abudukelimu1

The model reproduces Figure 1 of the paper.

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Title

Complex Stability and an Irreversible Transition Reverted by Peptide and Fibroblasts in a Dynamic Model of Innate Immunity.

Authors

Abulikemu Abudukelimu (1,2), Matteo Barberis (1,3), Frank Redegeld (4), Nilgun Sahin (2) and Hans V. Westerhoff (1,2,5)

Affiliations

1) Synthetic Systems Biology and Nuclear Organization, Swammerdam Institute for Life Sciences, University of Amsterdam, Amsterdam, Netherlands, 2) Molecular Cell Physiology, VU University Amsterdam, Amsterdam, Netherlands, 3) Faculty of Health and Medical Sciences, Systems Biology, School of Biosciences and Medicine, University of Surrey, Guildford, United Kingdom, 4) Division of Pharmacology, Department of Pharmaceutical Sciences, Faculty of Science, Utrecht University, Utrecht, Netherlands, 5) School for Chemical Engineering and Analytical Science, University of Manchester, Manchester, United Kingdom

Abstract

We here apply a control analysis and various types of stability analyses to an in silico model of innate immunity that addresses the management of inflammation by a therapeutic peptide. Motivation is the observation, both in silico and in experiments, that this therapy is not robust. Our modeling results demonstrate how (1) the biological phenomena of acute and chronic modes of inflammation may reflect an inherently complex bistability with an irreversible flip between the two modes, (2) the chronic mode of the model has stable, sometimes unique, steady states, while its acute-mode steady states are stable but not unique, (3) as witnessed by TNF levels, acute inflammation is controlled by multiple processes, whereas its chronic-mode inflammation is only controlled by TNF synthesis and washout, (4) only when the antigen load is close to the acute mode’s flipping point, many processes impact very strongly on cells and cytokines, (5) there is no antigen exposure level below which reduction of the antigen load alone initiates a flip back to the acute mode, and (6) adding healthy fibroblasts makes the transition from acute to chronic inflammation reversible, although (7) there is a window of antigen load where such a therapy cannot be effective. This suggests that triple therapies may be essential to overcome chronic inflammation. These may comprise (1) anti-immunoglobulin light chain peptides, (2) a temporarily reduced antigen load, and (3a) fibroblast repopulation or (3b) stem cell strategies.

Journal

Frontiers in Immunology (doi: 10.3389/fimmu.2019.03091)

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
60.0 second
1e-15 mole
Id Name Spatial dimensions Size
compartment compartment 3.0 1.0
Id Name Initial quantity Compartment Fixed
Bcells Bcells 1.0 compartment (compartment)
CRA CRA 0.00999412 compartment (compartment)
DyingBacteria DyingBacteria 0.0 compartment (compartment)
DyingFibr DyingFibr 0.0 compartment (compartment)
FLC FLC 0.000999412 compartment (compartment)
FLC_drug FLC_drug 0.0 compartment (compartment)
HealthyBacteria HealthyBacteria 0.000001 compartment (compartment)
HealthyFibr HealthyFibr 999.509 compartment (compartment)
MMP7 MMP7 99951.0 compartment (compartment)
MMP8 MMP8 999509.0 compartment (compartment)
MastCells MastCells 0.0998992 compartment (compartment)
MastCells_FLC MastCells_FLC 0.0000998404 compartment (compartment)
MastCells_FLC_CRA MastCells_FLC_CRA 0.000000997816000000001 compartment (compartment)
Protease Protease 1.0 compartment (compartment)
TNFalpha TNFalpha 4.75162 compartment (compartment)
Total_space Total space 1000.0 compartment (compartment)
drug drug 0.0 compartment (compartment)
free_space free_space 0.491000000000099 compartment (compartment)
washout washout 1.0 compartment (compartment)

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
R10_drug_washout R10_drug_washout drug + washout > washout

compartment * k1 * drug * washout
R11_FLC_drug_binding R11_FLC_drug_binding drug + FLC = FLC_drug

compartment * (k1 * drug * FLC - k2 * FLC_drug)
R12_FLC_drug_washout R12_FLC_drug_washout FLC_drug + washout > washout

compartment * k1 * FLC_drug * washout
R13_CRA_Secretion_DyingFibr R13_CRA_Secretion_DyingFibr DyingFibr > CRA

compartment * k1 * DyingFibr
R14_CRAClipOffHealthyFibr R14_CRAClipOffHealthyFibr HealthyFibr + MMP7 > CRA + MMP7 + HealthyFibr

compartment * Rate_Law_for_BAFF_clipoff(k1, HealthyFibr, MMP7)
R15_DyingFibroblast_death R15_DyingFibroblast_death DyingFibr > ∅

compartment * k1 * DyingFibr
R16_Healthy_to_Dying_fibroblast R16_Healthy_to_Dying_fibroblast HealthyFibr + TNFalpha > DyingFibr + TNFalpha

compartment * k1 * HealthyFibr * TNFalpha
R17_HealthyBacteriaProduction R17_HealthyBacteriaProduction HealthyBacteria > {2.0}HealthyBacteria

compartment * k1 * HealthyBacteria
R18_HealthyFibProduction R18_HealthyFibProduction free_space + HealthyFibr > {2.0}HealthyFibr

compartment * k1 * free_space * HealthyFibr
R19_MMP7_release_HealthyFibr R19_MMP7_release_HealthyFibr HealthyFibr > HealthyFibr + MMP7

compartment * k1 * HealthyFibr
R1_CRA_degradation R1_CRA_degradation CRA + MMP8 > MMP8

compartment * k1 * CRA * MMP8
R20_MMP8_release_HealthyFibr R20_MMP8_release_HealthyFibr HealthyFibr > HealthyFibr + {100.0}MMP8

