Global sensitivity analysis of a mathematical model of acute inflammation identifies nonlinear dependence of cumulative tissue damage on host interleukin-6 responses

Journal of Theoretical Biology

Volumn 358, Issue , 2014, Pages 132-148

  Mathew, Shibin ^a   Bartels, John ^b   Banerjee, Ipsita ^a,d   Vodovotz, Yoram ^b,c,d  

^a University of Pittsburgh   (United States)

^b IMMUNETRICS INC   (United States)

^c UNIVERSITY OF PITTSBURGH MEDICAL CENTER   (United States)

^d UNIVERSITY OF PITTSBURGH   (United States)

Author keywords

Cytokines; Endotoxin; Inflammation dynamics; Meta modeling; Nitric oxide

Indexed keywords

ENDOTOXIN; INDUCIBLE NITRIC OXIDE SYNTHASE; INTERLEUKIN 10; INTERLEUKIN 6; LIPOPOLYSACCHARIDE; NITRIC OXIDE; TUMOR NECROSIS FACTOR ALPHA;

IMMUNE RESPONSE; IMMUNE SYSTEM; MONTE CARLO ANALYSIS; NITRIC OXIDE; NUMERICAL MODEL; PROTEIN; SENSITIVITY ANALYSIS;

ANIMAL EXPERIMENT; ANTIINFLAMMATORY ACTIVITY; AREA UNDER THE CURVE; ARTICLE; ENDOTOXEMIA; ENZYME INHIBITION; IMMUNE RESPONSE; INFLAMMATION; LETHAL DOSE; MATHEMATICAL MODEL; MONTE CARLO METHOD; MOUSE; NONHUMAN; POSITIVE FEEDBACK; PRIORITY JOURNAL; RANDOM SAMPLE; RANDOM SAMPLING HIGH DIMENSIONAL MODEL REPRESENTATION; SENSITIVITY ANALYSIS; STIMULUS RESPONSE; TISSUE INJURY; ACUTE DISEASE; BIOSYNTHESIS; HUMAN; NONLINEAR SYSTEM; STATISTICAL MODEL; THEORETICAL MODEL;

ACUTE DISEASE; HUMANS; INTERLEUKIN-6; MODELS, STATISTICAL; MODELS, THEORETICAL; MONTE CARLO METHOD; NONLINEAR DYNAMICS;

EID: 84904611856     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2014.05.036     Document Type: Article

References (88)

