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BIOMD0000000463 - Heldt2012 - Influenza Virus Replication

 

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Reference Publication
Publication ID: 22593159
Heldt FS, Frensing T, Reichl U.
Modeling the intracellular dynamics of influenza virus replication to understand the control of viral RNA synthesis.
J. Virol. 2012 Aug; 86(15): 7806-7817
Bioprocess Engineering Group, Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany. heldt@mpi-magdeburg.mpg.de  [more]
Model
Original Model: BIOMD0000000463.origin
Submitter: Frank Stefan Heldt
Submission ID: MODEL1307270000
Submission Date: 27 Jul 2013 15:48:02 UTC
Last Modification Date: 08 Apr 2016 18:34:34 UTC
Creation Date: 07 Aug 2013 14:32:58 UTC
Encoders:  Nick Juty
   Vijayalakshmi Chelliah
   Frank Stefan Heldt
set #1
bqmodel:isDerivedFrom PubMed 9894006
set #2
bqbiol:hasTaxon Taxonomy Mammalia
Taxonomy Influenza A virus
set #3
bqbiol:isVersionOf Gene Ontology viral life cycle
Gene Ontology viral entry into host cell
Gene Ontology defense response, incompatible interaction
set #4
bqbiol:hasProperty Mathematical Modelling Ontology MAMO_0000046
set #5
bqbiol:hasProperty Human Disease Ontology influenza
Notes
Heldt2012 - Influenza Virus Replication

The model describes the life cycle of influenza A virus in a mammalian cell including the following steps: attachment of parental virions to the cell membrane, receptor-mediated endocytosis, fusion of the virus envelope with the endosomal membrane, nuclear import of vRNPs, viral transcription and replication, translation of the structural viral proteins, nuclear export of progeny vRNPs and budding of new virions. It also explicitly accounts for the stabilization of cRNA by viral polymerases and NP and the inhibition of vRNP activity by M1 protein binding. In short, the model focuses on the molecular mechanism that controls viral transcription and replication.

This model is described in the article:

Heldt FS, Frensing T, Reichl U.
J Virol.

Abstract:

Influenza viruses transcribe and replicate their negative-sense RNA genome inside the nucleus of host cells via three viral RNA species. In the course of an infection, these RNAs show distinct dynamics, suggesting that differential regulation takes place. To investigate this regulation in a systematic way, we developed a mathematical model of influenza virus infection at the level of a single mammalian cell. It accounts for key steps of the viral life cycle, from virus entry to progeny virion release, while focusing in particular on the molecular mechanisms that control viral transcription and replication. We therefore explicitly consider the nuclear export of viral genome copies (vRNPs) and a recent hypothesis proposing that replicative intermediates (cRNA) are stabilized by the viral polymerase complex and the nucleoprotein (NP). Together, both mechanisms allow the model to capture a variety of published data sets at an unprecedented level of detail. Our findings provide theoretical support for an early regulation of replication by cRNA stabilization. However, they also suggest that the matrix protein 1 (M1) controls viral RNA levels in the late phase of infection as part of its role during the nuclear export of viral genome copies. Moreover, simulations show an accumulation of viral proteins and RNA toward the end of infection, indicating that transport processes or budding limits virion release. Thus, our mathematical model provides an ideal platform for a systematic and quantitative evaluation of influenza virus replication and its complex regulation.

With the current parameter set, the model reproduces an infection at a multiplicity of infection (MOI) of 10. Figure 2A of the paper is reproduced here, with parameters kDegRnp and kSynP changed to zeros.

Initial conditions and parameter changes that were used to obtain specific figures in the article can be found in Table A2.

The model has the correct value for kAttLo as 4.55e-04. The value of this parameter mentioned as 4.55e-02 in Table 1 of the paper is incorrect. This is checked with the author.

To the extent possible under law, all copyright and related or neighbouring rights to this encoded model have been dedicated to the public domain worldwide. Please refer to CC0 Public Domain Dedication for more information.