compartment * k1 * HealthyFibr
R21_Healthy_to_Dying_Bacteria R21_Healthy_to_Dying_Bacteria HealthyBacteria + Protease > DyingBacteria + Protease

compartment * k1 * HealthyBacteria * Protease
R22_CRA_binding R22_CRA_binding MastCells_FLC + CRA = MastCells_FLC_CRA

compartment * (k1 * MastCells_FLC * CRA - k2 * MastCells_FLC_CRA)
R23_FLC_binding R23_FLC_binding FLC + MastCells = MastCells_FLC

compartment * (k1 * FLC * MastCells - k2 * MastCells_FLC)
R24_TNFalpha_production R24_TNFalpha_production MastCells_FLC_CRA > TNFalpha + MastCells_FLC_CRA

compartment * k1 * MastCells_FLC_CRA
R25_Protease_production R25_Protease_production MastCells_FLC_CRA > Protease + MastCells_FLC_CRA

compartment * k1 * MastCells_FLC_CRA
R26_DyingBacteria_secrete_CRA R26_DyingBacteria secrete CRA DyingBacteria > {1000.0}CRA

compartment * k1 * DyingBacteria
R27_Dyingbacteria_die R27_Dyingbacteria die DyingBacteria > ∅

compartment * k1 * DyingBacteria
R28_Proteaseinflux R28_Proteaseinflux ∅ > Protease

compartment * Constant_flux__irreversible(k_protease_influx)
R2_CRA_washout R2_CRA_washout CRA + washout > washout

compartment * k1 * CRA * washout
R3_CRAinflux R3_CRAinflux ∅ > CRA

compartment * Constant_flux__irreversible(k_CRA_influx)
R4_FLC_washout R4_FLC_washout FLC + washout > washout

compartment * k1 * FLC * washout
R5_MMP7_washout R5_MMP7_washout MMP7 + washout > washout

compartment * k1 * MMP7 * washout
R6_MMP8_washout R6_MMP8_washout MMP8 + washout > washout

compartment * k1 * MMP8 * washout
R7_Protease_washout R7_Protease_washout Protease + washout > washout

compartment * k1 * Protease * washout
R8_TNFalpha_washout R8_TNFalpha_washout TNFalpha + washout > washout

compartment * k1 * TNFalpha * washout
R9_FLC_production R9_FLC_production CRA + Bcells > FLC + CRA + Bcells

compartment * Rate_Law_for_B_FLC_production(k1, CRA, Bcells)

Global parameters

Id Value
Metabolite_18 1000.0
k_CRA_influx 0.0
k_protease_influx 0.0

Local parameters

Id Value Reaction
k1 0.0001 R1_CRA_degradation (R1_CRA_degradation)
k1 0.01 R2_CRA_washout (R2_CRA_washout)
k1 0.01 R4_FLC_washout (R4_FLC_washout)
k1 0.01 R5_MMP7_washout (R5_MMP7_washout)
k1 0.01 R6_MMP8_washout (R6_MMP8_washout)
k1 0.01 R7_Protease_washout (R7_Protease_washout)
k1 0.01 R8_TNFalpha_washout (R8_TNFalpha_washout)
k1 0.001 R9_FLC_production (R9_FLC_production)
k1 0.0001 R10_drug_washout (R10_drug_washout)
k1 0.00001 R11_FLC_drug_binding (R11_FLC_drug_binding)
k2 0.00001 R11_FLC_drug_binding (R11_FLC_drug_binding)
k1 0.0001 R12_FLC_drug_washout (R12_FLC_drug_washout)
k1 0.001 R13_CRA_Secretion_DyingFibr (R13_CRA_Secretion_DyingFibr)
k1 0.00000001 R14_CRAClipOffHealthyFibr (R14_CRAClipOffHealthyFibr)
k1 0.2 R15_DyingFibroblast_death (R15_DyingFibroblast_death)
k1 0.0000005 R16_Healthy_to_Dying_fibroblast (R16_Healthy_to_Dying_fibroblast)
k1 0.01 R17_HealthyBacteriaProduction (R17_HealthyBacteriaProduction)
k1 0.000000485 R18_HealthyFibProduction (R18_HealthyFibProduction)
k1 1.0 R19_MMP7_release_HealthyFibr (R19_MMP7_release_HealthyFibr)
k1 0.1 R20_MMP8_release_HealthyFibr (R20_MMP8_release_HealthyFibr)
k1 0.005 R21_Healthy_to_Dying_Bacteria (R21_Healthy_to_Dying_Bacteria)
k1 0.1 R22_CRA_binding (R22_CRA_binding)
k2 0.1 R22_CRA_binding (R22_CRA_binding)
k1 0.1 R23_FLC_binding (R23_FLC_binding)
k2 0.1 R23_FLC_binding (R23_FLC_binding)
k1 5000.0 R24_TNFalpha_production (R24_TNFalpha_production)
k1 65.0 R25_Protease_production (R25_Protease_production)
k1 10.0 R26_DyingBacteria_secrete_CRA (R26_DyingBacteria secrete CRA)
k1 0.1 R27_Dyingbacteria_die (R27_Dyingbacteria die)

Assignment rules

Definition
free_space = Metabolite_18 - (HealthyFibr + DyingFibr)
Total_space = Metabolite_18

Rate rules

Definition

Algebraic rules

Definition
Definition
Rate_Law_for_BAFF_clipoff(k1, s1, s2) = k1 * s1 * s2
Rate_Law_for_B_FLC_production(k1, s1, s2) = k1 * s1 * s2
Constant_flux__irreversible(v) = v
Trigger Assignments