Functional Data Analysis of DNA Molecular Dynamics

An important problem in contemporary biophysics is that of understanding the mechanical/dynamical properties of DNA strands, and linking them to base-pair sequence composition. Since moving DNAcannot (yet) be reliably "video recorded" experimentally, scientists rely on molecular dynamics simulations obtained by numerically solving atomic level interaction models. These are extraordinary in their computational and mathematical complexity, and often are not amenable to the extraction of interpretable dynamics in some idealised smooth limit. The following statistical challenge presents itself: can one infer qualitative informationby empirical observation of a molecular dynamics DNA trajectory, and indeed link it to the DNA base-pair sequence composition by means of some quantification of its statistical significance? Can this be done with minimal or no structural assumptions on the nature ofthe dynamics (such as linearity or Gaussianity)? We will attempt to answer some of these questions by means of a functional time series framework, where one is precisely interested in probing the dynamical structure of sequences of random curves on the basis of a realisation of a finite stretch of such a sequence (based on joint work with S. Tavakoli).