  The local opening of DNA is an intriguing phenomenon from a statistical
physics point of view, but is also essential for its biological function. For
instance, the transcription and replication of our genetic code can not take
place without the unwinding of the DNA double helix. Although these biological
processes are driven by proteins, there might well be a relation between these
biological openings and the spontaneous bubble formation due to thermal
fluctuations. Mesoscopic models, like the Peyrard-Bishop-Dauxois model, have
fairly accurately reproduced some experimental denaturation curves and the
sharp phase transition in the thermodynamic limit. It is, hence, tempting to
see whether these models could be used to predict the biological activity of
DNA. In a previous study, we introduced a method that allows to obtain very
accurate results on this subject, which showed that some previous claims in
this direction, based on molecular dynamics studies, were premature. This could
either imply that the present PBD should be improved or that biological
activity can only be predicted in a more complex frame work that involves
interactions with proteins and super helical stresses. In this article, we give
detailed description of the statistical method introduced before. Moreover, for
several DNA sequences, we give a thorough analysis of the bubble-statistics as
function of position and bubble size and the so-called $l$-denaturation curves
that can be measured experimentally. These show that some important
experimental observations are missing in the present model. We discuss how the
present model could be improved.
