Journal Club Theme of January 2007: Biomechanics and Non-Affine Kinematics
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:
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.
great first post for jClub!
Submitted by John E. Dolbow on Tue, 2007-01-09 00:22.
Michelle,
You're definitely setting the bar high for jClub! Nice job!
-John
It is a pleasure to see a wonderful post for J-Club
Submitted by Kilho Eom on Tue, 2007-01-09 14:26.
It is a pleasure to see a wonderful posting for J-Club. Especially, I think that it would be very good to consider polymer/biopolymer networks and their mechanical response in biomechanics issue in J-Club. The three papers you suggested for J-Club would guide many people (including me) in further interests in biopolymers and protein networks. Furthermore, I have known that van der Giessen, who wrote the paper you provided in this issue, is a member of iMechanica. So I hope that we may have a chance in communication and/or discussion on this topic with one of the authors who wrote the paper. Anyway, I am looking forward to seeing the fruitful discussions here for learning and broadening the biomechanics area. Dr. Oyen, thank you for your efforts in J-club for guiding the biomechanica area that I am also interested in.
Kilho
Discussions across disciplines
Submitted by Erik Van der Giessen on Tue, 2007-01-09 16:45.
First of all, I want to complement Michelle with having taken the lead on this endeavour and to congratulate her with a job well done.
Several people involved in initializing the Journal Club have emphasized the importance of allowing for discussion across disciplines. As a simple example of this, let me share with you a bit if my own "head-scratching" when I first looked into the behaviour of semi-flexible polymers. In the WLC model, axial deformation is enabled by pulling out undulations in the filament, i.e. by internal bending (much like post-buckling compression, but in the opposite direction). To my initial surprise, however, the WLC model says that the axial stiffness scales with the bending stiffness squared. Why was I surprised? Because I was not familiar enough with statistical mechancis to know (or immediately see) that axial stiffness is also inversely proportional to the amplitude of the undulations. And, for a given temperature, the amplitude is inversely proportional with the bending stiffness. Hence, one factor of bending stiffness arises from the stiffness of the filament itself, the other one from the magnitude of the undulations. A definite "eureka" for me when I saw this. Many have followed once I got into the subject that is referenced here as Ref. (2).
More to the point of affinity (or not), I cannot agree more with Michelle in that this is a major issue in network modeling. One problem I see with it, in general, is that it depends on many factors, in particular the ratio between bending (and torsional) stiffness and axial stiffness. This ratio varies quite a bit in biological systems; in the actin networks that Patrick Onck and I have focused on so far, this ratio is extremely small (one can get a feeling for the behavior of an actin filament by noting that it has an aspect ratio similar to that of a human hair of 1 meter long). MacKintosh and co-workers have developed a map between affinity and stiffness properties in two-deimensional networks -- in three dimensions it is still an open issue.
How does the Journal Club work?
If you are wondering how the Journal Club works, you might want to take a look at previous discussions and tentative operating notes: