Fractal kinetic behavior of plasmin on the surface of fibrin meshwork

Intravascular fibrin clots are resolved by plasmin acting at the interface of gel-phase 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.