Pathophysiology of Haemostasis and Thrombosis
Mathematical Modeling and Computer Simulation in Blood CoagulationAtaullakhanov F.I.a, b, c · Panteleev M.A.aaLaboratory of Physical Biochemistry of Blood, National Research Center for Hematology, Russian Academy of Medical Sciences, Moscow, bLaboratory of Metabolic Modeling and Bioinformatics, Institute of Theoretical and Experimental Biophysics, Pushchino, Moscow Region, and cFaculty of Physics, Moscow State University, Leninskie Gory, Moscow, Russia
F.I. Ataullakhanov Laboratory of Physical Biochemistry of Blood, National Research Center for Hematology Russian Academy of Medical Sciences, Novozykovskii pr. 4a Moscow 125167 (Russia) Tel. +7 095 212 55 31, Fax +7 095 212 88 70, E-Mail fazly@hc.comcor.ru |
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Abstract
Over the last two decades, mathematical modeling has become a popular tool in study of blood coagulation. The in silico methods were able to yield interesting and significant results in the understanding of both individual reaction mechanisms and regulation of large sections of the coagulation cascade. The objective of this paper is to review the development of theoretical research in hemostasis and thrombosis, to summarize the main findings, and outline problems and possible prospects in the use of mathematical modeling and computer simulation approaches. This review is primarily focused on the studies dealing with: (1) the membrane-dependent reactions of coagulation; (2) regulation of the coagulation cascade, including effects of positive and negative feedback loops, diffusion of coagulation factors, and blood flow.
© 2005 S. Karger AG, Basel
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References
- Schenone M, Furie BC, Furie B: The blood coagulation cascade. Curr Opin Hematol 2004;11:272–277.
-
Hemostasis and Thrombosis: Basic Principles and Clinical Practice. Philadelphia, Lippincott Williams & Wilkins, 2001.
-
Turitto VT, Hall CL: Mechanical factors affecting hemostasis and thrombosis. Thromb Res 1998;92:S25–S31.
External Resources
-
Heinrich R, Schuster S: The Regulation of Cellular Systems. New York, Chapman & Hall, 1996.
-
Heinrich R, Reder C: Metabolic control analysis of relaxation processes. J Theor Biol 1991;151:343–350.
External Resources
- Acerenza L, Sauro HM, Kacser H: Control analysis of time-dependent metabolic systems. J Theor Biol 1989;137:423–444.
- Reijenga KA, Westerhoff HV, Kholodenko BN, Snoep JL: Control analysis for autonomously oscillating biochemical networks. Biophys J 2002;82:99–108.
- Jesty J, Beltrami E, Willems G: Mathematical analysis of a proteolytic positive-feedback loop: dependence of lag time and enzyme yields on the initial conditions and kinetic parameters. Biochemistry 1993;32:6266–6274.
-
Levine SN: Enzyme amplifier kinetics. Science 1966;152:651–653.
External Resources
- Khanin MA, Semenov VV: A mathematical model of the kinetics of blood coagulation. J Theor Biol 1989;136:127–134.
- Xu CQ, Zeng YJ, Gregersen H: Dynamic model of the role of platelets in the blood coagulation system. Med Eng Phys 2002;24:587–593.
-
Hirayama H, Yoshii K, Ojima H, Kawai N, Gotoh S, Fukuyama Y: Linear systems analysis of blood clotting system. IEICE Trans Fundamentals 1995;E78-A:1419–1431.
- Peletier MA, Westerhoff HV, Kholodenko BN: Control of spatially heterogeneous and time-varying cellular reaction networks: a new summation law. J Theor Biol 2003;225:477–487.
- Davie EW, Ratnoff OD: Waterfall sequence for intrinsic blood clotting. Science 1964;145:1310–1312.
- Macfarlane RG: An enzyme cascade in the blood clotting mechanism, and its function as a biochemical amplifier. Nature 1964;202:498–499.
-
Moro A, Bharucha-Reid AT: On the kinetics of enzyme amplifier systems. Math Biosci 1969;5:391–402.
External Resources
-
Martorana F, Moro A: On the kinetics of enzyme amplifier systems with negative feedbacks. Math Biosci 1974;21:77–84.
External Resources
- Semenov VV, Khanin MA: Nonlinear effects in kinetics of blood coagulation. Biofizika 1990;35:139–141.
