Fig 1.
Microscale model of a fibrin fiber cross-section.
The 72.7 nm diameter fibrin fiber cross-section is composed of 49 squares representing the 49 protofibril cross-sections. Each protofibril cross-section is a stack of 6 binding doublets, representing the 6 chains of a protofibril. A binding doublet is a pair of binding sites (represented by the sideways ‘Y’ shapes), to which plasmin may bind. Lysis is initiated in the model by randomly placing a plasmin molecule (black disk) on a binding doublet at a protofibril on the outer edge of the fiber.
Fig 2.
A: There are 11 reactions considered in the model: 5 involving unbinding, degradation, or exposure (non-crawling reactions), and 6 crawling reactions (4 within the same protofibril and 2 to a neighboring protofibril). N is a cryptic doublet, N00 is an exposed doublet with nothing bound, N03 is an exposed doublet with a plasmin bound, ϕ00 is a degraded doublet with nothing bound, and ϕ03 is a degraded doublet with a plasmin bound. Solid black arrows indicate an unbinding reaction, dashed arrows indicate a degradation or exposure reaction, and red arrows indicate a crawling reaction. Reactions are labeled as ‘Ri’ with i = 1, …, 11. The unbinding reactions are R1 (plasmin unbinds from N03 resulting in N00) and R4 (plasmin unbinds from ϕ03 resulting in ϕ00). The exposure reaction is R5 (cryptic doublet N is exposed by plasmin to create N00). The degradation reactions are R2 (plasmin degrades N00, turning it into ϕ00) and R3 (plasmin degrades N03, turning it into ϕ03). There are 4 possible crawling reactions within the same protofibril: R6 (plasmin crawls from N03 to ϕ00, resulting in N00 and ϕ03), R7 (plasmin crawls from ϕ03 to N00, resulting in ϕ00 and N03), R8 (plasmin crawls from N03 to N00, resulting in N00 and N03), and R9 (plasmin crawls from ϕ03 to ϕ00 resulting in ϕ00 and ϕ03). Note that R8 and R9 do not change the state of the system, but do take time to occur, so we include them in the Gillespie algorithm. Finally, there are 2 possible crawling reactions from the given protofibril to a neighboring protofibril: R10 (plasmin crawls from N03 at this protofibril to a randomly chosen exposed doublet on a neighboring protofibril) and R11 (plasmin crawls from ϕ03 at this protofibril to a randomly chosen exposed doublet on a neighboring protofibril). B: The degradation reaction results in loss of doublets (degraded doublets represented by a red X in the leftmost figure). If some but not all of the doublets (protofibril chains) are degraded, then that protofibril is considered to be partially degraded (blue X). If all 6 doublets are degraded, then that protofibril is considered to be fully degraded (red X in middle figure cross-section). At a given fraction of degraded doublets, say 2/3, there will be a mix of undegraded, partially degraded, and fully degraded protofibrils (rightmost figure).
Table 1.
Baseline parameter values.
Fig 3.
Cartoon of different degraded doublet fractions and the effect of tension.
Since fibers are under tension, we assume that they cleave into two pieces before all the fibrin (doublets) in a cross-section is degraded by plasmin. In the top figure, only 20% of the doublets need to be degraded (red X’s), before tension causes the fiber to snap (orange star). In the middle figure, 50% of the doublets need to be degraded before tension causes the fiber to snap. In the bottom figure, 80% of the doublets need to be degraded before tension causes the fiber to snap. Blue arrows indicate the direction of force acting on the fiber, and their thickness scales with the magnitude of the force. Time increases from left to right.
Fig 4.
Median fiber cleavage time (black) and the fraction of successful runs (red) for different parameter values.
A: Median cleavage time and cleavage success rate as a function of the kinetic unbinding rate of plasmin from fibrin, kunbind. B: Median cleavage time and cleavage success rate as a function of the degradation and exposure rates of fibrin by plasmin, kdeg and kexp, respectively. C: Median cleavage time and cleavage success rate as a function of the crawling rate of plasmin, kcrawl. The top and bottom error bars show the 95th and 5th percentiles, respectively.
Fig 5.
Degradation pattern for four different parameter sets.
Snapshots were taken when the percentage of degraded doublets in the cross-section was 18%, 36%, 54%, and 72%, from left to right. Each pixel represents a protofibril. The color bar indicates the number of degraded doublets at the given protofibril from 0 (blue) to 6 (yellow). The small red square shows the initial location of plasmin and the small black square shows where degradation first occurred. A: Baseline parameter values. B: Lower unbinding rate (kunbind = 0.01 s−1), other parameters at baseline values. C: Higher crawling rate (kcrawl = 120 s−1), other parameters at baseline values. D: Higher degradation and exposure rates (kdeg = kexp = 45 s−1), other parameters at baseline values.
Fig 6.
Median fiber cleavage time at different degraded doublet fractions.
The results are obtained from 10,000 simulations. A: Baseline parameter values. The top and bottom error bars show the 95th and 5th percentiles, respectively. B: Different parameter values. All parameter values are held fixed at the values listed in Table 1 except for the following: kunbind = 0.01 s−1 (red diamond), kkrawl = 120 s−1 (empty blue triangle), kexp = kdeg = 45 s−1 (solid orange triangle).
Fig 7.
Median cleavage time of different fiber sizes at different degradation fractions.
The median cleavage times were measured with rate constants at their baseline values. The maximum degraded doublet fraction reached in the simulations decreases with thicker fibers because plasmin leaves the cross-section before it can degrade more doublets.
Fig 8.
Cleavage time as a function of scaled fiber diameter.
A: Experimental data showing the cleavage time as a function of the scaled fiber diameter. The line of best fit had slope 18.487. B: Model data with baseline parameters showing cleavage time as a function of the scaled fiber diameter. cleavage was defined as when 0.05 (black, 5%), 0.10 (blue, 10%), 0.25 (pink, 25%), or 0.5 (cyan, 50%) of the doublets in the cross-section had been degraded. Lines of best fit were computed for each of those four different sets of data. C: The same model data as in B, but with lines of slope 18.5 passing through the median cleavage time at scaled fiber diameter 1.0.