Kinetics of formation of fibrin oligomers. I. Theory

The course of formation of fibrin oligomers is treated theoretically for the condition that self-assembly of fibrin monomers is rapid compared with the loss of A peptides by the enzymatic action of thrombin. The rate constant for removal of the second A peptide is taken to be larger than that for the first by an arbitrary factor q; the association of activated A sites with their complementary a sites is assumed to be random and independent of oligomer size. Two types of oligomers are considered: noncovalently bonded protofibrils formed by the staggered overlap of thrombin-activated monomers and covalently bonded linear oligomers formed by factor XIIIa-mediated end-to-end ligation of adjacent monomers within protofibrils. Oligomers of the first type, if ligated, are dissociated to oligomers of the second type by solubilization in SDS–urea. Theoretical curves are presented for x _w and x ′_w (weight-average degree of polymerization of staggered overlap and linear ligated oligomers, respectively) and for the weight fractions of monomer, dimer, and decamer of both ligated and unligated species as functions of y, the fraction of A peptide removed; and also for w_x and w′_x, the weight fractions of x-mer of the respective oligomer types, as a function of x at y = 0.5. With increasing q, the maximum w_x or w′_x that a low oligomer will reach during the reaction decreases and the size distribution is broadened toward larger oligomers. Comparison with experiment is made in a companion paper.