zbMATH — the first resource for mathematics

Multigrid analysis of spatially resolved hepatitis C virus protein simulations. (English) Zbl 1388.92004
Summary: Viruses are a major challenge to human health and prosperity. This holds true for various viruses which are either threatening Europe (like Dengue and Yellow fever) or which are currently causing big health problems like the hepatitis C virus (HCV). HCV causes chronic liver diseases like cirrhosis and cancer and is the main reason for liver transplantations. Exploring biophysical properties of virus-encoded components and viral life cycle is an exciting new area of current virological research. In this context, spatial resolution is an aspect that has not yet been received much attention despite strong biological evidence suggesting that intracellular spatial dependence is a crucial factor in the viral replication process. We are developing first spatio-temporal resolved models which mimic the behavior of the important components of virus replication within single liver cells. HCV replication is strongly associated to the intracellular Endoplasmatic Reticulum (ER) network. Here, we present the computational basis for the estimation of the diffusion constant of a central component of HCV genome (viral RNA) replication, namely the NS5a protein, on the surface of realistic reconstructed ER geometries. The basic surface partial differential equation (sPDE) evaluations are performed with UG4 using fast massively parallel multigrid solvers. The numerics of the simulations are studied in detail. Integrated concentrations within special subdomains correspond to experimental FRAP time series. In particular, we analyze the refinement stability in time and space for these integrated concentrations based on diffusion sPDEs upon large unstructured surface grids using heuristic values for the NS5a diffusion constant. This builds up a solid basis for future research not included in this presentation. e.g. the presented refinement stability analysis of the single sPDEs allows for parameter estimations for the NS5a diffusion constant. Our advanced Finite Volume/multigrid techniques also could be applied for studying life cycles of other viruses.
92-08 Computational methods for problems pertaining to biology
92C60 Medical epidemiology
65C05 Monte Carlo methods
Full Text: DOI
[1] Moradpour, D; Penin, F; Rice, CM, Replication of hepatitis c virus, Nat. Rev. Microbiol., 5, 453-463, (2007)
[2] Paul, D; Bartenschlager, R, Architecture and biogenesis of plus- strand RNA virus replication factories, World J. Virol, 2, 1-000, (2013)
[3] Guzman, M.G., Halstead, S.B., Artsob, H., Buchy, P., Farrar, J., Gubler, D.J., Hunsperger, E., Kroeger, A., Margolis, H.S., Martnez, E., Nathan, M.B., Pelegrino, J.L., Simmons, C., Yoksan, S., Peeling, R.W.: Dengue: a continuing global threat. Nat. Rev. Microbiol. S7 (2010)
[4] Welsch, S; Miller, S; Romero-Brey, I; Merz, A; Bleck, CK; Walther, P; Fuller, SD; Antony, C; Krijnse-Locker, J; Bartenschlager, R, Composition and three-dimensional architecture of the dengue virus replication and assembly sites, Cell Host Micr., 5, 365-375, (2009)
[5] Kohli, A; Shaffer, A; Sherman, A; Kottilil, S, Treatment of hepatitis C: a systematic review, JAMA, 312, 631-640, (2014)
[6] Binder, M; Sulaimanov, N; Clausznitzer, D; Schulze, M; Hüber, CM; Lenz, SM; Schlöder, JP; Trippler, M; Bartenschlager, R; Lohmann, V; Kaderali, L, Replication vesicles are load- and choke-points in the hepatitis C virus lifecycle, PLoS Path., 9, e1003561, (2013)
[7] Guedj, J; Rong, L; Dahari, H; Perelson, AS, A perspective on modelling hepatitis C virus infection, J. Virol Hepat., 17, 825-833, (2010)