- Beltrami E, Jesty J: Mathematical analysis of activation thresholds in enzyme-catalyzed positive feedbacks: application to the feedbacks of blood coagulation. Proc Natl Acad Sci USA 1995;92:8744–8748.
- Jesty J, Rodriguez J, Beltrami E: Demonstration of a threshold response in a proteolytic feedback system: control of the autoactivation of factor XII. Pathophysiol Haemost Thromb 2005;34:71–79.
- Zarnitsina VI, Pokhilko AV, Ataullakhanov FI: A mathematical model for the spatio-temporal dynamics of intrinsic pathway of blood coagulation. II. Results. Thromb Res 1996;84:333–344.
- Qiao YH, Xu CQ, Zeng YJ, Xu XH, Zhao H, Xu H: The kinetic model and simulation of blood coagulation – the kinetic influence of activated protein C. Med Eng Phys 2004;26:341–347.
- Khanin MA, Leytin VL, Popov AP: A mathematical model of the kinetics of platelets and plasma hemostasis system interaction. Thromb Res 1991;64:659–666.
- Fogelson AL, Kuharsky AL: Membrane binding site density can modulate activation thresholds in enzyme systems. J Theor Biol 1998;193:1–18.
- Kuharsky AL, Fogelson AL: Surface-mediated control of blood coagulation: the role of binding site densities and platelet deposition. Biophys J 2001;80:1050–1074.
- Ataullakhanov FI, Volkova RI, Pokhilko AV, Sinauridze EI: Threshold behavior of the blood coagulation system upon changes in calcium concentration. Biofizika 1994;39:713–720.
-
Ataullakhanov FI, Molchanova DA, Pokhilko AV: A simulated mathematical model of the blood coagulation system intrinsic pathway. Biofizika 1995;40:434–442.
External Resources
- Al Dieri R, Peyvandi F, Santagostino E, Giansily M, Mannucci PM, Schved JF, Beguin S, Hemker HC: The thrombogram in rare inherited coagulation disorders: its relation to clinical bleeding. Thromb Haemost 2002;88:576–582.
- Basmadjian D, Sefton MV, Baldwin SA: Coagulation on biomaterials in flowing blood: some theoretical considerations. Biomaterials 1997;18:1511–1522.
- Pokhilko AV, Ataullakhanov FI: Contact activation of blood coagulation: trigger properties and hysteresis. Kinetic recognition of foreign surfaces upon contact activation of blood coagulation: a hypothesis. J Theor Biol 1998;191:213–219.
- Zwaal RF, Comfurius P, Bevers EM: Lipid-protein interactions in blood coagulation. Biochim Biophys Acta 1998;1376:433–453.
- Liniger W, Karreman G, Rawala R, Colman R: Mathematical model of the activation of prothrombin by factor Xa and factory Vt. Bull Math Biol 1980;42:861–870.
- Nesheim ME, Tracy RP, Mann KG: ‘Clotspeed’, a mathematical simulation of the functional properties of prothrombinase. J Biol Chem 1984;259:1447–1453.
- van Rijn JL, Govers-Riemslag JW, Zwaal RF, Rosing J: Kinetic studies of prothrombin activation: effect of factor Va and phospholipids on the formation of the enzyme-substrate complex. Biochemistry 1984;23:4557–4564.
- Boskovic DS, Giles AR, Nesheim ME: Studies of the role of factor Va in the factor Xa-catalyzed activation of prothrombin, fragment 1.2-prethrombin-2, and dansyl-L-glutamyl-glycyl-L-arginine-meizothrombin in the absence of phospholipid. J Biol Chem 1990;265:10497–10505.
- Jesty J: Interaction of feedback control and product inhibition in the activation of factor X by factors IXa and VIII. Haemostasis 1991;21:208–218.
- Scandura JM, Walsh PN: Factor X bound to the surface of activated human platelets is preferentially activated by platelet-bound factor IXa. Biochemistry 1996;35:8903–8913.
- Panteleev MA, Saenko EL, Ananyeva NM, Ataullakhanov FI: Kinetics of factor X activation by the membrane-bound complex of factor IXa and factor VIIIa. Biochem J 2004;381:779–794.
