Abstract
During the hemostatic phase of wound healing, vascular injury leads to endothelial cell damage, initiation of a coagulation cascade involving platelets, and formation of a fibrin-rich clot. As this cascade culminates, activation of the protease thrombin occurs and soluble fibrinogen is converted into an insoluble polymerized fibrin network. Fibrin polymerization is critical for bleeding cessation and subsequent stages of wound healing. We develop a cooperative enzyme kinetics model for in vitro fibrin matrix polymerization capturing dynamic interactions among fibrinogen, thrombin, fibrin, and intermediate complexes. A tailored parameter subset selection technique is also developed to evaluate parameter identifiability for a representative data curve for fibrin accumulation in a short-duration in vitro polymerization experiment. Our approach is based on systematic analysis of eigenvalues and eigenvectors of the classical information matrix for simulations of accumulating fibrin matrix via optimization based on a least squares objective function. Results demonstrate robustness of our approach in that a significant reduction in objective function cost is achieved relative to a more ad hoc curve-fitting procedure. Capabilities of this approach to integrate non-overlapping subsets of the data to enhance the evaluation of parameter identifiability are also demonstrated. Unidentifiable reaction rate parameters are screened to determine whether individual reactions can be eliminated from the overall system while preserving the low objective cost. These findings demonstrate the high degree of information within a single fibrin accumulation curve, and a tailored model and parameter subset selection approach for improving optimization and reducing model complexity in the context of polymerization experiments.
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Notes
For example, if \({\mathbf {q}} = [k^{+}_4, k^{-}_2, k^{+}_1, k, k^{+}_2]\) and \(\bar{\mathbf {q}} = [ k^{-}_3 , k^{+}_3 , k^{-}_1 , k^{-} , k^{-}_4 , k^{+}]\), then \(\mathbf {q_k}= \langle {\mathbf {q}},\bar{\mathbf {q}} \rangle = [{\mathbf {q}}[3], \bar{\mathbf {q}}[3], {\mathbf {q}}[5], {\mathbf {q}}[2], \bar{\mathbf {q}}[2], \bar{\mathbf {q}}[1], {\mathbf {q}}[1], \bar{\mathbf {q}}[5], {\mathbf {q}}[4], \bar{\mathbf {q}}[6], \bar{\mathbf {q}}[4]].\) Note that this notation throughout the paper does not denote an inner product.
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Funding
This study was funded in part by grants DMS-1638521 and DMR-1847488 (CAREER) from the National Science Foundation and NHLBI R01HL146701 from the National Institutes of Health.
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Pearce, K.J., Nellenbach, K., Smith, R.C. et al. Modeling and Parameter Subset Selection for Fibrin Polymerization Kinetics with Applications to Wound Healing. Bull Math Biol 83, 47 (2021). https://doi.org/10.1007/s11538-021-00876-6
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DOI: https://doi.org/10.1007/s11538-021-00876-6