Journal of Pharmacokinetics and Pharmacodynamics

, Volume 41, Issue 5, pp 479–491 | Cite as

Complex pattern of interleukin-11-induced inflammation revealed by mathematically modeling the dynamics of C-reactive protein

  • Yuri Kheifetz
  • Moran Elishmereni
  • Zvia AgurEmail author
Original Paper


Inflammation underlies many diseases and is an undesired effect of several therapy modalities. Biomathematical modeling can help unravel the complex inflammatory processes and the mechanisms triggering their emergence. We developed a model for induction of C-reactive protein (CRP), a clinically reliable marker of inflammation, by interleukin (IL)-11, an approved cytokine for treatment of chemotherapy-induced thrombocytopenia. Due to paucity of information on the mechanisms underlying inflammation-induced CRP dynamics, our model was developed by systematically evaluating several models for their ability to retrieve variable CRP profiles observed in IL-11-treated breast cancer patients. The preliminary semi-mechanistic models were designed by non-linear mixed-effects modeling, and were evaluated by various performance criteria, which test goodness-of-fit, parsimony and uniqueness. The best-performing model, a robust population model with minimal inter-individual variability, uncovers new aspects of inflammation dynamics. It shows that CRP clearance is a nonlinear self-controlled process, indicating an adaptive anti-inflammatory reaction in humans. The model also reveals a dual IL-11 effect on CRP elevation, whereby the drug has not only a potent immediate influence on CRP incline, but also a long-term influence inducing elevated CRP levels for several months. Consistent with this, model simulations suggest that periodic IL-11 therapy may result in prolonged low-grade (chronic) inflammation post treatment. Future application of the model can therefore help design improved IL-11 regimens with minimized long-term CRP toxicity. Our study illuminates the dynamics of inflammation and its control, and provides a prototype for progressive modeling of complex biological processes in the medical realm and beyond.


CRP Non-linear mixed-effects model Acute inflammation Chronic inflammation Akaike information criterion Model parsimony 



The authors thank Dr. Marina Kleiman, Prof. Gerard Wagemaker and Yuri Kogan for helpful discussions. This work was supported by the Chai Foundation.

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

10928_2014_9383_MOESM1_ESM.pdf (473 kb)
Supplementary material 1 (PDF 472 kb)


  1. 1.
    Mantovani A, Allavena P, Sica A, Balkwill F (2008) Cancer-related inflammation. Nature 454(7203):436–444. doi: 10.1038/nature07205 PubMedCrossRefGoogle Scholar
  2. 2.
    Colotta F, Allavena P, Sica A, Garlanda C, Mantovani A (2009) Cancer-related inflammation, the seventh hallmark of cancer: links to genetic instability. Carcinogenesis 30(7):1073–1081. doi: 10.1093/carcin/bgp127 PubMedCrossRefGoogle Scholar
  3. 3.
    Abou-Raya A, Abou-Raya S (2006) Inflammation: a pivotal link between autoimmune diseases and atherosclerosis. Autoimmun Rev 5(5):331–337. doi: 10.1016/j.autrev.2005.12.006 PubMedCrossRefGoogle Scholar
  4. 4.
    Davies M (2014) New modalities of cancer treatment for NSCLC: focus on immunotherapy. Cancer Manag Res 6:63–75. doi: 10.2147/CMAR.S57550 PubMedCrossRefPubMedCentralGoogle Scholar
  5. 5.
    Pellegrini M, Mak TW, Ohashi PS (2010) Fighting cancers from within: augmenting tumor immunity with cytokine therapy. Trends Pharmacol Sci 31(8):356–363. doi: 10.1016/ PubMedCrossRefGoogle Scholar
  6. 6.
    Xu XJ, Tang YM (2014) Cytokine release syndrome in cancer immunotherapy with chimeric antigen receptor engineered T cells. Cancer Lett 343(2):172–178. doi: 10.1016/j.canlet.2013.10.004 PubMedCrossRefGoogle Scholar
  7. 7.
    Vodovotz Y, Csete M, Bartels J, Chang S, An G (2008) Translational systems biology of inflammation. PLoS Comput Biol 4(4):e1000014. doi: 10.1371/journal.pcbi.1000014 PubMedCrossRefPubMedCentralGoogle Scholar
  8. 8.