[8] Dahari, H; Ribeiro, RM; Rice, CM; Perelson, AS, Mathematical modeling of subgenomic hepatitis C virus replication in huh-7 cells, J. Virol, 81, 750-760, (2007)
[9] Guedj, J; Rong, L; Dahari, H; Perelson, AS, A perspective on modeling hepatitis C virus infection, J. Virol Hepat., 17, 825-833, (2010)
[10] Guedj, J; Dahari, H; Rong, L; Sansone, N; Nettles, RE; Cotler, SJ; Layden, TJ; Uprichard, SL; Perelson, AS, Modeling shows that the NS5A inhibitor daclatasvir has two modes of action and yields a new estimate of the hepatitis C virus half-life, PNAS, 110, 3991-3996, (2013)
[11] Targett-Adams, P; Graham, EJ; Middleton, J; Palmer, A; Shaw, SM; Lavender, H; Brain, P; Tran, TD; Jones, LH; Wakenhut, F; Stammen, B; Pryde, D; Pickford, C; Westby, M, Small molecules targeting hepatitis C virus-encoded ns5a cause subcellular redistribution of their target: insights into compound modes of action, J. Virol, 85, 6353-6368, (2011)
[12] Chukkapalli, V; Berger, KL; Kelly, SM; Thomas, M; Deiters, A; Randall, G, Daclatasvir inhibits hepatitis C virus NS5A motility and hyper-accumulation of phosphoinositides, Virol, 476, 168-179, (2015)
[13] Wölk, B; Büchele, B; Moradpour, D; Rice, CM, A dynamic view of hepatitis C virus replication complexes, J Virol, 82, 10519-10531, (2008)
[14] Eyre, NS; Fiches, GN; Aloia, AL; Helbig, KJ; McCartney, EM; McErlean, CSP; Li, K; Aggarwal, A; Turville, SG; Bearda, MR, Dynamic imaging of the hepatitis C virus NS5A protein during a productive infection, J. Virol, 88, 3636-3652, (2014)
[15] Romero-Brey, I; Merz, A; Chiramel, A; Lee, JY; Chlanda, P; Haselman, U; Santarella-Mellwig, R; Habermann, A; Hoppe, S; Kallis, S; Walther, P; Antony, C; Krijnse-Locker, J; Bartenschlager, R, Three-dimensional architecture and biogenesis of membrane structures associated with hepatitis c virus replication, PLoS Path, 8, e1003056, (2012)
[16] Vega, S; Neira, JL; Marcuello, C; Lostao, A; Abian, O; Velazquez-Campoy, A, NS3 protease from hepatitis c virus: biophysical studies on an intrinsically disordered protein domain, Int. J. Mol. Sci., 14, 13282-13306, (2013)
[17] Dukhovny, A; Papadopulos, A; Hirschberg, K, Quantitative live-cell analysis of microtubule-uncoupled cargo-protein sorting in the ER, J. Cell Sci., 121, 865-876, (2008)
[18] Nevo-Yassaf, I; Yaffe, Y; Asher, M; Ravid, O; Eizenberg, S; Henis, YI; Nahmias, Y; Hirschberg, K; Sklan, EH, Role for TBC1D20 and rab1 in hepatitis C virus replication via interaction with lipid droplet-bound nonstructural protein 5A, J. Virol, 86, 6491, (2012)
[19] Appel, N; Zayas, M; Miller, S; Krijnse-Locker, J; Schaller, T; etal., Essential role of domain III of nonstructural protein 5A for hepatitis C virus infectious particle assembly, PLoS Path, 4, e1000035, (2010)
[20] Ishikawa-Ankerhold, HC; Ankerhold, R; Drummen, GPC, Advanced fluorescence microscopy techniques—frap, flip, flap, fret and flim, Molecules, 17, 4047-4132, (2012)
[21] Müller, F; Mazza, D; Stasevich, TJ; McNally, JG, Frap and kinetic modeling in the analysis of nuclear protein dynamics: what do we really know?, Curr Opin. Cell Biol., 22, 403-411, (2010)
[22] Broser, PJ; Schulte, R; Roth, A; Helmchen, F; Waters, J; Lang, S; Sakmann, B; Wittum, G, Nonlinear anisotropic diffusion filtering of three-dimensional image data from 2-photon microscopy, J. Biomed. Opt., 9, 1253-1264, (2004)
[23] Jungblut, D; Queisser, G; Wittum, G, Inertia based filtering of high resolution images using a gpu cluster, Comput. Vis. Sci., 14, 181-186, (2011)
[24] Heppner, I; Lampe, M; Nägel, A; Reiter, S; Rupp, M; Vogel, A; Wittum, G; Nagel, WE (ed.); Kröner, DH (ed.); Resch, MM (ed.), Software framework ug4: parallel multigrid on the Hermit supercomputer, (2013), Berlin
