## Hockin2002 - Mathematical model depicting blood coagulation cascade and control by anti-coagulants

April 2019, model of the month by Krishna Kumar Tiwari
Original model: BIOMD0000000335

### Introduction

The blood coagulation system is intricate balance of pro- and anti-coagulant systems that maintain the balance of blood fluidity broadly called “hemostatis”. Imbalance in this system can result in either thrombotic or bleeding disorders. Qualitative or quantitative alterations in this hemostatis balance can have devastating effects, producing hemorrhagic diseases (hemophilia a,b,c) [1, 2] or thrombotic diseases (antithrombin III (AT-III) deficiency, protein c deficiency) [3, 4]. Mathematical model always proved helpful in representing, quantifying and analysing complex biological process [5]. Over last many years, a reasonably detailed understanding of the proteins and the associated physiochemical processes involved in blood clotting has been developed through the efforts of numerous scientists. Hockin et al, 2002 [6] model further adds up to the present understand by explaining the robust kinetic regulation of thrombin activation (amplitude and time) determined by the presence and absence of anti-coagulants (e.g. tissue factor pathway inhibitor (TFPI), anti-thrombin III (AT-III), etc.) in extrinsically (Tissue factor (TF)) activated coagulation pathway. This model is a major base for study of many recent models like Chatterjee 2010 [7], Nayak 2015 [8] etc.

### Model

This model consists TF activation of blood coagulation cascade including multiple mechanistic regulation of blood coagulation cascade by TFPI, ATIII. Model also explains the binding competition and kinetic activation steps that exist between TF and factors VII and VIIa and the activation of factor VII by IIa (Thrombin mediated positive feedback regulation of VII), factor Xa, and factor IXa. A simplified diagram representing the same is expressed as figure 1. Model in total contains 34 species with 42 rate constants along with 27 independent equilibrium expressions. Model aims to study the regulation of thrombin activation amplitude and time by TF (extrinsic activation) along with impact of anti-coagulants like TFPI and ATIII on the same.

Figure1: Simplistic representation of blood coagulation pathway containing pro and anticoagulation regulators studies in Hockin et al. 2002 model ([6]).

### Result

Model simulation for different time courses, with absence and presence of pro and anti-coagulants aligned well with the reported literature [6]. Model accurately depicts the impact of TF (dose dependent (1, 5, and 25 pM)) on thrombin generation time and amplitude in the presence or absence of TFPI (2.5 nM) (Figure 2A). Presence of TFPI delays the thrombin activation time which reflects the delay in overall blood coagulation. Presence of ATIII (3.4uM) along with TFPI further decrease the thrombin generation time and amplitude both (Figure 2B) by directly inhibiting thrombin generation process. When challenged with 25 pM TF in the presence of 3.4 μM AT-III (Figure 2B), thrombin production is slightly delayed, is at a maximum near 150 sec, subsequently decreases, and is nearly consumed by 400 sec. Reactions with TFPI, in the absence of AT-III, 25 pM TF yield maximal rates of thrombin production at ∼200 sec and quantitative activation by 300 sec. Presence of both TFPI and ATIII delays the thrombin activation stimulated by different doses of TF (Figure 2C). Thus, model correctly quantifies the impact of anti-coagulants of blood coagulation cascade time and amplitude.

A

B

C

Figure 2. Impact of pro and anticoagulants on Thrombin activation (time and amplitude). A. Dose dependent impact of TF on thrombin activation in the presence and absence of TFPI (2.5nM) B. Impact of TFPI (2.5 nM) and ATIII (3.4 uM) alone and in combination on TF mediated Thrombin activation C. Dose dependent impact of TF in the presence of both TFPI and ATIII. All the simulation are done using COPASI 4.23 (built 184) and data plotted using Number.

### Conclusion

As predicted by Hockin et al 2002 ([6]), presence of anticoagulation keeps thrombin activation time and amplitude in control. Defects in the regulators leads to untimely and in excess activation of thrombin and blood coagulation which causes thrombotic disorders. This model serves as a good example how modelling can offer biological insights and aid drug discovery. Also, this model played a key role in the blood coagulation mathematical model development/enhancement in past and will add value in future.

## References

1. Leon W. Hoyer (1994). Hemophilia A. N Engl J Med., 209(6):330:38-47 DOI:https://doi.org/10.1056/NEJM199401063300108
2. S R Poort, J J Michiels, P H Reitsma, R M Bertina (1994). Homozygosity for a Novel Missense Mutation in the Prothrombin Gene Causing a Severe Bleeding Disorder. Thromb Haemost., 72(06): 819-824 DOI:https://doi.org/10.1055/s-0038-1648968.
3. C.H.Beresford (1988). Antithrombin III deficiency Blood Reviews, 2(4) DOI:https://doi.org/10.1016/0268-960X(88)90013-6.
4. Pieter H Reitsma (1997). Protein C Deficiency: from Gene Defects to Disease. Thromb Haemost; 78(01): 344-350. DOI:https://doi.org/10.1055/s-0038-1657550.
5. Santo Motta Francesco Pappalardo (2013). Mathematical modelling of biological systems. Briefings in Bioinformatics, 14 (4). DOI:https://doi.org/10.1093/bib/bbs061.
6. Hockin MF, Jones KC, Everse SJ, Mann KG. (2013). A model for the stoichiometric regulation of blood coagulation. J Biol Chem. 2002;277(21):18322-33 DOI:https://doi.org/10.1074/jbc.M201173200.
7. Manash S. Chatterjee, William S. Denney, Huiyan Jing, Scott L. Diamond (2010). Systems Biology of Coagulation Initiation: Kinetics of Thrombin Generation in Resting and Activated Human Blood. PLoS Comput Biol. 6(9) DOI:https://doi.org/10.1371/journal.pcbi.1000950.
8. Nayak S, Lee D, Patel-Hett S, Pittman DD, Martin SW, Heatherington AC, Vicini P, Hua F (2015). Using a Systems Pharmacology Model of the Blood Coagulation Network to Predict the Effects of Various Therapies on Biomarkers. CPT Pharmacometrics Syst Pharmacol. 4(7):396-405 DOI:https://doi.org/10.1002/psp4.50.