Physics of Flexible Polymers
Now that you have learned a bit about DNA, RNA and protein structure,
you will note that there are fundamental similarities between these molecules.
First, all these molecules can be thought of in the most gross way as
strings of symbols (`sequences'), with a definite direction.
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DNAs are arbitrary strings of the symbols {a,t,c,g}
e.g. 5'-gattaca-3'
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RNAs are arbitrary strings of the symbols {a,u,c,g}
e.g. 5'-gauuaca-3'
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proteins are arbitrary strings of the symbols {A,I,L,M,F,P,W,V,N,C,Q,G,S,T,Y,R,H,K,D,E}
e.g. MTKDELIARLRSLGEQLNRDVSLTGT
Nucleic acid sequences are always listed in 5' to 3' order; proteins from
the NH2- (or amino or N) end to the -COOH (or carboxyl or C) end.
Proteins always have M (methionine) as their first aa at the amino-terminus.
At the next level of chemical detail,
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they are linear molecules made of (nearly) repeated units (DNAs and RNAs
are strings of polymerized nucleotides; proteins are strings of amino acids)
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the backbones are homogeneous in structure, with the sequence variation
in the `side chain' chemical groups attached to the backbone (either nucleic
acid bases, or amino acid residues)
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they are long (DNAs are up to 109 nt long; RNAs typically
103 nt long, proteins 102-103 aa long)
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their backbones are chemically directed, soluble in water,
and are singly-bonded with
rotational freedom at many points
-for DNA and RNA, rotations can occur freely around
the phosophodiester bonds O-PO2-O
-for proteins rotations can occur freely around
the two bonds attached to the alpha-carbon N-Ca-C
In many ways these biopolymers are rather similar to the standard polymers
of chemical engineering, such as
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polyethylene (PE), the polymer of CH2 (e.g. the
polymer of N units, H-[CH2]N-H)
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polystyrene (PS), H-[CH2-C(C6H5)H-CH2]N-H,
basically PE with a benzene ring stuck onto every 2nd monomer
These two familiar polymers also have singly-bonded non-directed backbones
which are essentially flexible - if they are dispersed into a liquid in
which the backbone is soluble (for PE and PS, toluene is a good choice)
Flexibility means that at room temperature, these polymers will explore
a large number of conformations (shapes) which are all nearly the same
free energy.
Of course, in the cell most biopolymers have secondary structure
stabilized by interactions between the monomers:
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complementary DNA strands H-bond and twist together to form a double helix
-
complementary RNA bases H-bond together to form stem-loop structures
-
proteins fold into complicated 3d structures, largely as a result of hydrophobic
residues sticking together and hydrophilic (charged) residues having lowest
free energy when on the outside of the protein
Now we will discuss the basic theory of flexible polymers, and how it can
be applied to biopolymer structure. This theory is based in statistical
mechanics, so we will make a lot of use of the Boltzmann distribution to
calculate things. We will pay quite a bit of attention to mechanical
properties of polymers, which are especially relevant to biopolymers.
If you want to stare at sequences, look at the genome of the lambda
bacteriophage, which was sequenced in the mid-1980s. This is
the genome of a virus that infects E. coli, and was the source for the
translation sequence on problem set 2.
Many more sequences are publicly available at Genbank
(your tax dollars at work).
More databases are available at the National
Center for Biotechnology Information
including PubMed
(biomedical literature searching - good for your projects!),
Structure
(3d pictures of a lot of biomolecules, you need to download some softwarel,
it is amazing),