Skip to main content
Log in

A model for the formation, growth, and dissolution of clots in vitro. Effect of the intrinsic pathway on antithrombin III deficiency and protein C deficiency

  • Original Research
  • Published:
International Journal of Advances in Engineering Sciences and Applied Mathematics Aims and scope Submit manuscript

Abstract

The mechanics of blood flow with clot formation, growth, and dissolution is affected by the biochemical reactions underlying clot formation, growth, and dissolution. A framework of models combining the biochemistry and mechanics of the phenomenon should include a model for the biochemistry underlying the same. A mathematical model to describe the biochemical changes underlying the formation, growth and dissolution of clots in vitro has been developed in Anand et al. (J Theor Biol 253(4):725–738, 2008). In this paper, the model is extended to include the equations for the intrinsic pathway thereby addressing a shortcoming of the previous model. The effect of the intrinsic pathway on clot formation, growth and dissolution in quiescent plasma, as well as the effect on the impact of ATIII and Protein C deficiencies on clot growth parameters is documented. The inclusion of the intrinsic pathway leads to faster appearance of the clot, and a larger clot. The intrinsic pathway has minimal impact on the effects of ATIII and Protein C deficiencies.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Ahmad, S.S., Rawalasheikh, R., Walsh, P.N.: Comparative interactions of factor-IX and factor-IXa with human platelets. J. Biol. Chem. 264(6), 3244–3251 (1989)

    Google Scholar 

  2. Anand, M., Rajagopal, K., Rajagopal, K.R.: A model incorporating some of the mechanical and biochemical factors underlying clot formation and dissolution in flowing blood. J. Theor. Med. 5(3–4), 183–218 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  3. Anand, M., Rajagopal, K., Rajagopal, K.R.: A model for the formation, growth, and lysis of clots in quiescent plasma. A comparison between the effects of antithrombin III deficiency and protein C deficiency. J. Theor. Biol. 253(4), 725–738 (2008)

    Article  Google Scholar 

  4. Bergel, D.H.: The dynamic elastic properties of the arterial wall. J. Physiol. 156, 458–469 (1961)

    Google Scholar 

  5. Bodnar, T., Sequeira, A.: Numerical simulation of the coagulation dynamics of blood. Comput. Math. Method Med. 9(2), 83–104 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Booth, N.A.: Fibrinolysis and thrombosis. Baillière Clin. Haem. 12(3), 423–433 (1999)

    Google Scholar 

  7. Bridges, C., Rajagopal, K.R.: Pulsatile flow of a chemically-reacting nonlinear fluid. Comput. Math. Appl. 52(6–7), 1131–1144 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  8. Brummel-Ziedins, K., Orfeo, T., Jenny, N.S., Everse, S.J., Mann, K.G.: Blood coagulation and fibrinolysis. In: Wintrobe’s Hematology, 11th edn. Lippncott, Williams, and Wilkins, Philadelphia (2004)

  9. Bungay, S.D., Gentry, P.A., Gentry, R.D.: A mathematical model of lipid-mediated thrombin generation. Math. Med. Biol. 20, 105–129 (2003)

    Article  MATH  Google Scholar 

  10. Butenas, S., Mann, K.G.: Blood coagulation. Biochemistry (Moscow) 67(1), 3–12 (2002)

    Article  Google Scholar 

  11. Chien, S., Usami, S., Dellenback, R.J., Gregersen, M.I.: Blood viscosity: influence of erythrocyte aggregation. Science 157(3790), 829–831 (1967)

    Article  Google Scholar 

  12. Chien, S., Usami, S., Dellenback, R.J., Gregersen, M.I.: Blood viscosity: influence of erythrocyte deformation. Science 157(3790), 827–829 (1967)

    Article  Google Scholar 

  13. Colman, R.W., Clowes, A.W., George, J.N., Hirsh, J., Marder, V.J.: Overview of hemostasis. In: Colman, R.W., Hirsh, J., Marder, V.J., Clowes, A.W., George, J.N. (eds) Hemostasis and Thrombosis, 4th edition., pp. 1–16. Lippincott, Williams and Wilkins (2001)

    Google Scholar 

  14. Danforth, C.M., Orfeo, T., Mann, K.G., Brummel-Ziedins, K.E., Everse, S.J.: The impact of uncertainty in a blood coagulation model. Math. Med. Biol. 26(4), 323–336 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  15. Davie, E.W., Ratnoff, O.D.: Waterfall sequence for intrinsic blood clotting. Science 145, 1310–1311 (1964)

