Biological materials are frequently constructed of hydrated biopolymer networks. Examples include fibrous collagen in the extracellular matrix and actin within the cell's cytoskeleton. There are differences in the molecular composition of the biopolymer subunits as well as differences in the network density and organization. Images can be seen here and here for dense collagen networks and for portions of actin networks look at images here and here.

The mechanical response of these biopolymer network-based materials is nonlinear and concave-up (exhibiting strain-stiffening). The fundamental mechanics of this response has been widely studied and examined since the 1960s, when Viidik and others started characterizing responses of collagenous tissues to uniaxial loading as analogous to the sequential recruitment of linear spring elements.

More recently, attention has shifted to the nonlinear response of the molecules themselves. The individual biopolymer molecules are typically characterized using a worm-like chain (WLC) model or a more complicated model based on the WLC (such as the Marko-Siggia model or bead-spring chains). Armed with information on this response, a network can be conceivably "built up" from individual WLC elements to represent networks with different densities and different molecular orientation characteristics.

Thus there are two primary possibilities for mechanical stiffening in these networks: stiffening due to a structural effect in the network or stiffening due to a stiffening effect in the individual molecules themselves. Obviously both effects could be at play in real non-idealized networks.

A key question in the construction of "bottom-up" models of biopolymer network mechanics regards the reorganization of the networks under applied mechanical loading. In many cases, the deformation has been modeled as affine, or preserving parallelism (see, for example, the work of Storm et al. mentioned previously on iMechanica). However, recently this assumption has been questioned. There are also interesting, and frequently ignored, possibilities for viscous drag on the networks since the reorganization occurs in a fluid environment. Finally, there are likely length-scale effects in terms of the observation length-scale compared with the material length-scale, especially when the hierarchical structure of biological materials is considered.

In this month's inaugural iMechanica journal club, we examine mechanical deformation in biopolymer networks by first considering three papers that all argue for non-affine network behavior based on experimental and modeling results on collagen-type extracellular networks and actin-type cellular networks.

The three papers are included here for discussion are:

(1) "A method to quantify the fiber kinematics of planar tissues under biaxial stretch" by KL Billiar and MS Sacks. J. Biomech. 30 (1997) 753-6.

(2) "Alternative explanation of stiffening in cross-linked semiflexible networks" by Onck PR, Koeman T, van Dillen T and van der Giessen E. Phys. Rev. Lett. 95 (2005) 178102.

(3) "Affine versus non-affine fibril kinematics in collagen networks: theoretical studies of network behavior" by Chandran PL and Barocas VH. J. Biomech. Eng. 128 (2006) 259-70.

Initial points to consider in discussing these papers are the fidelity of the experimental and modeling approaches, the different assumptions made, and the strength of the conclusions of non-affine behavior based on the results presented by the authors. However, please feel free to initiate discussions on any aspect of the papers including forward-thinking ideas about the future of biopolymer network modeling.