Abstract basins of attraction

Abstract basins appear naturally in different areas of several complex variables. In this survey we want to describe three different topics in which they play an important role, leading to interesting open problems

Experimental determination of the frequency and field dependence of Specific Loss Power in Magnetic Fluid Hyperthermia

Magnetic nanoparticles are promising systems for biomedical applications and in particular for Magnetic Fluid Hyperthermia, a promising therapy that utilizes the heat released by such systems to damage tumor cells. We present an experimental study of the physical properties that influences the capability of heat release, i.e. the Specific Loss Power, SLP, of three biocompatible ferrofluid samples having a magnetic core of maghemite with different core diameter d= 10.2, 14.6 and 19.7 nm. The SLP was measured as a function of frequency f and intensity of the applied alternating magnetic field H, and it turned out to depend on the core diameter, as expected. The results allowed us to highlight experimentally that the physical mechanism responsible for the heating is size-dependent and to establish, at applied constant frequency, the phenomenological functional relationship SLP=cH^x, with 2<x<3 for all samples. The x-value depends on sample size and field frequency/ intensity, here chosen in the typical range of operating magnetic hyperthermia devices. For the smallest sample, the effective relaxation time Teff=19.5 ns obtained from SLP data is in agreement with the value estimated from magnetization data, thus confirming the validity of the Linear Response Theory model for this system at properly chosen field intensity and frequency

Microfluidics for protein biophysics

Microfluidics has the potential to transform experimental approaches across the life sciences. In this review, we discuss recent advances enabled by the development and application of microfluidic approaches to protein biophysics. We focus on areas where key fundamental features of microfluidics open up new possibilities and present advantages beyond low volumes and short time-scale analysis, conventionally provided by microfluidics. We discuss the two most commonly used forms of microfluidic technology, single-phase laminar flow and multiphase microfluidics. We explore how the understanding and control of the characteristic physical features of the microfluidic regime, the integration of microfluidics with orthogonal systems and the generation of well-defined microenvironments can be used to develop novel devices and methods in protein biophysics for sample manipulation, functional and structural studies, detection and material processing

NMR and μ+\mu^{+}SR detection of unconventional spin dynamics in Er(trensal) and Dy(trensal) molecular magnets

Measurements of proton Nuclear Magnetic Resonance (1H NMR) spectra and relaxation and of Muon Spin Relaxation ($\mu^{+}$SR) have been performed as a function of temperature and external magnetic field on two isostructural lanthanide complexes, Er(trensal) and Dy(trensal) featuring crystallographically imposed trigonal symmetry. Both the nuclear 1/T1 and muon $\lambda$ longitudinal relaxation rates, LRR, exhibit a peak for temperatures T lower than 30K, associated to the slowing down of the spin dynamics, and the width of the NMR absorption spectra starts to increase significantly at T ca. 50K, a temperature sizably higher than the one of the LRR peaks. The LRR peaks have a field and temperature dependence different from those previously reported for all Molecular Nanomagnets. They do not follow the Bloembergen-Purcell-Pound scaling of the amplitude and position in temperature and field and thus cannot be explained in terms of a single dominating correlation time $\tau$c determined by the spin slowing down at low temperature. Further, for T lower than 50K the spectral width does not follow the temperature behavior of the magnetic susceptibility chi. We suggest, using simple qualitative considerations, that the observed behavior is due to a combination of two different relaxation processes characterized by the correlation times $\tau$LT and $\tau$HT, dominating for T lower than 30K and T higher than 50K, respectively. Finally, the observed flattening of LRR for T lower than 5K is suggested to have a quantum origin

Particle-Based Monte-Carlo Simulations of Steady-State Mass Transport at Intermediate Péclet Numbers