    Article  Google Scholar 

  16. De Cristofaro, R., De Filippis, V.: Interaction of the 268–282 region of glycoprotein Ib alpha with the heparin-binding site of thrombin inhibits the enzyme activation of factor VIII. Biochem. J. 373(2), 593–601 (2003)

    Article  Google Scholar 

  17. Diamond, S.L., Anand, S.: Inner clot diffusion and permeation during fibrinolysis. Biophys. J. 65, 2622–2643 (1993)

    Article  Google Scholar 

  18. Ferry, J.D., Morrison, P.R.: Preparation and properties of serum and plasma proteins. VIII. The conversion of human fibrinogen to fibrin under various conditions. J. Am. Chem. Soc. 69, 388–400 (1947)

    Article  Google Scholar 

  19. Freyssinet, J.M., Orfanoudakis, F.T., Ravanat, C., Grunebaum, L., Gauchy, J., Cazenave, J.P., Wiesel, M.L.: The catalytic role of anionic phospholipids in the activation of protein C by factor Xa and expression of its anticoagulant function in human plasma. Blood. Coagul. Fibrin. 2, 691–698 (1991)

    Article  Google Scholar 

  20. Gailani, D., Broze, G.J.: Factor XI activation in a revised model of blood coagulation. Science 253(5022), 909–912 (1991)

    Article  Google Scholar 

  21. Heeb, M.J., Bischoff, R., Courtney, M., Griffin, J.H.: Inhibition of activated protein C by recombinant α1-antitrypsin variants with substitution of arginine or leucine for methionine. J. Biol. Chem. 265(4), 2365–2389 (1990)

    Google Scholar 

  22. Kalafatis, M., Egan, J.O., vant Veer, C., Cawthern, K.M., Mann, K.G.: The regulation of clotting factors. Crit. Rev. Eukar. Gene 7(3), 241–280 (1997)

    Google Scholar 

  23. Kaplan, K.L., Mather, T., DeMarco, L., Solomon, S.: Effect of fibrin on endothelial cell production of prostacyclin and tissue plasminogen activator. Arteriosclerosis 9(1), 43–49 (1989)

    Article  Google Scholar 

  24. Karsan, A.L., Harlan, J.M.: The blood vessel wall. In: Hoffman, R., Benz, E.J., Shattil, S.J., Furie, B., Cohen, H.J., Silberstein, L.E., McGlave, P. (eds) Hematology: Basic Principles and Practice, 3rd edn., pp. 1770–1782. Churchill Livingstone, New York (2000)

    Google Scholar 

  25. Kolev, K., L, C., Lerant, I., Tenekkejiev, K., Machovich, R.: Regulation of fibrinolytic activity of neutrophil leukocyte elastase, plasmin, and miniplasmin by plasma protease inhibitors. J. Biol. Chem. 269(25), 17030–17034 (1994)

    Google Scholar 

  26. Kolev, K., Longstaff, C., Machovich, R.: Fibrinolysis at the fluid–solid interface of thrombi. J. Biol. Chem. 3(4), 341–355 (2005)

    Google Scholar 

  27. Kolev, K., Machovich, R.: Molecular and cellular modulation of fibrinolysis. Thromb. Haemost. 89(4), 610 (2003)

    Google Scholar 

  28. Komiyama, Y., L, C., Lerant, I., Tenekkejiev, K., Machovich, R.: Proteolytic activation of human factors IX and X by recombinant human factor VIIa: effects of calcium, phospholipids, and tissue factor. Biochemistry (US) 29(40), 9418–9425 (1990)

    Article  Google Scholar 

  29. Krishnaswamy, S., Church, W.R., Nesheim, M.E., Mann, K.G.: Activation of human prothrombin by human prothrombinase. Influence of factor Va on the reaction mechanism. J. Biol. Chem. 262(7), 3291–3299 (1987)

    Google Scholar 

  30. Kuharsky, A., Fogelson, A.F.: Surface mediated control of blood coagulation: the role of binding site densities and platelet deposition. Biophys. J. 80, 1050–1094 (2001)

    Article  Google Scholar 

  31. Levin, E.G., Marzec, U., Anderson, J., Harker, L.A.: Thrombin stimulates tissue plasminogen activator release from cultured human endothelial cells. J. Clin. Invest. 74, 1988–1995 (1984)

    Article  Google Scholar 

  32. Levine, S.N.: Enzyme amplifier kinetics. Science 152, 651–653 (1966)

    Article  Google Scholar 

  33. Lijnen, H.R., Collen, D.: Molecular and cellular basis of fibrinolysis. In: Hoffman, R., Benz, E.J., Shattil, S.J., Furie, B., Cohen, H.J., Silberstein, L.E., McGlave, P. (eds) Hematology: Basic Principles and Practice, 3rd edn., pp. 1804–1814. Churchill Livingstone, New York (2000)