Model
Publication ID: 22593159 Submission Date: 27 Jul 2013 15:48:02 UTC Last Modification Date: 08 Apr 2016 18:34:34 UTC Creation Date: 07 Aug 2013 14:32:58 UTC
Mathematical expressions
Reactions
Binding of virions to high-affinity sites Binding of virions to low-affinity sites Endocytosis of virions bound to high-affinity sites Endocytosis of virions bound to low-affinity sites
Fusion of virions with endosomes Degradation of virions in endosomes Nuclear import of vRNPs Synthesis of cRNA
Binding of polymerase to nascent cRNA Binding of NP to RdRp-cRNA complexes Binding of M1 to vRNPs in the nucleus Nuclear export of vRNPs
Synthesis of vRNA Binding of polymerase to nascent vRNA Binding of NP to RdRp-vRNA complexes Synthesis of mRNA of segment 1
Synthesis of mRNA of segment 2 Synthesis of mRNA of segment 3 Synthesis of mRNA of segment 4 Synthesis of mRNA of segment 5
Synthesis of mRNA of segment 6 Synthesis of mRNA of segment 7 Synthesis of mRNA of segment 8 Synthesis of PB1
Synthesis of PB2 Synthesis of PA Formation of polymerases Synthesis of NP
Synthesis of M1 Synthesis of NEP Synthesis of HA Synthesis of NA
Synthesis of M2 Virus release Degradation of vRNPs in the nucleus Degradation of nascent cRNA
Degradation of nascent vRNA Degradation of RdRp-cRNA Degradation of RdRp-vRNA Degradation of cRNPs
Degradation of M1-vRNP complexes in the nucleus Degradation of M1-vRNP complexes in the cytoplasm Degradation of mRNA of segment 1 Degradation of mRNA of segment 2
Degradation of mRNA of segment 3 Degradation of mRNA of segment 4 Degradation of mRNA of segment 5 Degradation of mRNA of segment 6
Degradation of mRNA of segment 7 Degradation of mRNA of segment 8    
Rules
Assignment Rule (variable: kSynP_Drib) Assignment Rule (variable: kDisHi) Assignment Rule (variable: kDisLo) Assignment Rule (variable: kDegVen)
Assignment Rule (variable: kSynM5) Assignment Rule (variable: kSynM6) Assignment Rule (variable: kSynP_M1) Assignment Rule (variable: kSynM8)
Assignment Rule (variable: kSynM2) Assignment Rule (variable: kSynM3) Assignment Rule (variable: kSynM1) Assignment Rule (variable: kSynM4)
Assignment Rule (variable: kSynP_M2) Assignment Rule (variable: kSynP_NEP) Assignment Rule (variable: kSynM7) Assignment Rule (variable: total vRNA)
Assignment Rule (variable: total cRNA) Assignment Rule (variable: total vRNA of a segment) Assignment Rule (variable: total cRNA of a segment)  
Physical entities
Compartments Species
cell Bhi VattHi Vex
Blo VattLo Ven
Vfus VpCyt VpNuc
Rc P_Rdrp RcRdrp
P_Np P_M1 VpNucM1
VpCytM1 Cp Rv
RvRdrp Rm1 Rm2
Rm3 Rm4 Rm5
Rm6 Rm7 Rm8
P_Pb1 P_Pb2 P_Pa
P_Nep P_Ha P_Na
P_M2 Vrel total cRNA
total cRNA of a segment total vRNA total vRNA of a segment
Global parameters
kAttHi kAttLo kDisHi kDisLo
kEn kFus kDegVen kImp
kSynP kSynV kSynC kBindRdrp
kBindNp kBindM1 kExp kSynP_Drib
kRdrp kRel kDegR kDegRnp
kDegM kDegRrdrp Ffus Drib
Fspl7 Fspl8 kSynP_M1 kSynP_M2
kSynP_NEP L1 L2 L3
L4 L5 L6 L7
L8 kSynM kSynM1 kSynM2
kSynM3 kSynM4 kSynM5 kSynM6
kSynM7 kSynM8 kEqHi kEqLo
Reactions (50)
 
 Binding of virions to high-affinity sites [Vex] + [Bhi] ↔ [VattHi];   {Vex} , {Bhi} , {VattHi}
 
 Binding of virions to low-affinity sites [Vex] + [Blo] ↔ [VattLo];   {Vex} , {Blo} , {VattLo}
 
 Endocytosis of virions bound to high-affinity sites [VattHi] → [Ven] + [Bhi];   {VattHi}
 