1. An G., Nieman G., Vodovotz Y. Toward computational identification of multiscale "Tipping Points" in acute inflammation and multiple organ failure. Ann. Biomed. Eng. 2012, 1-11.
2. Barton R.R. Metamodels for Simulation Input-Output Relations 1992, 289-299. ACM.
3. Beutler B., Cerami A. The biology of cachectin/Tnf-a primary mediator of the host response. Annu. Rev. Immunol. 1989, 7:625-655. 10.1146/Annurev.Iy.07.040189.003205.
4. Beutler B., Rietschel E.T. Innate immune sensing and its roots: the story of endotoxin. Nat. Rev. Immunol. 2003, 3:169-176. 10.1038/nri1004.
5. Bogdan C., Vodovotz Y., Letterio J. TGFß and IL-10: inhibitory cytokines regulating immunity and the response to infection. Novel Cytokine Inhib. 2000, 217-242.
6. Chow C.C., Clermont G., Kumar R., Lagoa C., Tawadrous Z., Gallo D., Betten B., Bartels J., Constantine G., Fink M.P. The acute inflammatory response in diverse shock states. Shock 2005, 24:74-84.
7. Chu Y., Hahn J. Generalization of a parameter set selection procedure based on orthogonal projections and the D-optimality criterion. AlChE J. 2012, 58:2085-2096.
8. Clermont G., Bartels J., Kumar R., Constantine G., Vodovotz Y., Chow C. In silico design of clinical trials: a method coming of age. Crit. Care Med. 2004, 32:2061-2070.
9. Copeland S., Warren H.S., Lowry S.F., Calvano S.E., Remick D. Acute inflammatory response to endotoxin in mice and humans. Clin. Diagn. Lab. Immunol. 2005, 12:60-67.
10. Croft M., Duan W., Choi H., Eun S.Y., Madireddi S., Mehta A. TNF superfamily in inflammatory disease: translating basic insights. Trends Immunol. 2012, 33:144-152. 10.1016/j.it.2011.10.004.
11. Daun S., Rubin J., Vodovotz Y., Clermont G. Equation-based models of dynamic biological systems. J. Crit. Care 2008, 23:585-594. 10.1016/j.jcrc.2008.02.003.
12. Daun S., Rubin J., Vodovotz Y., Roy A., Parker R., Clermont G. An ensemble of models of the acute inflammatory response to bacterial lipopolysaccharide in rats: results from parameter space reduction. J. Theor. Biol. 2008, 253:843-853.
13. Davis M.J., Skodje R.T., Tomlin A.S. Global sensitivity analysis of chemical-kinetic reaction mechanisms: construction and deconstruction of the probability density function. J. Phys. Chem. A 2011, 115:1556.
14. Day J., Rubin J., Vodovotz Y., Chow C.C., Reynolds A., Clermont G. A reduced mathematical model of the acute inflammatory response. II. Capturing scenarios of repeated endotoxin administration. J. Theor. Biol. 2006, 242:237-256. 10.1016/j.jtbi.2006.02.015.
15. Fayad L., Keating M.J., Reuben J.M., O'Brien S., Lee B.N., Lerner S., Kurzrock R. Interleukin-6 and interleukin-10 levels in chronic lymphocytic leukemia: correlation with phenotypic characteristics and outcome. Blood 2001, 97:256-263.
16. Feil, B., Kucherenko, S., Shah, N., 2009. Comparison of monte carlo and quasi monte carlo sampling methods in high dimensional model representation. In: IEEE First International Conference on Advances in System Simulation, SIMUL'09, pp. 12-17.
17. Feng X., Hooshangi S., Chen D., Li G., Weiss R., Rabitz H. Optimizing genetic circuits by global sensitivity analysis. Biophysical journal 2004, 87:2195-2202.
18. Foteinou P., Yang E., Androulakis I. Networks, biology and systems engineering: a case study in inflammation. Comput. Chem. Eng. 2009, 33:2028-2041.
19. Foteinou P., Calvano S., Lowry S., Androulakis I. Modeling endotoxin-induced systemic inflammation using an indirect response approach. Math. Biosci. 2009, 217:27-42.
20. Gallucci S., Matzinger P. Danger signals: SOS to the immune system. Curr. Opin. Immunol. 2001, 13:114-119.
21. Hahn J., Edgar T.F. An improved method for nonlinear model reduction using balancing of empirical gramians. Comput. Chem. Eng. 2002, 26. (1379-1397% at 0098-1354).
