A Model for the Stoichiometric Regulation of Blood Coagulation
2002; Elsevier BV; Volume: 277; Issue: 21 Linguagem: Inglês
10.1074/jbc.m201173200
ISSN1083-351X
AutoresMatthew F. Hockin, Kenneth C. Jones, Stephen J. Everse, Kenneth G. Mann,
Tópico(s)Hemophilia Treatment and Research
ResumoWe have developed a model of the extrinsic blood coagulation system that includes the stoichiometric anticoagulants. The model accounts for the formation, expression, and propagation of the vitamin K-dependent procoagulant complexes and extends our previous model by including: (a) the tissue factor pathway inhibitor (TFPI)-mediated inactivation of tissue factor (TF)·VIIa and its product complexes; (b) the antithrombin-III (AT-III)-mediated inactivation of IIa, mIIa, factor VIIa, factor IXa, and factor Xa; (c) the initial activation of factor V and factor VIII by thrombin generated by factor Xa-membrane; (d) factor VIIIa dissociation/activity loss; (e) the binding competition and kinetic activation steps that exist between TF and factors VII and VIIa; and (f) the activation of factor VII by IIa, factor Xa, and factor IXa. These additions to our earlier model generate a model consisting of 34 differential equations with 42 rate constants that together describe the 27 independent equilibrium expressions, which describe the fates of 34 species. Simulations are initiated by “exposing” picomolar concentrations of TF to an electronic milieu consisting of factors II, IX, X, VII, VIIa, V, and VIIII, and the anticoagulants TFPI and AT-III at concentrations found in normal plasma or associated with coagulation pathology. The reaction followed in terms of thrombin generation, proceeds through phases that can be operationally defined as initiation, propagation, and termination. The generation of thrombin displays a nonlinear dependence upon TF, AT-III, and TFPI and the combination of these latter inhibitors displays kinetic thresholds. At subthreshold TF, thrombin production/expression is suppressed by the combination of TFPI and AT-III; for concentrations above the TF threshold, the bolus of thrombin produced is quantitatively equivalent. A comparison of the model with empirical laboratory data illustrates that most experimentally observable parameters are captured, and the pathology that results in enhanced or deficient thrombin generation is accurately described. We have developed a model of the extrinsic blood coagulation system that includes the stoichiometric anticoagulants. The model accounts for the formation, expression, and propagation of the vitamin K-dependent procoagulant complexes and extends our previous model by including: (a) the tissue factor pathway inhibitor (TFPI)-mediated inactivation of tissue factor (TF)·VIIa and its product complexes; (b) the antithrombin-III (AT-III)-mediated inactivation of IIa, mIIa, factor VIIa, factor IXa, and factor Xa; (c) the initial activation of factor V and factor VIII by thrombin generated by factor Xa-membrane; (d) factor VIIIa dissociation/activity loss; (e) the binding competition and kinetic activation steps that exist between TF and factors VII and VIIa; and (f) the activation of factor VII by IIa, factor Xa, and factor IXa. These additions to our earlier model generate a model consisting of 34 differential equations with 42 rate constants that together describe the 27 independent equilibrium expressions, which describe the fates of 34 species. Simulations are initiated by “exposing” picomolar concentrations of TF to an electronic milieu consisting of factors II, IX, X, VII, VIIa, V, and VIIII, and the anticoagulants TFPI and AT-III at concentrations found in normal plasma or associated with coagulation pathology. The reaction followed in terms of thrombin generation, proceeds through phases that can be operationally defined as initiation, propagation, and termination. The generation of thrombin displays a nonlinear dependence upon TF, AT-III, and TFPI and the combination of these latter inhibitors displays kinetic thresholds. At subthreshold TF, thrombin production/expression is suppressed by the combination of TFPI and AT-III; for concentrations above the TF threshold, the bolus of thrombin produced is quantitatively equivalent. A comparison of the model with empirical laboratory data