I was at a dinner the other night at a restaurant when we moaned about the fact that the rectangular table was so long that those of us at one end could hardly speak to those at the other. Restaurant designers are acutely aware of the fact for a given perimeter, a circle occupies the greatest area of all possible shapes.
Talk therefore turned to circles and my colleague said the volume of a sphere is obtained by integrating the area of a circle.
I did a quick differentiation in my mind- 4/3 pi r^3 differentiates to 4 pi r^2, so it was easy to prove him wrong.
I just found out why- the area of a sphere is given by 4 pi r^2.
But hey, did you know this? For a cone, sphere and cylinder, where radius equals height:
Volume of a cone= 1/3 pi r^2. h= 1/3 pi r^2.2r= 2/3 pi.r^3 X 1
Volume of a sphere= 4/3 pi r^3= 2/3 pi. r^3 X 2
Volume of a cylinder= pi.r^2.h= pi.r^2.2r= 2/3 pi.r^3 X 3
Therefore the volume of equiradial cone, sphere and cylinder has a ratio of 1:2:3.
The relationshiip between the cone and cylinder is a bit obvious, but I had no idea that you could make a sphere out of 2 cones or a cylinder out of 1.5 spheres. Did you?
Saturday 23 July 2011
Sunday 26 June 2011
The Worm That Won Three Nobels
Meet Caenorhabditis elegans, or simply C.elegans. Roundworm extraordinaire, 1 mm long. Multicellular eukaryote. Superstar.
Simple to study, it was the organism that has 35% homology (similarity) to human DNA. The prototype organism, where apoptosis- programmed cell death- was studied. Apoptosis is the reason why the cells of your immune system wither and die in an orderly fashion after killing the bad bugs, rather than running out of control and killing you off instead. When things go wrong with apoptosis, bad things happen- like autoimmune diseases, or cancer. Brenner, Horvitz & Sulston walked with the Medicine Nobel for this work in 2002.
Want to study the function of a particular gene? No problem. Catch a C.elegans, douse it in some double stranded RNA with a complimentary sequence to the bit of DNA you want to study. The dsRNA will home in to the complimentary sequence of the DNA like a long lost brother and join up (hybridise). Result? The protein produced by the gene will be silenced, and presto, because C.elegans stops producing that protein, you know the function of that gene. Cue Nobel for Fire & Mello for Physiology & Medicine in 2006.
Want to label a protein produced by a living organism with a fluorescent biomarker without killing the organism? Try Green Fluorescent Protein or GFP as it's known, first isolated from a jellyfish. Chalfie, Shimomura and Tsien introduced the gene for GFP adjacent to the regulatory sequence (big brother gene) governing the transcription of a certain protein in C.elegans. The protein lit up like Guy Fawkes night under blue light, fluorescing a bright green. It's been used many many times since then to tag proteins, a use that earned the trio, and C.elegans its 3rd Nobel Prize in 6 years, this time in Chemistry, in 2008.
Inspirational worm, C.elegans. Rewarded by my university, the University of Nottingham, with an all expenses paid two week jaunt on The International Space Station to study the effect of zero gravity on muscle. It even has its own social networking site, called- you guessed it- Wormbook.
Simple to study, it was the organism that has 35% homology (similarity) to human DNA. The prototype organism, where apoptosis- programmed cell death- was studied. Apoptosis is the reason why the cells of your immune system wither and die in an orderly fashion after killing the bad bugs, rather than running out of control and killing you off instead. When things go wrong with apoptosis, bad things happen- like autoimmune diseases, or cancer. Brenner, Horvitz & Sulston walked with the Medicine Nobel for this work in 2002.
Want to study the function of a particular gene? No problem. Catch a C.elegans, douse it in some double stranded RNA with a complimentary sequence to the bit of DNA you want to study. The dsRNA will home in to the complimentary sequence of the DNA like a long lost brother and join up (hybridise). Result? The protein produced by the gene will be silenced, and presto, because C.elegans stops producing that protein, you know the function of that gene. Cue Nobel for Fire & Mello for Physiology & Medicine in 2006.
Want to label a protein produced by a living organism with a fluorescent biomarker without killing the organism? Try Green Fluorescent Protein or GFP as it's known, first isolated from a jellyfish. Chalfie, Shimomura and Tsien introduced the gene for GFP adjacent to the regulatory sequence (big brother gene) governing the transcription of a certain protein in C.elegans. The protein lit up like Guy Fawkes night under blue light, fluorescing a bright green. It's been used many many times since then to tag proteins, a use that earned the trio, and C.elegans its 3rd Nobel Prize in 6 years, this time in Chemistry, in 2008.
Inspirational worm, C.elegans. Rewarded by my university, the University of Nottingham, with an all expenses paid two week jaunt on The International Space Station to study the effect of zero gravity on muscle. It even has its own social networking site, called- you guessed it- Wormbook.
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