Embracing Integrability in Stellar and Planetary Dynamics

Hamiltonian systems in stellar and planetary dynamics are typically near integrable. For example, Solar System planets are almost in two-body orbits, and in simulations of the Galaxy, the orbits of stars seem regular. For such systems, sophisticated numerical methods can be developed through integrable approximations. Following this theme, we discuss three distinct problems. We start by considering numerical integration techniques for planetary systems. Perturbation methods (that utilize the integrability of the two-body motion) are preferred over conventional "blind" integration schemes. We introduce perturbation methods formulated with Cartesian variables. In our numerical comparisons, these are superior to their conventional counterparts, but, by definition, lack the energy-preserving properties of symplectic integrators. However, they are exceptionally well suited for relatively short-term integrations in which moderately high positional accuracy is required. The next exercise falls into the category of stability questions in solar systems. Traditionally, the interest has been on the orbital stability of planets, which have been quantified, e.g., by Liapunov exponents. We offer a complementary aspect by considering the protective effect that massive gas giants, like Jupiter, can offer to Earth-like planets inside the habitable zone of a planetary system. Our method produces a single quantity, called the escape rate, which characterizes the system of giant planets. We obtain some interesting results by computing escape rates for the Solar System. Galaxy modelling is our third and final topic. Because of the sheer number of stars (about 10^11 in Milky Way) galaxies are often modelled as smooth potentials hosting distributions of stars. Unfortunately, only a handful of suitable potentials are integrable (harmonic oscillator, isochrone and Stäckel potential). This severely limits the possibilities of finding an integrable approximation for an observed galaxy. A solution to this problem is torus construction; a method for numerically creating a foliation of invariant phase-space tori corresponding to a given target Hamiltonian. Canonically, the invariant tori are constructed by deforming the tori of some existing integrable toy Hamiltonian. Our contribution is to demonstrate how this can be accomplished by using a Stäckel toy Hamiltonian in ellipsoidal coordinates.

External signal-activated liposomal drug delivery systems

Modern drug discovery gives rise to a great number of potential new therapeutic agents, but in some cases the efficient treatment of patient may not be achieved because the delivery of active compounds to the target site is insufficient. Thus, drug delivery is one of the major challenges in current pharmaceutical research. Numerous nanoparticle-based drug carriers, e.g. liposomes, have been developed for enhanced drug delivery and targeting. Drug targeting may enhance the efficiency of the treatment and, importantly, reduce unwanted side effects by decreasing drug distribution to non-target tissues. Liposomes are biocompatible lipid-based carriers that have been studied for drug delivery during the last 40 years. They can be functionalized with targeting ligands and sensing materials for triggered activation. In this study, various external signal-assisted liposomal delivery systems were developed. Signals can be used to modulate drug permeation or release from the liposome formulation, and they provide accurate control of time, place and rate of activation. The study involved three types of signals that were used to trigger drug permeation and release: electricity, heat and light. Electrical stimulus was utilized to enhance the permeation of liposomal DNA across the skin. Liposome/DNA complex-mediated transfections were performed in tight rat epidermal cell model. Various transfection media and current intensities were tested, and transfection efficiency was evaluated non-invasively by monitoring the concentration of secreted reporter protein in cell culture medium. Liposome/DNA complexes produced gene expression, but electrical stimulus did not enhance the transfection efficiency significantly. Heat-sensitive liposomal drug delivery system was developed by coating liposomes with biodegradable and thermosensitive poly(N-(2-hydroxypropyl) methacrylamide-mono/dilactate polymer. Temperature-triggered liposome aggregation and contents release from liposomes were evaluated. The cloud point temperature (CP) of the polymer was set to 42 °C. Polymer-coated liposome aggregation and contents release were observed above CP of the polymer, while non-coated liposomes remained intact. Polymer precipitates above its CP and interacts with liposomal bilayers. It is likely that this induces permeabilization of the liposomal membrane and contents release. Light-sensitivity was introduced to liposomes by incorporation of small (< 5 nm) gold nanoparticles. Hydrophobic and hydrophilic gold nanoparticles were embedded in thermosensitive liposomes, and contents release was investigated upon UV light exposure. UV light-induced lipid phase transitions were examined with small angle X-ray scattering, and light-triggered contents release was shown also in human retinal pigment epithelial cell line. Gold nanoparticles absorb light energy and transfer it into heat, which induces phase transitions in liposomes and triggers the contents release. In conclusion, external signal-activated liposomes offer an advanced platform for numerous applications in drug delivery, particularly in the localized drug delivery. Drug release may be localized to the target site with triggering stimulus that results in better therapeutic response and less adverse effects. Triggering signal and mechanism of activation can be selected according to a specific application.