[25] Reiter, S; Vogel, A; Heppner, I; Rupp, M; Wittum, G, A massively parallel geometric multigrid solver on hierarchically distributed grids, Comput. Vis. Sci., 16, 151-164, (2013) · Zbl 1380.65463
[26] Vogel, A; Reiter, S; Rupp, M; Nägel, A; Wittum, G, UG 4: a novel flexible software system for simulating PDE based models on high performance computers, Comput. Vis. Sci., 16, 165-179, (2013) · Zbl 1375.35003
[27] Knodel, M.M., Nägel, A., Reiter, S., Rupp, M., Vogel, A., Targett-Adams, P., McLauchlan, J., Herrmann, E., Wittum, G.: Quantitative analysis of hepatitis C NS5A viral protein dynamics on the ER surface (submitted) (2015)
[28] Knodel, M.M., Nägel, A., Reiter, S., Rupp, M., Vogel, A., Targett-Adams, P., Herrmann, E., Wittum, G.: On estimation of a viral protein diffusion constant on the curved intracellular ER surface. In: Nagel, W.E., Kröner, D.H., Resch, M.M. (eds.) High Performance Computing in Science and Engineering’15: transactions of the high performance computing center, Stuttgart (HLRS), p. 641-657. Springer, Cham (2016)
[29] Knodel, M.M., Reiter, S., Rupp, M., Vogel, A., Targett-Adams, P., Herrmann, E., Wittum, G.: Mechanistic dynamics of hepatitis C virus replication in single liver cells: Simple full 3D (surface) PDE models (in preparation) (2016)
[30] Chatel-Chaix, L; Bartenschlager, R, Dengue virus and hepatitis C virus-induced replication and assembly compartments: the enemy inside—caught in the web, J. Virol, 88, 5907-5911, (2014)
[31] Quinkert, D; Bartenschlager, R; Lohmann, V, Quantitative analysis of the hepatitis C virus replication complex, J. Virol, 79, 13594-13605, (2005)
[32] Keum, SJ; Park, SM; Park, JH; Jung, JH; Shin, EJ; Jang, SK, The specific infectivity of hepatitis C virus changes through its life cycle, Virol, 433, 462-470, (2012)
[33] Jones, DM; Gretton, SN; McLauchlan, J; Targett-Adams, P, Mobility analysis of an NS5A-GFP fusion protein in cells actively replicating hepatitis C virus subgenomic RNA, J. Gen. Virol., 88, 470-475, (2007)
[34] Belda, O; Targett-Adams, P, Small molecule inhibitors of the hepatitis C virus-encoded NS5A protein, Virus Res., 170, 1-14, (2012)
[35] Targett-Adams, P; Boulant, S; McLauchlan, J, Visualization of double-stranded RNA in cells supporting hepatitis C virus RNA replication, J. Virol, 82, 2182-2195, (2008)
[36] Netherlands. Scientific Volume Imaging B.V., Hilversum. Huygens comute engine. Software (2014) http://www.svi.nl/HuygensSoftware
[37] Kano, H; Voort, HTM; Schrader, M; Kempen, GMP; Hell, SW, Avalanche photodiode detection with object scanning and image restoration provides 2-4 fold resolution increase in two-photon fluorescence microscopy, Bioimaging, 4, 87-197, (1996)
[38] van der Voort, H.T.M., Brakenhoff, G.J.: 3-d image formation in high-aperture fluorescence confocal microscopy: a numerical analysis. J. Microsc. 158(1), 43-54 (1990)
[39] Reiter, S.: Effiziente algorithmen und datenstrukturen für die realisierung von adaptiven, hierarchischen gittern auf massiv parallelen systemen. Ph.D. thesis. University of Frankfurt (2015)
[40] Sbalzarini, I.F., Mezzacasa, A., Helenius, A., Koumoutsakos, P.: Effects of organelle shape on fluorescence recovery after photobleaching. Biophys. J. 89, 1482-1492 (2005)
[41] Bank, RE; Rose, D, Some error estimates for the box method, SIAM J. Numer. Anal., 24, 777-787, (1987) · Zbl 0634.65105
[42] Means, S; Smith, AJ; Shepherd, J; Shadid, J; Fowler, J; Wojcikiewicz, RJH; Mazel, T; Smith, Gregory D; Wilson, BS, Reaction diffusion modeling of calcium dynamics with realistic er geometry, Biophys. J., 91, 537-557, (2006)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.