Mathematical model of plant-virus interactions mediated by RNA interference.

Cross-protection, which refers to a process whereby artificially inoculating a plant with a mild strain provides protection against a more aggressive isolate of the virus, is known to be an effective tool of disease control in plants. In this paper we derive and analyse a new mathematical model of the interactions between two competing viruses with particular account for RNA interference. Our results show that co-infection of the host can either increase or decrease the potency of individual infections depending on the levels of cross-protection or cross-enhancement between different viruses. Analytical and numerical bifurcation analyses are employed to investigate the stability of all steady states of the model in order to identify parameter regions where the system exhibits synergistic or antagonistic behaviour between viral strains, as well as different types of host recovery. We show that not only viral attributes but also the propagating component of RNA-interference in plants can play an important role in determining the dynamics.

[1]  A. Perelson.  Modelling viral and immune system dynamics , 2002, Nature Reviews Immunology.

[2]  M. Heinen,et al.  Analytical growth equations and their Genstat 5 equivalents , 1999 .

[3]  R. May,et al.  The maintenance of strain structure in populations of recombining infectious agents , 1996, Nature Medicine.

[4]  T. Sasaba,et al.  An Experimental Validation of the Systems Model for the Prediction of Rice Dwarf Virus Infection , 1978 .

[5]  O. Mathieu,et al.  RNA-directed DNA methylation , 2004, Journal of Cell Science.

[6]  Ming-Bo Wang,et al.  Virus resistance and gene silencing: killing the messenger. , 1999, Trends in plant science.

[7]  N. Caplen,et al.  Gene Therapy Progress and Prospects. Downregulating gene expression: the impact of RNA interference , 2004, Gene Therapy.

[8]  P. Waterhouse,et al.  Gene Silencing in Arabidopsis Spreads from the Root to the Shoot, through a Gating Barrier, by Template-Dependent, Nonvascular, Cell-to-Cell Movement1[W][OA] , 2012, Plant Physiology.

[9]  A. Fereres,et al.  A Plant Virus Manipulates the Behavior of Its Whitefly Vector to Enhance Its Transmission Efficiency and Spread , 2013, PloS one.

[10]  M. Roossinck.  Symbiosis versus competition in plant virus evolution , 2005, Nature Reviews Microbiology.

[11]  R. M. Goodman.  Encyclopedia of Plant and Crop Science , 2004 .

[12]  Vitali Sintchenko,et al.  Infectious disease informatics , 2010 .

[13]  C. Himber,et al.  The tracking of intercellular small RNA movement. , 2015, Methods in molecular biology.

[14]  M. Mescher,et al.  Deceptive chemical signals induced by a plant virus attract insect vectors to inferior hosts , 2010, Proceedings of the National Academy of Sciences.

[15]  Caroline O. Buckee,et al.  A Network Approach to Understanding Pathogen Population Structure , 2010 .

[16]  P. A. Moore,et al.  The ecology of Aphis craccivora Koch and Subterranean Clover Stunt Virus in south-east Australia. II. A model of cowpea aphid populations in temperate pastures. , 1974 .

[17]  P. Roggero,et al.  A history of plant virology. Cross protection. , 2001, The new microbiologica.

[18]  G. Ruvkun,et al.  New insights into siRNA amplification and RNAi , 2012, RNA biology.

[19]  I. Maia,et al.  Viral Counter Defense X Antiviral Immunity in Plants: Mechanisms for Survival , 2013 .

[20]  Mario Recker,et al.  Immunological serotype interactions and their effect on the epidemiological pattern of dengue , 2009, Proceedings of the Royal Society B: Biological Sciences.

[21]  B. Ownley,et al.  Co-infection of Soybean with Soybean mosaic virus and Alfalfa mosaic virus Results in Disease Synergism and Alteration in Accumulation Level of Both Viruses. , 2009, Plant disease.

[22]  J. Carrington,et al.  Plant viral synergism: the potyviral genome encodes a broad-range pathogenicity enhancer that transactivates replication of heterologous viruses. , 1997, The Plant cell.

[23]  T. Sijen,et al.  Post‐transcriptional gene‐silencing: RNAs on the attack or on the defense? , 2000, BioEssays : news and reviews in molecular, cellular and developmental biology.

[24]  Katia Koelle,et al.  The effects of host contact network structure on pathogen diversity and strain structure. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[25]  F. van den Bosch,et al.  The dynamics of infectious diseases in orchards with roguing and replanting as control strategy , 1996 .

[26]  R. Beachy.  Coat-protein-mediated resistance to tobacco mosaic virus: discovery mechanisms and exploitation. , 1999, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[27]  C. W. Gear,et al.  Equation-free modelling of evolving diseases: coarse-grained computations with individual-based models , 2003, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[28]  J. Holt,et al.  Mathematical models of cross protection in the epidemiology of plant-virus diseases. , 2001, Phytopathology.