illustrates that most experimentally observable parameters are captured, and the pathology that results in enhanced or deficient thrombin generation is accurately described. The blood coagulation system is composed of a set of pro- and anticoagulant systems that maintain the balance of blood fluidity. Defects in this balance can result in either thrombotic or bleeding tendencies. Qualitative or quantitative alterations in this hemostatic balance can have devastating effects, producing hemorrhagic diseases (hemophilia A, hemophilia B, hemophilia C, para-hemophilia, hypoprothrombinemia) (1Mannucci P.M. Tuddenham E.G. N. Engl. J. Med. 2001; 344: 1773-1779Crossref PubMed Scopus (841) Google Scholar, 2Hoyer L.W.N. Engl. J. Med. 1994; 330: 38-47Crossref PubMed Scopus (375) Google Scholar, 3Ozsoylu S. Ozer F.L. Acta Haematol. 1973; 50: 305-314Crossref PubMed Scopus (29) Google Scholar, 4Poort S.R. Michiels J.J. Reitsma P.H. Thromb. Haemostasis. 1994; 72: 819-824Crossref PubMed Scopus (48) Google Scholar, 5Bolton-Maggs P.H. Baillieres Clin. Haematol. 1996; 9: 355-368Abstract Full Text PDF PubMed Scopus (36) Google Scholar, 6Chiu H.C. Whitaker E. Colman R.W. J. Clin. Invest. 1983; 72: 493-503Crossref PubMed Scopus (31) Google Scholar) or thrombotic diseases (antithrombin III (AT-III) 1The abbreviations used are: AT-IIIantithrombin IIITFPItissue factor pathway inhibitorTFtissue factorPCPSphospholipid vesicles composed of 25% phosphatidylserine and 75% phosphatidylcholine deficiency, protein C deficiency, protein S deficiency, and factor VLeiden) (7Beresford C.H. Blood Rev. 1988; 2: 239-250Crossref PubMed Scopus (46) Google Scholar, 8Reitsma P.H. Thromb. Haemostasis. 1997; 78: 344-350Crossref PubMed Scopus (67) Google Scholar, 9Griffin J.H. Heeb M.J. Schwarz H.P. Prog. Hematol. 1987; 15: 39-49PubMed Google Scholar, 10Bertina R.M. Koeleman B.P. Koster T. Rosendaal F.R. Dirven R.J. de Ronde H. van der Velden P.A. Reitsma P.H. Nature. 1994; 369: 64-67Crossref PubMed Scopus (3873) Google Scholar). The initial protein components involved in the essential coagulation cascade and its stoichiometric regulation includes 10 species. However, during thrombin generation by the tissue factor (TF)-initiated reaction, multiple transitory species are produced, bringing the total to 27, many of which play multiple roles at different stages of the process. An example of these multiple roles is presented in the activation of prothrombin. The product, thrombin, participates in feed back processes leading to its own generation by activating factor V, factor VIII, and factor VII; using a different binding partner, it initiates the anticoagulation cascade through protein C activation (11Esmon C.T. J. Biol. Chem. 1989; 264: 4743-4746Abstract Full Text PDF PubMed Google Scholar). It is in the balance of this complex interplay that the response to each injury or stimulus is determined. antithrombin III tissue factor pathway inhibitor tissue factor phospholipid vesicles composed of 25% phosphatidylserine and 75% phosphatidylcholine The rational design of therapeutic antihemorrhagic and antithrombotic strategies has primarily relied upon intuitive approaches to judge how qualitative or quantitative alterations in a natural product or a therapeutic agent might behave in this complex reaction milieu. These estimates are usually made on the basis of oversimplifications, which ignore the dynamic interplay between coagulation factor reactions; consequently, judgments are made based upon the presumption of isolated defective functions. In even the simplest cases, such as the single gene deficiencies (hemophilia A or B) in which a fundamental knowledge of the defect is available, less than satisfactory algorithms exist for determining the dosage required of the missing factor. Even less obvious is the case in which an otherwise “normal” individuals present with complex disorders such as venous or coronary thrombosis, or an unaccounted for bleeding diathesis (12Zoller B. Garcia de Frutos P. Hillarp A. Dahlback B. Haematologica. 