Whatever the origin and condition of extraction of type I collagen ﬁbrils, in vitro as well as in vivo, the radii of their circular circular cross sections stay distributed in a range going from 50 to 100 nm for the most part of them. Jean Charvolin and Jean-Francois Sadoc from the solid state physique laboratory at the Paris-Sud University propose therefore that, once the growth of the ﬁbrils has been triggered by external biological factors, their lateral size be limited by internal physical stresses generated during the growth. Their conjecture is based on the remark that the assembly of the long triple helices building a ﬁbril is a place of conﬂict between two incompatible requirements: (1) a double-twist around the ﬁbril axis induced by the chirality of those molecules, and (2) a periodic layering normal to the ﬁbril axis associated with their Hodge-Petrushka staggering.
If the initial planar conﬁguration of the layering is kept unchanged as the growth proceeds, the stresses associated with this incompatibility increase and limit this growth rapidly. But if this conﬁguration can switch to a helicoidal ones this increase can be limited and the growth pursued. However such changes require that the triple helices can slide along each other, i.e. their lateral cohesion must be weakened at the cylindrical surfaces along which the changes occurs.
The opportunity for this is contained in a recent model using the algorithm of phyllotaxis to build a dense organization of triple helices in ﬁbrils with circular symmetry (see J. Charvolin and J.-F. Sadoc (2013), Biophysical Reviews and Letters, 8, 33-49 (2013). This organization shows indeed a succession of large rings or grains, in which each triple helices has six ﬁrst neighbors and the cohesion is at its highest, separated by narrow rings of defects or grain boundaries in which this number is no longer maintained and the cohesion lowered.
Those grain boundaries can therefore be extended all along the cylindrical surfaces on which the conﬁguration of the layering should change. However, as their radii follow the Fibonacci series, they are more and more spaced out when moving away from the center of the phyllotactic pattern: (1) they stay sufficiently close to each other not too far from the center so that the stresses can be relaxed before they become too important to prevent the growth, (2) they become too distant far from the center so that the stresses cannot be relaxed before they become sufficiently important and limit the growth.
The radius in the vicinity of which one situation changes to the other and the size limitation occurs compares well with those observed. The distribution of the grain boundaries in the phyllotactic pattern might therefore be determinant for the control of the lateral growth of type I collagen ﬁbrils.
This conjecture relies upon a geometrical analysis of the structural distortions imposed by the very nature of the triple helices building the ﬁbrils of type I collagen. Although crude at this level of development, the agreement obtained calls for an extension to similar systems of ﬁbrils built by molecules different from the triple helices, as displayed by the wide variety of collagenic structures. Beyond its eventual interest for the conception of artiﬁcial tissues, such a program should also contribute to the most sensitive issue of the respective roles of genetics and physical chemistry in the building of morphologies needed for biological materials to ﬁll their functions.
The study can be found in the upcoming issue of Biophysical Reviews and Letters. The full paper can be read at the following link, http://www.worldscientific.com/doi/pdf/10.1142/S1793048014500027.
Biophysical Reviews and Letters