    Agur Z, Elishmereni M, Kheifetz Y (2013) Personalizing oncology treatments in solid cancer diseases by predicting drug efficacy, side-effects, and improved therapy: mathematics, statistics and their integration. WIREs Systems Biology and Medicine In PressGoogle Scholar
  9. 9.
    Radosavljevic V, Ristovski K, Obradovic Z (2013) A data-driven acute inflammation therapy. BMC Med Genomics 6(3):1–9. doi: 10.1186/1755-8794-6-S3-S7 Google Scholar
  10. 10.
    Machavaram KK, Almond LM, Rostami-Hodjegan A, Gardner I, Jamei M, Tay S, Wong S, Joshi A, Kenny JR (2013) A physiologically based pharmacokinetic modeling approach to predict disease-drug interactions: suppression of CYP3A by IL-6. Clin Pharmacol Ther 94(2):260–268. doi: 10.1038/clpt.2013.79 PubMedCrossRefGoogle Scholar
  11. 11.
    Reynolds A, Rubin J, Clermont G, Day J, Vodovotz Y, Bard Ermentrout G (2006) A reduced mathematical model of the acute inflammatory response: I. Derivation of model and analysis of anti-inflammation. J Theor Biol 242(1):220–236. doi: 10.1016/j.jtbi.2006.02.016 PubMedCrossRefGoogle Scholar
  12. 12.
    Vodovotz Y, Clermont G, Chow C, An G (2004) Mathematical models of the acute inflammatory response. Curr Opin Crit Care 10(5):383–390. doi: 10.1097/00075198-200410000-00014 PubMedCrossRefGoogle Scholar
  13. 13.
    Lauffenburger DA, Kennedy CR (1981) Analysis of a lumped model for tissue inflammation dynamics. Math Biosci 53(3–4):189–221. doi: 10.1016/0025-5564(81)90018-3 PubMedCrossRefGoogle Scholar
  14. 14.
    Schwertschlag US, Trepicchio WL, Dykstra KH, Keith JC, Turner KJ, Dorner AJ (1999) Hematopoietic, immunomodulatory and epithelial effects of interleukin-11. Leukemia 13(9):1307–1315PubMedCrossRefGoogle Scholar
  15. 15.
    Bhatia M, Davenport V, Cairo MS (2007) The role of interleukin-11 to prevent chemotherapy-induced thrombocytopenia in patients with solid tumors, lymphoma, acute myeloid leukemia and bone marrow failure syndromes. Leuk Lymphoma 48(1):9–15. doi: 10.1080/10428190600909115 PubMedCrossRefGoogle Scholar
  16. 16.
    Vadhan-Raj S (2009) Management of chemotherapy-induced thrombocytopenia: current status of thrombopoietic agents. Semin Hematol 46(1 Suppl 2):S26–S32. doi: 10.1053/j.seminhematol.2008.12.007 PubMedCrossRefGoogle Scholar
  17. 17.
    Gordon MS, McCaskill-Stevens WJ, Battiato LA, Loewy J, Loesch D, Breeden E, Hoffman R, Beach KJ, Kuca B, Kaye J, Sledge GW Jr (1996) A phase I trial of recombinant human interleukin-11 (neumega rhIL-11 growth factor) in women with breast cancer receiving chemotherapy. Blood 87(9):3615–3624PubMedGoogle Scholar
  18. 18.
    Smith JW 2nd (2000) Tolerability and side-effect profile of rhIL-11. Oncology (Williston Park) 14(9 Suppl 8):41–47Google Scholar
  19. 19.
    Wu S, Zhang Y, Xu L, Dai Y, Teng Y, Ma S, Ho SH, Kim JM, Yu SS, Kim S, Song S (2012) Multicenter, randomized study of genetically modified recombinant human interleukin-11 to prevent chemotherapy-induced thrombocytopenia in cancer patients receiving chemotherapy. Support Care Cancer 20(8):1875–1884. doi: 10.1007/s00520-011-1290-x PubMedCrossRefGoogle Scholar
  20. 20.
