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The geometry of biomolecular solvation

Years of research in biology have established that all cellular functions are deeply connected to the shape and dynamics of their molecular actors. As a response, structural molecular biology has emerged as a new line of experimental research focused on revealing the structure of biomolecules. The analysis of these structures has led to the development of computational biology, whose aim is to predict from molecular simulation properties inaccessible to experimental probes. Here we focus on the representation of biomolecules used in these simulations, and in particular on the hard sphere models. We review how the geometry of the union of such spheres is used to model their interactions with their environment, and how it has been included in simulations of molecular dynamics. In parallel, we review our own developments in mathematics and computer science on understanding the geometry of unions of balls, and their applications in molecular simulation.