  We relate open book decompositions of a 4-manifold M with its Engel
structures. Our main result is, given an open book decomposition of M whose
binding is a collection of 2-tori and whose monodromy preserves a framing of a
page, the construction of an En-gel structure whose isotropic foliation is
transverse to the interior of the pages and tangent to the binding. In
particular the pages are contact man-ifolds and the monodromy is a
contactomorphism. As a consequence, on a parallelizable closed 4-manifold,
every open book with toric binding carries in the previous sense an Engel
structure. Moreover, we show that amongst the supported Engel structures we
construct, there is a class of loose Engel structures.
