abudukelimu1
The model reproduces Figure 1 of the paper.
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Complex Stability and an Irreversible Transition Reverted by Peptide and Fibroblasts in a Dynamic Model of Innate Immunity.
Abulikemu Abudukelimu (1,2), Matteo Barberis (1,3), Frank Redegeld (4), Nilgun Sahin (2) and Hans V. Westerhoff (1,2,5)
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
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.
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) |
| Id | Value | |
|---|---|---|
| Metabolite_18 | 1000.0 | |
| k_CRA_influx | 0.0 | |
| k_protease_influx | 0.0 |
| 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) |
| Definition | |
|---|---|
| free_space = Metabolite_18 - (HealthyFibr + DyingFibr) | |
| Total_space = Metabolite_18 |
| Definition |
|---|
| 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 |
|---|