Figure 1.
Deep ultraviolet transmission imaging of fibronectin fibers.
Fn fibers (n = 8) were imaged in a deep ultraviolet transmission microscope at wavelengths 280 nm, 260 nm, and 220 nm. Panels A–C show optical density maps of the same Fn fiber at 280 nm (A), 260 nm (B), and 220 nm (C). These optical density maps were converted to maps of mass (D–F) using extinction coefficients calculated from the amino acid sequence of fibronectin (Uniprot P02751-9) and maps of concentration (G–I) by assuming the fibers have a cylindrical cross section to find the path length (scale bar 2 µm). Fn concentrations were averaged over a region in the center of the fiber to avoid edge effects due to errors in the assumed circular cross sectional profile. The resulting measurements of fibronectin concentration are shown in panel J, the error bars show one standard deviation. The Fn concentrations were 177±59 mg/ml, 270±102 mg/ml, and 160±42 mg/ml (mean ± SD) measured at 280 nm, 260 nm, and 220 nm respectively.
Figure 2.
Simulated fibronectin fiber tension and stress compared to in vitro data.
The tension of in silico fibers with 4 domains initially unfolded was scaled by the Fn concentration measured by UV microscopy. The model output is shown with experimental data from Klotzsch, 2009 [4]. The equal loading configuration (A) is shown scaled to the density determined by the UV microscope measurements (B) with wavelengths 280 nm (blue, 1.65e5 fibrils), 260 nm (green, 2.52e5 fibrils) and 220 nm (red, 1.49e5 fibrils), with the experimental data (blue dots). The tension along the equally loaded fiber (B) rises more quickly than the experiment before module unfolding begins to dominate the fiber mechanics slowing the rise in tension. Panel C shows the ratio of the model scaled by the 280 nm UV measurement to the experimental data. In the disparate loading case (E), the unequal distribution of forces causes the onset of unfolding at lower forces, smoothing the initial rise in tension (F). The ratio of force in the disparate simulation to the in vitro force reached was lower than in the equal fiber (G). The disparate loading case more closely matched the fiber tension of the experiment. The fiber stress was calculated for concentrations measured with each wavelength assuming a constant fiber volume and a fiber diameter of 3.0 µm at 0% strain (D, H). In the disparate loading condition (E) the force was scaled by the number of disparately loaded fibers (280 nm 5.50e4 fibrils; 260 nm 8.39e4 fibrils; 220 nm 4.98e4 fibrils).
Figure 3.
Comparison of fibers with initially unfolded domains.
Fibers were simulated in two configurations, equal loading (A) and disparate loading (D), with either no domains initially unfolded (orange), 4 domains per molecule initially unfolded (purple) or 8 domains per molecule initially unfolded (black) for both the equally loaded fibers (B,C) and the disparate loaded fibers (E,F). Changes in the fiber Force (B, E) and Stress (C, F) were predominantly in the low strain region (<200% strain) where increasing the number of unfolded domains reduced the initial stiffness of the fiber.
Figure 4.
Prediction of molecular forces from in vitro measurements.
The experimental results from Klotzsch 2009 were scaled using the UV absorption measurements of Fn concentration at 280 nm. The load on individual molecules in the equal loading configuration (A,B) was calculated by dividing the measured fiber tension by the calculated number of fibrils (1.65e5 fibrils). The loads in the disparate loading condition (C) were calculated by dividing the measured fiber tension by the number of disparately loaded fibrils (5.50e4 fibrils) then solving for the forces required to maintain the ratio between molecular forces found in the disparate loaded simulation (D). In the disparate loading condition there are two distinct populations of molecular forces. The more extended molecules (i) are under a higher load while the pair of molecules connected in series (ii) is shielded from force.
Figure 5.
The influence of segment initial length assumption on the match between simulation and experiment.
The assumption of initial molecular end-to-end length z impacts the calculation of the number of molecules in the cross section of the fiber. Small values of z (A) lead to fewer molecules in the fiber cross section than larger values of z (B) for the same Fn density. Thus, increasing values of z leads to a decrease in the average molecular force when scaling experimental whole fiber data to average molecular force (red dashed line in D and F). The value of z impacts the scaling of the simulated molecular strand by remapping the value of strain (black in D and F). The average molecular force at 300% strain estimated from scaling of experiment (red) and simulation (black) of equal loading configuration (C) and disparate loading configuration (E) is shown in plots (D) and (F) respectively. The value of z is directly correlated to the number of molecules in the fiber cross section. The equal loading configuration showed agreement at 54 nm of initial length. For the disparate loading configuration, the model matched experimental data at 86 nm initial length.