Degree and connectivity of the Internet's scale-free topology

In this paper we theoretically and empirically study the degree and connectivity of the Internet's scale-free topology at the autonomous system (AS) level. The basic features of the scale-free network have influence on the normalization constant of the degree distribution p(k). We develop a mathematics model of the Internet's scale-free topology. On this model we theoretically get the formulas of the average degree, the ratios of the kmin-degree (minimum degree) nodes and the kmax-degree (maximum degree) nodes, the fraction of the degrees (or links) in the hands of the richer (top best-connected) nodes. We find the average degree is larger for smaller power-law exponent {\lambda} and larger minimum or maximum degree. The ratio of the kmin-degree nodes is larger for larger {\lambda} and smaller kmin or kmax. The ratio of the kmax-degree ones is larger for smaller {\lambda} and kmax or larger kmin. The richer nodes hold most of the total degrees of the AS-level Internet topology. In addition, we reveal the ratio of the kmin-degree nodes or the rate of the increase of the average degree has power-law decay with the increase of the kmin. The ratio of the kmax-degree nodes has power-law decay with the increase of the kmax, and the fraction of the degrees in the hands of the richer 27% nodes is about 73% (the '73/27 rule'). At last, we empirically calculate, based on empirical data extracted from BGP, the average degree and the ratio and fraction using our method and other methods, and find that our method is rigorous and effective for the AS-level Internet topology.Comment: 22 pages, 8 figure

G-CSF/anti-G-CSF antibody complexes drive the potent recovery and expansion of CD11b+Gr-1+ myeloid cells without compromising CD8+ T cell immune responses

BACKGROUND: Administration of recombinant G-CSF following cytoreductive therapy enhances the recovery of myeloid cells, minimizing the risk of opportunistic infection. Free G-CSF, however, is expensive, exhibits a short half-life, and has poor biological activity in vivo. METHODS: We evaluated whether the biological activity of G-CSF could be improved by pre-association with anti-G-CSF mAb prior to injection into mice. RESULTS: We find that the efficacy of G-CSF therapy can be enhanced more than 100-fold by pre-association of G-CSF with an anti-G-CSF monoclonal antibody (mAb). Compared with G-CSF alone, administration of G-CSF/anti-G-CSF mAb complexes induced the potent expansion of CD11b(+)Gr-1(+) myeloid cells in mice with or without concomitant cytoreductive treatment including radiation or chemotherapy. Despite driving the dramatic expansion of myeloid cells, in vivo antigen-specific CD8(+) T cell immune responses were not compromised. Furthermore, injection of G-CSF/anti-G-CSF mAb complexes heightened protective immunity to bacterial infection. As a measure of clinical value, we also found that antibody complexes improved G-CSF biological activity much more significantly than pegylation. CONCLUSIONS: Our findings provide the first evidence that antibody cytokine complexes can effectively expand myeloid cells, and furthermore, that G-CSF/anti-G-CSF mAb complexes may provide an improved method for the administration of recombinant G-CSF

In situ growth of a stoichiometric PEG-like conjugate at a protein's N-terminus with significantly improved pharmacokinetics

The challenge in the synthesis of protein-polymer conjugates for biological applications is to synthesize a stoichiometric (typically 1:1) conjugate of the protein with a monodisperse polymer, with good retention of protein activity, significantly improved pharmacokinetics and increased bioavailability, and hence improved in vivo efficacy. Here we demonstrate, using myoglobin as an example, a general route to grow a PEG-like polymer, poly(oligo(ethylene glycol) methyl ether methacrylate) [poly(OEGMA)], with low polydispersity and high yield, solely from the N-terminus of the protein by in situ atom transfer radical polymerization (ATRP) under aqueous conditions, to yield a site-specific (N-terminal) and stoichiometric conjugate (1:1). Notably, the myoglobin-poly(OEGMA) conjugate [hydrodynamic radius (Rh): 13 nm] showed a 41-fold increase in its blood exposure compared to the protein (Rh: 1.7 nm) after IV administration to mice, thereby demonstrating that comb polymers that present short oligo(ethylene glycol) side chains are a class of PEG-like polymers that can significantly improve the pharmacological properties of proteins. We believe that this approach to the synthesis of N-terminal protein conjugates of poly(OEGMA) may be applicable to a large subset of protein and peptide drugs, and thereby provide a general methodology for improvement of their pharmacological profiles