Extended Data Fig. 4: Agent-based computational model for a fibrillar matrix. | Nature

Extended Data Fig. 4: Agent-based computational model for a fibrillar matrix.

From: Matrix viscoelasticity promotes liver cancer progression in the pre-cirrhotic liver

Extended Data Fig. 4

a-c. Fibrils (grey, “f”), cross-linkers (yellow, “xl”), and bundlers (red, “bu”) are simplified by cylindrical segments in the model. Cross-linkers connect pairs of fibrils without preference of a cross-linking angle by binding-to-binding sites in any part of two fibrils. By contrast, bundlers connect pairs of fibrils with a specific angle and then maintain the angle. The first binding site of bundlers is always located at the end of fibrils, and the second binding site is located at specified part of fibrils. The specific part available for binding is defined by two boundaries, b1 and b2, between 0 and 1. Various bending (κb) and extensional (κs) stiffnesses maintain angles and lengths near their equilibrium values, respectively. Stiffnesses, equilibrium lengths, and equilibrium angles are listed in the Supplementary Table 5. d-g. Different types of matrices. Without bundlers, a matrix is comprised of individual fibrils cross-linked to each other, resulting in small mesh size (d). With bundlers which bind only to the ends of fibrils, a matrix consists of short bundles. Depending on the angle between fibrils connected by bundlers, the shape of short bundles varies (e, f). With bundlers that bind to the end of one fibril and the mid of another fibril, a matrix consists of longer bundles (g). Cross-linkers can connect fibrils within each bundle or fibrils that belong to different bundles. h-j: Snapshots of matrices employed for rheological measurements. The length of fibrils used for creating matrices is either 3 μm (top row) or 5 μm (bottom row). (Images displayed are representatives of 4 independent simulations). h. Matrix structures with a homogeneous, fine mesh, which is created without bundlers as shown in d. i. Matrix structures consisting of long, tight bundles with different lengths. Fibrils are connected in parallel by bundlers as shown in g. The length of bundles can be changed by varying b1 and b2. If the second binding site can bind only to part near one end of fibrils (e.g., b1 = 0.8, b2 = 1), the average length of bundles (LB) becomes large. By contrast, if the binding can take place only near the other end of fibrils (e.g., b1 = 0, b2 = 0.1), LB is slightly longer than the length of individual fibrils. j. Matrix structures consisting of short, loose bundles with different bundling angles, θ. In these cases, both binding sites of bundlers bind to the end of fibrils (i.e., b1 = b2 = 0) as shown in e and f. The shape of the bundle is varied by changing θ.

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