1999; 84: 59-70PubMed Google Scholar, 13de Moerloose, P., Bounameaux, H. R., and Mannucci, P. M. (1998) Semin. Thromb. Hemostasis(1998) 24, 321–327Google Scholar). A more complete understanding of the interplay between the pro- and anticoagulant factors involved in hemostasis should permit the kinetics of “composite” deficiencies to be better understood. Toward this end, we have extended our numerical model (14Jones K.C. Mann K.G. J. Biol. Chem. 1994; 269: 23367-23373Abstract Full Text PDF PubMed Google Scholar) for the thrombin generation reaction by including the stoichiometric inhibitor systems and updating the mechanism to the current level of knowledge. Over the past 25 years, a reasonably comprehensive understanding of the inventory of the proteins and the associated biophysical and enzymologic processes involved in blood clotting has been developed through the efforts of numerous investigators (15Mann K.G. Gaffney D. Bovill E.G. Lichtman M.A. Coller B.S. Kipps T.J. Williams Hematology. 5th Ed. McGraw-Hill, Inc., New York1995: 1206-1226Google Scholar). A large body of rigorously obtained data describes association states, membrane binding thermodynamics, enzyme complex assembly kinetics, and reaction kinetics for the inventory of processes (16Lawson J.H. Krishnaswamy S. Butena S. Mann K.G. Methods Enzymol. 1993; 222: 177-195Crossref PubMed Scopus (43) Google Scholar). This in turn has led to the description of an increasingly overwhelming network of pathways and interactions (17Esmon C.T. Biochim. Biophys. Acta. 2000; 1477: 349-360Crossref PubMed Scopus (274) Google Scholar, 18Broze G.J., Jr. Thromb. Haemostasis. 1995; 74: 90-93Crossref PubMed Scopus (311) Google Scholar, 19Davie E.W. Fujikawa K. Kisiel W. Biochemistry. 1991; 30: 10363-10370Crossref PubMed Scopus (1691) Google Scholar). In the face of this complexity, intuition frequently leads to paradox. For example, increasing the concentration of a procoagulant factor such as factor VII “should” lead to an increase in thrombin generation and decreased clotting time. In empirical studies and in laboratory experiments, the opposite is true (20van't Veer C. Golden N.J. Mann K.G. Blood. 2000; 95: 1330-1335Crossref PubMed Google Scholar). Computational modeling provides the opportunity to integrate and quantify reaction details, which, in turn, aids in the design of the more expensive empirical “wet” experiments. Rapid advances in mathematical algorithm development and computational power have enabled modeling of ever more complex systems (21Nesheim M.E. Tracy R.P. Mann K.G. J. Biol. Chem. 1984; 259: 1447-1453Abstract Full Text PDF PubMed Google Scholar, 22Hockin M.F. Cawthern K.M. Kalafatis M. Mann K.G. Biochemistry. 1999; 38: 6918-6934Crossref PubMed Scopus (35) Google Scholar, 23Mounts W.M. Liebman M.N. Int. J. Biol. Macromol. 1997; 20: 265-281Crossref PubMed Scopus (11) Google Scholar, 24Beltrami E. Jesty J. Proc. Natl. Acad. Sci. U. S. A. 1995; 92: 8744-8748Crossref PubMed Scopus (67) Google Scholar, 25Gentry R., Ye, L. Nemerson Y. Biophys. J. 1995; 69: 356-361Abstract Full Text PDF PubMed Scopus (13) Google Scholar, 26Kessels H. Willems G. Hemker H.C. Comput. Biol. Med. 1994; 24: 277-288Crossref PubMed Scopus (34) Google Scholar). These technologies, when coupled with the expanding base of empirically defined mechanism, allow the development of rational models that predict the product generation profiles to be expected for diverse experimental conditions. The construction of models also provide the ability to look into reactions at a “microscopic” level, at which the concentrations of substrates and products being investigated are below detection limits accessible through direct analysis. Such evaluations can provide estimations of the initiating events in a process and lead to the design of laboratory experiments that are designed to explore unforeseen computational results. Our laboratory provided one of the first computational models successful in predicting empirical outcomes in the biochemistry of the TF-initiated procoagulant pathway (14Jones K.C. Mann K.G. J. Biol. Chem. 1994; 269: 23367-23373Abstract Full Text PDF PubMed Google Scholar). Subsequent empirical studies have evaluated the influence of combinations of the stoichiometric and dynamic anticoagulant systems on the thrombin generation process (27Butenas S. van't Veer C. Mann K.G. Blood. 