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heldt1

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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.

Unit definitions have no effect on the numerical analysis of the model. It remains the responsibility of the modeler to ensure the internal numerical consistency of the model. If units are provided, however, the consistency of the model units will be checked.

Name Definition
1.0 metre
1.0 metre^(2.0)
1.0 dimensionless
3600.0 second
1.0 dimensionless
1.0 litre
1.0 mole
Id Name Spatial dimensions Size
compartment_1 cell 3.0 1.0 litre
Id Name Initial quantity Compartment Fixed
species_1 Bhi 150.0 mole/litre compartment_1 (cell)
species_10 Rc 0.0 mole/litre compartment_1 (cell)
species_11 P_Rdrp 0.0 mole/litre compartment_1 (cell)
species_12 RcRdrp 0.0 mole/litre compartment_1 (cell)
species_13 P_Np 0.0 mole/litre compartment_1 (cell)
species_14 P_M1 0.0 mole/litre compartment_1 (cell)
species_15 VpNucM1 0.0 mole/litre compartment_1 (cell)
species_16 VpCytM1 0.0 mole/litre compartment_1 (cell)
species_17 Cp 0.0 mole/litre compartment_1 (cell)
species_18 Rv 0.0 mole/litre compartment_1 (cell)
species_19 RvRdrp 0.0 mole/litre compartment_1 (cell)
species_2 VattHi 0.0 mole/litre compartment_1 (cell)
species_20 Rm1 0.0 mole/litre compartment_1 (cell)
species_21 Rm2 0.0 mole/litre compartment_1 (cell)
species_22 Rm3 0.0 mole/litre compartment_1 (cell)
species_23 Rm4 0.0 mole/litre compartment_1 (cell)
species_24 Rm5 0.0 mole/litre compartment_1 (cell)
species_25 Rm6 0.0 mole/litre compartment_1 (cell)
species_26 Rm7 0.0 mole/litre compartment_1 (cell)
species_27 Rm8 0.0 mole/litre compartment_1 (cell)
species_28 P_Pb1 0.0 mole/litre compartment_1 (cell)
species_29 P_Pb2 0.0 mole/litre compartment_1 (cell)
species_3 Vex 10.0 mole/litre compartment_1 (cell)
species_30 P_Pa 0.0 mole/litre compartment_1 (cell)
species_31 P_Nep 0.0 mole/litre compartment_1 (cell)
species_32 P_Ha 0.0 mole/litre compartment_1 (cell)
species_33 P_Na 0.0 mole/litre compartment_1 (cell)
species_34 P_M2 0.0 mole/litre compartment_1 (cell)
species_35 Vrel 0.0 mole/litre compartment_1 (cell)
species_36 total cRNA <assignment rule> mole/litre compartment_1 (cell)
species_37 total cRNA of a segment <assignment rule> mole/litre compartment_1 (cell)
species_38 total vRNA <assignment rule> mole/litre compartment_1 (cell)
species_39 total vRNA of a segment <assignment rule> mole/litre compartment_1 (cell)
species_4 Blo 1000.0 mole/litre compartment_1 (cell)
species_5 VattLo 0.0 mole/litre compartment_1 (cell)
species_6 Ven 0.0 mole/litre compartment_1 (cell)
species_7 Vfus 0.0 mole/litre compartment_1 (cell)
species_8 VpCyt 0.0 mole/litre compartment_1 (cell)
species_9 VpNuc 0.0 mole/litre compartment_1 (cell)

Initial assignments are expressions that are evaluated at time=0. It is not recommended to create initial assignments for all model entities. Restrict the use of initial assignments to cases where a value is expressed in terms of values or sizes of other model entities. Note that it is not permitted to have both an initial assignment and an assignment rule for a single model entity.

Definition
Id Name Objective coefficient Reaction Equation and Kinetic Law Flux bounds
reaction_1 Binding of virions to high-affinity sites species_3 + species_1 = species_2

compartment_1 * (parameter_1 * species_3 * species_1 - parameter_3 * species_2)
reaction_10 Binding of NP to RdRp-cRNA complexes species_12 + {71.0}species_13 > species_17

compartment_1 * function_1(parameter_13, species_12, species_13)
reaction_11 Binding of M1 to vRNPs in the nucleus species_9 + {8.5}species_14 > species_15

compartment_1 * function_1(parameter_14, species_9, species_14)
reaction_12 Nuclear export of vRNPs species_15 + species_31 > species_16

compartment_1 * parameter_15 * species_15 * species_31
reaction_13 Synthesis of vRNA species_17 > species_17 + species_18

compartment_1 * parameter_10 * species_17
reaction_14 Binding of polymerase to nascent vRNA species_18 + species_11 > species_19

compartment_1 * parameter_12 * species_18 * species_11
reaction_15 Binding of NP to RdRp-vRNA complexes species_19 + {71.0}species_13 > species_9

compartment_1 * function_1(parameter_13, species_19, species_13)
reaction_16 Synthesis of mRNA of segment 1 species_9 > species_9 + species_20

compartment_1 * parameter_39 * species_9
reaction_17 Synthesis of mRNA of segment 2 species_9 > species_9 + species_21

compartment_1 * parameter_40 * species_9
reaction_18 Synthesis of mRNA of segment 3 species_9 > species_9 + species_22

compartment_1 * parameter_41 * species_9
reaction_19 Synthesis of mRNA of segment 4 species_9 > species_9 + species_23

compartment_1 * parameter_42 * species_9
reaction_2 Binding of virions to low-affinity sites species_3 + species_4 = species_5

compartment_1 * (parameter_2 * species_3 * species_4 - parameter_4 * species_5)
reaction_20 Synthesis of mRNA of segment 5 species_9 > species_9 + species_24

compartment_1 * parameter_43 * species_9
reaction_21 Synthesis of mRNA of segment 6 species_9 > species_9 + species_25

compartment_1 * parameter_44 * species_9
reaction_22 Synthesis of mRNA of segment 7 species_9 > species_9 + species_26

compartment_1 * parameter_45 * species_9
reaction_23 Synthesis of mRNA of segment 8 species_9 > species_9 + species_27

compartment_1 * parameter_46 * species_9
reaction_24 Synthesis of PB1 species_21 > species_21 + species_28

compartment_1 * parameter_16 * species_21
reaction_25 Synthesis of PB2 species_20 > species_20 + species_29

compartment_1 * parameter_16 * species_20
reaction_26 Synthesis of PA species_22 > species_22 + species_30

compartment_1 * parameter_16 * species_22
reaction_27 Formation of polymerases species_28 + species_29 + species_30 > species_11

compartment_1 * parameter_17 * species_28 * species_29 * species_30
reaction_28 Synthesis of NP species_24 > species_24 + species_13

compartment_1 * parameter_16 * species_24
reaction_29 Synthesis of M1 species_26 > species_26 + species_14

compartment_1 * parameter_27 * species_26
reaction_3 Endocytosis of virions bound to high-affinity sites species_2 > species_6 + species_1

compartment_1 * parameter_5 * species_2
reaction_30 Synthesis of NEP species_27 > species_27 + species_31

compartment_1 * parameter_29 * species_27
reaction_31 Synthesis of HA species_23 > species_23 + species_32

compartment_1 * parameter_16 * species_23
reaction_32 Synthesis of NA species_25 > species_25 + species_33

compartment_1 * parameter_16 * species_25
reaction_33 Synthesis of M2 species_26 > species_26 + species_34

compartment_1 * parameter_28 * species_26
reaction_34 Virus release {8.0}species_16 + {37.0}species_11 + {433.0}species_13 + {2932.0}species_14 + {157.0}species_31 + {500.0}species_32 + {100.0}species_33 + {40.0}species_34 > species_35

compartment_1 * function_2(parameter_18, species_16, species_11, KmB, species_32, KmC, species_13, KmD, species_33, KmE, species_14, KmF, species_34, KmG, species_31, KmH)
reaction_35 Degradation of vRNPs in the nucleus species_9 > ∅

compartment_1 * parameter_20 * species_9
reaction_36 Degradation of nascent cRNA species_10 > ∅

compartment_1 * parameter_19 * species_10
reaction_37 Degradation of nascent vRNA species_18 > ∅

compartment_1 * parameter_19 * species_18
reaction_38 Degradation of RdRp-cRNA species_12 > ∅

compartment_1 * parameter_22 * species_12
reaction_39 Degradation of RdRp-vRNA species_19 > ∅

compartment_1 * parameter_22 * species_19
reaction_4 Endocytosis of virions bound to low-affinity sites species_5 > species_6 + species_4

compartment_1 * parameter_5 * species_5
reaction_40 Degradation of cRNPs species_17 > ∅

compartment_1 * parameter_20 * species_17
reaction_41 Degradation of M1-vRNP complexes in the nucleus species_15 > ∅

compartment_1 * parameter_20 * species_15
reaction_42 Degradation of M1-vRNP complexes in the cytoplasm species_16 > ∅

compartment_1 * parameter_20 * species_16
reaction_43 Degradation of mRNA of segment 1 species_20 > ∅

compartment_1 * parameter_21 * species_20
reaction_44 Degradation of mRNA of segment 2 species_21 > ∅

compartment_1 * parameter_21 * species_21
reaction_45 Degradation of mRNA of segment 3 species_22 > ∅

compartment_1 * parameter_21 * species_22
reaction_46 Degradation of mRNA of segment 4 species_23 > ∅

compartment_1 * parameter_21 * species_23
reaction_47 Degradation of mRNA of segment 5 species_24 > ∅

compartment_1 * parameter_21 * species_24
reaction_48 Degradation of mRNA of segment 6 species_25 > ∅

compartment_1 * parameter_21 * species_25
reaction_49 Degradation of mRNA of segment 7 species_26 > ∅

compartment_1 * parameter_21 * species_26
reaction_5 Fusion of virions with endosomes species_6 > species_7 + {8.0}species_8

compartment_1 * parameter_6 * species_6
reaction_50 Degradation of mRNA of segment 8 species_27 > ∅

compartment_1 * parameter_21 * species_27
reaction_6 Degradation of virions in endosomes species_6 > ∅

compartment_1 * parameter_7 * species_6
reaction_7 Nuclear import of vRNPs species_8 > species_9

compartment_1 * parameter_8 * species_8
reaction_8 Synthesis of cRNA species_9 > species_9 + species_10

compartment_1 * parameter_11 * species_9
reaction_9 Binding of polymerase to nascent cRNA species_10 + species_11 > species_12

compartment_1 * parameter_12 * species_10 * species_11

Global parameters

Id Value
parameter_1 0.0809
parameter_10 13.86
parameter_11 1.38
parameter_12 1.0
parameter_13 0.000301
parameter_14 0.00000139
parameter_15 0.000001
parameter_16 405.0
parameter_17 1.0
parameter_18 0.0037
parameter_19 36.36
parameter_2 0.000455
parameter_20 0.09
parameter_21 0.33
parameter_22 4.25
parameter_23 0.51
parameter_24 160.0
parameter_25 0.02
parameter_26 0.125
parameter_27 396.9
parameter_28 8.1
parameter_29 50.625
parameter_3 7.15929203539823
parameter_30 2320.0
parameter_31 2320.0
parameter_32 2211.0
parameter_33 1757.0
parameter_34 1540.0
parameter_35 1392.0
parameter_36 1005.0
parameter_37 868.0
parameter_38 250000.0
parameter_39 13.4698275862069
parameter_4 5.46218487394958
parameter_40 13.4698275862069
parameter_41 14.1338760741746
parameter_42 17.7859988616961
parameter_43 20.2922077922078
parameter_44 22.4497126436782
parameter_45 31.0945273631841
parameter_46 36.0023041474654
parameter_47 0.0113
parameter_48 0.0000833
parameter_5 4.8
parameter_6 3.21
parameter_7 3.08411764705882
parameter_8 6.0
parameter_9 64800.0

Local parameters

Id Value Reaction
KmB 450.0 reaction_34 (Virus release)
KmC 5000.0 reaction_34 (Virus release)
KmD 10000.0 reaction_34 (Virus release)
KmE 1000.0 reaction_34 (Virus release)
KmF 30000.0 reaction_34 (Virus release)
KmG 400.0 reaction_34 (Virus release)
KmH 1650.0 reaction_34 (Virus release)

Assignment rules

Definition
parameter_7 = (1.0 - parameter_23) / parameter_23 * parameter_6
parameter_4 = parameter_2 / parameter_48
parameter_3 = parameter_1 / parameter_47
parameter_16 = parameter_9 / parameter_24
species_37 = species_36 / 8.0
species_39 = species_38 / 8.0
species_36 = species_10 + species_12 + species_17
species_38 = 8.0 * (species_2 + species_5 + species_6) + species_8 + species_9 + species_18 + species_19 + species_15 + species_16
parameter_45 = parameter_38 / parameter_36 / 8.0
parameter_29 = parameter_9 / parameter_24 * parameter_26
parameter_28 = parameter_9 / parameter_24 * parameter_25
parameter_42 = parameter_38 / parameter_33 / 8.0
parameter_39 = parameter_38 / parameter_30 / 8.0
parameter_41 = parameter_38 / parameter_32 / 8.0
parameter_40 = parameter_38 / parameter_31 / 8.0
parameter_46 = parameter_38 / parameter_37 / 8.0
parameter_27 = parameter_9 / parameter_24 * (1.0 - parameter_25)
parameter_44 = parameter_38 / parameter_35 / 8.0
parameter_43 = parameter_38 / parameter_34 / 8.0

Rate rules

Definition

Algebraic rules

Definition
Definition
function_2(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))
function_1(k, substratea, substrateb) = k * substratea * substrateb
Trigger Assignments