CNRS

Certain papillomaviruses (PVs) are a major public health concern as in humans they are responsible for virtually all cases of cervical and anal cancer, and for a fraction of cancers on the penis, vagina, vulva and oropharynx. But oncogenic PVs are actually an unfortunate exception, as most PVs cause asymptomatic infections, and a few cause benign, wart-like lesions. Despite the efforts directed towards the understanding of the different clinical manifestations of infection, our knowledge on PV evolution remains fragmentary. Oncogenic human PVs arose recently, after acquiring the E5, E6 and E7 genes. The integration of the E5 proto-oncogene in the ancestral AlphaPV genome allowed viruses to evade host immune response. Thereafter E6 and E7 acquired the ability to target essential tumor suppressor proteins, paving the way for carcinogenesis. Tracking the evolutionary history of the E5, E6 and E7 oncogenes will thus help understand the emergence of oncogenic human PVs. Regarding the deep roots of PVs, small DNA viruses may share a common ancestor as they encode proteins sharing similar functions and domains, but their evolutionary origin is still an enigma. Here I propose to apply an evolutionary medicine approach, combining in silico and wet-lab approaches, to study key events that occurred during PV genome evolution. We will go back into history and study how and when certain PVs became oncogenic. We will resurrect the ancestral oncogenes, and experimentally test hypotheses about the function of the resurrected proteins in different environmental contexts. We will then generate a comprehensive scenario modelling the appearance of the modern PV genome and the emergence of the oncogenic phenotype of certain PVs. Finally we will explore the relationships between small DNA viruses and test whether they may have a common origin. Our ultimate aim is to understand why a few PVs are oncogenic for a few host species, while most PVs cause asymptomatic infections in most hosts.

In 2006 Cohn and Kumar have conjectured that the A2 lattice is universally optimal, meaning that it has the lowest potential energy among all configurations of the same density for all completely monotone potentials. This conjecture has several very important corollaries. Among other consequences, it is known that it implies a positive solution to the 2D crystallization problem, a major unsolved problem coming from materials science, and it also implies a conjecture on the emergence of the triangular lattice of Abrikosov vortices in the Landau-Ginzburg theory of superconductivity. Recently, the 8 and 24-dimensional cases of the Cohn-Kumar conjecture have been positively resolved using novel interpolation formulas for radial Schwartz functions. This formula recovers a radial function from the data of it and its Fourier transform on a discrete set of radii, and its construction uses classical modular and quasi-modular forms. In this project we will prove a significant generalization of these interpolation formulas with a view towards applications in extremal problems in Fourier analysis. To prove these formulas we will develop new analytic and numerical techniques for solving certain types of functional equations in one complex variable. Finally, based on these proposed interpolation formulas we will give a refinement of the Cohn-Kumar conjecture in dimension 2 and use it to attack the full conjecture in this case.