1999; 94: 2169-2178Crossref PubMed Google Scholar, 28Butenas S. van't Veer C. Mann K.G. J. Biol. Chem. 1997; 272: 21527-21533Abstract Full Text Full Text PDF PubMed Scopus (126) Google Scholar, 29van't Veer C. Golden N.J. Kalafatis M. Mann K.G. J. Biol. Chem. 1997; 272: 7983-7994Abstract Full Text Full Text PDF PubMed Scopus (118) Google Scholar, 30van't Veer C. Mann K.G. J. Biol. Chem. 1997; 272: 4367-4377Abstract Full Text Full Text PDF PubMed Scopus (174) Google Scholar, 31Rand M.D. Lock J.B. van't Veer C. Gaffney D.P. Mann K.G. Blood. 1996; 88: 3432-3445Crossref PubMed Google Scholar, 32Brummel K.E. Butenas S. Mann K.G. J. Biol. Chem. 1999; 274: 22862-22870Abstract Full Text Full Text PDF PubMed Scopus (118) Google Scholar). However, our attempts to develop a model that would produce the unique kinetic forms observed in empirical experiments were limited by insufficient mechanistic and kinetic data. The elucidation of robust kinetic schemes for TFPI (33Baugh R.J. Broze G.J., Jr. Krishnaswamy S. J. Biol. Chem. 1998; 273: 4378-4386Abstract Full Text Full Text PDF PubMed Scopus (194) Google Scholar) and AT-III inhibition (34Jordan R.E. Oosta G.M. Gardner W.T. Rosenberg R.D. J. Biol. Chem. 1980; 255: 10081-10090Abstract Full Text PDF PubMed Google Scholar, 35Chuang Y.J Swanson R. Raja S.M. Olson S.T. J. Biol. Chem. 2001; 276: 14961-14971Abstract Full Text Full Text PDF PubMed Scopus (144) Google Scholar, 36Lawson J.H. Butenas S. Ribarik N. Mann K.G. J. Biol. Chem. 1993; 268: 767-770Abstract Full Text PDF PubMed Google Scholar, 37Schoen P. Lindhout T. J. Biol. Chem. 1987; 262: 11268-11274Abstract Full Text PDF PubMed Google Scholar), factor VII/VIIa competition (20van't Veer C. Golden N.J. Mann K.G. Blood. 2000; 95: 1330-1335Crossref PubMed Google Scholar), factor VIIIa dissociation (38Lollar P. Parker E.T. Fay P.J. J. Biol. Chem. 1992; 267: 23652-23657Abstract Full Text PDF PubMed Google Scholar, 39Fay P.J. Smudzin T.M. J. Biol. Chem. 1992; 267: 13245-13250Abstract Full Text PDF Google Scholar, 40Fay P.J. Beattie T.L. Regan L.M. O'Brien L.M. Kaufman R.J. J. Biol. Chem. 1996; 271: 6027-6032Abstract Full Text Full Text PDF PubMed Scopus (99) Google Scholar), and factor VII (41Butenas S. Mann K.G. Biochemistry. 1996; 35: 1904-1910Crossref PubMed Scopus (94) Google Scholar), prothrombin (42Krishnaswamy S. Church W.R. Nesheim M.E. Mann K.G. J. Biol. Chem. 1987; 262: 3291-3299Abstract Full Text PDF PubMed Google Scholar), and factor V activation (43Nesheim M.E. Katzmann J.A. Tracy P.B. Mann K.G. Methods Enzymol. 1981; 80: 249-274Crossref PubMed Scopus (115) Google Scholar), which adequately account for empirical observations, has enabled undertaking the integration of the stoichiometric anticoagulation system into a more comprehensive model of the coagulation system. The present model includes 34 species, 42 rate constants, and accounts for the peculiar inhibitory “thresholds” produced by combinations of TFPI and AT-III. A software package was written to enable rapid transformation of chemical equilibrium expressions to the necessary time-dependent partial differential equations required for this model and their solution. The software package Speed Rx utilizes an Internet-based interface with a generally applicable fourth order Runge-Kutta solver that provides solutions to a family of time-dependent differential equations. After the user inputs the chemical equations, initial concentrations, and rate constants for all relevant species and steps, the software generates a series of time-dependent concentration profiles for any/all reactants over any time frame of interest. A set of simulations can be developed representing titration of individual species or varying individual rate constants to represent qualitative or quantitative alterations in the reactant. The results of each simulation are stored in a relational data base architecture utilizing SQL standards. For this work all computations were carried out on a Pentium III computer running LINUX (RedHat version 7.1); however, the software may be installed on any computer capable of running UNIX. The validity of our implementation of the fourth order Runge-Kutta solver was tested through use of the freely available backward differentiational formula in the livermore solver for ordinary differential equations (LSODE) that utilizes third order polynomials (www.llnl.gov/casc/odepak). LSODE utilizes dynamic