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© Copyright 1993 Mario Hilgemeier

DNA and protein folding

      When the DNA is decoded, the chain of its four bases is 
interpreted to produce proteins which can influence the enviroment. 
These proteins may be considered as a "meaning" of the DNA. For 
instance, enzymes, hair and nails are made of proteins. Seen 
chemically, proteins are strings of amino acids which are folded in 
three dimensional space to give rise to the most complex forms. The 
folding is governed by the attraction between certain parts of the 
amino acids and the environment of the protein molecule.

      The DNA is interpreted by ribosomes. Ribosomes are cell 
particles that work with partial copies of the DNA to produce 
proteins. Each triplet of DNA bases can be the code for an amino 
acid or a control sign like "stop here". Again, there is an iterated 
system (the cell with its DNA in a biological context) that produces 
beautiful fractals [20].

Stop and Think

      Molecular scientists often use "folding" programs to join 
particular regions of a linear sequence into a 2-D pattern. Can you 
fold any of the longer strings of the Gleichniszahlenreihe, let's 
say the 23rd iteration or so? Are there beautiful 2-D (or even 3- D) 
foldings of the Gleichniszahlenreihe? You can use the following laws 
(or a variation of them) as attracting force: - equal ciphers (or 
elements) attract with a strength of 1 - a pair of mutually 
attractive ciphers attracts stronger than single ciphers, a trio more 
than a pair and so on. - the "bonds" between the ciphers cannot be 
overstretched (else they would break up the "chemical bond") - 
different ciphers (or elements) repel each other.

Figure (7.)9 I've tried to fold the element 4Be, which is one of the two longest elements. The result is shown in figure 9. Thin dashed lines represent weak bonds between the ciphers. The fat lines denote the order of the string (strong bonds). Note the shorter strong bonds between equal ciphers (because of their attraction). The folding is essentially governed by the weak bonds. Can you find similar patterns for other cipher (or element) strings? I've shown a folding in the plane (two dimensions). What happens if three or more dimensions are allowed?

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