Fractal kinetic models of plasmin-catalyzed dissolution of fibrin

Background: Intravascular fibrin clots are resolved through the proteolytic action of plasmin acting at the interface of gel-phase substrate and fluid-borne enzyme. The classic Michaelis-Menten (MM) 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 constant Km = Km0.(1 + t)exp(hF), where hF is a fractal exponent of time, t. Furthermore, a realistic kinetic model should take into account sequestration of plasmin due to kringle binding to C-terminal lysines (CTL), newly exposed during fibrin degradation. Aim: The aim of the present study is to build up and experimentally validate a mathematical model that adequately describes the kinetics of plasmin-catalyzed fibrin dissolution and thus contributes to a better understanding of the factors that influence plasmin efficiency at the fluid-gel interface.

Method: Two modifications of the basic MM scheme were introduced: a term reducing the enzyme concentration through rapid equilibrium binding of plasmin to continuously increasing unproductive sites including an association constant Ka and a fractal exponent, hF resulting in apparent Km, which accounts for the time-dependent clustering of the enzyme. A broad range of biochemical (fibrin turbidimetry, densitometry of electrophoretic samples, amidolytic assay on synthetic plasmin substrate) and imaging (atomic force microscopy, AFM; confocal laser microscopy, CLM) techniques were applied to test the predictions of the fibrinolytic model. The power of the predictions was assessed using known modifiers of fibrinolysis; e-amino caproic acid (EACA) which blocks the kringle-dependent binding and carboxypeptidase B (CPB) which removes CTLs. The clustering of plasmin was evaluated with AFM using nanogold-labeled anti-plasmin antibodies in an experimental setup where plasmin was applied to a mica surface decorated with fibrinogen using microcontact printing and with CLM using fluorescent protein-fusion derivative of plasminogen.

Results: Using a range of fibrin and plasmin concentrations, variants of the kinetic model were fitted to the turbidimetric data for lysis of fibrin by plasmin applied to the surface of the clots. A global fit to 32 time-course curves with 90 measured points each yielded four model parameters with optimal values Km0 = 1.5 µM, hF = 0.25, Ka = 1.3 µM^-1 and k_cat = 32.4 min^-1. Addition of 1 mM EACA or 8 U/mL CPB increased the lysis rate, which could be satisfactorily explained with unchanged Km0 and k_cat model parameters accompanied by a decrease in hF to 0.031 and in to 0.001 µM^-1 in line with the interpretation of these parameters as measures of spatial clustering (hF) and sequestration of enzyme molecules in solution (Ka). This concept gained further support from imaging techniques. AFM images revealed significant changes in plasmin distribution on the patterned fibrinogen surface: the ratio of surface occupied by plasmin/intact substrate area decreased by 25% over a 5-min interval in line with the time-dependent clustering of fluorescent plasminogen in CLM.

Conclusion: These data, from multi-faceted, complementary approaches, support a mechanism for time-dependent loss of plasmin activity resulting from spatial redistribution in this heterogeneous system. Thus, plasmin-CTL binding retards lysis, opposing the stimulatory effect of CTLs in plasminogen activation.