 Endocytosis of virions bound to low-affinity sites [VattLo] → [Ven] + [Blo];   {VattLo}
 
 Fusion of virions with endosomes [Ven] → [Vfus] + 8.0 × [VpCyt];   {Ven}
 
 Degradation of virions in endosomes [Ven] → ;   {Ven}
 
 Nuclear import of vRNPs [VpCyt] → [VpNuc];   {VpCyt}
 
 Synthesis of cRNA [VpNuc] → [VpNuc] + [Rc];   {VpNuc}
 
 Binding of polymerase to nascent cRNA [Rc] + [P_Rdrp] → [RcRdrp];   {Rc} , {P_Rdrp}
 
 Binding of NP to RdRp-cRNA complexes [RcRdrp] + 71.0 × [P_Np] → [Cp];   {RcRdrp} , {P_Np}
 
 Binding of M1 to vRNPs in the nucleus [VpNuc] + 8.5 × [P_M1] → [VpNucM1];   {VpNuc} , {P_M1}
 
 Nuclear export of vRNPs [VpNucM1] + [P_Nep] → [VpCytM1];   {VpNucM1} , {P_Nep}
 
 Synthesis of vRNA [Cp] → [Cp] + [Rv];   {Cp}
 
 Binding of polymerase to nascent vRNA [Rv] + [P_Rdrp] → [RvRdrp];   {Rv} , {P_Rdrp}
 
 Binding of NP to RdRp-vRNA complexes [RvRdrp] + 71.0 × [P_Np] → [VpNuc];   {RvRdrp} , {P_Np}
 
 Synthesis of mRNA of segment 1 [VpNuc] → [VpNuc] + [Rm1];   {VpNuc}
 
 Synthesis of mRNA of segment 2 [VpNuc] → [VpNuc] + [Rm2];   {VpNuc}
 
 Synthesis of mRNA of segment 3 [VpNuc] → [VpNuc] + [Rm3];   {VpNuc}
 
 Synthesis of mRNA of segment 4 [VpNuc] → [VpNuc] + [Rm4];   {VpNuc}
 
 Synthesis of mRNA of segment 5 [VpNuc] → [VpNuc] + [Rm5];   {VpNuc}
 
 Synthesis of mRNA of segment 6 [VpNuc] → [VpNuc] + [Rm6];   {VpNuc}
 
 Synthesis of mRNA of segment 7 [VpNuc] → [VpNuc] + [Rm7];   {VpNuc}
 
 Synthesis of mRNA of segment 8 [VpNuc] → [VpNuc] + [Rm8];   {VpNuc}
 
 Synthesis of PB1 [Rm2] → [Rm2] + [P_Pb1];   {Rm2}
 
 Synthesis of PB2 [Rm1] → [Rm1] + [P_Pb2];   {Rm1}
 
 Synthesis of PA [Rm3] → [Rm3] + [P_Pa];   {Rm3}
 
 Formation of polymerases [P_Pb1] + [P_Pb2] + [P_Pa] → [P_Rdrp];   {P_Pb1} , {P_Pb2} , {P_Pa}
 
 Synthesis of NP [Rm5] → [Rm5] + [P_Np];   {Rm5}
 
 Synthesis of M1 [Rm7] → [Rm7] + [P_M1];   {Rm7}
 
 Synthesis of NEP [Rm8] → [Rm8] + [P_Nep];   {Rm8}
 
 Synthesis of HA [Rm4] → [Rm4] + [P_Ha];   {Rm4}
 
 Synthesis of NA [Rm6] → [Rm6] + [P_Na];   {Rm6}
 
 Synthesis of M2 [Rm7] → [Rm7] + [P_M2];   {Rm7}
 
 Virus release 8.0 × [VpCytM1] + 37.0 × [P_Rdrp] + 433.0 × [P_Np] + 2932.0 × [P_M1] + 157.0 × [P_Nep] + 500.0 × [P_Ha] + 100.0 × [P_Na] + 40.0 × [P_M2] → [Vrel];   {VpCytM1} , {P_Rdrp} , {P_Ha} , {P_Np} , {P_Na} , {P_M1} , {P_M2} , {P_Nep}
 
