This project aims to deliver a microfluidic platform capable of isolating bacteria and Extracellular Vesicles (EVs) at high throughput and high recovery rates from clinical samples, and perform the necessary downstream analysis for the diagnosis of diseases requiring earlier/urgent treatment. Currently, long incubation steps required for identification and susceptibility testing of pathogens make clinicians to prescribe broad-spectrum antibiotic treatments in sepsis cases upon hospital admission, and in nearly half of cases this treatment fails. On a different timescale, the lack of symptoms until late stages of some cancer types such as pancreatic cancer means a high mortality rate. Profiling molecules contained in EVs —most importantly DNA, RNA, proteins and lipids— promises a powerful diagnostic tool as biomarkers for cancer, but current EV isolation methods relying on ultracentrifugation are lengthy and can potentially damage the information enclosed. Microfluidics could provide a high yield, high throughput solution for isolation and enrichment of such particles. However, current approaches do not meet requirements of throughput and/or detection limit, and lack insightful physical understanding. I propose to use novel fluid dynamic and electrokinetic models for particle manipulation in microfluidics, with state-of-the-art fabrication methods to deliver a device capable of rapidly isolating and enriching samples containing (a) bacteria at low concentration (few hundreds per mL) to be integrated in a platform with the potential to identify and perform ASTs in possible bacterial infections in body fluids that avoid culture steps in current gold standards and potentially allow a ten-fold time reduction from sample to answer; (b) EVs to replace current ultracentrifugation methods. Thus, a future clinical implementation of the project outcomes will have large economic and societal impact.

The research of this proposal is focused on solving problems that involve the evolution of fluid interfaces. The project will investigate the dynamics of free boundaries arising between incompressible fluids of different nature. The main concern is well-posed scenarios which include the possible formation of singularities in finite time or existence of solutions for all time. These contour dynamics issues are governed by fundamental fluid mechanics equations such as the Euler, Navier-Stokes, Darcy and quasi-geostrophic systems. They model important problems such as water waves, viscous waves, Muskat, interface Hele-Shaw and SQG sharp front evolution. All these contour dynamics frameworks will be studied with emphasis on singularity formation and global existence results, not only for their importance in mathematical physics, but also for their mathematical interest. This presents huge challenges which will in particular require the use of different tools and methods from several areas of mathematics. A new technique, introduced to the field by the Principal Investigator, has already enabled the analysis of several singularity formations for the water waves and Muskat problems, as well as to obtain global existence results for Muskat. The main goal of this proposal is to develop upon this work, going far beyond the state of the art in these contour dynamics problems for incompressible fluids.

Oxygen (O2) is essential for life on Earth. This proposal deals with the study of the molecular mechanisms underlying acute O2 sensing by cells, a long-standing issue that is yet to be elucidated. In recent years, the discovery of hypoxia inducible transcription factors and their regulation by the O2-dependent hydroxylases has provided a solid framework for understanding genetic responses to sustained (chronic) hypoxia. However the mechanisms of acute O2 sensing, necessary for the activation of rapid, life-saving, compensatory respiratory and cardiovascular reflexes (e.g. hyperventilation and sympathetic activation), are unknown. While the primary goal of the project is to characterize the molecular mechanisms underlying acute O2 sensing by arterial chemoreceptors (carotid body –CB- and adrenal medulla –AM-), we will also extend our study to other organs (e.g. pulmonary and systemic arteries) of the homeostatic acute O2-sensing system. We will investigate the role of mitochondria, in particular complex I (MCI), in acute O2 sensing. Previous data from our group demonstrated that rotenone, a MCI blocker, selectively occludes responsiveness to hypoxia in CB cells. In addition, our unpublished data indicate that sensitivity to hypoxia (but not to other stimuli) is lost in mice with genetic disruption of MCI genes in CB and AM cells. We have shown that the adult CB is a plastic organ that contains a population of multipotent neural stem cells. Hence, another objective of the project is to study the role of these stem cells in CB modulation (over- or infra-activation), which may participate in the pathogenesis of diseases. In the past, our group has made seminal contributions to unveiling the cellular bases of arterial chemoreception. The discovery of stem cells in the CB and the generation of new genetically modified mouse models, put us in a leading position to elucidate the molecular bases of acute O2 sensing and their biomedical implications.

The GDSFLOWS project aims to re-shape the mathematics we use to understand fluid flows. More precisely, the goal is to develop completely new tools, at the crossroads of differential topology, harmonic analysis, and dynamical systems, to address two of the most pressing problems on the PDEs of incompressible fluids: (1) if, and how, do solutions “blow-up” (that is: after a smooth start, do the physical magnitudes of the problem become irregular in finite time)? and (2) when solutions do not blow-up, what are the qualitative dynamics (attractors, equilibrium solutions) of the trajectories in the phase space (that is, in the space of velocity or vorticity fields? The project proposes 3 horizons: 1) Extending the recently obtained universality results for the Euler equation on certain Riemannian manifolds to the case of PDEs modelling the evolution of fluid interfaces, where the existence of solutions blowing-up in finite time is rigurously known. 2) Proving that the Euler equations on high-dimensional Euclidean spaces are universal, and using this to study whether solutions in very high dimensions that blow-up in finite time exist. 3) Proving the existence of chaotic invariant sets in the infinite dimensional phase space of the 2D Euler equation. The GDSFLOWS project will be carried out by the researcher, an expert in the study of geometric properties of PDEs coming from mathematical physics and hydrodynamics. He recently developed a method for embedding any finite-dimensional dynamical system into the Euler equation on certain high-dimensional Riemannian manifolds, building on T. Tao's recent program to prove blow-up of solutions to the high-dimensional Euler equation. The researcher will collaborate with the Supervisor, a prominent expert in the formation of singularities in the PDEs of fluid dynamics, and one of the authors of the first rigurous proof of blow-up in well-posed PDEs modelling incompressible fluids.