Conventional approaches for simulating steady-state distributions of dilute particles under diffusive and advective transport involve solving the diffusion and advection equations in at least two dimensions. Here, we present an alternative computational strategy by combining a particle-based rather than a field-based approach with the initialisation of particles in proportion to their flux. This method allows accurate prediction of the steady state and is applicable even at intermediate and high Péclet numbers (Pe>1) swhere traditional particle-based Monte-Carlo methods starting from randomly initialised particle distributions fail. We demonstrate that generating a flux of particles according to a predetermined density and velocity distribution at a single fixed time and initial location allows for accurate simulation of mass transport under flow. Specifically, upon initialisation in proportion to their flux, these particles are propagated individually and detected by summing up their Monte-Carlo trajectories in predefined detection regions. We demonstrate quantitative agreement of the predicted concentration profiles with the results of experiments performed with fluorescent particles in microfluidic channels under continuous flow. This approach is computationally advantageous and readily allows non-trivial initial distributions to be considered. In particular, this method is highly suitable for simulating advective and diffusive transport in microfluidic devices, for instance in the context of diffusive sizing.Financial support from the Biotechnology and Biological Sciences Research Council (BBSRC), the European Research Council (ERC), the Frances and Augustus Newman Foundation as well as the Swiss National Science Foundation is gratefully acknowledged

Self-assembling peptide and protein amyloids: from structure to tailored function in nanotechnology

Self-assembled peptide and protein amyloid nanostructures have traditionally been considered only as pathological aggregates implicated in human neurodegenerative diseases. In more recent times, these nanostructures have found interesting applications as advanced materials in biomedicine, tissue engineering, renewable energy, environmental science, nanotechnology and material science, to name only a few fields. In all these applications, the final function depends on: (i) the specific mechanisms of protein aggregation, (ii) the hierarchical structure of the protein and peptide amyloids from the atomistic to mesoscopic length scales and (iii) the physical properties of the amyloids in the context of their surrounding environment (biological or artificial). In this review, we will discuss recent progress made in the field of functional and artificial amyloids and highlight connections between protein/peptide folding, unfolding and aggregation mechanisms, with the resulting amyloid structure and functionality. We also highlight current advances in the design and synthesis of amyloid-based biological and functional materials and identify new potential fields in which amyloid-based structures promise new breakthroughs

Particle-Based Monte-Carlo Simulations of Steady-State Mass Transport at Intermediate Péclet Numbers

Conventional approaches for simulating steady-state distributions of dilute particles under diffusive and advective transport numbers involve solving the diffusion and advection equations in at least two dimensions. Here, we present an alternative computational strategy by combining a particle-based rather than a field-based approach with the initialisation of particles in proportion to their flux. This method allows accurate prediction of the steady state and is applicable even at intermediate and high Péclet numbers (Pe>1) where traditional particle-based Monte-Carlo methods starting from randomly initialised particle distributions fail. We demonstrate that generating a flux of particles according to a predetermined density and velocity distribution at a single fixed time and initial location allows for accurate simulation of mass transport under flow. Specifically, upon initialisation in proportion to their flux, these particles are propagated individually and detected by summing up their Monte-Carlo trajectories in predefined detection regions. We demonstrate quantitative agreement of the predicted concentration profiles with the results of experiments performed with fluorescent particles in microfluidic channels under continuous flow. This approach is computationally advantageous and readily allows non-trivial initial distributions to be considered. In particular, this method is highly suitable for simulating advective and diffusive transport in microfluidic devices, for instance in the context of diffusive sizing.Financial support from the Biotechnology and Biological Sciences Research Council (BBSRC), the European Research Council (ERC), the Frances and Augustus Newman Foundation as well as the Swiss National Science Foundation is gratefully acknowledged

Synthesis and Biological Evaluation (in Vitro and in Vivo) of Cyclic RGD Peptidomimetic - Paclitaxel Conjugates Targeting Integrin alphaVbeta3

A small library of integrin ligand - Paclitaxel conjugates 10-13 was synthesized with the aim of using the tumor-homing cyclo[DKP-RGD] peptidomimetics for site-directed delivery of the cytotoxic drug. All the Paclitaxel-RGD constructs 10-13 inhibited biotinylated vitronectin binding to the purified alphaVbeta3 integrin receptor at low nanomolar concentration and showed in vitro cytotoxic activity against a panel of human tumor cell lines similar to that of Paclitaxel. Among the cell lines, the cisplatin-resistant IGROV-1/Pt1 cells expressed high levels of integrin alphaVbeta3, making them attractive to be tested in in vivo models. Cyclo[DKP-f3-RGD]-PTX 11 displayed sufficient stability in physiological solution and in both human and murine plasma to be a good candidate for in vivo testing. In tumor-targeting experiments against the IGROV-1/Pt1 human ovarian carcinoma xenotransplanted in nude mice, compound 11 exhibited a superior activity than Paclitaxel, despite the lower (ca. half) molar dosage used