    Kurzrock R (2005) Thrombopoietic factors in chronic bone marrow failure states: the platelet problem revisited. Clin Cancer Res 11(4):1361–1367. doi: 10.1158/1078-0432.CCR-04-1094 PubMedCrossRefGoogle Scholar
  21. 21.
    Cotreau MM, Stonis L, Strahs A, Schwertschlag US (2004) A multiple-dose, safety, tolerability, pharmacokinetics and pharmacodynamic study of oral recombinant human interleukin-11 (oprelvekin). Biopharm Drug Dispos 25(7):291–296. doi: 10.1002/bdd.415 PubMedCrossRefGoogle Scholar
  22. 22.
    Ellis M, Hedstrom U, Frampton C, Alizadeh H, Kristensen J, Shammas FV, al-Ramadi BK (2006) Modulation of the systemic inflammatory response by recombinant human interleukin-11: a prospective randomized placebo controlled clinical study in patients with hematological malignancy. Clin Immunol 120(2):129–137. doi: 10.1016/j.clim.2006.03.003 PubMedCrossRefGoogle Scholar
  23. 23.
    Coventry BJ, Ashdown ML, Quinn MA, Markovic SN, Yatomi-Clarke SL, Robinson AP (2009) CRP identifies homeostatic immune oscillations in cancer patients: a potential treatment targeting tool? J Transl Med 7:102. doi: 10.1186/1479-5876-7-102 PubMedCrossRefPubMedCentralGoogle Scholar
  24. 24.
    Eklund CM (2009) Proinflammatory cytokines in CRP baseline regulation. Adv Clin Chem 48:111–136PubMedCrossRefGoogle Scholar
  25. 25.
    Pradhan AD, Manson JE, Rifai N, Buring JE, Ridker PM (2001) C-reactive protein, interleukin 6, and risk of developing type 2 diabetes mellitus. JAMA 286(3):327–334PubMedCrossRefGoogle Scholar
  26. 26.
    Yousuf O, Mohanty BD, Martin SS, Joshi PH, Blaha MJ, Nasir K, Blumenthal RS, Budoff MJ (2013) High-sensitivity C-reactive protein and cardiovascular disease: a resolute belief or an elusive link? J Am Coll Cardiol 62(5):397–408. doi: 10.1016/j.jacc.2013.05.016 PubMedCrossRefGoogle Scholar
  27. 27.
    Danesh J, Wheeler JG, Hirschfield GM, Eda S, Eiriksdottir G, Rumley A, Lowe GD, Pepys MB, Gudnason V (2004) C-reactive protein and other circulating markers of inflammation in the prediction of coronary heart disease. N Engl J Med 350(14):1387–1397PubMedCrossRefGoogle Scholar
  28. 28.
    Ridker PM (2003) Cardiology patient page. C-reactive protein: a simple test to help predict risk of heart attack and stroke. Circulation 108(12):e81–e85. doi: 10.1161/01.CIR.0000093381.57779.67 PubMedCrossRefGoogle Scholar
  29. 29.
    de Martino M, Klatte T, Seemann C, Waldert M, Haitel A, Schatzl G, Remzi M, Weibl P (2013) Validation of serum C-reactive protein (CRP) as an independent prognostic factor for disease-free survival in patients with localised renal cell carcinoma (RCC). BJU Int 111(8):E348–E353. doi: 10.1111/bju.12067 PubMedCrossRefGoogle Scholar
  30. 30.
    Allin KH, Nordestgaard BG (2011) Elevated C-reactive protein in the diagnosis, prognosis, and cause of cancer. Crit Rev Clin Lab Sci 48(4):155–170. doi: 10.3109/10408363.2011.599831 PubMedCrossRefGoogle Scholar
  31. 31.
    Heikkila K, Ebrahim S, Rumley A, Lowe G, Lawlor DA (2007) Associations of circulating C-reactive protein and interleukin-6 with survival in women with and without cancer: findings from the British Women’s Heart and Health Study. Cancer Epidemiol Biomarkers Prev 16(6):1155–1159. doi: 10.1158/1055-9965.EPI-07-0093 PubMedCrossRefGoogle Scholar
  32. 32.