22. Hindmarsh A.C. ODEPACK, A Systematized Collection of ODE Solvers 1983, vol. 1:55-64. North-Holland, Amsterdam, (IMACS transactions on scientific computation 1, pp. 55-64).
23. Hofmann S.R., Rösen-Wolff A., Tsokos G.C., Hedrich C.M. Biological properties and regulation of IL-10 related cytokines and their contribution to autoimmune disease and tissue injury. Clin. Immunol. 2012.
24. Ivady B., Beres B.J., Szabo D. Recent advances in sepsis research: novel biomarkers and therapeutic targets. Curr. Med. Chem. 2011, 18:3211-3225.
25. Jayaraman A., Hahn J. Methods in Bioengineering: Systems Analysis of Biological Networks 2009, Artech House Publishers.
26. Kiparissides A., Kucherenko S., Mantalaris A., Pistikopoulos E. Global sensitivity analysis challenges in biological systems modeling. Ind. Eng. Chem. Res. 2009, 48:7168-7180.
27. Kiparissides A., Koutinas M., Kontoravdi C., Mantalaris A., Pistikopoulos E.N. 'Closing the loop' in biological systems modeling-From the in silico to the in vitro. Automatica 2011, 47:1147-1155.
28. Kopf, M., Baumann, H., Freer, G., Freudenberg, M., Lamers, M., Kishimoto, T., Zinkernagel, R., Bluethmann, H., Köhler, G., 1994. Impaired Immune and Acute-phase Responses in Interleukin-6-deficient Mice.
29. Kovacs E.J., Palmer J.L., Fortin C.F., Fulop T., Goldstein D.R., Linton P.J. Aging and innate immunity in the mouse: impact of intrinsic and extrinsic factors. Trends Immunol. 2009, 30:319-324. 10.1016/j.it.2009.03.012.
30. Krakauer T., Buckley M.J., Fisher D. Proinflammatory mediators of toxic shock and their correlation to lethality. Mediators Inflamm. 2010.
31. Kruttgen A., Rose-John S. Interleukin-6 in sepsis and capillary leakage syndrome. J. Interferon Cytokine Res. 2012, 32:60-65. 10.1089/jir.2011.0062.
32. Kumar R., Clermont G., Vodovotz Y., Chow C.C. The dynamics of acute inflammation. J. Theor. Biol. 2004, 230:145-155.
33. Lagoa C.E., Bartels J., Baratt A., Tseng G., Clermont G., Fink M.P., Billiar T.R., Vodovotz Y. The role of initial trauma in the host[U+05F3]s response to injury and hemorrhage: insights from a correlation of mathematical simulations and hepatic transcriptomic analysis. Shock 2006, 26:592-600.
34. Li G., Rabitz H. General formulation of HDMR component functions with independent and correlated variables. J. Math. Chem. 2012, 50:99-130.
35. Li G., Rosenthal C., Rabitz H. High dimensional model representations. J. Phys. Chem. A 2001, 105:7765-7777.
36. Li G., Wang S.W., Rabitz H. Practical approaches to construct RS-HDMR component functions. J. Phys. Chem. A 2002, 106:8721-8733.
37. Li G., Wang S.W., Rabitz H., Wang S., Jaffé P. Global uncertainty assessments by high dimensional model representations (HDMR). Chem. Eng. Sci. 2002, 57:4445-4460.
38. Li G., Rabitz H., Yelvington P.E., Oluwole O.O., Bacon F., Kolb C.E., Schoendorf J. Global sensitivity analysis for systems with independent and/or correlated inputs. J. Phys. Chem. A 2010, 114:6022-6032.
39. Lyakh L., Trinchieri G., Provezza L., Carra G., Gerosa F. Regulation of interleukin-12/interleukin-23 production and the T-helper 17 response in humans. Immunol. Rev. 2008, 226:112-131. 10.1111/j.1600-065X.2008.00700.x.
40. MacMicking J.D., Nathan C., Hom G., Chartrain N., Fletcher D.S., Trumbauer M., Stevens K., Xie Q., Sokol K., Hutchinson N. Altered responses to bacterial infection and endotoxic shock in mice lacking inducible nitric oxide synthase. Cell 1995, 81:641-650.
41. Marino S., Hogue I.B., Ray C.J., Kirschner D.E. A methodology for performing global uncertainty and sensitivity analysis in systems biology. J. Theor. Biol. 2008, 254:178-196. 10.1016/j.jtbi.2008.04.011.
42. Mathew, S., Sundararaj, S., Mamiya, H., Banerjee, I., 2014. Regulatory interactions maintaining self-renewal of human embryonic stem cells as revealed through a systems analysis of PI3K/AKT pathway. Bioinformatics Accepted, in press, (E-pub ahead of print). http://dx.doi.org/10.1093/bioinformatics/btu209.
