replication - What is the mechanism of labeling a DNA molecule with deuterated water?

I would assume that the labeling occurs in the reduction of NTPs to form dNTPS.

This process (catalyzed by ribonucleotide reductase) involves protonating the hydroxyl group on the 2' carbon, allowing it to leave as water, and then adding a hydride to the newly formed carbocation. The two hydrogen atoms (the proton and the hydride) come from two thiols on the enzyme, which in the process are oxidized to form a disulfide bond.

The crux is that, in the presence of heavy water, the two thiols would rapidly exchange their hydrogen for deuterium. That means that the hydride that gets added to the carbocation would be a deuterium, and the resulting dNTP would be deuterium labeled.

This is the only step that I can imagine the labeling working for, as a carbon-hydrogen bond is formed (which doesn't exchange rapidly with the solvent) using the hydrogen from a sulfer-hydrogen bond (which does exchange rapidly with the solvent).

fa.functional analysis - Self-adjoint extension of locally defined differential operators

The following is well known. Given a symmetric differential operator, like $partial_x^2$, defined on smooth functions of compact support on $mathbb{R}$, $C_0^infty(mathbb{R})$, one can count the number of independent $L^2$-normalizable solutions of $partial_xpm i$ and use the von Neumann index theorem to classify possible self-adjoint extensions of this operator on $L^2(mathbb{R})$. This can be generalized to more complicated differential operators, to $mathbb{R}^n$ as well as bounded open subsets thereof.

On the other hand, suppose that I have a manifold $M$ that is covered by a set of open charts $U_i$ with differential operators $D_i$ defined in corresponding local coordinates. It is easy to check if the $D_i$ are restrictions of a globally defined differential operator $D$ on $M$: the transition functions on intersections of charts $U_icap U_j$ must transform $D_i$ into $D_j$ and vice versa. Suppose that is the case and that I am interested in self-adjoint extensions of $D$ to $L^2(M)$ (supposing that an integration measure is given and that $D$ is symmetric with respect to it). Now, the question:

Is there way of classifying the self-adjoint extensions of $D$ on $L^2(M)$ in terms of its definition in local coordinates, the actions of $D_i$ on $C_0^infty(U_i)$.

A simple example would be the cover of $S^1$ by two overlapping charts. I know that a self-adjoint extension of $partial_x^2$ on $[0,1]$ with periodic boundary conditions gives the naturally defined self-adjoint Laplacian on $S^1$. Then $(0,1)$ is interpreted as a chart on $S^1$ that excludes one point. However, I don't know how to define the self-adjoint Laplacian on $S^1$ if it's given on two overlapping charts.

mg.metric geometry - How to compare finite point sets in normed spaces?

Consider the complete bipartite graph $G$ with bipartition $(A,B)$, and let the weight of an edge $ab$ be $d(a,b)$. Then $d(A,B)$ is simply the weight of a minimum weight perfect matching of $G$. Finding minimum weight perfect matchings is a well-studied problem. In particular, we can compute $d(A,B)$ in polynomial-time. Indeed, even in the case that the edge weights do not come from a metric, efficient algorithms exist. Also, even in the case that the graph is not bipartite, we can find minimum weight perfect matchings in polynomial-time. See Combinatorial Optimization, by Cook, Cunningham, Pulleyblank, and Schrijver for the sordid details.

stem cells - potency in preformed germ-line

In almost all metazoa, the pro-germline cells get segregated from other stem cells at an early stage of development and they thrive and differentiate in their neighborhood. This is important in order to preserve the germline. This post provides some basic explanation.

However, even drosophila have adult multipotent stem cells and help in the formation of midgut as reported by this study.

muscles - Does a piezoelectric organic substance exist?

I don't know if it would contract by the amount that you are after, but bone (which has both organic and inorganic components) is piezoelectric.

For an overview, see http://silver.neep.wisc.edu/~lakes/BoneElectr.html.

They suggest that two different mechanisms are responsible for these effects: classical piezoelectricity due to the molecular asymmetry of collagen in dry bone, and fluid flow effects, possibly streaming potentials in wet bone.

mg.metric geometry - Bounding the product of lengths of basis vectors of a unimodular lattice

I don't know how good the bound is you can obtain from this, but what about taking a Korkine-Zolotarev reduced basis of $Lambda$, say $(b_1, dots, b_n)$: then, by this paper, $|b_i|_2^2 le frac{i + 3}{4} lambda_i(Lambda)^2$, where $lambda_i(Lambda)$ is the $i$-th successive minimum of $Lambda$. By Minkowski, $prod_{i=1}^n lambda_i(Lambda) le gamma_n^{n/2} det Lambda = gamma_n^{n/2}$ (in your case), $gamma_n$ being the $n$-th Hermite constant, whence you get $A le prod_{i=1}^n |b_i|_2 le frac{gamma_n^{n/2}}{2^n} prod_{i=1}^n sqrt{i + 3}$.

blood circulation - Do body lotions enter into bloodstream of people? And how do they do it?

Lotions, like any other drug, can effectively enter the blood system. However, the fraction of the applied lotion that actually enters is really small, and it only achieves a significant concentration in the zone near the application. The skin, if healthy, offers a very high resistance to the passage of substances. Moreover, the bloodstream actually dilutes even more the little fraction it achieves to enter, further reducing its effects. If the skin is damaged the penetration is greater, though you'll never be able to get drunk by dropping booze in an injury.