Coalescence times for critical Galton-Watson processes with immigration

Let $X^I_n$ be the coalescence time of two particles picked at random from the $n$th generation of a critical Galton-Watson process with immigration, and let $A^I_n$ be the coalescence time of the whole population in the $n$th generation. In this paper, we study the limiting behaviors of $X^I_n$ and $A^I_n$ as $n\to\infty$

Development of small interfering RNA delivery system using PEI-PEG-APRPG polymer for antiangiogenic vascular endothelial growth factor tumor-targeted therapy

Zong-Xia Lu1, Li-Ting Liu1,2, Xian-Rong Qi11Department of Pharmaceutics, School of Pharmaceutical Sciences, Peking University, Beijing, People's Republic of China; 2Department of Pharmacy, School and Hospital of Stomatology, Peking University, Beijing, People's Republic of ChinaBackground: Small interfering RNA (siRNA) can silence target genes in the cytoplasm and be a major tool in gene therapy. Vascular endothelial growth factor (VEGF), a potent regulator of angiogenesis, is overexpressed in most tumors and is closely associated with tumor growth and metastasis. It has been shown that inhibition of VEGF expression by siRNA is an effective and useful method for antiangiogenic tumor therapy.Methods: In the present study, we synthesized a targeted delivery system of PEI-PEG-APRPG incorporating angiogenic vessel-homing Ala-Pro-Arg-Pro-Gly (APRPG) peptide into cationic polyethylenimine (PEI) via a hydrophilic poly(ethylene glycol) (PEG) spacer.Results: PEI-PEG-APRPG effectively condensed siRNA into 20–50 nm nanoparticles with a positive surface charge using a suitable N/P ratio. The siRNA/PEI-PEG-APRPG complex effectively enhanced the stability of siRNA in RNase A, and improved the proliferation-inhibiting ability and transfection efficiency of siRNA in vitro and tumor accumulation in vivo. In addition, the siRNA/PEI-PEG-APRPG complex exhibited high efficiency as antitumor therapy with regard to tumor growth, microvessel density, and VEGF protein and mRNA levels.Conclusion: These findings suggest that PEI-PEG-APRPG effectively delivers siRNA to tumors overexpressing VEGF and thereby inhibits tumor growth.Keywords: PEI-PEG-APRPG, VEGF siRNA, gene delivery, tumor-targeted, antiangiogenic therap