Curvature-induced cross-hatched order in two-dimensional semi flexible polymer networks


A recurring motif in the organization of biological tissues is the occurrence of networks of long, fibrillar protein strands effectively confined to thin non-flat shells. A prominent example is the arterial wall, where collagen forms quasi-2D layers that envelop and strengthen the cylindrical vessel lumen (Fig.1a). Another example can be found in the wall of cylindrical shaped cells. A prime example of this is the cell wall of the Pinus Radiata where cellulose forms a cross-hatched structure (Fig.1b). A third example is the annulus fibrosus, where concentric lamellae of quasi-2D collagen cylindrically surround the soft nucleus pulposus (Fig.1c). Strikingly, in each of these cases, the biopolymers fibers are highly ordered: neither circumferentially nor axial, the fibers rather wrap around the central axis at an angle which varies radially and, in several cases, is strongly bimodally distributed.
In this study we investigate the role of the mechanics of the fibers in the formation of those network structures. Therefore we investigate the problem of a 2D crosslinked network of stiff polymers confined to a curved surface. We do this by simulating a network of worm-like chains on smooth geometrical shaped substrates, e.g. cylinders or tori. We demonstrate that in the case of the cylinder, starting with an isotropic network, the tradeoff between bending and stretching energies, very generically, passively gives rise to this cross-hatched order. The simulation begins with a disordered network, which is shown in Fig.1d, and the network relaxes towards a cross-hatched structure (Fig.1e).
This study shed new light on the potential origin of some curiously universal collagen orientation distributions in tissue biology, and suggests novel ways in which synthetic polymeric soft materials may be instructed in terms of their macromolecular ordering.
A second part of the project, which is in collaborating with the group of prof. Weitz of the Harvard University, is related to the mechanics of polymer networks with two crosslinker types. In those networks permanent crosslinks fix fibers together. In addition to this, each fiber can form several reversible crosslinkers. Those reversible crosslinkers gives rise to a polymeric structure with has extraordinary mechanical behavior which we study by molecular dynamics simulations.


  1. Andreas J. Schriefl, Andreas J. Reinisch, Sethuraman Sankaran, David M. Pierce and Gerhard A. Holzapfel. Quantitative assessment of collagen fibre orientations from two-dimensional images of soft biological tissues, Journal of the Royal Society, Interface9:3081–3093, 2012.
  2. Lloyd A. Donaldson; Jenny Grace and Geoff M. Downes. Within tree variation in anatomical properties of compression wood in radiata pine, IAWA Journal, 25(3):253–271, 2004.
  3. Anthony J. Hayes, Michael Benjamin and James R. Ralphs. Role of actin stress fibres in the development of the intervertebral disc: Cytoskeletal control of extracellular matrix assembly, Developmental Dynamics215(3):179–189, 1999.

Researchers: C.H.M.P. (Cyril) Vrusch.
Supervisors: C. (Kees) Storm, C.V.C. (Carlijn) Bouten.

Funding by the Institute for Complex Molecular Systems (ICMS).