miao2

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000546) Biomodels notes: Parameter scan was done with varying values (1e-06 to 1)of beta_a. The green plot in figure 6A for Ep and Ep* (Eps in the model) that correspond to beta_a=1e-06 has been reproduced here. JWS Online curation: This model was curated by reproducing the figures as described in the BioModels Notes. No additional changes were made.

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Quantifying the early immune response and adaptive immune response kinetics in mice infected with influenza A virus.

  • Hongyu Miao
  • Joseph A Hollenbaugh
  • Martin S Zand
  • Jeanne Holden-Wiltse
  • Tim R Mosmann
  • Alan S Perelson
  • Hulin Wu
  • David J Topham
J. Virol. 2010; 84 (13): 6687-6698
Abstract
Seasonal and pandemic influenza A virus (IAV) continues to be a public health threat. However, we lack a detailed and quantitative understanding of the immune response kinetics to IAV infection and which biological parameters most strongly influence infection outcomes. To address these issues, we use modeling approaches combined with experimental data to quantitatively investigate the innate and adaptive immune responses to primary IAV infection. Mathematical models were developed to describe the dynamic interactions between target (epithelial) cells, influenza virus, cytotoxic T lymphocytes (CTLs), and virus-specific IgG and IgM. IAV and immune kinetic parameters were estimated by fitting models to a large data set obtained from primary H3N2 IAV infection of 340 mice. Prior to a detectable virus-specific immune response (before day 5), the estimated half-life of infected epithelial cells is approximately 1.2 days, and the half-life of free infectious IAV is approximately 4 h. During the adaptive immune response (after day 5), the average half-life of infected epithelial cells is approximately 0.5 days, and the average half-life of free infectious virus is approximately 1.8 min. During the adaptive phase, model fitting confirms that CD8(+) CTLs are crucial for limiting infected cells, while virus-specific IgM regulates free IAV levels. This may imply that CD4 T cells and class-switched IgG antibodies are more relevant for generating IAV-specific memory and preventing future infection via a more rapid secondary immune response. Also, simulation studies were performed to understand the relative contributions of biological parameters to IAV clearance. This study provides a basis to better understand and predict influenza virus immunity.

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^(2.0)
1.0 metre
1.0 second
1.0 mole
1.0 litre
Id Name Spatial dimensions Size
default 3.0 1.0 volume
Id Name Initial quantity Compartment Fixed
s1 Ep 580000.0 default
s2 Eps 0.0 default
s3 V 1473.0 default
s4 s4 0.0 <substance_units>/volume default
s5 s5 0.0 <substance_units>/volume default
s6 s6 0.0 <substance_units>/volume default
s7 s7 0.0 <substance_units>/volume default

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
s1 = 5.800000e+05
s2 = 0
s3 = 1.473000e+03
Id Name Objective coefficient Reaction Equation and Kinetic Law Flux bounds
re1 s1 > s2

beta_a * s1 * s3
re3 s4 > s1

rho_E * s1
re5 s2 > s5

delta_Es * s2
re6 s3 > s6

c_V * s3
re7 s7 > s3

pi_a * s2

Global parameters

Id Value
beta_a 2.4e-06 substance
c_V 4.2 substance
delta_Es 0.6 substance
pi_a 100.0 substance
rho_E 6.2e-08 substance

Local parameters

Id Value Reaction

Assignment rules

Definition

Rate rules

Definition

Algebraic rules

Definition
Trigger Assignments