Table 1.
Bivalent binding reactions and kinetic constants.
Fig 1.
Schematic of single molecule stochastic binding model.
(A) A single thrombin molecule binding at a junction of fibrin monomers without bivalent binding (AA junction). Thrombin can be unbound (Tfree), bound to fibrin via two E-domain binding sites (BE1), or removed from the system (R), which is an absorbing (end state). Thrombin is in yellow, fibrin in purple, and red is the removed state. (B) A single thrombin molecule binding at a junction of fibrin monomers with bivalent binding (AP junction). Thrombin can be unbound (Tfree), bound to fibrin via two E-domain binding sites (BE1 and BE), bound to a single γ′ binding site (BG), or can transition from BE and BG to the bivalently bound state (B), or can be removed from the system to state (R), an absorbing (end state).
Fig 2.
Schematic of the four main stages in the polymerization model.
(A) Thrombin forms fibrin I and fibrin II monomers. Thrombin (yellow shape) binds the the E-domain of fibrinogen (purple with blue and green dots), cleaving FpA (green dots), which converts fibrinogen into fibrin I (purple with blue dots). Thrombin binds to the E-domain to cleave FpB (blue dots), converting fibrin I into fibrin II (purple with no dots). (B) Fibrin I and II bind together forming half-staggered chains called oligomers. Fibrin I and II also bind to existing oligomers, increasing them in length. When an oligomer reaches a critical length (11 monomers in length for this study), it becomes a protofibril. (C) Protofibrils aggregate laterally, forming fibers, which are cable-like bundles of protofibrils. Additional protofibrils can bind to an existing fiber, increasing its diameter. (D) As protofibrils and fibers are formed, FpB continues to be cleaved from fibrin I that is incorporated into protofibrils and fibers. Fibrin I is considered to have a limiting effect of lateral aggregation, slowing the process as the ratio of fibrin I to fibrin II increases. The bottom of the figure shows a diagram of the model flow, particularly how key components of the model are connected and which estimated parameters affect each component. The colors in the flow diagram match those in the schematics above.
Table 2.
Parameters for the polymerization model.
Fig 3.
Time of thrombin in free and bound states within AA, AP, and wild-type junctions.
Reported means and credibility intervals for quantities of interest from the stochastic binding model for various junctions and removal rates. Free and bound states of single thrombin molecules were tracked within AA junctions (γA/γA fibrin), AP junctions (γA/γ′ fibrin). Wild type fibrin was represented as a weighted average of these two cases. Thrombin was removed from the system at removal rates, kr. A) Mean time to removal starting from bound states, to either an E-domain or bivalently, fraction of mean time to removal spent (B) susceptible to removal, (C) bound to high-affinity bivalent sites, and (D) bound to low-affinity sites.
Fig 4.
Number of protofibrils per fiber during polymerization.
Model output for protofibril number as a function of thrombin concentration and ratio of γ′:E-domains. Varying thrombin concentration, 0.1 nM—purple, 1.0 nM—yellow, 10 nM—red, 100 nM—blue, using previously published parameters. B) The ratio γ′ binding sites to fibrin(ogen) monomers (0:1—purple, 0.3:1—yellow, 1:1—red, and 2:1—blue) is varied and model uses previously-published parameters. Varied thrombin from 0.1 nM—purple, 1.0 nM—yellow, 10 nM—red,100 nM—blue, (C) and varied ratio of γ′ binding sites to fibrin(ogen) monomers, from 0:1—purple, 0.3:1—yellow, 1:1—red, and 2:1—blue, (D) from the model evaluated with best-fit parameters.
Fig 5.
Box plot of parameter estimates and relative clot time vs. fibrinogen.
Left: Box and whisker plot for 300 parameter sets with the smallest least squares errors from the parameter estimation process. The parameter values are shown in log-scale and the units are those in Table 2. Right: The ratio of clot times showing the relative clot time between γA/γ′ to γA/γA fibrinogen. Clot time being defined as the time to half-maximal turbidity measurement. The model output (solid line) is below the experimental data from Kim et al. [38] (dots with error bars).
Fig 6.
Protofibril number and structural quantities after long periods of time: Comparing model output with experiments.
Shown are the experimentally measured fiber radii [32] in (A). Model outputs as a function of both the thrombin concentration and γ′:E-domain ratio: (B) protofibril number, (C) protein density and (D) distance between protofibrils. The quantities in C,D are computed by combining the measurements in A with a post-processing of the model output in B.
Fig 7.
Fiprinopeptide cleavage and thrombin binding.
Three typed of fibrin(ogen) are considered: γ′/γ′ fibrinogen (blue), γA/γ′ fibrinogen (red), and γA/γA fibrinogen (yellow). Shown are time courses of (A) the percent of FpA (dashed lines) and FpB (solid lines) cleaved due in the presence of 0.1 nM thrombin and 0.1 mg/ml fibrinogen, (B) the percent of free thrombin, (C) the percent of thrombin bound to low-affinity binding sites (those not associated with bivalent binding), BE1 and BG, and (D) the percent of thrombin bound to high-affinity, bivalent sites: BE, BG, and B.
Fig 8.
Estimates of percent of bound thrombin that is trapped within fibers as a function of increasing: A) thrombin (0.1 nM—purple, 1.0 nM—yellow, 10 nM—red,100 nM—blue) and B) the ratio γ′ binding sites to fibrin(ogen) monomers (0:1—purple, 0.3:1—yellow, 1:1—red, and 2:1—blue). As thrombin is increased, percent of thrombin trapped decreases following the protofibril number, with the exception of the 0.1 nM where enough time has not elapsed for it to surpass the yellow curve. As the γ′ ratio increases, the trapped thrombin monotonically increases.