An accurate and efficient scheme for function extensions on smooth domains

A new scheme is proposed to construct an n-times differentiable function extension of an n-times differentiable function defined on a smooth domain D in d-dimensions. The extension scheme relies on an explicit formula consisting of a linear combination of n+1 function values in D, which extends the function along directions normal to the boundary. Smoothness tangent to the boundary is automatic. The performance of the scheme is illustrated by using function extension as a step in a numerical solver for the inhomogeneous Poisson equation on multiply connected domains with complex geometry in two and three dimensions. We show that the modest additional work needed to do function extension leads to considerably more accurate solutions of the partial differential equation.Comment: 22 pages, 38 figure

Biological characterization of purified native 20-kDa human growth hormone

Because of the propensity of the 20-kDa variant of human growth human (GH) to aggregate with itself and with 22-kDa human GH, it has been difficult to prepare monomeric 20-kDa GH in highly purified form. This has been a major complicating factor in determining whether 20-kDa GH has a biological activity profile distinct from that of 22-kDa GH. In the present study, native 20-kDa GH was isolated from a human GH dimer concentrate and purified by a procedure that included column electrophoresis in agarose suspension as a final separation step. This procedure yielded highly purified monomeric 20-kDa GH, which was contaminated to an extent of less than 1% with 22-kDa GH, and which exhibited only a small degree of dimerization upon storage. The native 20-kDa Gh was quite active in stimulating growth in hypophysectomized rats, when growth was assessed by body weight gain, longitudinal bone growth, the stimulation of sulfation of cartilage, and the elevation of serum IGF-1 level. However, in all of these growth assays, the 20-kDa GH was somewhat less active than the native 22-kDa GH to which it was compared; e.g., in the body weight gain and longitudinal bone growth assays, it had an estimated potency of 0.6 relative to the 22-kDa GH. The 20-kDa GH exhibited substantial diabetogenic activity when tested for the ability to raise fasting blood glucose concentration and to impair glucose tolerance in ob/ob mice. Also, the native 20-kDa GH had significant in vitro insulin-like activity, although its potency was approximately 20% that of the native 22-kDa GH to which it was compared. Thus, the biological activity profile of native 20-kDa GH differs from that of 22-kDa GH primarily in that insulin-like activity is markedly attenuated.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/26576/1/0000115.pd

Identification and Structural Characterization of a New Three-Finger Toxin Hemachatoxin from Hemachatus haemachatus Venom

10.1371/journal.pone.0048112PLoS ONE710