Mathematical Modeling of Blood Clotting: From Surface-Mediated Coagulation to Fibrin Polymerization

Monday, June 14 at 09:30am (PDT)
Monday, June 14 at 05:30pm (BST)
Tuesday, June 15 01:30am (KST)

SMB2021 SMB2021 Follow Monday (Tuesday) during the "MS01" time block.
Note: this minisymposia has multiple sessions. The second session is MS07-MMPB (click here).

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Karin Leiderman (Colorado School of Mines, United States), Anna Nelson (University of Utah, USA)


Blood clotting is an intricate and nonlinear process that occurs under flow and on multiple spatial and temporal scales. Clots form normally during hemostasis, where an injured vessel is sealed to stop bleeding. Regulation of hemostasis depends on platelet adhesion, aggregation, and contraction, the cell-surface mediated enzyme reactions of coagulation, and formation of stabilizing fibrin matrix. Defects or perturbations can lead to serious bleeding or pathological clot formation (thrombosis). Due the complex nature of the clotting system as a whole, responses to these perturbations are challenging to predict and underlying mechanisms are difficult to determine. Here, we bring together researchers taking mathematical and computational approaches to gain insight into the complexity of the clotting system. This minisymposium will consist of two sessions: one with a focus on aspects of fibrin, fibrin polymerization, and clot mechanics and one with a focus on coagulation biochemistry, both static and under flow, and the interplay with coronavirus. The mathematical approaches include continuum and particle-based modeling of various spatial-temporal processes under flow, system biology approaches for complex biochemical systems, as well as uncertainty quantification and parameter estimation using experimental data.

Anna Nelson

(University of Utah, USA)
"Understanding the effect of fibrinogen interactions on fibrin gel structure"
Fibrin polymerization, an important component of blood clotting, involves the conversion of soluble fibrinogen molecules in the blood plasma to fibrin monomers. These monomers can then polymerize to form a gel that is a major structural component of a blood clot. Oligomers composed of both fibrinogen and fibrin have been observed experimentally and are thought to impact the kinetics of the fibrin gelation process. Fibrinogen plays a dual role in fibrin polymerization; it can occupy available binding sites by binding to fibrin, inhibiting gelation, and monomeric fibrinogen and fibrinogen contained in oligomers can be converted to fibrin. To study the effects of fibrin-fibrinogen interactions on fibrin polymerization and fibrin gel structure, we developed a kinetic polymerization model with two monomers, where the reaction sites on the different species of monomers can participate in different binding reactions. With the chosen framework, gelation can occur, which is defined to be the finite time blow-up of a particular second moment of the oligomer distribution. We characterize the conditions under which a gel forms and examine the impact of fibrin-fibrinogen binding and fibrinogen conversion to fibrin on the branch point density in a gel, if one forms.

Michael Kelley

(Colorado School of Mines, USA)
"Modeling the effects of bivalently bound thrombin on fibrin polymerization"
Thrombin is an enzyme generated during the blood coagulation process and is crucial to the formation of a stable blood clot. Thrombin cleaves fibrinogen into fibrin, which polymerizes to form a stabilizing gel matrix. Thrombin can also bind directly to fibrin and become sequestered for long periods of time. Experimental models support the dogma that this retention is due to the dynamic interplay of thrombin binding to both low- and high-affinity binding sites on fibrinogen and an alternative splice variant of fibrinogen, $gamma’$ that makes up about 15% of the total fibrinogen pool. Recent experimental studies have suggested that $gamma’$ decreases the rate of fibrin polymerization but there are conflicting results in the literature regarding its effects on other aspects of fibrin polymerization such as rates of fibrinopeptide release and clot morphology. The goal of this study was to use a mathematical modeling approach to help interpret some of the disparate results. We built on an existing model of fibrin polymerization and added our previous model of bivalent thrombin-fibrin binding to investigate how thrombin and fibrin interact dynamically during polymerization. Preliminary results show that during dynamic fibrin polymerization, a large fraction of thrombin can become trapped within fibers as they form. Additionally, we show that the $gamma’$ binding of thrombin to fibrin acts to increase fiber thickness, modulating the formation of and polymerization of fibrin.

Francesco Pancaldi

(University of California Riverside, USA)
"Modeling study of clot contraction"
Blood clots are one major cause of death and disability worldwide. Blood clot formation has been relatively well studied, however, little is known about the contraction or retraction of clots. Clot contraction is driven by activated platelets that pull on fibrin fibers, causing a reduction in clot volume. In this talk, we present a model to quantify platelet and fibrin-mediated blood clot contraction mechanisms. The model combines a fibrin network mechanical model and a sub-model accounting for the forces generated by activated platelets. We used experimental measurements to calibrate model parameters and model simulations were used to reveal contraction mechanisms. The contraction was shown to depend on how pulling forces, generated by platelets, change based on local fiber stiffness and the number of filopodia per platelet. In particular, the number of filopodia per platelet contributed to the formation of distinct numbers and length of contraction phases, as defined by peaks in the change of fibrin density. Our simulations show that the number of filopodia per platelet is important to obtain the correct number and length of contraction phases. Finally, the model reproduced experimentally observed clustering of platelets within the contracting clot and predicted more rapid clustering at the initial stages of contraction.

Sumith Yesudasan

(Sam Houston State University, USA)
"Coarse-grained Molecular Model for Fibrin Polymerization"
The study on the polymerization of fibrinogen molecules into fibrin monomers and eventually a stable, mechanically robust fibrin clot is a persistent and enduring topic in the field of thrombosis and hemostasis. Despite many research advances in fibrin polymerization, the change in the structure of fibrin clots and its influence on the formation of a fibrous protein network are still poorly understood. In this paper, we develop a new computational method to simulate fibrin clot polymerization using dissipative particle dynamics simulations. With an effective combination of reactive molecular dynamics formularies and many body dissipative particle dynamics principles, we constructed the reactive dissipative particle dynamics (RDPD) model to predict the complex network formation of fibrin clots and branching of the fibrin network. The 340 kDa fibrinogen molecule is converted into a spring-bead coarse-grain system with 11 beads using a topology representing network algorithm, and using RDPD, we simulated polymerization and formation of the fibrin clot. The final polymerized structure of the fibrin clot qualitatively agrees with experimental results from the literature, and to the best of our knowledge this is the first molecular-based study that simulates polymerization and structure of fibrin clots.

Hosted by SMB2021 Follow
Virtual conference of the Society for Mathematical Biology, 2021.