[29]  S. Hammond,et al.  RNA interference: a promising approach to antiviral therapy? , 2002, Trends in molecular medicine.

[30]  G. Loebenstein.  Natural resistance mechanisms of plants to viruses , 2005 .

[31]  Yan Zhou,et al.  Strategies for viral cross protection in plants. , 2012, Methods in molecular biology.

[32]  W. Dong,et al.  Molecular interaction between two cassava geminiviruses exhibiting cross-protection. , 2012, Virus research.

[33]  R. Anderson,et al.  Population structure of pathogens: the role of immune selection. , 1999, Parasitology today.

[34]  Wei Jiang,et al.  A Two-Scale Discretization Scheme for Mixed Variational Formulation of Eigenvalue Problems , 2012 .

[35]  Alan S. Perelson,et al.  Mathematical Analysis of HIV-1 Dynamics in Vivo , 1999, SIAM Rev..

[36]  S. Hammond,et al.  An RNA-directed nuclease mediates post-transcriptional gene silencing in Drosophila cells , 2000, Nature.

[37]  A. Caudy,et al.  Role for a bidentate ribonuclease in the initiation step of RNA interference , 2001 .

[38]  James Watmough,et al.  Further Notes on the Basic Reproduction Number , 2008 .

[39]  J. Dijkstra,et al.  A history of plant virology , 2006, Archives of Virology.

[40]  Michel Langlais,et al.  The dynamics of two viral infections in a single host population with applications to hantavirus. , 2003, Mathematical biosciences.

[41]  J. O. Irwin,et al.  MATHEMATICAL EPIDEMIOLOGY , 1958 .

[42]  J. Laliberté,et al.  Turnip mosaic virus Moves Systemically through Both Phloem and Xylem as Membrane-Associated Complexes1 , 2015, Plant Physiology.

[43]  W. Frommer,et al.  Transport mechanisms for organic forms of carbon and nitrogen between source and sink. , 2004, Annual review of plant biology.

[44]  M. Takeshita,et al.  Spatial analysis for exclusive interactions between subgroups I and II of Cucumber mosaic virus in cowpea. , 2004, Virology.

[45]  J. Shaw,et al.  A hypersensitive response-like mechanism is involved in resistance of potato plants bearing the Ry(sto) gene to the potyviruses potato virus Y and tobacco etch virus. , 1998, The Journal of general virology.

[46]  J. Holt,et al.  Mathematical models of host plant infection by helper-dependent virus complexes: why are helper viruses always avirulent? , 2000, Phytopathology.

[47]  K. Blyuss,et al.  Time-delayed model of immune response in plants. , 2015, Journal of theoretical biology.

[48]  A. Purcell,et al.  Insects as Vectors of Disease Agents , 2004 .

[49]  D. Baulcombe,et al.  Gene Silencing without DNA: RNA-Mediated Cross-Protection between Viruses , 1999, Plant Cell.

[50]  Bryan T Grenfell,et al.  Dynamics and selection of many-strain pathogens , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[51]  C. Hollier,et al.  Crop losses due to diseases and their implications for global food production losses and food security , 2012, Food Security.

[52]  Charles W. Melnyk,et al.  Intercellular and systemic movement of RNA silencing signals , 2011, The EMBO journal.

[53]  Zhenqing Li,et al.  Dynamical Analysis of Delayed Plant Disease Models with Continuous or Impulsive Cultural Control Strategies , 2012 .

[54]  Ulf Dieckmann,et al.  On State-Space Reduction in Multi-Strain Pathogen Models, with an Application to Antigenic Drift in Influenza A , 2007, PLoS Comput. Biol..

[55]  D. Bisaro,et al.  Viral Genome Methylation as an Epigenetic Defense against Geminiviruses , 2008, Journal of Virology.

[56]  K. Dietz.  The estimation of the basic reproduction number for infectious diseases , 1993, Statistical methods in medical research.

[57]  N. Ferguson,et al.  Ecological and immunological determinants of influenza evolution , 2003, Nature.

[58]  Daniel Zeng,et al.  Infectious Disease Informatics: Syndromic Surveillance for Public Health and BioDefense , 2009 .

[59]  S. Gupta,et al.  Antigenic diversity and the transmission dynamics of Plasmodium falciparum. , 1994, Science.

[60]  B. Dumas,et al.  Mechanism of the Hypersensitivity Reaction of Plants , 2007 .

[61]  Steven A. Frank,et al.  Immunology and Evolution of Infectious Disease , 2002 .

[62]  M. Yeager,et al.  Movement of rice yellow mottle virus between xylem cells through pit membranes. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[63]  Lindsay A. Turnbull,et al.  How to fit nonlinear plant growth models and calculate growth rates: an update for ecologists , 2012 .

