Epi-Genetics and DNA Computing

I am busy making plans for a long-distance move and so I will have only limited time to put up a stub where questions go today. Will attempt to flesh this out later.

At the local Eugene Science Pub event, a Professor from Pacific University spoke about the concept of nature and nurture in the context of recent work in epigenetics. The topic itself is fascinating and in a nutshell studies the effects of how methyl-groups (CH3) are tagged onto the DNA sequence to disable gene expression (and presumably protein synthesis) as well as tagged onto the proteins around which the DNA sequences are coiled around. In the latter case, the methyl-groups causes the DNA strands to be less tightly wound, exposing them for expression (the reverse of the former case).

On this topic, as a computer scientist and an engineer, I have several vectors of interest:

1) The methyl-groups according to her, are tagged through the aid of enzymes. If I remember my microbiology correctly, this should be similar to the way proteins are constructed - that one part of the enzyme should bind with the methyl-group while the other latches on to other identifier markers on the DNA strand or the proteins. The question really is "how?". I would like to understand the mechanics of it. Surely, this process has to be statistical, right? How would a consistent template of gene expression toggling be achieved by the mechanics of methyl-group tagging across the entire human genome and all the cells in our body? She was talking about how the tags change the regular nature of dominant and recessive gene interplay. Also, even if one assumes some statistical modeling, how do the enzymes tag, so cleanly, some set of specific genes? Do those enzymes identify an entire sub-sequence for tagging? How does the methyl-groups chemically prevent the usual protein synthesis process from working?

2) Now for the stuff I am really excited about (in the long term). Can I make use of this information to design and construct more complex scenarios using methyl-groups to enable yet another model (maybe one that is more flexible) for DNA-based computing? Can I model an environment where I do not have to mimic biology? All I need to do is to respect the chemistry and statistics involved, correct?

Deriving the Leibniz Formula for Pi/4

A while back, I picked up a fascinating book by Clifford Pickover ("The Math Book" - not exact, "a" is alpha, "B" is capital beta. I have yet to learn to put math symbols onto blogspot, and I'm feeling lazy right now) summarizing the chronological history of mathematical discoveries.

Today, I read the entry on the "Discovery of Series Formula for Pi" (page 110 - c.1500) and realized that while I had learned this, I had never appreciated its significance nor how it was derived.

So, given the sparse details of the entry, my question is:

"How did Leibniz, Gregory and (possibly) Somayaji independently derive the series formula for Pi? Was there a first-principles approach?"

Wikipedia, sadly, provides the proof using the Arctan series:

http://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80

My impression, having read the text, was that the series for arctan and pi/4 were independently derived, with arctan having been found by Gregory and Somayaji. Apparently, Gregory had not realized that arctan(1) was pi/4, which seemed a little strange.

Time to find out!

Gene Therapy - A Mechanism

Read an article on gene therapy on the BBC and wondered how they expect to efficiently deliver the correction to the right part of the sequence of the genetic code in sufficient numbers of cells so the right proteins get synthesized in the right amounts and for the right duration to help the patient ... will need to follow up on the following article:

http://pubs.rsc.org/en/Content/ArticleLanding/2005/CS/b307062j

The link to the BBC article:

http://www.bbc.co.uk/news/health-18926892

Docking two vessels in orbit

So, it was in the news that the Chinese had become the third nation to achieve manual orbital docking of a spacecraft with the International Space Station. I wondered why this would be considered a feat and so I consulted Wikipedia:

http://en.wikipedia.org/wiki/Proximity_operations

Turns out this is not an intuitive operation. The primary reason is due to the effects of accelerating while under the influence of gravity - it raises the craft into a higher orbit which decreases relative velocities. Buzz Aldrin has written a Phd Thesis on the issues of Orbital Mechanics. So, the answers to my (would be) question are probably here:

http://en.wikipedia.org/wiki/Orbital_mechanics

So, what I really want to do in this entry is to work out the simplest cases. If I have a spacecraft just behind (and slightly off to the side of) another in the same orbital plane:

1. What happens when I try to accelerate and then decelerate in order to catch up with it intuitively?

2. What do I have to do (I'll need to fill in the necessary parameters) in order to actually dock with the leading craft?