    Steffens S, Kohler A, Rudolph R, Eggers H, Seidel C, Janssen M, Wegener G, Schrader M, Kuczyk MA, Schrader AJ (2012) Validation of CRP as prognostic marker for renal cell carcinoma in a large series of patients. BMC Cancer 12:399. doi: 10.1186/1471-2407-12-399 PubMedCrossRefPubMedCentralGoogle Scholar
  33. 33.
    Han Y, Mao F, Wu Y, Fu X, Zhu X, Zhou S, Zhang W, Sun Q, Zhao Y (2011) Prognostic role of C-reactive protein in breast cancer: a systematic review and meta-analysis. Int J Biol Markers 26(4):209–215. doi: 10.5301/JBM.2011.8872 PubMedGoogle Scholar
  34. 34.
    Mazhar D, Ngan S (2006) C-reactive protein and colorectal cancer. QJM 99(8):555–559. doi: 10.1093/qjmed/hcl056 PubMedCrossRefGoogle Scholar
  35. 35.
    Zhou B, Liu J, Wang ZM, Xi T (2012) C-reactive protein, interleukin 6 and lung cancer risk: a meta-analysis. PLoS ONE 7(8):e43075. doi: 10.1371/journal.pone.0043075 PubMedCrossRefPubMedCentralGoogle Scholar
  36. 36.
    Shimura T, Kitagawa M, Yamada T, Ebi M, Mizoshita T, Tanida S, Kataoka H, Kamiya T, Joh T (2012) C-reactive protein is a potential prognostic factor for metastatic gastric cancer. Anticancer Res 32(2):491–496PubMedGoogle Scholar
  37. 37.
    Aoyama K, Uchida T, Takanuki F, Usui T, Watanabe T, Higuchi S, Toyoki T, Mizoguchi H (1997) Pharmacokinetics of recombinant human interleukin-11 (rhIL-11) in healthy male subjects. Br J Clin Pharmacol 43(6):571–578PubMedCrossRefPubMedCentralGoogle Scholar
  38. 38.
    Akaike H (1973) Information theory as an extension of the maximum likelihood principle. 2nd International Symposium on Information Theory. Akademiai Kiado, BudapestGoogle Scholar
  39. 39.
    Akaike H (1974) A new look at the statistical model identification. IEEE Trans Automat Contr 19(6):716–723. doi: 10.1109/tac.1974.1100705 CrossRefGoogle Scholar
  40. 40.
    Forster M, Sober E (1994) How to tell when simpler, more unified, or less ad hoc theories will provide more accurate predictions. Br J Philos Sci 45(1):1–35. doi: 10.1093/bjps/45.1.1 CrossRefGoogle Scholar
  41. 41.
    Davidian M, Giltinan DM (1995) Nonlinear models for repeated measurement data. Monographs on Statistics and Applied Probability, vol 62. Chapman and Hall, LondonGoogle Scholar
  42. 42.
    Davidian M, Giltinan DM (2003) Nonlinear models for repeated measurements: an overview and update. J Agric Biol Environ Stat 8:387–419. doi: 10.1198/1085711032697
  43. 43.
    Delyon B, Lavielle M, Moulines E (1999) Convergence of a stochastic approximation version of the EM algorithm. Ann Statist 27(1):94–128CrossRefGoogle Scholar
  44. 44.
    Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J Roy Statist Soc Ser B 39(1):1–38Google Scholar
  45. 45.
    Kuhn E, Lavielle M (2004) Coupling a stochastic approximation version of EM with an MCMC procedure. ESAIM: Probab Stat 8:115–131. doi: 10.1051/ps:2004007 CrossRefGoogle Scholar
  46. 46.
    Kuhn E, Lavielle M (2005) Maximum likelihood estimation in nonlinear mixed effects models. Comput Stat Data Anal 49(4):1020–1038. doi: 10.1016/j.csda.2004.07.002 CrossRefGoogle Scholar
  47. 47.
    Faller D, Klingmüller U, Timmer J (2003) Simulation methods for optimal experimental design in systems biology. Simulation 79(12):717–725CrossRefGoogle Scholar
  48. 48.
    Louis TA (1982) Finding the observed information matrix when using the EM algorithm. J Roy Statist Soc Ser B 44(2):226–233Google Scholar
  49. 49.