43. Matzinger P. The danger model: a renewed sense of self. Sci. Signalling 2002, 296:301.
44. Medzhitov R. Origin and physiological roles of inflammation. Nature 2008, 454:428-435. 10.1038/nature07201.
45. Mi Q., Constantine G., Ziraldo C., Solovyev A., Torres A., Namas R., Bentley T., Billiar T.R., Zamora R., Puyana J.C., Vodovotz Y. A dynamic view of trauma/hemorrhage-induced inflammation in mice: principal drivers and networks. PLoS One 2011, 6:e19424. 10.1371/journal.pone.0019424.
46. Mihara M., Hashizume M., Yoshida H., Suzuki M., Shiina M. IL-6/IL-6 receptor system and its role in physiological and pathological conditions. Clin. Sci. 2012, 122:143-159.
47. Miki S., Takeyama N., Tanaka T., Nakatani T. Immune dysfunction in endotoxicosis: role of nitric oxide produced by inducible nitric oxide synthase. Crit. Care Med. 2005, 33:716-720.
48. Miller M.A., Feng X.J., Li G., Rabitz H.A. Identifying biological network structure, predicting network behavior, and classifying network state with high dimensional model representation (hdmr). PLoS One 2012, 7:e37664.
49. Namas R.A., Bartels J., Hoffman R., Barclay D., Billiar T.R., Zamora R., Vodovotz Y. Combined in silico, in vivo, and in vitro studies shed insights into the acute inflammatory response in middle-aged mice. PLoS One 2013, 8:e67419. 10.1371/journal.pone.0067419.
50. Nathan C. Inducible nitric oxide synthase: what difference does it make?. J. Clin. Invest. 1997, 100:2417.
51. Nathan C. Points of control in inflammation. Nature 2002, 420:846-852. 10.1038/nature01320.
52. Neugebauer E.A.M., Willy C., Sauerland S. Complexity and non-linearity in shock research: reductionism or synthesis?. Shock 2001, 16:252-258.
53. Nieman G., Brown D., Sarkar J., Kubiak B., Ziraldo C., Dutta-Moscato J., Vieau C., Barclay D., Gatto L., Maier K. A two-compartment mathematical model of endotoxin-induced inflammatory and physiologic alterations in swine*. Crit. Care Med. 2012, 40:1052.
54. Okino M.S., Mavrovouniotis M.L. Simplification of mathematical models of chemical reaction systems. Chem. Rev. 1998, 98:391-408.
55. Parker R.S., Clermont G. Systems engineering medicine: engineering the inflammation response to infectious and traumatic challenges. J. R. Soc. Interface 2010, 7:989-1013. 10.1098/rsif.2009.0517.
56. Parker S.J., Watkins P.E. Experimental models of Gram-negative sepsis. Br. J. Surg. 2001, 88:22-30.
57. Pinsky M.R. Dysregulation of the immune response in severe sepsis. Am. J. Med. Sci. 2004, 328:220-229.
58. Plackett T.P., Boehmer E.D., Faunce D.E., Kovacs E.J. Aging and innate immune cells. J. Leukocyte Biol. 2004, 76:291-299. 10.1189/jlb.1103592.
59. Prince J.M., Levy R.M., Bartels J., Baratt A., Kane J.M., Lagoa C., Rubin J., Day J., Wei J., Fink M.P. In silico and in vivo approach to elucidate the inflammatory complexity of CD14-deficient mice. Mol. Med. 2006, 12:88.
60. Purswani M.U., Eckert S.J., Arora H.K., Noel G.J. Effect of ciprofloxacin on lethal and sublethal challenge with endotoxin and on early cytokine responses in a murine in vivo model. J. Antimicrob. Chemother. 2002, 50:51-58.
61. Reynolds A., Rubin J., Clermont G., Day J., Vodovotz Y., Bard Ermentrout G. A reduced mathematical model of the acute inflammatory response: I. Derivation of model and analysis of anti-inflammation. J. Theor. Biol. 2006, 242:220-236.
62. Rice R.G., Do D.D. Applied Mathematics and Modeling for Chemical Engineers 2012, John Wiley & Sons.
63. Romani L., Puccetti P., Bistoni F. Interleukin-12 in infectious diseases. Clin. Microbiol. Rev. 1997, 10:611-636.
64. Sahle S., Mendes P., Hoops S., Kummer U. A new strategy for assessing sensitivities in biochemical models. Philos. Trans. R. Soc. London, Ser. A 2008, 366:3619-3631.
65. Saltelli A., Tarantola S., Chan K.-S. A quantitative model-independent method for global sensitivity analysis of model output. Technometrics 1999, 41:39-56.
