Singular stochastic equations on Hilbert spaces: Harnack inequalities for their transition semigroups

We consider stochastic equations in Hilbert spaces with singular drift in the framework of [Da Prato, R\"ockner, PTRF 2002]. We prove a Harnack inequality (in the sense of [Wang, PTRF 1997]) for its transition semigroup and exploit its consequences. In particular, we prove regularizing and ultraboundedness properties of the transition semigroup as well as that the corresponding Kolmogorov operator has at most one infinitesimally invariant measure $\mu$ (satisfying some mild integrability conditions). Finally, we prove existence of such a measure $\mu$ for non-continuous drifts

Combining Transfer of TTF-1 and Pax-8 Gene: a Potential Strategy to Promote Radioiodine Therapy of Thyroid Carcinoma

Cotransfer of TTF-1 and Pax-8 gene to tumor cells, resulting in the reexpression of iodide metabolism-associated proteins, such as sodium iodide symporter (NIS), thyroglobulin (Tg), thyroperoxidase (TPO), offers the possibility of radioiodine therapy to non-iodide-concentrating tumor because the expression of iodide metabolism-associated proteins in thyroid are mediated by the thyroid transcription factors TTF-1 and Pax-8. The human TTF-1 and Pax-8 gene were transducted into the human thyroid carcinoma (K1 and F133) cells by the recombinant adenovirus, AdTTF-1 and AdPax-8. Reexpression of NIS mRNA and protein, but not TPO and Tg mRNA and protein, was detected in AdTTF-1-infected F133 cells, following with increasing radioiodine uptake (6.1~7.4 times), scarcely iodide organification and rapid iodide efflux (t1/2≈8 min in vitro, t1/2≈4.7 h in vivo).
In contrast, all of the reexpression of NIS, TPO and Tg mRNA and proteins in F133 cells were induced by the synergetic effect of TTF-1 and Pax-8. AdTTF-1 and AdPax-8 coinfected K1 and F133 cells could effectively accumulate radioiodine (6.6-7.5 times) and obviously retarded radioiodine retention (t1/2≈25-30 min in vitro, t1/2≈12 h in vivo) (p<0.05).
Accordingly, the effect of radioiodine therapy of TTF-1 and Pax-8 cotransducted K1 and
F133 cells (21-25% survival rate in vitro) was better than that of TTF-1-transducted cells
(40% survival rate in vitro) (p<0.05). These results indicate that single TTF-1 gene transfer may have limited efficacy of radioiodine therapy because of rapid radioiodine efflux. The cotransduction of TTF-1 and Pax-8 gene, with resulting NIS-mediated radioiodine accumulation and TPO and Tg-mediated radioiodine organification and intracellular retention, may lead to effective radioiodine therapy of thyroid carcinoma

Acyclic Congeners of Cucurbit[n]uril and a Related Mechanistic Study on the Cucurbit[n]uril Forming Reaction.

Supramolecular chemistry has been a very important research area in the past several decades. In this research field, molecular containers, such as cyclodextrin, attracts special attention due to their wide applications both in academia and industry. Cucurbit[n]uril (CB[n]), as a new generation molecular container, has selective and tight binding towards lots of cations and neutral molecules. A homologous family of CB[n] has been discovered including CB[5]-CB[8], CB[10], iCB[n], ns-CB[10] and ns-CB[6]. CB[n] analogues and derivatives have also been developed. CB[n] still has several issues, such as low solubility in water, difficulty to be functionalized, and slow association and dissociation kinetics. This thesis describes efforts to address these issues by developing new CB[n] type molecular containers and carrying out mechanistic investigations. Three chapters are included in this thesis. Chapter 1 is a literature review of molecular encapsulation and molecular container chemistry. We first introduced general concepts of molecular encapsulation and present examples of molecular container, such as cyclodextrin. This is followed by an introduction to CB[n] molecular containers and their supramolecular chemistry. Chapter 2 introduces new acyclic CB[n] congeners II-5a and II-5b. II-5a and II-5b are obtained from step-wise synthesis with reasonable yields. This step-wise synthetic route avoids difficult separation process. We measured the binding constants of II-5a towards a number of guests and found the binding affinity is usually comparable to CB[7]. The recognition property of II-5a is investigated in depth. We found that the length and functional groups of the guests greatly influence the binding affinity. Nevertheless, the charge and size of the guests do not have as a big influence on the binding constants as CB[7]. We discovered that the ionic strength of the buffer is critical for the binding constant. By comparing the recognition property of II-5a and II-6, it is discovered that the substituted o-xylyene walls are important for the tight binding compounds. II-5a and II-5b are new examples of CB[n] type molecular containers. They retain most of the good recognition property of CB[n] and have advantages compared to CB[n], including 1) aromatic walls that makes further functionalization possible; 2) acyclic structure that enables fast association and dissociation kinetics. Chapter 3 describes the mechanistic study of CB[n] forming reactions. Another possible way to synthesize CB[n] molecular container is to use aldehydes instead of paraformaldehyde. But neither previous researchers nor our work has succeeded to make the aldehydes participating CB[n] forming reactions happen. Mechanistic investigation was carried out to explain why this reaction simply does not occur. We used III-7 instead of glycoluril to avoid cyclization reactions. Several reasons are discovered: 1) side products are formed, such as III-SP1 and III-SP2; 2) S-shape intermediates are yielded, such as III-15S, III-16S, III-17S and III-18S, which are not able to continue the reaction to form macrocycles; 3) a small equilibrium constant for the chain grouth reaction. This study explains why aldehydes usually do not participate in CB[n] forming reactions. This work could also lead to the discovery of certain aldehydes that can form CB[n] type macrocycles