 Degradation of vRNPs in the nucleus [VpNuc] → ;   {VpNuc}
 
 Degradation of nascent cRNA [Rc] → ;   {Rc}
 
 Degradation of nascent vRNA [Rv] → ;   {Rv}
 
 Degradation of RdRp-cRNA [RcRdrp] → ;   {RcRdrp}
 
 Degradation of RdRp-vRNA [RvRdrp] → ;   {RvRdrp}
 
 Degradation of cRNPs [Cp] → ;   {Cp}
 
 Degradation of M1-vRNP complexes in the nucleus [VpNucM1] → ;   {VpNucM1}
 
 Degradation of M1-vRNP complexes in the cytoplasm [VpCytM1] → ;   {VpCytM1}
 
 Degradation of mRNA of segment 1 [Rm1] → ;   {Rm1}
 
 Degradation of mRNA of segment 2 [Rm2] → ;   {Rm2}
 
 Degradation of mRNA of segment 3 [Rm3] → ;   {Rm3}
 
 Degradation of mRNA of segment 4 [Rm4] → ;   {Rm4}
 
 Degradation of mRNA of segment 5 [Rm5] → ;   {Rm5}
 
 Degradation of mRNA of segment 6 [Rm6] → ;   {Rm6}
 
 Degradation of mRNA of segment 7 [Rm7] → ;   {Rm7}
 
 Degradation of mRNA of segment 8 [Rm8] → ;   {Rm8}
 
Rules (19)
 
 Assignment Rule (name: parameter_16) kSynP_Drib = parameter_9/parameter_24
 
 Assignment Rule (name: parameter_3) kDisHi = parameter_1/parameter_47
 
 Assignment Rule (name: parameter_4) kDisLo = parameter_2/parameter_48
 
 Assignment Rule (name: parameter_7) kDegVen = (1-parameter_23)/parameter_23*parameter_6
 
 Assignment Rule (name: parameter_43) kSynM5 = parameter_38/parameter_34/8
 
 Assignment Rule (name: parameter_44) kSynM6 = parameter_38/parameter_35/8
 
 Assignment Rule (name: parameter_27) kSynP_M1 = parameter_9/parameter_24*(1-parameter_25)
 
 Assignment Rule (name: parameter_46) kSynM8 = parameter_38/parameter_37/8
 
 Assignment Rule (name: parameter_40) kSynM2 = parameter_38/parameter_31/8
 
 Assignment Rule (name: parameter_41) kSynM3 = parameter_38/parameter_32/8
 
 Assignment Rule (name: parameter_39) kSynM1 = parameter_38/parameter_30/8
 
 Assignment Rule (name: parameter_42) kSynM4 = parameter_38/parameter_33/8
 
 Assignment Rule (name: parameter_28) kSynP_M2 = parameter_9/parameter_24*parameter_25
 
 Assignment Rule (name: parameter_29) kSynP_NEP = parameter_9/parameter_24*parameter_26
 
 Assignment Rule (name: parameter_45) kSynM7 = parameter_38/parameter_36/8
 
 Assignment Rule (name: species_38) total vRNA = 8*(species_2+species_5+species_6)+species_8+species_9+species_18+species_19+species_15+species_16
 
 Assignment Rule (name: species_36) total cRNA = species_10+species_12+species_17
 
 Assignment Rule (name: species_39) total vRNA of a segment = species_38/8
 
 Assignment Rule (name: species_37) total cRNA of a segment = species_36/8
 
Functions (2)
 
 Virus release kinetic lambda(k, substrateA, substrateB, KmB, substrateC, KmC, substrateD, KmD, substrateE, KmE, substrateF, KmF, substrateG, KmG, substrateH, KmH, k*substrateA*substrateB*substrateC*substrateD*substrateE*substrateF*substrateG*substrateH/((substrateB+KmB)*(substrateC+KmC)*(substrateD+KmD)*(substrateE+KmE)*(substrateF+KmF)*(substrateG+KmG)*(substrateH+KmH)))
 
 Protein binding lambda(k, substratea, substrateb, k*substratea*substrateb)
 
 cell Spatial dimensions: 3.0  Compartment size: 1.0  (Units: litre)
 
 Bhi
Compartment: cell
Initial concentration: 150.0  (Units: mole)
 
 VattHi
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
 Vex
Compartment: cell
Initial concentration: 10.0  (Units: mole)
 