step sizing and a matrix of partial differential equations to approach the solution. Utilizing the Livermore algorithm, we were able to demonstrate exact correspondence to the solutions obtained with our Runge-Kutta solver. This correspondence was found between both simple chemical systems and numerous pre-publication versions of the coagulation model. The present effort is based upon our prior publications describing a procoagulant model of blood coagulation (14Jones K.C. Mann K.G. J. Biol. Chem. 1994; 269: 23367-23373Abstract Full Text PDF PubMed Google Scholar). Extensive revisions were made to incorporate additional steps to our procoagulant system. In all cases the processes and rate constants described are representative of reaction paths and rates experimentally observed under the condition of saturating phospholipid concentrations. In the instances for which experimental data are not available for the processes modeled, rate constants and mechanisms were incorporated by analogy with similar processes within the coagulation cascade. The entire model, in tabular form, is presented as Table I. The rate constants are presented in Table II, and the initial (“normal”) concentrations for all reactants are presented in Table III.Table IChemical expressions for the coagulation cascadeLineChemical expressions1TF + VII TF==VII2TF + VIIa TF==VIIa3TF==VIIa + VII-5 > TF==VIIa + VIIa4Xa + VII-6 > Xa + VIIa5IIa + VII-7 > IIa + VIIa6TF==VIIa + X TF==VIIa==X-10 > TF==VIIa==Xa7TF==VIIa + Xa TF==VIIa==Xa8TF==VIIa + IX TF==VIIa==IX-15 > TF==VIIa + IXa9Xa + II-16 > Xa + IIa10IIa + VIII-17 > IIa + VIIIa11VIIIa + IXa IXa==VIIIa12IXa==VIIIa + X IXa==VIIIa==X-22 > IXa==VIIIa + Xa13VIIIa VIIIa1 · L + VIIIa214IXa==VIIIa==X-25 > VIIIa1 · L + VIIIa2 + X + IXa15IXa==VIIIa-25 > VIIIa1 · L + VIIIa2 + IXa16IIa + V-26 > IIa + Va17Xa + Va Xa==Va18Xa==Va + II Xa==Va==II-31 > Xa==Va + mIIa19mIIa + Xa==Va-32 > IIa + Xa==Va20Xa + TFPI Xa==TFPI21TF==VIIa==Xa + TFPI TF==VIIa==Xa==TFPI22TF==VIIa + Xa==TFPI-37 > TF==VIIa==Xa==TFPI23Xa + ATIII-38 > Xa==ATIII24mIIa + ATIII-39 > mIIa==ATIII25IXa + ATIII-40 > IXa==ATIII26IIa + ATIII-41 > IIa==ATIII27TF==VIIa + ATIII-42 > TF==VIIa==ATIIIThe notation -2> signifies a forward reaction dictated by rate constant “2” (Table II). The notation indicates an equilibrium expression with a forward rate constant of k2 and a reverse rate constant of k1. Binding between components is indicated by the = notation, i.e. A + B A = B. Open table in a new tab Table IIListing of rate constants utilized in the model and a summary of literature referencesRate no.Model valueCitationLiterature ranges−1m −1 s−113.1 × 10−3 2-aIndicates that the rate constant used in the model was derived through fitting of computational results to empirical data, these values were usually seeded with literature values when available or generated based upon analogy to other known similar processes.44, 456.29 × 10−4 to 3.1 × 10−3· 2-dUnit of measure is indicated by a dot in the appropriate column.23.2 × 106 2-aIndicates that the rate constant used in the model was derived through fitting of computational results to empirical data, these values were usually seeded with literature values when available or generated based upon analogy to other known similar processes.44, 453.14 × 106 to 1.6 × 105·33.1 × 10−3 2-aIndicates that the rate constant used in the model was derived through fitting of computational results to empirical data, these values were usually seeded with literature values when available or generated based upon analogy to other known similar processes.44, 468.76 × 10−4 to 1.6 × 10−3·42.3 × 107 2-aIndicates that the rate constant used in the model was derived through fitting of computational results to empirical data, these values were usually seeded with literature values when available or generated based upon analogy to other known similar processes.44, 461.6 × 105 to 1.9 × 105·54.4 × 10541·61.3 × 10741·72.3 × 10441·81.052-aIndicates that the rate constant used in the model was derived through fitting of computational results to empirical data, these values were usually seeded with literature values when available or generated based upon analogy to other known similar processes.Km in 33, 4669 nm (PCPS) to 4.35 μm (PC)·92.5 × 107 2-aIndicates that the rate constant used in the model was derived through fitting of computational results to empirical data, these values were usually seeded with literature values when available or generated based upon analogy to other known similar processes.Km in 33, 4669 nm (PCPS) to 4.35 μm (PC)·10657, 587.0–5.69·11192-aIndicates that the rate constant used in the model was derived through fitting of computational results to empirical data, these values were usually seeded with literature values when available or generated based upon analogy to other known similar processes.2-bRefs. 