66. Saltelli A., Ratto M., Andres T., Campolongo F., Cariboni J., Gatelli D., Saisana M., Tarantola S. Global Sensitivity Analysis: The Primer 2008, Wiley-Interscience.
67. Salvemini D., Billiar T.R., Vodovotz Y. Nitric Oxide and Inflammation 2001, Birkhauser.
68. Scheff J.D., Calvano S.E., Androulakis I.P. Predicting critical transitions in a model of systemic inflammation. J. Theor. Biol. 2013, 338:9-15. 10.1016/j.jtbi.2013.08.011.
69. Scheff J.D., Mavroudis P.D., Foteinou P.T., An G., Calvano S.E., Doyle J., Dick T.E., Lowry S.F., Vodovotz Y., Androulakis I.P. A multiscale modeling approach to inflammation: a case study in human endotoxemia. J. Comput. Phys 2012.
70. Scheller J., Chalaris A., Schmidt-Arras D., Rose-John S. The pro- and anti-inflammatory properties of the cytokine interleukin-6. Biochim. Biophys. Acta 2011, 1813:878-888. 10.1016/j.bbamcr.2011.01.034.
71. Schilders W.H.A., Van der Vorst H.A., Rommes J. Model Order Reduction: Theory, Research Aspects and Applications 2008, Springer.
72. Sobol' I.M. On quasi-monte carlo integrations. Math. Comput. Simul. 1998, 47:103-112.
73. Sobol' I.M. Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math. Comput. Simul. 2001, 55:271-280.
74. Song M., Kellum J.A. Interleukin-6. Crit. Care Med. 2005, 33:S463.
75. Teukolski S.A., Flannery B.P., Press W.H., Vetterling W.T. Numerical Recipes in FORTRAN-The Art of Scientific Computing 1989, University Press.
76. Torres A., Bentley T., Bartels J., Sarkar J., Barclay D., Namas R., Constantine G., Zamora R., Puyana J.C., Vodovotz Y. Mathematical modeling of posthemorrhage inflammation in mice: studies using a novel, computer-controlled, closed-loop hemorrhage apparatus. Shock 2009, 32:172-178.
77. Vincent J.L., Abraham E. The last 100 years of sepsis. Am. J. Respir. Crit. Care Med. 2006, 173:256-263.
78. Vodovotz Y., An G. Systems biology and inflammation. Syst. Biol. Drug Discovery Dev.: Methods Protoc. 2009, 181-201.
79. Vodovotz Y., Billiar T.R. In silico modeling: methods and applications to trauma and sepsis. Crit. Care Med. 2013, 41:2008-2014. 10.1097/CCM.0b013e31829a6eb4.
80. Vodovotz Y., Clermont G., Chow C., An G. Mathematical models of the acute inflammatory response. Curr. Opin. Crit. Care 2004, 10:383-390.
81. Vodovotz Y., Csete M., Bartels J., Chang S., An G. Translational systems biology of inflammation. PLoS Comput. Biol. 2008, 4:e1000014. 10.1371/journal.pcbi.1000014.
82. Vodovotz Y., Constantine G., Rubin J., Csete M., Voit E.O., An G. Mechanistic simulations of inflammation: current state and future prospects. Math. Biosci. 2009, 217:1-10.
83. Vodovotz Y., Chow C.C., Bartels J., Lagoa C., Prince J.M., Levy R.M., Kumar R., Day J., Rubin J., Constantine G. In silico models of acute inflammation in animals. Shock 2006, 26:235-244.
84. Wada Y., Otu H., Wu S., Abid M.R., Okada H., Libermann T., Kodama T., Shih S.-C., Minami T., Aird W.C. Preconditioning of primary human endothelial cells with inflammatory mediators alters the "set point" of the cell. FASEB J. 2005, 19:1914-1916.
85. Wakahara K., Kobayashi H., Yagyu T., Matsuzaki H., Kondo T., Kurita N., Sekino H., Inagaki K., Suzuki M., Kanayama N. Major articles and brief report-bacteria-bikunin suppresses lipopolysaccharide-induced lethality through down-regulation of tumor necrosis factor-a and interleukin-1b in macrophages. J. Infect. Dis. 2005, 191:930-938.
86. Wei X., Charlesi I.G., Smithi A., Xu D., Muller W. Mice lacking inducible nitric oxide synthase. Nature 1995, 375:1.
87. Wright C.E., Rees D.D., Moncada S. Protective and pathological roles of nitric oxide in endotoxin shock. Cardiovasc. Res. 1992, 26:48-57.
88. Zamora R., Vodovotz Y., Billiar T.R. Inducible nitric oxide synthase and inflammatory diseases. Mol. Med. 2000, 6:347-373.