Monday, 28 July 2014

Vectors in maths, disease and molecular biology: understanding terms in context.

I was asked by a student to explain the logic behind the structure of Buckminsterfullerene, or BF, the C60 "spherical" form of carbon that was recently the focus of an outreach visit to the Widnes Catalyst museum by Sir Harry Kroto, who like me, is an alumnus of the University of Sheffield, but unlike me is a Nobel Laureate! The plastic model was thrust in front of me by a UTC student and I asked: "what else does it remind you off?" (as I stood in front of a 3D print of Bacteriophage T4). "Oh yes, a phage capsid" came the reply. Followed by, "But why is it so stable?". I immediately thought back to my school days and applied maths. My maths teacher had given me a taste for the use of maths to describe and calculate forces, such as friction etc. I said "vectors: it's all a matter of balancing forces". Of course I was then challenged by the comment: "aren't they the carriers of malaria?" And I thought to myself, vectors as agents for delivering recombinant DNA (even in the form of bacteriophage DNA), but I meant the vectors as defined by mathematicians, physicists and engineers:  "A quantity having direction as well as magnitude, especially as determining the position of one point in space relative to another". The word being originally Latin and related to the verb vehere to convey and here it is being used as a noun to mean a carrier.

So the word vector is context dependent. In Maths, it means a number that carries with it direction, in Molecular Biology, it means a plasmid or bacteriophage DNA molecule that carries foreign DNA and in Parasitology, it means an organism that carries a pathogen, in the case of malaria, the plasmodium parasite is carried by a mosquito vector. I like the fact that the word vector can be such a good match for multiple scientific concepts. It is a versatile word, just as the red case of a Swiss army knife houses multiple functions. Indeed, as we have touched on this in earlier blogs; genes and proteins can be used in different contexts to provide different functions. This also reminds me of the use of the word "parsimonious" (or thrifty) in a seminar I attended some years ago by Professor Richard Perham when he described the sharing of protein subunits between the two multienzyme complexes: Pyruvate and 2-oxoglutarate dehydrogenase; both key enzymes in 9OR NEAR) the Krebs Cycle.  The synthesis of a pool of subunits for sharing, is something that is now known to be common amongst multi-protein complexes in human cells in particular. In language, we often use words in a context dependent manner, the same is true of biological molecules!

Returning to the "Bucky Ball" and the bacteriophage capsid for a moment. As I understand it, the occurrence in Nature of regular arrangements of proteins in bacteriophage and viral capsids matches sound engineering principles, just as the architect Buckminster Fuller employed in order to design his geodesic domes (Top left). The adenovirus capsid shown top right, is an example of how, like in BF, a combination of pentameric and hexameric rings of subunits (proteins instead of carbon atoms) provides a stable shell in which the genome of the virus is accommodated until the virus infects the host cell. The sum of all of the force vectors (imagine you are building the frame in the same way that you would assemble a tent from tubular struts) across all of the pentagons and hexagons will equal zero in a stable structure. Thus mathematical vectors underpin the stability bacteriophage cloning vectors and we have squared the circle.....well not quite! 

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