    Google Scholar 

  34. Luan, D., Zai, M., Varner, J.D.: Computationally derived points of fragility of a human cascase are consistent with current therapeutic strategies. PLOS Comput. Biol. 3(7), e142 (2007)

    Article  Google Scholar 

  35. MacFarlane, R.G.: An enzyme cascade model in the blood clotting mechanism, and its function as a biochemical amplifier. Nature 202, 498–499 (1964)

    Article  Google Scholar 

  36. Madison, E.L., Coombs, G.S., Corey, D.R.: Substrate-specificity of tissue-type plasminogen-activator—characterization of the fibrin-dependent specificity of t-PA for plasminogen. J. Biol. Chem. 270(13), 7558–7562 (1995)

    Article  Google Scholar 

  37. Mann, K.G.: The assembly of blood clotting complexes on membranes. Trends Biochem. Sci. 12(6), 229–233 (1987)

    Article  Google Scholar 

  38. Mann, K.G., Brummel-Ziedins, K., Orfeo, T., Butenas, S.: Models of blood coagulation. Blood Cell. Mol. Dis. 36, 108–117 (2006)

    Article  Google Scholar 

  39. Mann, K.G., Gaffney, D., Bovill, E.G.: Molecular biology, biochemistry, and lifespan of plasma coagulation factors. In: Beutler, E. (ed) Williams Hematology, 5th edn., pp. 1206–1226. McGraw Hill Inc., New York (1995)

    Google Scholar 

  40. Meijers, J.C.M., Vlooswijk, R.A.A., Bouma, B.N.: Inhibition of human blood coagulation factor XIa byC1-inhibitor. Biochemistry 27(12), 959–963 (1988)

    Article  Google Scholar 

  41. Monkovic, D.D., Tracy, P.B.: Functional characterization of human platelet-released factor V and its activation by factor Xa and thrombin. J. Biol. Chem. 265(28), 17132–17140 (1990)

    Google Scholar 

  42. Nesheim, M.E., Tracy, R.P., Mann, K.G.: “Clotspeed,” a mathematical simulation of the functional properties of prothrombinase. J. Biol. Chem. 259(3), 1447–1453 (1984)

    Google Scholar 

  43. Neuenschwander, P.F., Jesty, J.: Thrombin-activated and factor Xa-activated human factor VIII: differences in cofactor activity and decay rate. Arch. Biochem. Biophys. 296(2), 426–434 (1992)

    Article  Google Scholar 

  44. Orfeo, T., Butenas, S., Brummel-Ziedins, K.E., Mann, K.G.: The tissue factor requirement in blood coagulation. J. Biol. Chem. 280(52), 42887–42896 (2005)

    Article  Google Scholar 

  45. Ovanesov, M.V., Krasotkina, J.V., Ulyanova, L.I., Abushinova, K.V., Plyushch, O.P., Domogatskii, S.P., Vorobev, A.I., Ataullakhanov, F.I.: Hemophilia a and b are associated with abnormal spatial dynamics of clot growth. BBA Gen. Subj. 1572(1), 45–57 (2002)

    Article  Google Scholar 

  46. Panteleev, M.A., Ovanesov, M.V., Kireev, D.A., Shibeko, A.M., Sinauridze, E.I., Ananyeva, N.M., Butylin, A.A., Saenko, E.L., Ataullakhanov, F.I.: Spatial propagation and localization of blood coagulation are regulated by intrinsic and protein C pathways, respectively. Biophys. J. 90(5), 1489–1500 (2006)

    Article  Google Scholar 

  47. Perktold, K., Rappitsch, G.: Computer simulation of local blood flow and vessel mechanics in a compliant carotid artery bifurcation model. J. Biomech. 28(7), 845–856 (1995)

    Article  Google Scholar 

  48. Pixley, R.A., Schapira, M., Colman, R.W.: The regulation of human factor XIIa by plasma proteinase inhibitors. J. Biol. Chem. 260(3), 1723–1729 (1985)

    Google Scholar 

  49. Rawalasheikh, R., Ahmed, S.S., Ashby, B., Walsh, P.N.: Kinetics of coagulation factor X activation by platelet-bound factor IXa. Biochemistry (US) 29(10), 2606–2611 (1990)

    Article  Google Scholar 

  50. Schousboe, I., Feddersen, K., Rojkjaer, R.: Factor XIIa is a kinetically favorable plasminogen activator. Thromb. Haemost. 82, (1999)