- Nemerson Y, Gentry R: An ordered addition, essential activation model of the tissue factor pathway of coagulation: evidence for a conformational cage. Biochemistry 1986;25:4020–4033.
- Gentry R, Ye L, Nemerson Y: Surface-mediated enzymatic reactions: simulations of tissue factor activation of factor X on a lipid surface. Biophys J 1995;69:362–371.
- Baugh RJ, Broze GJ Jr, Krishnaswamy S: Regulation of extrinsic pathway factor Xa formation by tissue factor pathway inhibitor. J Biol Chem 1998;273:4378–4386.
- Panteleev MA, Zarnitsina VI, Ataullakhanov FI: Tissue factor pathway inhibitor: a possible mechanism of action. Eur J Biochem 2002;269:2016–2031.
- Lu G, Broze GJ Jr, Krishnaswamy S: Formation of factors IXa and Xa by the extrinsic pathway: differential regulation by tissue factor pathway inhibitor and antithrombin III. J Biol Chem 2004;279:17241–17249.
- Hemker HC, Beguin S: Phenotyping the clotting system. Thromb Haemost 2000;84:747–751.
- Willems GM, Lindhout T, Hermens WT, Hemker HC: Simulation model for thrombin generation in plasma. Haemostasis 1991;21:197–207.
- Jones KC, Mann KG: A model for the tissue factor pathway to thrombin. II. A mathematical simulation. J Biol Chem 1994;269:23367–23373.
- Hockin MF, Jones KC, Everse SJ, Mann KG: A model for the stoichiometric regulation of blood coagulation. J Biol Chem 2002;277:18322–18333.
- Lo K, Denney WS, Diamond SL: Stochastic modeling of blood coagulation initiation. Pathophysiol Haemost Thromb 2005;34:80–90.
- Leipold RJ, Bozarth TA, Racanelli AL, Dicker IB: Mathematical model of serine protease inhibition in the tissue factor pathway to thrombin. J Biol Chem 1995;270:25383–25387.
- Nagashima H: Studies on the different modes of action of the anticoagulant protease inhibitors DX-9065a and Argatroban. I. Effects on thrombin generation. J Biol Chem 2002;277:50439–50444.
- Bungay SD, Gentry PA, Gentry RD: A mathematical model of lipid-mediated thrombin generation. Math Med Biol 2003;20:105–129.
- Pohl B, Beringer C, Bomhard M, Keller F: The quick machine – a mathematical model for the extrinsic activation of coagulation. Haemostasis 1994;24:325–337.
-
Stortelder WJH, Hemker PW, Hemker HC: Mathematical modelling in blood coagulation. CWI Reports 1997;MAS-R9720:1–11.
- Tyurin KV, Khanin MA: Optimality principle and determination of kinetic constants for biochemical reactions. Math Med Biol 2005;22:1–14.
- Khanin MA, Rakov DV, Kogan AE: Mathematical model for the blood coagulation prothrombin time test. Thromb Res 1998;89:227–232.
- Kogan AE, Kardakov DV, Khanin MA: Analysis of the activated partial thromboplastin time test using mathematical modeling. Thromb Res 2001;101:299–310.
- Kramoroff A, Nigretto JM: In vitro factor XI activation mechanism according to an optimized model of activated partial thromboplastin time test. Blood Coagul Fibrinolysis 2001;12:289–299.
- Peyrou V, Lormeau JC, Herault JP, Gaich C, Pfliegger AM, Herbert JM: Contribution of erythrocytes to thrombin generation in whole blood. Thromb Haemost 1999;81:400–406.
- Griffin JH, Fernandez JA, Deguchi H: Plasma lipoproteins, hemostasis and thrombosis. Thromb Haemost 2001;86:386–394.
- London FS, Marcinkiewicz M, Walsh PN: A subpopulation of platelets responds to thrombin- or SFLLRN-stimulation with binding sites for factor IXa. J Biol Chem 2004;279:19854–19859.
- Baldwin SA, Basmadjian D: A mathematical model of thrombin production in blood coagulation. I. The sparsely covered membrane case. Ann Biomed Eng 1994;22:357–370.
- Chung TW, O’Rear EA: A model for analyzing the formation of thrombin in vessels. Comput Biol Med 1994;24:31–41.
