Narrow Results

This discussion about diagnostic tests for cancer incorporates a powerful branch of Physics namely X-ray diffraction. Although this technique was used to solve the DNA structure using the X-ray diffraction pictures of Rosalind Franklin,¹ and the structure of vitamin B12 by Dorothy Hodgkin² and hosts of other medical related structures, it is poorly understood by the general medical profession and the community at large. To the nonphysicist the patterns appear to have no relation to the results produced. It might as well be written in Greek. The well-known quote of Poincaré, the famous French mathematician and scientist, in 1885 comes to mind: "Science is built up with facts as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house."

In order therefore to build a true understanding of this powerful technique it is necessary to build a firm understanding of the basic facts about this technique, so that the final results will be clear to all, as they will be held up by a firm house of knowledge. So let us take up the first stone.

Type I collagen fibrils have circular cross sections with radii mostly distributed in between 50 and 100 nm and are characterized by an axial banding pattern with a period of 67 nm. The constituent long molecules of those fibrils, the so-called triple helices, are densely packed but their nature is such that their assembly must conciliate two conflicting requirements. One is a double-twist around the axis of the fibril induced by their chirality and the other is a periodic layered organization, corresponding to the axial banding, built by specific lateral interactions. We examine here how such a conflict could contribute to the control of the radius of a fibril. We develop our analysis with the help of two geometrical archetypes: the Hopf fibration and the algorithm of phyllotaxis. The first one provides an ideal template for a twisted bundle of fibres and the second ensures the best homogeneity and local isotropy possible for a twisted dense packing with circular symmetry. This approach shows that, as the radius of a fibril with constant double-twist increases, the periodic layered organization can not be preserved without moving from planar to helicoidal configurations. Such changes of configurations are indeed made possible by the edge dislocations naturally present in the phyllotactic pattern. The distribution of those defects is such that the lateral growth of a fibril should stay limited in the observed range. Because of our limited knowledge about the elastic constants involved, this purely geometrical development stays at a quite conjectural level.

Tumor invasion, the process by which tumor cells break away from their primary tumor and gain access to vascular systems, is an important step in cancer metastasis. Most current 3D tumor invasion assays consisted of a single tumor cell embedded within an extracellular matrix (ECM). These assays taught us much of what we know today on how key biophysical (e.g., ECM stiffness) and biochemical (e.g., cytokine gradients) parameters within the tumor microenvironment guided and regulated tumor invasion. One limitation of the single tumor cell invasion assays was that it did not account for cell–cell adhesion within the tumor. In this paper, we developed a micrometer scale 3D co-culture spheroid invasion assay that recapitulated physiologically realistic tumor microenvironment and was compatible with microscopic imaging. Micrometer scale co-culture spheroids (1:1 ratio of metastatic breast cancer MDA-MB-231 and non-tumorigenic epithelial MCF-10A cells) were made using an array of microwells, and then were embedded within a collagen matrix in a microfluidic platform. Real time imaging of tumor spheroid invasion revealed that the spatial distribution of the two cell types within the tumor spheroid critically regulated tumor invasion. This work linked tumor architecture with tumor invasion and highlighted the importance of the biophysical cues within the bulk of the tumor in tumor invasion.