Physical Measures for Certain Partially Hyperbolic Attractors on 3-Manifolds

In this work, we study ergodic properties of certain partially hyperbolic attractors whose central direction has a neutral behavior, the main feature is a condition of transversality between unstable leaves when projected by the stable holonomy. We prove that partial hyperbolic attractors satisfying conditions of transversality between unstable leaves via the stable holonomy, neutrality in the central direction and regularity of the stable foliation admits a finite number of physical measures, coinciding with the ergodic u-Gibbs States, whose union of the basins has full Lebesgue measure. Moreover, we describe the construction of a family of robustly nonhyperbolic attractors satisfying these properties

Multiscale sensing of antibody-antigen interactions by organic transistors and single-molecule force spectroscopy

Antibody–antigen (Ab–Ag) recognition is the primary event at the basis of many biosensing platforms. In label-free biosensors, these events occurring at solid–liquid interfaces are complex and often difficult to control technologically across the smallest length scales down to the molecular scale. Here a molecular-scale technique, such as single-molecule force spectroscopy, is performed across areas of a real electrode functionalized for the immunodetection of an inflammatory cytokine, viz. interleukin-4 (IL4). The statistical analysis of force–distance curves allows us to quantify the probability, the characteristic length scales, the adhesion energy, and the time scales of specific recognition. These results enable us to rationalize the response of an electrolyte-gated organic field-effect transistor (EGOFET) operated as an IL4 immunosensor. Two different strategies for the immobilization of IL4 antibodies on the Au gate electrode have been compared: antibodies are bound to (i) a smooth film of His-tagged protein G (PG)/Au; (ii) a 6-aminohexanethiol (HSC6NH2) self-assembled monolayer on Au through glutaraldehyde. The most sensitive EGOFET (concentration minimum detection level down to 5 nM of IL4) is obtained with the first functionalization strategy. This result is correlated to the highest probability (30%) of specific binding events detected by force spectroscopy on Ab/PG/Au electrodes, compared to 10% probability on electrodes with the second functionalization. Specifically, this demonstrates that Ab/PG/Au yields the largest areal density of oriented antibodies available for recognition. More in general, this work shows that specific recognition events in multiscale biosensors can be assessed, quantified, and optimized by means of a nanoscale technique.Peer reviewe