticulum (ER), such as the NS5a protein. The diffusion of NSPs has been studied by in-vitro fluorescence recovery after photobleaching (FRAP) experiments. The diffusive evolution of the concentration field of NSPs on the ER can be described by means of surface partial differential equations (sufPDE). Knodel et al, Viruses 2018, 10, 28 estimated the diffusion coefficient of the NS5a protein by minimizing the discrepancy of an extended set of sufPDE simulations and experimental FRAP time series data. Here, we provide a scaling analysis of the sufPDEs that describe the diffusive evolution of the concentration field of NSPs on the ER. This analysis provides an estimate of the diffusion coefficient that is based only on the ratio of the membrane surface area in the FRAP region and its contour length. The quality of this estimate is explored by comparison to numerical solutions of the sufPDE for a flat geometry and for ten different 3D embedded 2D ER grids that are derived from fluorescence z-stack data of the ER. Finally, we apply the new data analysis to the experimental FRAP time-series data analyzed in our previous paper, and we discuss the opportunities of the new approach.

show abstract

“…Finally, we discuss the numerical solution techniques used for conducting in silico simulations on the present supercomputers. While we provide a high-level overview of the mathematical and numerical properties in this section, for a more detailed description, we refer readers to a peer-reviewed proceedings paper [35] and to another peer-reviewed proceedings paper that is currently under review [36].…”

Section: Materials Models and Methodsmentioning

confidence: 99%

Intracellular “In Silico Microscopes”—Comprehensive 3D Spatio-Temporal Virus Replication Model Simulations

Knodel,

Nägel,

Herrmann

et al. 2024

Viruses

Self Cite

View full text Add to dashboard Cite

Despite their small and simple structure compared with their hosts, virus particles can cause severe harm and even mortality in highly evolved species such as humans. A comprehensive quantitative biophysical understanding of intracellular virus replication mechanisms could aid in preparing for future virus pandemics. By elucidating the relationship between the form and function of intracellular structures from the host cell and viral components, it is possible to identify possible targets for direct antiviral agents and potent vaccines. Biophysical investigations into the spatio-temporal dynamics of intracellular virus replication have thus far been limited. This study introduces a framework to enable simulations of these dynamics using partial differential equation (PDE) models, which are evaluated using advanced numerical mathematical methods on leading supercomputers. In particular, this study presents a model of the replication cycle of a specific RNA virus, the hepatitis C virus. The diffusion–reaction model mimics the interplay of the major components of the viral replication cycle, including non structural viral proteins, viral genomic RNA, and a generic host factor. Technically, surface partial differential equations (sufPDEs) are coupled on the 3D embedded 2D endoplasmic reticulum manifold with partial differential equations (PDEs) in the 3D membranous web and cytosol volume. The membranous web serves as a viral replication factory and is formed on the endoplasmic reticulum after infection and in the presence of nonstructural proteins. The coupled sufPDE/PDE model was evaluated using realistic cell geometries based on experimental data. The simulations incorporate the effects of non structural viral proteins, which are restricted to the endoplasmic reticulum surface, with effects appearing in the volume, such as host factor supply from the cytosol and membranous web dynamics. Because the spatial diffusion properties of genomic viral RNA are not yet fully understood, the model allows for viral RNA movement on the endoplasmic reticulum as well as within the cytosol. Visualizing the simulated intracellular viral replication dynamics provides insights similar to those obtained by microscopy, complementing data from in vitro/in vivo viral replication experiments. The output data demonstrate quantitative consistence with the experimental findings, prompting further advanced experimental studies to validate the model and refine our quantitative biophysical understanding.

show abstract

PDE Models of Virus Replication Coupling 2D Manifold and 3D Volume Effects Evaluated at Realistic Reconstructed Cell Geometries

Cited by 4 publications

References 6 publications

Efficient Estimates of Surface Diffusion Parameters for Spatio-Temporally Resolved Virus Replication Dynamics

Efficient Estimates of Surface Diffusion Parameters for Spatio-Temporally Resolved Virus Replication Dynamics

Efficient Estimates of Surface Diffusion Parameters for Spatio-Temporal Resolved Virus Replication Dynamics

Intracellular “In Silico Microscopes”—Comprehensive 3D Spatio-Temporal Virus Replication Model Simulations

Contact Info

Product

Resources

About