Surface-dependent coagulation enzymes. Flow kinetics of factor Xa generation on live cell membranes

Blood flow and mass transfer regulation of coagulation

Blood flow regulates coagulation and fibrin formation by controlling the transport, or mass transfer, of zymogens, co-factors, enzymes, and inhibitors to, from, and within a growing thrombus. The rate of mass transfer of these solutes relative to their consumption or production by coagulation reactions determines, in part, the rate of thrombin generation, fibrin deposition, and thrombi growth. Experimental studies on the influence of blood flow on specific coagulation reactions are reviewed here, along with a theoretical framework that predicts how flow influences surface-bound coagulation binding and enzymatic reactions. These flow-mediated transport mechanisms are also used to interpret the role of binding site densities and injury size on initiating coagulation and fibrin deposition. The importance of transport of coagulation proteins within the interstitial spaces of thrombi is shown to influence thrombi architecture, growth, and arrest.

A multiscale model of venous thrombus formation with surface-mediated control of blood coagulation cascade

A combination of the extended multiscale model, new image processing algorithms, and biological experiments is used for studying the role of Factor VII (FVII) in venous thrombus formation. A detailed submodel of the tissue factor pathway of blood coagulation is introduced within the framework of the multiscale model to provide a detailed description of coagulation cascade. Surface reactions of the extrinsic coagulation pathway on membranes of platelets are studied under different flow conditions. It is shown that low levels of FVII in blood result in a significant delay in thrombin production, demonstrating that FVII plays an active role in promoting thrombus development at an early stage.

Diffusion and reaction in the cell glycocalyx and the extracellular matrix

Many biologically important macromolecular reactions are assembled and catalyzed at the cell lipid-surface and thus, the extracellular matrix and the glycocalyx layer mediate transfer and exchange of reactants and products between the flowing blood and the catalytic lipid-surface. This paper presents a mathematical model of reaction-diffusion equations that simply describes the transfer process and explores its influence on surface reactivity for a prototypical pathway, the tissue factor (Tf) pathway of blood coagulation. The progressively increasing friction offered by the matrix and glycocalyx to reactants and to the product (coagulation factors X, VIIa and Xa) approaching the reactive surface is simulated and tested by solving the equations numerically with both, monotonically decreasing and constant diffusion profiles. Numerical results show that compared to isotropic transfer media, the anisotropic structure of the matrix and glycocalyx sharply decreases overall reaction rates and significantly increases the mean transit time of reactants; this implies that the anisotropy modifies the distribution of reactants. Results also show that the diffusional transfer, whether isotropic or anisotropic, influences reaction rates according to the order at which the reactants arrive at the boundary. Faster rates are observed when at least one of the reactants is homogeneously distributed before the other arrives at the boundary than when both reactants transfer simultaneously from the boundary.

Multistage adsorption of diffusing macromolecules and viruses

We derive the equations that describe adsorption of diffusing particles onto a surface followed by additional surface kinetic steps before being transported across the interface. Multistage surface kinetics occurs during membrane protein insertion, cell signaling, and the infection of cells by virus particles. For example, viral entry into healthy cells is possible only after a series of receptor and coreceptor binding events occurs at the cellular surface. We couple the diffusion of particles in the bulk phase with the multistage surface kinetics and derive an effective, integrodifferential boundary condition that contains a memory kernel embodying the delay induced by the surface reactions. This boundary condition takes the form of a singular perturbation problem in the limit where particle-surface interactions are short ranged. Moreover, depending on the surface kinetics, the delay kernel induces a nonmonotonic, transient replenishment of the bulk particle concentration near the interface. The approach generalizes that of Ward and Tordai [J. Chem. Phys. 14, 453 (1946)] and Diamant and Andelman [Colloids Surf. A 183-185, 259 (2001)] to include surface kinetics, giving rise to qualitatively new behaviors. Our analysis also suggests a simple scheme by which stochastic surface reactions may be coupled to deterministic bulk diffusion.

Kinetics of bimolecular reactions in model bilayers and biological membranes. A critical review

The quantitative study of the probability of molecular encounters giving rise to a reaction in membranes is a challenging discipline. Model systems, model in the sense that they use model bilayers and model reactants, have been widely used for this purpose, but the methodologies employed for the analysis of the results obtained in experiments, and for experimental design, are so disparate that a concerned experimentalist has difficulty in deciding about the value of each approach. This review intends to examine the several approaches that can be found in the literature showing, when feasible, the weakness, strengths and limits of application of each of them. There is not, so far, a full experimental validation of the most promising theories for the analysis of reactions in two dimensions, what leaves open a large field for new research. The major challenge resides in the time range in which the processes take place, but the possibilities of the existing techniques for these studies are far from exhausted. We review also the attempts of several authors to quantitatively analyze the kinetics of reactions in biological membranes. Especially in this field, the recently developed microspectroscopies enclose a still unexplored potential.