Why should a protein have just one shape (or any shape for that matter) ?


This is something I posted on “The Skeptical Chymist” 4/08.  It (and the next post) are relevant to the discussion which (hopefully) will ensue.  Stuart Cantril, the editor, says that since I wrote these posts, I can put them on my blog. 

Well of course they don’t, but the proteins we know the most about (because they can be crystallized and their structure determined by X-ray diffraction) do have a shape. Sperm whale myoglobin, the first protein to have its 3-dimensional structure determined, showed that this couldn’t be the whole story. Sperm whales (air breathing mammals after all) use their myoglobin to carry oxygen during their hour-long dives down to 1000 meters. Kendrew and Perutz’s crystal structure showed no way for oxygen to find its way in to the embedded porphyrin ring. Amazingly, the 153 amino acids of myoglobin must themselves breathe to let the oxygen in. All it takes to denature (seriously change its tertiary structure so it is no longer functional) a protein of 100 amino acids is 10 kcal/mole (Voet & Voet – Biochemistry 3rd Edition p. 258). That’s two hydrogen bonds – not much. Sight your eye at the alpha carbon of one of the amino acids of this protein, looking toward the carbonyl carbon. There are three conformational energy minima the carbonyl can adopt. That’s potentially 3^99 = 10^48 conformations (clearly an overestimate because of self intersection, but still, a huge number). Yet to be crystallizable, this protein must choose just one of them, and it must be lower in energy by 2 hydrogen bonds than all the rest. In addition, to get to this single structure, the protein can’t possibly sample all the conformations available to it. The rotation barrier of ethane is 12 kJ/mole and a barrier of 73 kJ/mole allows a rotation rate of 1 per second, and every 6 kJ changes the barrier by a factor of 10 at 25 deg C (Clayden et al. Organic Chemistry pp. 450-1). So the maximum rate of rotation of ethane is 10^11 per second (at a body temperature of around 37 deg C) rather than 10^10 at 25 deg C. This is clearly an upper bound on the rotation rate as the mass attached to the alpha carbons of a protein will make the rotation far slower, but let it pass (that’s why I chose ethane in the first place). That’s 10^37 seconds to sample the conformations available, far longer than the age of the universe. This is the Levinthal paradox. So for the crystallizable proteins (all of biological interest so far) one conformation out of all those available must be more stable (but only by two hydrogen bonds) than all the rest, and the particular conformation must be findable quickly (or we’d all be dead). How likely is this for a ‘random’ sequence of amino acids. We’ll probably never know (but we might if we’re lucky). This is the subject of the next post…

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  • Wavefunction  On August 5, 2010 at 7:35 am

    -How likely is this for a ‘random’ sequence of amino acids.

    Not just very likely but certain! As you know, the Levinthal paradox is a paradox only if we assume completely random conformational space searching. Plus, sequence space is much less conserved than structure space and therefore there are many options (for instance, many ‘random’ sequences can form alpha helices). Preservation of favored structures like helices and sheets followed by long-range attraction can make the process much more facile. It’s incremental. The trick is to figure out the details. See the previous post. More to come.

  • luysii  On August 5, 2010 at 5:51 pm

    I’m going to put in one more old post from the Skeptical Chymist, before responding to the comments on this, and those on “How many proteins can we make?” — but it’s great to have comments like these. Should be ready to roll by Monday next week.

  • Yggdrasil  On August 5, 2010 at 11:15 pm

    A random sequence of amino acids probably is unlikely to fold into only one structure. Proteins have evolved such that they exhibit significant cooperativity in their folding, their native structures represent a significant minimum in the surrounding energy landscape, and their native structures are fairly robust to mutation. This is not the case when people have done computational studies on random amino acid sequences. See Shakhnovich 2006 Chem. Rev. 106(5):1559–1588 doi:10.1021/cr040425u for example.

    • luysii  On August 12, 2010 at 4:58 pm

      Yggdrasil: Thanks for the tip. I’m going to print it out and read it when I’m at band camp 15 – 22 Aug.
      More later.

  • Wavefunction  On August 6, 2010 at 9:36 am

    One of the more entertaining calculations indicates the following:

    The mass of all possible 18 amino acid sequences would be that of a baseball

    The mass of all possible 37 amino acid sequences would be that of the earth

    The mass of all possible 42 amino acid sequences would be that of the sun

    The mass of all possible 59 amino acid sequences would be that of the observable universe

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