[64]  L. Madden,et al.  A theoretical assessment of the effects of vector-virus transmission mechanism on plant virus disease epidemics. , 2000, Phytopathology.

[65]  Carlos Castillo-Chavez,et al.  Competitive Exclusion in Gonorrhea Models and Other Sexually Transmitted Diseases , 1996, SIAM J. Appl. Math..

[66]  Man-Suen Chan,et al.  An analytical model of plant virus disease dynamics with roguing and replanting. , 1994 .

[67]  L. Madden,et al.  Modelling virus- and host-limitation in vectored plant disease epidemics. , 2011, Virus research.

[68]  Graham F Medley,et al.  On the determinants of population structure in antigenically diverse pathogens , 2002, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[69]  H. Vaucheret,et al.  Post-transcriptional gene silencing in plants. , 2001, Journal of cell science.

[70]  S. Elena,et al.  A Viral Protein Mediates Superinfection Exclusion at the Whole-Organism Level but Is Not Required for Exclusion at the Cellular Level , 2014, Journal of Virology.

[71]  H. Soifer,et al.  MicroRNAs in disease and potential therapeutic applications. , 2007, Molecular therapy : the journal of the American Society of Gene Therapy.

[72]  W. G. Ruesink,et al.  Mitigating epidemics caused by non-persistently transmitted aphid-borne viruses: the role of the pliant environment. , 2000, Virus research.

[73]  P. A. Moore,et al.  [Dynamics of community structure in successional process of needle and broad-leaved mixed forest in Heishiding of Guangdong]. , 1974 .

[74]  J. Dushoff,et al.  Evolution and persistence of influenza A and other diseases. , 2004, Mathematical biosciences.

[75]  O. Voinnet,et al.  RNA silencing suppression by plant pathogens: defence, counter-defence and counter-counter-defence , 2013, Nature Reviews Microbiology.

[76]  C. Rice,et al.  Dual Mechanisms of Pestiviral Superinfection Exclusion at Entry and RNA Replication , 2005, Journal of Virology.

[77]  C. Wege,et al.  Synergism of a DNA and an RNA virus: enhanced tissue infiltration of the begomovirus Abutilon mosaic virus (AbMV) mediated by Cucumber mosaic virus (CMV). , 2007, Virology.

[78]  Klaus Dietz,et al.  The concept of RO in epidemic theory , 1996 .

[79]  Y. Kuang,et al.  Modeling the interaction of cytotoxic T lymphocytes and influenza virus infected epithelial cells. , 2010, Mathematical biosciences and engineering : MBE.

[80]  Simon A. Levin,et al.  The dynamics of cocirculating influenza strains conferring partial cross-immunity , 1997, Journal of mathematical biology.

[81]  Jan Barciszewski,et al.  Noncoding RNAs : molecular biology and molecular medicine , 2003 .

[82]  Stanca M. Ciupe,et al.  Modeling the mechanisms of acute hepatitis B virus infection. , 2007, Journal of theoretical biology.

[83]  R. Beachy,et al.  Studies of coat protein-mediated resistance to tobacco mosaic tobamovirus: correlation between assembly of mutant coat proteins and resistance , 1997, Journal of virology.

[84]  R. Beachy,et al.  Tobacco mosaic virus infection spreads cell to cell as intact replication complexes. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[85]  Dominik Wodarz,et al.  The importance of lytic and nonlytic immune responses in viral infections. , 2002, Trends in immunology.

[86]  Herbert W. Hethcote,et al.  The Mathematics of Infectious Diseases , 2000, SIAM Rev..

[87]  J. Burdon,et al.  The fitness costs to plants of resistance to pathogens , 2003, Genome Biology.

[88]  M. Kreitman,et al.  Fitness costs of R-gene-mediated resistance in Arabidopsis thaliana , 2003, Nature.

[89]  G. Wunderlich,et al.  Antigenic Diversity and Immune Evasion by Malaria Parasites , 2004, Clinical Diagnostic Laboratory Immunology.

[90]  Marc Lipsitch,et al.  Patterns of antigenic diversity and the mechanisms that maintain them , 2007, Journal of The Royal Society Interface.

[91]  M. Takeshita.  Molecular biological study of host specificity and cross-protection of Cucumber mosaic virus , 2005, Journal of General Plant Pathology.

[92]  B. D. Frazer.  PLANT VIRUS EPIDEMIOLOGY AND COMPUTER SIMULATION OF APHID POPULATIONS , 1977 .

[93]  M. Kuntz.  Is It Possible to Overcome the GMO Controversy? Some Elements for a Philosophical Perspective , 2021, Plant Biotechnology.

[94]  Mikhail M. Pooggin,et al.  Silencing and Innate Immunity in Plant Defense Against Viral and Non-Viral Pathogens , 2012, Viruses.