    Stuart J, Whicher JT (1988) Tests for detecting and monitoring the acute phase response. Arch Dis Child 63(2):115–117PubMedCrossRefPubMedCentralGoogle Scholar
  50. 50.
    Catsburg C, Gunter MJ, Chen C, Cote ML, Kabat GC, Nassir R, Tinker L, Wactawski-Wende J, Page DL, Rohan TE (2014) Insulin, estrogen, inflammatory markers, and risk of benign proliferative breast disease. Cancer Res 74(12):3248–3258. doi: 10.1158/0008-5472.CAN-13-3514 PubMedCrossRefGoogle Scholar
  51. 51.
    Putoczki T, Ernst M (2010) More than a sidekick: the IL-6 family cytokine IL-11 links inflammation to cancer. J Leukoc Biol 88(6):1109–1117. doi: 10.1189/jlb.0410226 PubMedCrossRefGoogle Scholar
  52. 52.
    Gurfein BT, Zhang Y, Lopez CB, Argaw AT, Zameer A, Moran TM, John GR (2009) IL-11 regulates autoimmune demyelination. J immunol 183(7):4229–4240. doi: 10.4049/jimmunol.0900622 PubMedCrossRefPubMedCentralGoogle Scholar
  53. 53.
    Hermann JA, Hall MA, Maini RN, Feldmann M, Brennan FM (1998) Important immunoregulatory role of interleukin-11 in the inflammatory process in rheumatoid arthritis. Arthritis Rheum 41(8):1388–1397. doi: 10.1002/1529-0131(199808)41:8<1388:AID-ART7>3.0.CO;2-F PubMedCrossRefGoogle Scholar
  54. 54.
    Walmsley M, Butler DM, Marinova-Mutafchieva L, Feldmann M (1998) An anti-inflammatory role for interleukin-11 in established murine collagen-induced arthritis. Immunology 95(1):31–37PubMedCrossRefPubMedCentralGoogle Scholar
  55. 55.
    Trepicchio WL, Ozawa M, Walters IB, Kikuchi T, Gilleaudeau P, Bliss JL, Schwertschlag U, Dorner AJ, Krueger JG (1999) Interleukin-11 therapy selectively downregulates type I cytokine proinflammatory pathways in psoriasis lesions. J Clin Investig 104(11):1527–1537. doi: 10.1172/JCI6910 PubMedCrossRefPubMedCentralGoogle Scholar
  56. 56.
    Bozza M, Bliss JL, Dorner AJ, Trepicchio WL (2001) Interleukin-11 modulates Th1/Th2 cytokine production from activated CD4 + T cells. J Interferon Cytokine Res 21(1):21–30. doi: 10.1089/107999001459123 PubMedCrossRefGoogle Scholar
  57. 57.
    Kapina MA, Shepelkova GS, Avdeenko VG, Guseva AN, Kondratieva TK, Evstifeev VV, Apt AS (2011) Interleukin-11 drives early lung inflammation during Mycobacterium tuberculosis infection in genetically susceptible mice. PLoS ONE 6(7):e21878. doi: 10.1371/journal.pone.0021878 PubMedCrossRefPubMedCentralGoogle Scholar
  58. 58.
    Wong PK, Campbell IK, Robb L, Wicks IP (2005) Endogenous IL-11 is pro-inflammatory in acute methylated bovine serum albumin/interleukin-1-induced (mBSA/IL-1)arthritis. Cytokine 29(2):72–76. doi: 10.1016/j.cyto.2004.09.011 PubMedCrossRefGoogle Scholar
  59. 59.
    Vial T, Descotes J (1995) Clinical toxicity of cytokines used as haemopoietic growth factors. Drug Saf 13(6):371–406PubMedCrossRefGoogle Scholar
  60. 60.
    van Leeuwen MA, van Rijswijk MH, Sluiter WJ, van Riel PL, Kuper IH, van de Putte LB, Pepys MB, Limburg PC (1997) Individual relationship between progression of radiological damage and the acute phase response in early rheumatoid arthritis. Towards development of a decision support system. J Rheumatol 24(1):20–27PubMedGoogle Scholar
  61. 61.