57 and58 provide evidence that factor Xa or similar proteolytic fragments of factor Xa will bind the TF · VIIa complex with affinity similar factor X, the rate constants illustrated are derived based on this assumption and are not contained in the reference.None·122.2 × 107 2-aIndicates that the rate constant used in the model was derived through fitting of computational results to empirical data, these values were usually seeded with literature values when available or generated based upon analogy to other known similar processes.2-bRefs. 57 and58 provide evidence that factor Xa or similar proteolytic fragments of factor Xa will bind the TF · VIIa complex with affinity similar factor X, the rate constants illustrated are derived based on this assumption and are not contained in the reference.58, 59·132.42-aIndicates that the rate constant used in the model was derived through fitting of computational results to empirical data, these values were usually seeded with literature values when available or generated based upon analogy to other known similar processes.2-cThese values were based upon a knowledge of the rates for factor X activation by TF · VIIa as referenced, and the relative ratio between the rate of activation of X versus IX in a TF-dependent system (60).13, 6024·141.0 × 107 2-aIndicates that the rate constant used in the model was derived through fitting of computational results to empirical data, these values were usually seeded with literature values when available or generated based upon analogy to other known similar processes.2-cThese values were based upon a knowledge of the rates for factor X activation by TF · VIIa as referenced, and the relative ratio between the rate of activation of X versus IX in a TF-dependent system (60).13, 601.0 × 108·151.82-aIndicates that the rate constant used in the model was derived through fitting of computational results to empirical data, these values were usually seeded with literature values when available or generated based upon analogy to other known similar processes.2-cThese values were based upon a knowledge of the rates for factor X activation by TF · VIIa as referenced, and the relative ratio between the rate of activation of X versus IX in a TF-dependent system (60).13, 600.3·167.5 × 103In preparation·172.0 × 10733·185.0 × 10−313·191.0 × 10713·201.0 × 10−313·211.0 × 10813·228.213·232.2 × 104 2-aIndicates that the rate constant used in the model was derived through fitting of computational results to empirical data, these values were usually seeded with literature values when available or generated based upon analogy to other known similar processes.38, 39Based on Ref. 38Lollar P. Parker E.T. Fay P.J. J. Biol. Chem. 1992; 267: 23652-23657Abstract Full Text PDF PubMed Google Scholar and Kd (Ref. 39Fay P.J. Smudzin T.M. J. Biol. Chem. 1992; 267: 13245-13250Abstract Full Text PDF Google Scholar)·246.0 × 10−338·251.0 × 10−340·262.0 × 10713·270.213·284.0 × 10813·2910313·301.0 × 10813·3163.513·321.5 × 10713·333.6 × 10−433·349.0 × 105 2-aIndicates that the rate constant used in the model was derived through fitting of computational results to empirical data, these values were usually seeded with literature values when available or generated based upon analogy to other known similar processes.331.35 × 106·351.1 × 10−4 2-aIndicates that the rate constant used in the model was derived through fitting of computational results to empirical data, these values were usually seeded with literature values when available or generated based upon analogy to other known similar processes.331.1 × 10−3·363.2 × 108 2-aIndicates that the rate constant used in the model was derived through fitting of computational