plant physiology - Measuring sugar content of a tree

The difficult step will be getting samples of sap: have a look at the WP page for maple syrup for ideas about methods of tapping into the xylem of your trees.

You will then need to assay sucrose in the sample of sap. There are many commercial assay kits available (Google: sucrose assay), which rely on an enzyme, invertase, to convert the sucrose to glucose + fructose. The released glucose is then measured by a glucose oxidase assay. You would need some kind of colorimeter/spectrophotometer for quantitative results but there is a visible color change, so you could probably get a rough idea of what is going on by visual comparison with a set of glucose standards.

Supplementary
An alternative would be to measure sugar concentration by refractometry: see here and here.

human biology - Extremely rare occurence of Heart cancer?

This is a specific version of the great cancer question: "Why are some cancers more common than others?" The answer is either "Some have more common causes", and (or) "Some are cured spontaneously more often". So now all you are asking is "What causes cancer?" and "How do we cure it?"

Given that, I don't expect a general definitive answer will be forthcoming. A specific answer might be possible, but I doubt there will be any existing experiments that address this. With the obvious caveat that only experimental or statistical results can really answer your question, here are a couple of off-the-cuff hypothesis for consideration:

1 - Differences in stem cell populations.

Apparently, differentiation can actually be targeted as part of a treatment in some neuroblastoma cases - see the section on "Differentiation therapy" in this page from Sloan-Kettering. Cardiac stem cells seem to exist, but a difference in relative population and turnover rates between brain and heart might be related to the relative frequencies of these types of cancers. @WYSYWIG referred to neural progenitors in his comment above.

2 - A filtering effect due to a more extreme selection pressure in the uniformly stressful environment of the a beating heart.

Although there is a relation between elevated levels of oxidative stress and cancer causing mutations, it could be that this only matters in a punctuated stress environment, where cells have down time to recover. A sustained stress environment might actually helps prevent cancer. The path from normal to cancer cell requires multiple mutations, and I would not expect most pre-cancerous cells to be more fit than correctly wired ones. The extra stress of the cardiac environment might produce an elevated mutation rate, but also produce an even higher rate of apoptosis in early "sick" cells before they accumulate enough mistakes to become become cancerous, resulting in a net decrease in the rate of cancer.

Both of these ideas fit with heart cancer being less common and with metastasis from elsewhere being more common in heart than primary cancer, but unfortunately, a higher rate of clearing of sick cells would necessitate a higher rate of replacement from stem cells, so these two hypotheses partially cancel each other. Again, hypotheses without experiments are not really answers.

Difference between genetic engineering and synthetic biology

My understanding is that synthetic biology is genetic engineering 2.0. The difference is in the approach. Whereas genetic engineering projects are usually ad hoc, synthetic biology aims to apply proper engineering principles such as standardisation, modularisation, and reusability. Synthetic biologists create and use libraries of standard parts that are characterised, so they can be easily reused in projects. A part could be a gene, a terminator, a promoter, etc.

Synthetic biology also has greater ambitions. The focus is on creating whole systems/circuits of genetic regulation. This means there is a need for computational modelling and understanding of how biological systems work. In this aspect synthetic biology is a sister of systems biology a bit like synthetic chemistry (engineering) is a sister of chemistry (science).

You could of course argue that it's just a marketing ploy to invent a new name for something that is just the next step in genetic engineering, but the differences in approach are quite large and a new name signifies it.

With regards to synthesised vs. PCRed DNA: It doesn't really matter which you use in synthetic biology. However, cheap synthesis is one of the technologies that enable easier synthetic biology. The idea for the future is that you will be able to synthesise whole plasmids and chromosomes instead of having to "cut and paste" DNA. When that happens physical parts repositories will be obsolete, but they will remain crucial in silico. Cheap synthesis is nice, but doesn't make or brake synthetic biology.

anatomy - Evolution of long necks in giraffes

There seems to consensus that it is not competition for tall food. Giraffes actually often feed on resources that are lower than their maximum possible height. See:

Simmons, R. E. & Scheepers, L. 1996. Winning by a Neck: Sexual Selection in the Evolution of Giraffe. The American Naturalist 148: 771–786

This paper put forth the idea that sexual selection is the reason behind long necks. The idea is that longer necked males are dominant. But this theory has also been questioned. See:

G. Mitchell, S. J. Van Sittert, J. D. Skinner. 2009.Sexual selection is not the origin of long necks in giraffes. Journal of Zoology 278, Issue 4: 281–286

So in the end there's no clear consensus. Some papers have returned to the theory of competition for research in the past few years.To put it simply, no there is no consensus.

microbiology - Is there a practical upper limit to amount of nucleotides or genes in a transformed plasmid?

From my experience in the mammalian world (and this may apply to bacterial systems as well), it's not so much the number of genes in the plasmid as its actual size. The larger the construct is, the more difficult it will be to get it into your target cells in one piece, without degradation or shearing. Since the transformation efficiency is lower, you are getting fewer whole constructs per cell, so depending on how you've set up your promoters, the overall expression level can be significantly lower. The trouble with splitting your genes amongst two or more plasmids is that each will have different transformation efficiencies, and there will be a certain (perhaps large) number of cells that don't get the full complement of genes, interfering with phenotype analysis. And again, you'll also have to consider differential expression rates.

However, once you get your vector into the cells in one piece, theoretically they should all get expressed at approximately equal levels (assuming identical promoters). It's possible that steric hindrance among multiple transcription complexes may occur - I just don't know enough about bacterial transcription and the effects of circular plasmids to say.

One way to get around many of these factors would be to use a bacterial artificial chromosome or BAC. BACs are 7-10 kb vectors that can have inserts of up to 1 million bp cloned into them and are then electroporated into cells. One of (the many) cool things about them is they control their own duplication and partitioning at cell division, so succeeding generations should have essentially the same copy number as the original. They were heavily used during the Human Genome Project to amplify large sections of DNA for sequencing, but they are also used in many other studies, including synthetic biology. OpenWetWare has a list of some common ones, and NEB sells pBeloBAC11 systems.

dna - How are atoms in benzopyridines and benzopurines numbered?

This is a question of chemical nomenclature and the principle source for this is the IUPAC (IUBMB in case of biological molecules; but not in this case). You can find all hetero-ring nomenclature references on the IUPAC web site:

http://www.acdlabs.com/iupac/nomenclature/

http://www.acdlabs.com/iupac/nomenclature/79/r79_702.htm

(I'm skipping the actual naming step)

Numbering is actually done according to
http://www.acdlabs.com/iupac/nomenclature/79/r79_72.htm

That means, if you take the skeleton without hetero atoms, you start

in a clockwise direction commencing with the carbon atom not engaged
in ring-fusion in the most counter-clockwise position of the uppermost
ring, or if there is a choice, of the uppermost ring farthest to the
right, and omitting atoms common to two or more rings.

Now, if there are more than one possibility due to symmetry, you chose the numbering that gives the heteros the smallest possible numbers (this means your purines would be actually wrongly numbered if they weren't an exception---see the List of retained names).

So, we have finally in dxC and dxT the start at the lower nitrogen, going anti-clockwise (the other N at 3, methyl at 6, ribose at 8), and in dxA and dxG similarly the start at the lower right N, going anti-clockwise with other Ns at 3, 6, and 8, and ribose at 8, as well.

genetics - Effect of single-gene overexpression in the cell's response

Which are the factors that modify the overall gene differential expression by introducing a vector for single-gene overexpression?

If you overexpress a gene for a protein involved in signal transduction (e.g., a kinase, scaffold, or receptor) by vector cell transfection, then you overdrive the cell using this signaling pathway, it's useful to isolate the pathway and study them.

Is there any way to modify the overall gene expression or cell differential expression pattern by gene transfection? I think this would work if you delivered a gene for overexpression in proteins involved for RNA processing (e.g., splicing, ribosomal proteins, etc.), RNA transcription (e.g., TFs) or protein translation.