Agent Based Modeling Traction Force Mediated Compaction of Cell Populated Collagen Gels Using Physically Realistic Fibril Mechanics

Abstract

Agentbased modeling was used to model collagen fibrils, composed of a string of nodes serially connected by links that act as Hookean springs. Bending mechanics are implemented as torsional springs that act upon each set of three serially connected nodes as a linear function of angular deflection about the central node. These fibrils were evaluated under conditions that simulated axial extension, simple threepoint bending and an endloaded cantilever. The deformation of fibrils under axial loading varied <0.001% from the analytical solution for linearly elastic fibrils. For fibrils between 100 خ¼m and 200 خ¼m in length experiencing small deflections, differences between simulated deflections and their analytical solutions were <1% for fibrils experiencing threepoint bending and <7% for fibrils experiencing cantilever bending. When these new rules for fibril mechanics were introduced into a model that allowed for crosslinking of fibrils to form a network and the application of cell traction force, the fibrous network underwent macroscopic compaction and aligned between cells. Further, fibril density increased between cells to a greater extent than that observed macroscopically and appeared similar to matrical tracks that have been observed experimentally in cellpopulated collagen gels. This behavior is consistent with observations in previous versions of the model that did not allow for the physically realistic simulation of fibril mechanics. The significance of the torsional spring constant value was then explored to determine its impact on remodeling of the simulated fibrous network. Although a stronger torsional spring constant reduced the degree of quantitative remodeling that occurred, the inclusion of torsional springs in the model was not necessary for the model to reproduce key qualitative aspects of remodeling, indicating that the presence of Hookean springs is essential for this behavior. These results suggest that traction force mediated matrix remodeling may be a robust phenomenon not limited to fibrils with a precise set of material properties.