title: Fractal-like kinetics of intracellular enzymatic reactions: a chemical framework of endotoxin tolerance and a possible non-specific contribution of macromolecular crowding to cross-tolerance.
abstract: BACKGROUND
  The response to endotoxin (LPS), and subsequent signal transduction lead to the production of cytokines such as tumor necrosis factor-α (TNF-α) by innate immune cells. Cells or organisms pretreated with endotoxin enter into a transient state of hyporesponsiveness, referred to as endotoxin tolerance (ET) which represents a particular case of negative preconditioning. Despite recent progress in understanding the molecular basis of ET, there is no consensus yet on the primary mechanism responsible for ET and for the more complex cases of cross tolerance. In this study, we examined the consequences of the macromolecular crowding (MMC) and of fractal-like kinetics (FLK) of intracellular enzymatic reactions on the LPS signaling machinery. We hypothesized that this particular type of enzyme kinetics may explain the development of ET phenomenon.
  
  
  METHODS
  Our aim in the present study was to characterize the chemical kinetics framework in ET and determine whether fractal-like kinetics explains, at least in part, ET. We developed an ordinary differential equations (ODE) mathematical model that took into account the links between the MMC and the LPS signaling machinery leading to ET. We proposed that the intracellular fractal environment (MMC) contributes to ET and developed two mathematical models of enzyme kinetics: one based on Kopelman's fractal-like kinetics framework and the other based on Savageau's power law model.
  
  
  RESULTS
  Kopelman's model provides a good image of the potential influence of a fractal intracellular environment (MMC) on ET. The Savageau power law model also partially explains ET. The computer simulations supported the hypothesis that MMC and FLK may play a role in ET.
  
  
  CONCLUSIONS
  The model highlights the links between the organization of the intracellular environment, MMC and the LPS signaling machinery leading to ET. Our FLK-based model does not minimize the role of the numerous negative regulatory factors. It simply draws attention to the fact that macromolecular crowding can contribute significantly to the induction of ET by imposing geometric constrains and a particular chemical kinetic for the intracellular reactions.
authors.affiliation: Fundeni Clinical Institute, Carol Davila University of Medicine and Pharmacy, 258 Fundeni Street, Bucharest, Romania. catvasilescu@gmail.com.
authors.forename: Catalin
authors.initials: C
authors.lastname: Vasilescu
authors.forename: Mircea
authors.initials: M
authors.lastname: Olteanu
authors.forename: Paul
authors.initials: P
authors.lastname: Flondor
authors.forename: George A
authors.initials: GA
authors.lastname: Calin
mesh_terms: D003429:Cross Reactions / Q000276:immunology*; D004731:Endotoxins / Q000276:immunology*; D017709:Fractals; D007108:Immune Tolerance; D042541:Intracellular Space / Q000201:enzymology*; D007700:Kinetics; D008070:Lipopolysaccharides / Q000276:immunology; D046911:Macromolecular Substances / Q000378:metabolism*; D008954:Models, Biological; D014409:Tumor Necrosis Factor-alpha / Q000378:metabolism
chemical_list: D004731:Endotoxins; D008070:Lipopolysaccharides; D046911:Macromolecular Substances; D014409:Tumor Necrosis Factor-alpha
references.citation: Math Biosci. 2009 Jan;217(1):53-63
references.pmid: 18835283
references.citation: Proc R Soc Lond B Biol Sci. 1969 Jul 1;173(1032):411-20
references.pmid: 4389515
references.citation: Math Biosci. 2009 Jan;217(1):19-26
references.pmid: 18950647
references.citation: Cell. 2009 May 1;137(3):586-586.e1
references.pmid: 19410551
references.citation: Math Biosci. 2009 Jan;217(1):43-52
references.pmid: 18950646
references.citation: Int Rev Cytol. 2000;192:189-221
references.pmid: 10553280
references.citation: Math Biosci. 2009 Jan;217(1):1-10
references.pmid: 18835282
references.citation: BMC Syst Biol. 2011 May 14;5:71
references.pmid: 21569565
references.citation: J Clin Invest. 1990 Apr;85(4):1108-18
references.pmid: 2318968
references.citation: PLoS One. 2012;7(6):e39418
references.pmid: 22761790
references.citation: Chemphyschem. 2006 Jul 17;7(7):1422-4
references.pmid: 16755640
references.citation: J Cell Sci. 2006 Jul 15;119(Pt 14):2863-9
references.pmid: 16825427
references.citation: Math Biosci. 2009 Jan;217(1):27-42
references.pmid: 18840451
references.citation: Math Biosci. 2009 Jan;217(1):11-8
references.pmid: 18851981
references.citation: Chirurgia (Bucur). 2009 Mar-Apr;104(2):195-201
references.pmid: 19499663
references.citation: FEBS Lett. 2013 Apr 17;587(8):1046-52
references.pmid: 23337873
references.citation: Front Physiol. 2011 Sep 21;2:50
references.pmid: 21960972
references.citation: Langenbecks Arch Surg. 2008 Jul;393(4):473-8
references.pmid: 18320210
references.citation: Exp Cell Res. 1991 Mar;193(1):127-33
references.pmid: 1995288
references.citation: Philos Trans A Math Phys Eng Sci. 2012 Jun 28;370(1969):3023-39
references.pmid: 22615474
references.citation: Science. 1988 Sep 23;241(4873):1620-6
references.pmid: 17820893
references.citation: J Cell Sci. 2004 Jun 1;117(Pt 13):2769-75
references.pmid: 15150320
references.citation: J Immunol. 2011 Feb 1;186(3):1723-34
references.pmid: 21178010
references.citation: BMC Biophys. 2011 Mar 02;4:3
references.pmid: 21595998
references.citation: J Trauma. 2003 Jan;54(1):104-12; discussion 112-3
references.pmid: 12544905
references.citation: Math Biosci. 2011 Aug;232(2):151-63
references.pmid: 21624378
references.citation: J Endotoxin Res. 2003;9(2):101-7
references.pmid: 12803883
references.citation: Trends Biochem Sci. 2001 Oct;26(10):597-604
references.pmid: 11590012
references.citation: J Cell Mol Med. 2003 Oct-Dec;7(4):417-24
references.pmid: 14754510
references.citation: Prog Biophys Mol Biol. 2004 Jun-Jul;85(2-3):235-60
references.pmid: 15142746
references.citation: Trends Immunol. 2009 Oct;30(10):475-87
references.pmid: 19781994
references.citation: FEBS Lett. 1994 May 9;344(1):1-4
references.pmid: 8181555
references.citation: Biophys J. 2002 Oct;83(4):1891-901
references.pmid: 12324410
references.citation: J Immunol. 2009 Jul 1;183(1):533-42
references.pmid: 19542464
references.citation: J Immunol. 2002 Feb 1;168(3):1389-96
references.pmid: 11801680
references.citation: Proc Natl Acad Sci U S A. 2010 Oct 26;107(43):18457-62
references.pmid: 20937902
references.citation: Biochim Biophys Acta. 2000 Jan 3;1500(1):125-36
references.pmid: 10564725
references.citation: Shock. 2003 Aug;20(2):176-82
references.pmid: 12865664
references.citation: C R Biol. 2003 Feb;326(2):149-59
references.pmid: 12754934
references.citation: Immunology. 2005 Oct;116(2):203-12
references.pmid: 16162269
references.citation: J Theor Biol. 1995 Sep 7;176(1):115-24
references.pmid: 7475096