Analysis of ion channel stochastic signals for biosensing

In biological world, life of cells is guaranteed by their ability to sense and to respond to a large variety of internal and external stimuli. In particular, excitable cells, like muscle or nerve cells, produce quick depolarizations in response to electrical, mechanical or chemical stimuli: this means that they can change their internal potential through a quick exchange of ions between cytoplasm and the external environment. This can be done thanks to the presence of ion channels, proteins that span the lipid bilayer and act like switches, allowing ionic current to flow opening and shutting in a stochastic way. For a particular class of ion channels, ligand-gated ion channels, the gating processes is strongly influenced by binding between receptive sites located on the channel surface and specific target molecules. These channels, inserted in biomimetic membranes and in presence of a proper electronic system for acquiring and elaborating the electrical signal, could give us the possibility of detecting and quantifying concentrations of specific molecules in complex mixtures from ionic currents across the membrane; in this thesis work, this possibility is investigated. In particular, it reports a description of experiments focused on the creation and the characterization of artificial lipid membranes, the reconstitution of ion channels and the analysis of their electrical and statistical properties. Moreover, after a chapter about the basis of the modelling of the kinetic behaviour of ligand gated ion channels, a possible approach for the estimation of the target molecule concentration, based on a statistical analysis of the ion channel open probability, is proposed. The fifth chapter contains a description of the kinetic characterisation of a ligand gated ion channel: the homomeric α2 isoform of the glycine receptor. It involved both experimental acquisitions and signal analysis. The last chapter represents the conclusions of this thesis, with some remark on the effective performance that may be achieved using ligand gated ion channels as sensing elements.

Permutation classes, sorting algorithms, and lattice paths

A permutation is said to avoid a pattern if it does not contain any subsequence which is order-isomorphic to it. Donald Knuth, in the first volume of his celebrated book "The art of Computer Programming", observed that the permutations that can be computed (or, equivalently, sorted) by some particular data structures can be characterized in terms of pattern avoidance. In more recent years, the topic was reopened several times, while often in terms of sortable permutations rather than computable ones. The idea to sort permutations by using one of Knuth’s devices suggests to look for a deterministic procedure that decides, in linear time, if there exists a sequence of operations which is able to convert a given permutation into the identical one. In this thesis we show that, for the stack and the restricted deques, there exists an unique way to implement such a procedure. Moreover, we use these sorting procedures to create new sorting algorithms, and we prove some unexpected commutation properties between these procedures and the base step of bubblesort. We also show that the permutations that can be sorted by a combination of the base steps of bubblesort and its dual can be expressed, once again, in terms of pattern avoidance. In the final chapter we give an alternative proof of some enumerative results, in particular for the classes of permutations that can be sorted by the two restricted deques. It is well-known that the permutations that can be sorted through a restricted deque are counted by the Schrӧder numbers. In the thesis, we show how the deterministic sorting procedures yield a bijection between sortable permutations and Schrӧder paths.

Sparse Signal Representation of Ultrasonic Signals for Structural Health Monitoring Applications

Assessment of the integrity of structural components is of great importance for aerospace systems, land and marine transportation, civil infrastructures and other biological and mechanical applications. Guided waves (GWs) based inspections are an attractive mean for structural health monitoring. In this thesis, the study and development of techniques for GW ultrasound signal analysis and compression in the context of non-destructive testing of structures will be presented. In guided wave inspections, it is necessary to address the problem of the dispersion compensation. A signal processing approach based on frequency warping was adopted. Such operator maps the frequencies axis through a function derived by the group velocity of the test material and it is used to remove the dependence on the travelled distance from the acquired signals. Such processing strategy was fruitfully applied for impact location and damage localization tasks in composite and aluminum panels. It has been shown that, basing on this processing tool, low power embedded system for GW structural monitoring can be implemented. Finally, a new procedure based on Compressive Sensing has been developed and applied for data reduction. Such procedure has also a beneficial effect in enhancing the accuracy of structural defects localization. This algorithm uses the convolutive model of the propagation of ultrasonic guided waves which takes advantage of a sparse signal representation in the warped frequency domain. The recovery from the compressed samples is based on an alternating minimization procedure which achieves both an accurate reconstruction of the ultrasonic signal and a precise estimation of waves time of flight. Such information is used to feed hyperbolic or elliptic localization procedures, for accurate impact or damage localization.