results to empirical data, these values were usually seeded with literature values when available or generated based upon analogy to other known similar processes.332.72 × 108·375.0 × 107 2-aIndicates that the rate constant used in the model was derived through fitting of computational results to empirical data, these values were usually seeded with literature values when available or generated based upon analogy to other known similar processes.337.34 × 106·381.5 × 10335·397.1 × 10337·404.9 × 10235·417.1 × 10337·422.3 × 10236·2-a Indicates that the rate constant used in the model was derived through fitting of computational results to empirical data, these values were usually seeded with literature values when available or generated based upon analogy to other known similar processes.2-b Refs. 57Baugh R.J. Dickinson C.D. Ruff W. Krishnaswamy S. J. Biol. Chem. 2000; 275: 28826-28833Abstract Full Text Full Text PDF PubMed Scopus (87) Google Scholar and58Baugh R.J. Krishnaswamy S. J. Biol. Chem. 1996; 271: 16126-16134Abstract Full Text Full Text PDF PubMed Scopus (53) Google Scholar, 59Bergum P.W. Cruikshank A. Maki S.L. Kelly C.R. Ruff W. Vlasuk G.P. J. Biol. Chem. 2001; 276: 10063-10071Abstract Full Text Full Text PDF PubMed Scopus (96) Google Scholar provide evidence that factor Xa or similar proteolytic fragments of factor Xa will bind the TF · VIIa complex with affinity similar factor X, the rate constants illustrated are derived based on this assumption and are not contained in the reference.2-c These values were based upon a knowledge of the rates for factor X activation by TF · VIIa as referenced, and the relative ratio between the rate of activation of X versus IX in a TF-dependent system (60Bom V.J. van Hinsberght V.W. Reinalda-Poot H.H. Mohanlal R.W. Bertina R.M. Thromb. Haemostasis. 1991; 66: 283-291Crossref PubMed Scopus (23) Google Scholar).2-d Unit of measure is indicated by a dot in the appropriate column. Open table in a new tab Table IIIMean plasma concentrations of pro- and anticoagulantsSpeciesInitial concentrationmTFVariedVII1.0 × 10−8TF==VII0.0VIIa1 × 10−10TF==VIIa0.0Xa0.0IIa0.0X1.6 × 10−7TF==VIIa==X0.0TF==VIIa==Xa0.0IX9 × 10−8TF==VIIa==IX0.0IXa0.0II1.4 × 10−6VIII0.7 × 10−9VIIIa0.0IXa-VIIIa0.0IXa==VIIIa==X0.0VIIIa1·L0.0VIIIa20.0V2.0 × 10−8Va0.0Xa==Va0.0Xa==Va==II0.0mIIa0.0TFPI2.5 × 10−9Xa==TFPI0.0TF==VIIa==Xa==TFPI0.0ATIII3.4 × 10−6Xa==ATIII0.0mIIa==ATIII0.0IXa==ATIII0.0IIa==ATIII0.0TF==VIIa==ATIII0.0 Open table in a new tab The notation -2> signifies a forward reaction dictated by rate constant “2” (Table II). The notation indicates an equilibrium expression with a forward rate constant of k2 and a reverse rate constant of k1. Binding between components is indicated by the = notation, i.e. A + B A = B. Literature values for rate constants were utilized as starting points. Additional fitting was required either because these values were evaluated under nonphysiologic conditions or because they made use of extensively modified proteins. For example, the reported equilibrium constant for factor VIIa-TF-membrane was estimated utilizing a truncated TF protein and evaluated by surface plasmon resonance utilizing chemical cross-linking to a substrate (44O'Brien D.P. Kemball-Cook G. Hutchinson A.M. Martin D.M. Johnson D.J. Byfield P.G. Takamiya O. Tuddenham E.G. McVey J.H. Biochemistry. 1994; 29: 14162-14169Crossref Scopus (66) Google Scholar). In this case, we maintained the ratio of the reported reverse and forward rate constants (Kd) to fit published kinetic functional data (45Krishnaswamy S. J. Biol. Chem. 1992; 267: 23696-23706Abstract Full Text PDF PubMed Google Scholar, 46Shobe J. Dickinson C.D. Edgington T.S. Ruf W. J. Biol. Chem. 1999; 274: 24171-24175Abstract Full Text Full Text PDF PubMed Scopus (44) Google Scholar, 47Butenas S. Lawson J.H. Kalafatis M. Mann K.G. Biochemistry. 1994; 33: 3449-3456Crossref PubMed Scopus (38) Google Scholar). For description purposes, it is convenient to define the coagulation reactions leading to thrombin generation in three phases:initiation, propagation, and termination. This oversimplification provides a convenient vehicle for communication. The extrinsic factor Xase (factor VIIa-TF-membrane) forms
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