 Blo
Compartment: cell
Initial concentration: 1000.0  (Units: mole)
 
 VattLo
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
 Ven
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
 Vfus
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
 VpCyt
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
 VpNuc
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
 Rc
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
 P_Rdrp
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
 RcRdrp
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
 P_Np
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
 P_M1
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
 VpNucM1
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
 VpCytM1
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
 Cp
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
 Rv
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
 RvRdrp
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
 Rm1
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
 Rm2
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
 Rm3
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
 Rm4
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
 Rm5
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
 Rm6
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
 Rm7
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
 Rm8
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
 P_Pb1
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
 P_Pb2
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
 P_Pa
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
 P_Nep
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
 P_Ha
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
 P_Na
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
 P_M2
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
 Vrel
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
  total cRNA
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
  total cRNA of a segment
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
  total vRNA
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
  total vRNA of a segment
Compartment: cell
Initial concentration: 0.0  (Units: mole)
 
Global Parameters (48)
 
 kAttHi
Value: 0.0809
Constant
 
 kAttLo
Value: 4.55E-4
Constant
 
  kDisHi
Value: 7.15929203539823
 
  kDisLo
Value: 5.46218487394958
 
 kEn
Value: 4.8
Constant
 
 kFus
Value: 3.21
Constant
 
  kDegVen
Value: 3.08411764705882
 
 kImp
Value: 6.0
Constant
 
 kSynP
Value: 64800.0
Constant
 
 kSynV
Value: 13.86
Constant
 
 kSynC
Value: 1.38
Constant
 
 kBindRdrp
Value: 1.0
Constant
 
 kBindNp
Value: 3.01E-4
Constant
 
 kBindM1
Value: 1.39E-6
Constant
 
 kExp
Value: 1.0E-6
Constant
 
  kSynP_Drib
Value: 405.0
 
 kRdrp
Value: 1.0
Constant
 
 kRel
Value: 0.0037
Constant
 
 kDegR
Value: 36.36
Constant
 
 kDegRnp
Value: 0.09
Constant
 
 kDegM
Value: 0.33
Constant
 
 kDegRrdrp
Value: 4.25
Constant
 
 Ffus
Value: 0.51
Constant
 
 Drib
Value: 160.0
Constant
 
 Fspl7
Value: 0.02
Constant
 
 Fspl8
Value: 0.125
Constant
 
  kSynP_M1
Value: 396.9
 
  kSynP_M2
Value: 8.1
 
  kSynP_NEP
Value: 50.625
 
 L1
Value: 2320.0
Constant
 
 L2
Value: 2320.0
Constant
 
 L3
Value: 2211.0
Constant
 
 L4
Value: 1757.0
Constant
 
 L5
Value: 1540.0
Constant
 
 L6
Value: 1392.0
Constant
 
 L7
Value: 1005.0
Constant
 
 L8
Value: 868.0
Constant
 
 kSynM
Value: 250000.0
Constant
 
  kSynM1
Value: 13.4698275862069
 
  kSynM2
Value: 13.4698275862069
 
  kSynM3
Value: 14.1338760741746
 
  kSynM4
Value: 17.7859988616961
 
  kSynM5
Value: 20.2922077922078
 
  kSynM6
Value: 22.4497126436782
 
  kSynM7
Value: 31.0945273631841
 
  kSynM8
Value: 36.0023041474654
 
 kEqHi
Value: 0.0113
Constant
 
 kEqLo
Value: 8.33E-5
Constant
 
Virus release (7)
 
   KmB
Value: 450.0
Constant
 
   KmC
Value: 5000.0
Constant
 
   KmD
Value: 10000.0
Constant
 
   KmE
Value: 1000.0
Constant
 
   KmF
Value: 30000.0
Constant
 
   KmG
Value: 400.0
Constant
 
   KmH
Value: 1650.0
Constant
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000463

Curator's comment: (updated: 07 Aug 2013 14:32:08 GMT)

Figure 2B of the reference publication is reproduced here. To obtain the figure, set kDegRnp and kSynP to zero. Note that, the model has time units in hrs and in the plot it is 120 mins. So, the model simulation has to be run for 2 hrs (=120mins).
The model was simulated using Copasi v4.10 (Build 55) and the plots were obtained using Gnuplot.

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