[A fundamental symmetry between morphogenesis and function of branched organs]

Small Cell Lung Cancer Therapeutic Responses Through Fractal Measurements: From Radiology to Mitochondrial Biology

Small cell lung cancer (SCLC) is an aggressive neuroendocrine disease with an overall 5 year survival rate of ~7%. Although patients tend to respond initially to therapy, therapy-resistant disease inevitably emerges. Unfortunately, there are no validated biomarkers for early-stage SCLC to aid in early detection. Here, we used readouts of lesion image characteristics and cancer morphology that were based on fractal geometry, namely fractal dimension (FD) and lacunarity (LC), as novel biomarkers for SCLC. Scanned tumors of patients before treatment had a high FD and a low LC compared to post treatment, and this effect was reversed after treatment, suggesting that these measurements reflect the initial conditions of the tumor, its growth rate, and the condition of the lung. Fractal analysis of mitochondrial morphology showed that cisplatin-treated cells showed a discernibly decreased LC and an increased FD, as compared with control. However, treatment with mdivi-1, the small molecule that attenuates mitochondrial division, was associated with an increase in FD as compared with control. These data correlated well with the altered metabolic functions of the mitochondria in the diseased state, suggesting that morphological changes in the mitochondria predicate the tumor’s future ability for mitogenesis and motogenesis, which was also observed on the CT scan images. Taken together, FD and LC present ideal tools to differentiate normal tissue from malignant SCLC tissue as a potential diagnostic biomarker for SCLC.

About the equilibrium shape of fibred structures, and biological shapes

Biological morphogenesis has often been modeled with reaction-diffusion models [A.M. Turing, The chemical basis of morphogenesis, Phil. Trans. R. Soc. Lond. B 237 (1952) 37-72]. The interplay of bio-chemical fields is supposed to generate shapes by positional information carried by the values in the field. However, the structure of the biological tissue at the microscopic scale is absent from these models. We show that the fibred nature of biological tissue induces specific morphogenic properties. Fibred shapes can be calculated from physical principles borrowed from the theory of crystallogenesis. These give an intuitive insight into the shape of fruits or vegetables, buds and pins in botany, fingers, muscles, insects abdomen and heart in the animal realm, and also into other fibred structures such as the mitotic spindle. We predict the existence of bumps, apices or cusps at poles of fibred structures. An extrapolation to out-of-equilibrium growth predicts that these structures grow forward in the direction of the cusp, and that fibred organs should have a regular branching ordering. However, our model does not take into account the elasto-plastic properties, or the composite nature of the living material.

Morphogenesis of fingers and branched organs: how collagen and fibroblasts break the symmetry of growing biological tissue

Understanding the growth of branching organs is an important scientific endeavour. It has crucial applications, from saving premature newborns, to repairing or even regenerating organs. Despite differences in timing and shape, branching morphogenesis of all branching organs or glands (lung, kidney, salivary, lachrymal, mammary glands, sebaceous and sweat glands, prostate, guts papillae etc.) is similar: an epithelial sheet of cells, forming a 2D layer, penetrates into a 3D mass of mesenchymal cells. Inside the epithelium, a lumen is filled with fluid. As the epithelium grows, it evolves into a branched structure. The pattern of branches is in some cases stereotypic, deterministic, and it has memory effects. We present a simple line of reasoning that predicts that viscous fingering of biological tissue will exhibit all of these features. The line of reasoning is based on the idea that surface tension selects the shape of a growing branch, as is well known in the context of moving boundary problems, except that in this case, the surface is akin to a liquid-crystal. The anisotropy of the surface tension comes from a symmetry breaking by collagen and fibroblasts. The equilibrium shape of the corresponding boundary is that of an actual fingertip, and the out-of-equilibrium shape is that of branched organs, such as the lung.