Stochastic stability at the boundary of expanding maps

We consider endomorphisms of a compact manifold which are expanding except for a finite number of points and prove the existence and uniqueness of a physical measure and its stochastical stability. We also characterize the zero-noise limit measures for a model of the intermittent map and obtain stochastic stability for some values of the parameter. The physical measures are obtained as zero-noise limits which are shown to satisfy Pesin?s Entropy Formula

Methods of probing the interactions between small molecules and disordered proteins

It is generally recognized that a large fraction of the human proteome is made up of proteins that remain disordered in their native states. Despite the fact that such proteins play key biological roles and are involved in many major human diseases, they still represent challenging targets for drug discovery. A major bottleneck for the identification of compounds capable of interacting with these proteins and modulating their disease-promoting behaviour is the development of effective techniques to probe such interactions. The difficulties in carrying out binding measurements have resulted in a poor understanding of the mechanisms underlying these interactions. In order to facilitate further methodological advances, here we review the most commonly used techniques to probe three types of interactions involving small molecules: (1) those that disrupt functional interactions between disordered proteins; (2) those that inhibit the aberrant aggregation of disordered proteins, and (3) those that lead to binding disordered proteins in their monomeric states. In discussing these techniques, we also point out directions for future developments.Gabriella T. Heller is supported by the Gates Cambridge Trust Scholarship. Francesco A. Aprile is supported by a Senior Research Fellowship award from the Alzheimer’s Society, UK (grant number 317, AS-SF-16-003)