Identification of Mechanisms Mediating Coagulation Factor Penetration into the Glycocalyx: Mathematical Modeling of Transfer to TF (Tissue Factor) Sites.
Authors: McGee Maria P. , Levivne Howard A. , Serna Susana 
Published: April 2020

Abstract
The endothelial glycocalyx is an ~0.5 μm thick extracellular layer of negatively charged polysaccharides, now emerging as a key dynamic regulator of vascular wall function. Relatively little is known about its role on hemostasis, particularly, at injury sites where TF- mediated generation of fXa (factor Xa) determines prothrombinase levels and thrombus formation. Regulating fXa generation is a critical target for antithrombotic therapy development, but progress is hampered by incomplete understanding of the reaction mechanisms on biological membranes. While on artificial vesicles, the overall reaction seems limited by intermediate surface steps related to lateral diffusion of reactants on the phospholipid layer, on natural procoagulant surfaces, both morphometric analyses and estimates of effective diffusion length suggest a more complex explanation of the rate-limiting intermediate step (McGee and Chou, 2001, J. Biol Chem276:7827-35). We propose to explore the potential regulatory role of the glycocalyx, using mathematical modeling and inverse problem approaches. Reactions are assembled on vero cells that express TF and a glycosaminoglycan-rich coat. The reaction parameters are determined from direct rate measurements by solving kinetic equations numerically and fitting them to fXa profiles. The transfer of reactants, factors VIIa and X, from the solution to the TF reactive sites is then modeled, via a system of reaction-diffusion equations that track the reactants’ concentration gradients as a function of time and penetration distance. The field under analysis is a rectangular area (0.5 × 2.5 mm) of the cell coat perpendicular to, and including the upper leaflet of the lipid bi-layer, containing discrete and fixed TF reactive-sites. The diffusion equations are solved numerically assuming periodic boundary conditions, an impermeable lipid layer, and Robbin-type boundary conditions at the fluid/glycocalyx interface. Reactants crossing this boundary and penetrating into the glycocalyx are assumed to meet progressive resistance, modeled as continuously decreasing (as the penetration distance increases) diffusion coefficients that may reflect viscosity changes and/or friction resulting from transient binding to low affinity non-specific sites. Results from the model indicate heterogeneous distribution of reactants, forming concentration gradients that increase with surface reactivity, and reactant transit times across the glycocalyx that decrease when the procoagulant surface reactivity increases. These results are consistent with rate and transit-time measurements on the live cells and predict that changes in TF reactivity, for example, by either “de-encryption” of existing molecules or new TF expression/inhibition, can influence the distribution of plasma coagulation reactants across the glycocalyx. Conversely, glycocalyx interactions with plasma reactants can regulate their functional transfer and reaction rates at TF sites. These studies quantitatively relate the physicochemical state of the glycocalyx to the procoagulant activity of the underlying membrane and suggest new therapeutic strategies based on modulating the former.