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Beta sheets have the peptide backbone parallel whilst the alpha helix has a curled backbone.

But the thing I can't get around my head is why would the same protein always fold into one of these shapes?

It looks to me like I could grab an alpha helix and just straighten it out to form a beta pleat. I can't see anything that wouldn't work - so if I could turn alpha into beta, then what ensures that these proteins will fold the same way each time they're made? I think there must be something that prevents me from turning alpha into beta but I'm not sure what.

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In the alpha helix structure as well as the beta pleated structure, the atoms are arranged in such a way that the number of hydrogen bonds is maximum. H bonding is a stabilizing factor, and consequently, any molecule (or polymer) would like to maximize their number. This answers your question as to why the protein would fold into one of these shapes.

Coming to why alpha and beta structures are not easily interconvertible, it is once again because of hydrogen bonding. The H bonds between H and electronegative atoms like oxygen and nitrogen are difficult to break, and hence we cannot simply smash an alpha helix into a beta pleated structure, since in doing so, we would inevitably have to break some hydrogen bonds. Thus, whether a protein exists in alpha or beta form depends on how it was formed.

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    $\begingroup$ You provide a kinetic argument but not a thermodynamic one. Why "choose" one secondary structure over another? $\endgroup$
    – Buck Thorn
    Commented Sep 19, 2020 at 13:28
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    $\begingroup$ Backbone h bonds are just one of many factors determining protein structures $\endgroup$
    – Andrew
    Commented Oct 19, 2020 at 14:05

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