Toroidal diffusions, this is, continuous-time Markovian processes on the torus, are useful
statistical tools for modelling the evolution of a protein's backbone throughout its dihedral
angles representation. This chapter reviews a class of time-reversible ergodic diffusions,
which can be regarded as the toroidal analogues of the celebrated Ornstein–Uhlenbeck
process, and presents their application to the construction of an evolutionary model for pairs
of related proteins that aims to provide new insights into the relationship between protein …

Eduardo Garcīıa-Portugueīs, 1 Michael Golden, 2 Michael Sørensen31Department of
Statistics, Carlos III University of Madrid (Spain) 2Department of Statistics, University of
Oxford (UK) 3Department of Mathematical Sciences, University of Copenhagen (Denmark)
4Department of Mathematics, University of Leeds (UK) Kanti V. Mardia, 2, 4 Thomas
Hamelryck, 5, 6 Jotun Hein25Department of Biology, University of Copenhagen (Denmark)
6Department of Computer Science, University of Copenhagen (Denmark) 4.1 …