- Ataullakhanov FI, Guriia GT, Safroshkina AI: Spatial aspects of the dynamics of blood coagulation. II. Phenomenological model. Biofizika 1994;39:97–106.
- Zarnitsina VI, Pokhilko AV, Ataullakhanov FI: A mathematical model for the spatio-temporal dynamics of intrinsic pathway of blood coagulation. I. The model description. Thromb Res 1996;84:225–236.
- Ovanesov MV, Ananyeva NM, Panteleev MA, Ataullakhanov FI, Saenko EL: Initiation and propagation of coagulation from tissue factor bearing cell monolayers to plasma: initiator cells do not regulate spatial growth rate. J Thromb Haemost 2005;3:321–331.
-
Ataullakhanov FI, Zarnitsina VI, Kondratovich AYu, Lobanova ES, Sarbash VI: A new class of stopping self-sustained waves: a factor determining the spatial dynamics of blood coagulation. Physics-Uspekhi 2002;45:619–636.
External Resources
-
Pokhilko AV, Ataullakhanov FI: Spatial dynamics of blood coagulation. Mathematical model. Biomembrany 2002;19:250–263.
External Resources
- Ovanesov MV, Krasotkina JV, Ul’yanova LI, Abushinova KV, Plyushch OP, Domogatskii SP, Vorob’ev AI, Ataullakhanov FI: Hemophilia A and B are associated with abnormal spatial dynamics of clot growth. Biochim Biophys Acta 2002;1572:45–57.
-
Zarnitsina VI, Ataullakhanov FI, Lobanov AI, Morozova OL: Dynamics of spatially nonuniform patterning in the model of blood coagulation. Chaos 2001;11:57–70.
External Resources
- Lobanova ES, Ataullakhanov FI: Unstable trigger waves induce various intricate dynamic regimes in a reaction-diffusion system of blood clotting. Phys Rev Lett 2003;91:138301.
-
Lobanova ES, Ataullakhanov FI: Running pulses of complex shape in a reaction-diffusion model. Phys Rev Lett 2004;93:098303.
External Resources
-
Lobanova ES, Shnol EE, Ataullakhanov FI: Complex dynamics of the formation of spatially localized standing structures in the vicinity of saddle-node bifurcations of waves in the reaction-diffusion model of blood clotting. Phys Rev E Stat Nonlin Soft Matter Phys 2004;70:032903.
External Resources
- Beltrami E, Jesty J: The role of membrane patch size and flow in regulating a proteolytic feedback threshold on a membrane: possible application in blood coagulation. Math Biosci 2001;172:1–13.
-
Fogelson AL, Tania N: Coagulation under flow: the influence of flow-mediated transport on the initiation and inhibition of coagulation. Pathophysiol Haemost Thromb 2005;34:91–108.
-
Chulichkov AL, Nikolaev AV, Lobanov AI, Guria GT: Threshold activation of blood coagulation and thrombus growth under flow conditions. Matematicheskoe modelirovanie 2000;12:75–96.
-
Guzevatykh AP, Lobanov AI, Guria GT: Threshold intervascular blood coagulation as a result of stenosis developement. Matematicheskoe modelirovanie 2000;12:39–60.
-
Lobanov AI, Starozhilova TK, Guria GT: Numerical investigation of pattern formation processes in blood coagulation. Matematicheskoe modelirovanie 1997;9:83–95.
-
Lobanov AI, Starozhilova TK: The effect of convective flows on blood coagulation processes. Pathophysiol Haemost Thromb 2005;34: 121–134.
-
Anand M, Rajagopal K, Rajagopal KR: A model incorporating some of the mechanical and biochemical factors underlying clot formation and dissolution in flowing blood. J Theor Med 2004;6:183–218.
- Anand M, Rajagopal K, Rajagopal KR: A model for the formation and lysis of blood clots. Pathophysiol Haemost Thromb 2005; 34:109–120.
-
Ermakova EA, Panteleev MA, Shnol EE: Blood coagulation and propagation of autowaves in flow. Pathophysiol Haemost Thromb 2005; 34:135–142.
External Resources
- Falati S, Gross P, Merrill-Skoloff G, Furie BC, Furie B: Real-time in vivo imaging of platelets, tissue factor and fibrin during arterial thrombus formation in the mouse. Nat Med 2002;8:1175–1181.
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Published online: January 26, 2006
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