Fractal Kinetic Behavior of Plasmin on the Surface of Fibrin Meshwork

Abstract

Intravascular fibrin clots are resolved by plasmin acting at the interface of gelphase substrate and fluid-borne enzyme. The classic Michaelis−Menten kinetic scheme cannot describe satisfactorily this heterogeneous-phase proteolysis because it assumes homogeneous well-mixed conditions. A more suitable model for these spatial constraints, known as fractal kinetics, includes a time-dependence of the Michaelis coefficient K m F = K m0 F (1 + t) h , where h is a fractal exponent of time, t. The aim of the present study was to build up and experimentally validate a mathematical model for surface-acting plasmin that can contribute to a better understanding of the factors that influence fibrinolytic rates. The kinetic model was fitted to turbidimetric data for fibrinolysis under various conditions. The model predicted K m0 F = 1.98 μM and h = 0.25 for fibrin composed of thin fibers and K m0 F = 5.01 μM and h = 0.16 for thick fibers in line with a slower macroscale lytic rate (due to a stronger clustering trend reflected in the h value) despite faster cleavage of individual thin fibers (seen as lower K m0 F ). ε-Aminocaproic acid at 1 mM or 8 U/mL carboxypeptidase-B eliminated the time-dependence of K m F and increased the lysis rate suggesting a role of C-terminal lysines in the progressive clustering of plasmin. This fractal kinetic concept gained structural support from imaging techniques. Atomic force microscopy revealed significant changes in plasmin distribution on a patterned fibrinogen surface in line with the time-dependent clustering of fluorescent plasminogen in confocal laser microscopy. These data from complementary approaches support a mechanism for loss of plasmin activity resulting from C-terminal lysine-dependent redistribution of enzyme molecules on the fibrin surface.

Basic mechanisms and regulation of fibrinolysis

“…The clustering of the enzyme optimizes the pattern of cleavage, but it has some negative impact on the kinetics of enzyme action. The macroscopic consequence of plasmin clustering was found to be a gradual decay of its lytic efficiency, which was quantitatively expressed in fractal kinetic terms as a time-dependent increase of the Michaelis constant (K F m ) of plasmin [34]. A further observation was that low concentrations of the lysine analogue aminohexanoic acid can promote plasmin digestion of fibrin by reducing clustering, in agreement with earlier studies [35].…”

Bleeding related to disturbed fibrinolysis

“…Another profibrinolytic mechanism has been ascribed to improved diffusion of plasmin through fibrin clots due to reduced binding to C‐terminal lysines. Thus, fibrinolysis was enhanced when plasmin was added to fibrin treated with carboxypepetidase (which removes C‐terminal lysines) (Kovacs et al , ) or in the presence of AHA (Varju et al , ), as shown in Fig B. The concentration of AHA used in (Varju et al , ) was 1 mmol/l, so applying the 6‐ to 10‐fold rule (McCormack, ), a therapeutic concentration of 100–150 μmol/l TXA may have the same pro‐fibrinolytic effect.…”

“…Thus, fibrinolysis was enhanced when plasmin was added to fibrin treated with carboxypepetidase (which removes C‐terminal lysines) (Kovacs et al , ) or in the presence of AHA (Varju et al , ), as shown in Fig B. The concentration of AHA used in (Varju et al , ) was 1 mmol/l, so applying the 6‐ to 10‐fold rule (McCormack, ), a therapeutic concentration of 100–150 μmol/l TXA may have the same pro‐fibrinolytic effect. Hence, profibrinolytic effects of TXA are possible under circumstances where uPA develops a significant role as activator; or when sufficient free plasmin has been generated and TXA protects plasmin from inhibition by α 2 ‐PI; or where TXA enhances plasmin diffusion and degradation of fibrin.…”

“…In Fig B, clot lysis achieved by adding plasmin to a preformed fibrin clot is stimulated by low concentrations of 6‐aminohexanoate ( AHA ) or by carboxypeptidase B ( CPB ) removal of C‐terminal lysines in fibrin. Reprinted with permission from: Varju et al (). Copyright 2014 American Chemical Society.…”

Biophysical Mechanisms Mediating Fibrin Fiber Lysis

“…Thus, although commonly used, Michaelis-Menten kinetics are not quite correct in describing the action of an enzyme on an insoluble substrate. Recent work on fractal kinetics has begun to explore this issue [33]. …”