  51. Schrauwen, Y., Kooistra, T., de Vries, R.E.M., Emeis, J.J.: Studies on the acute release of tissue-type plasminogen activator from human endothelial cells in vitro and in rats in vivo: evidence for a dynamic storage pool. Blood 85(12), 3510–3517 (1995)

    Google Scholar 

  52. Scott, C.F., Schapira, M., James, H.L., Cohen, A.B., Colman, R.W.: Inactivation of factor XIa by plasma protease inhibitors. J. Clin. Invest. 69(12), 844–852 (1982)

    Article  Google Scholar 

  53. Silverberg, M., Kaplan, A.P.: Enzymatic activities of activated and zymogen forms of human hageman factor (factor XII). Blood 60(1), 64–70 (1982)

    Google Scholar 

  54. Solymoss, S., Tucker, M.M., Tracy, P.B.: Kinetics of inactivation of membrane-bound factor Va by activated protein C. J. Biol. Chem. 263(29), 14884–14890 (1988)

    Google Scholar 

  55. Soons, H., Janssen-Claessen, T., Tans, G., Hemker, H.C.: Inhibition of factor XIa by antithrombin III. Biochemistry (US) 26(15), 4624–4629 (1987)

    Article  Google Scholar 

  56. Sun, Y., Gailani, D.: Identification of a factor IX binding site on the third apple domain of activated factor XI. J. Biol. Chem. 271(46), 29023–29028 (1996)

    Article  Google Scholar 

  57. Tankersly, D.L., Finlayson, J.S.: Kinetics of activation and auto-activation of human factor XII. Biochem 23, (1984)

  58. Thurston, G.B.: The viscoelasticity of blood. Biophys. J. 21(2), 1205–1217 (1972)

    Article  MathSciNet  Google Scholar 

  59. Tsiang, M., Paborsky, L.R., Li, W.X., Jain, A.K., Mao, C.T., Dunn, K.E., Lee, D.W., Matsumura, S.Y., Matteucci, M.D., Coutre, S.E., Leung, L.L.K., Gibbs, C.S.: Protein engineering thrombin for optimal specificity and potency of anticoagulant activity in vivo. Biochemistry (US) 35, 16449–16457 (1996)

    Article  Google Scholar 

  60. Van der Graaf, F., Koedam, J.A., Bouma, B.N.: Inactivation of kallikrein in human plasma. J. Clin. Invest. 71(1), 149–158 (1983)

    Article  Google Scholar 

  61. Virchow, R.: Über den faserstoff : V. phlogose und thrombose im gefäßsystem. In: Gesammelte Abhandlungen zur wissenschaftlichen Medicin, 1st edn. Verlag v. Meidinger, Sohn and Corp., Frankfurt am Main (1856)

  62. Wiebe, E.M., Stafford, A.R., Fredenburgh, J.C., Weitz, J.I.: Mechanism of catalysis of inhibition of factor IXa by antithrombin in the presence of heparin or pentasaccharide. J. Biol. Chem. 278(37), 35767–35774 (2003)

    Article  Google Scholar 

  63. Young, M.E., Carroad, P.A., Bell, R.L.: Estimation of diffusion coefficients of proteins. Biotechnol. Bioeng. 22, 947–955 (1980)

    Article  Google Scholar 

  64. Zarnitsina, V.I., Pokhilko, A.V., Ataullakhanov, F.I.: A mathematical model for the spatio-temporal dynamics of intrinsic pathway of blood coagulation. I. The model description. Thromb. Res. 84(4), 225–236 (1996)

    Article  Google Scholar 

  65. Zarnitsina, V.I., Pokhilko, A.V., Ataullakhanov, F.I.: A mathematical model for the spatio-temporal dynamics of intrinsic pathway of blood coagulation. II. Results. Thromb. Res. 84(5), 333–344 (1996)

    Article  Google Scholar 

Download references

Acknowledgements

DEL was supported from Professor K. R. Rajagopal’s endowment as a professor, and from an NSF grant: this support is gratefully acknowledged. MA thanks Kaminee Anand for drawing a major part of Fig. 1.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. Anand.

Additional information

Dedicated to Professor K. R. Rajagopal on his 60th birthday

Rights and permissions

Reprints and permissions

About this article

Cite this article

LaCroix, D.E., Anand, M. A model for the formation, growth, and dissolution of clots in vitro. Effect of the intrinsic pathway on antithrombin III deficiency and protein C deficiency. Int J Adv Eng Sci Appl Math 3, 93–105 (2011). https://doi.org/10.1007/s12572-011-0040-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12572-011-0040-0

Keywords

Navigation