    Wick MC, Lindblad S, Klareskog L, Van Vollenhoven RF (2004) Relationship between inflammation and joint destruction in early rheumatoid arthritis: a mathematical description. Ann Rheum Dis 63(7):848–852. doi: 10.1136/ard.2003.01517263/7/848 PubMedCrossRefPubMedCentralGoogle Scholar
  62. 62.
    Liu B, Zhang J, Tan PY, Hsu D, Blom AM, Leong B, Sethi S, Ho B, Ding JL, Thiagarajan PS (2011) A computational and experimental study of the regulatory mechanisms of the complement system. PLoS Comput Biol 7(1):e1001059. doi: 10.1371/journal.pcbi.1001059 PubMedCrossRefPubMedCentralGoogle Scholar
  63. 63.
    Bauer R, Guzy S, Ng C (2007) A survey of population analysis methods and software for complex pharmacokinetic and pharmacodynamic models with examples. AAPS J 9(1):E60–E83. doi: 10.1208/aapsj0901007 PubMedCrossRefPubMedCentralGoogle Scholar
  64. 64.
    Friberg LE, Henningsson A, Maas H, Nguyen L, Karlsson MO (2002) Model of chemotherapy-induced myelosuppression with parameter consistency across drugs. J Clin Oncol 20(24):4713–4721PubMedCrossRefGoogle Scholar
  65. 65.
    Friberg LE, Karlsson MO (2003) Mechanistic models for myelosuppression. Invest New Drugs 21(2):183–194PubMedCrossRefGoogle Scholar
  66. 66.
    Karlsson MO, Molnar V, Freijs A, Nygren P, Bergh J, Larsson R (1999) Pharmacokinetic models for the saturable distribution of paclitaxel. Drug Metab Dispos 27(10):1220–1223PubMedGoogle Scholar
  67. 67.
    Quartino AL, Friberg LE, Karlsson MO (2012) A simultaneous analysis of the time-course of leukocytes and neutrophils following docetaxel administration using a semi-mechanistic myelosuppression model. Invest New Drugs 30(2):833–845. doi: 10.1007/s10637-010-9603-3 PubMedCrossRefGoogle Scholar
  68. 68.
    Dartois C, Brendel K, Comets E, Laffont CM, Laveille C, Tranchand B, Mentre F, Lemenuel-Diot A, Girard P (2007) Overview of model-building strategies in population PK/PD analyses: 2002–2004 literature survey. Br J Clin Pharmacol 64(5):603–612. doi: 10.1111/j.1365-2125.2007.02975.x PubMedCrossRefPubMedCentralGoogle Scholar
  69. 69.
    Skomorovski K, Harpak H, Ianovski A, Vardi M, Visser TP, Hartong SC, van Vliet HH, Wagemaker G, Agur Z (2003) New TPO treatment schedules of increased safety and efficacy: pre-clinical validation of a thrombopoiesis simulation model. Br J Haematol 123(4):683–691PubMedCrossRefGoogle Scholar
  70. 70.
    Vainas O, Ariad S, Amir O, Mermershtain W, Vainstein V, Kleiman M, Inbar O, Ben-Av R, Mukherjee A, Chan S, Agur Z (2012) Personalising docetaxel and G-CSF schedules in cancer patients by a clinically validated computational model. Br J Cancer 107(5):814–822. doi: 10.1038/bjc.2012.316 PubMedCrossRefPubMedCentralGoogle Scholar
  71. 71.
    Vainstein V, Ginosar Y, Shoham M, Ranmar DO, Ianovski A, Agur Z (2005) The complex effect of granulocyte colony-stimulating factor on human granulopoiesis analyzed by a new physiologically-based mathematical model. J Theor Biol 234(3):311–327PubMedCrossRefGoogle Scholar
  72. 72.
    Gorelik B, Ziv I, Shohat R, Wick M, Hankins WD, Sidransky D, Agur Z (2008) Efficacy of weekly docetaxel and bevacizumab in mesenchymal chondrosarcoma: a new theranostic method combining xenografted biopsies with a mathematical model. Cancer Res 68(21):9033–9040. doi: 10.1158/0008-5472.can-08-1723 PubMedCrossRefPubMedCentralGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Institute for Medical Biomathematics (IMBM)Bene-AtarothIsrael

Personalised recommendations