Fibroblast-mediated compaction of collagen gels attracts extensive attention in studies of wound healing, cellular fate processes, and regenerative medicine. However, the underlying mechanism and the cellular mechanical niche still remain obscure. This study examines the mechanical behaviour of collagen fibrils during the process of compaction from an alternative perspective on the primary mechanical interaction, providing a new viewpoint on the behaviour of populated fibroblasts. We classify the collagen fibrils into three types - bent, stretched, and adherent - and deduce the respective equations governing the mechanical behaviour of each type; in particular, from a putative principle based on the stationary state of the instantaneous Hamiltonian of the mechanotransduction system, we originally quantify the stretching force exerted on each stretched fibrils. Via careful verification of a structural elementary model based on this classification, we demonstrate a clear physical picture of the compaction process, quantitatively elucidate the panorama of the micro mechanical niche and reveal an intrinsic biphasic relationship between cellular traction force and matrix elasticity. Our results also infer the underlying mechanism of tensional homoeostasis and stress shielding of fibroblasts. With this study, and sequel investigations on the putative principle proposed herein, we anticipate a refocus of the research on cellular mechanobiology, in vitro and in vivo.
In this paper, we present a general, fibril-based structural constitutive theory which accounts for three material aspects of crosslinked filamentous materials: the single fibrillar force response, the fibrillar network model, and the effects of alterations to the fibrillar network. In the case of the single fibrillar response, we develop a formula that covers the entropic and enthalpic deformation regions, and introduce the relaxation phase to explain the observed force decay after crosslink breakage. For the filamentous network model, we characterize the constituent element of the fibrillar network in terms its end-to-end distance vector and its contour length, then decompose the vector orientation into an isotropic random term and a specific alignment, paving the way for an expanded formalism from principal deformation to general 3D deformation; and, more important, we define a critical core quantity over which macroscale mechanical characteristics can be integrated: the ratio of the initial end-to-end distance to the contour length (and its probability function). For network alterations, we quantitatively treat changes in constituent elements and relate these changes to the alteration of network characteristics. Singular in its physical rigor and clarity, this constitutive theory can reproduce and predict a wide range of nonlinear mechanical behavior in materials composed of a crosslinked filamentous network, including: stress relaxation (with dual relaxation coefficients as typically observed in soft tissues); hysteresis with decreasing maximum stress under serial cyclic loading; strain-stiffening under uniaxial tension; the rupture point of the structure as a whole; various effects of biaxial tensile loading; strain-stiffening under simple shearing; the so-called "negative normal stress" phenomenon; and enthalpic elastic behaviors of the constituent element. Applied to compacted collagen gels, the theory demonstrates that collagen fibrils behave as enthalpic elasticas with linear elasticity within the gels, and that the macroscale nonlinearity of the gels originates from the curved fibrillar network. Meanwhile, the underlying factors that determine the mechanical properties of the gels are clarified. Finally, the implications of this study on the enhancement of the mechanical properties of compacted collagen gels and on the cellular mechanics with this model tissue are discussed.