Homework assignment and answer

A few days ago I gave the following homework assignment for the ace protein chemist, and promised an answer.

Here’s the assignment

Homework assignment for the protein chemist

As an ace protein chemist you are asked to design two proteins, both intrinsically disordered which form a tight complex with a picoMolar dissociation constant.  To make the problem ‘easier’ there is no need for specific amino acid interactions between the proteins.  To make the problem harder, even in the tight complex formed, the two proteins remain intrinsically disordered.

Hint: ‘nature’, ‘evolution’, ‘God’ —  whatever you chose to call it, has solved the problem.

Here’s the answer

The structure of an unstructured protein

Protein structure without structure.  No I haven’t fallen under the spell of a Zen master.  As Bill Clinton would say, it depends on what you mean by structure.

If you mean a segment of the protein chain which doesn’t settle down into one structure, you are talking about intrinsically disordered proteins. It is estimated that 40% of all human proteins contain at least one intrinsically disordered segment of 30 amino acids or more ( Nature vol. 471 pp. 151 – 153 ’11 ).   The same paper ‘estimates’ that 25% of all human proteins are likely to be disordered from beginning to end.

Frankly, I’ve always been amazed that any protein settles down into one shape — for details please see — https://luysii.wordpress.com/2010/08/04/why-should-a-protein-have-just-one-shape-or-any-shape-for-that-matter/. But that’s ‘old news’ as another Clinton would say.

Two fascinating papers in the current Nature (vol. 555 pp. 37 – 38, 61 – 66 ’18 1 March) describe the interaction of two very unstructured proteins.  One is prothymosin-alpha with 111 amino acids and a net negative charge of -44.  The other is Histone H1 with at least 189 amino acids and a net positive charge of + 53.  With such a charge imbalance it’s unlikely that they can coalesce into a compact single form.  So they are both intrinsically disordered proteins.

However the two proteins bind to each other quite tightly (dissociation constant is in the picoMolar range).  Even when they form a complex, a variety of techniques (NMR, single molecule fluorescent techniques, computation) show that neither settles down into a single form and are still unstructured.

So where’s the structure?  It isn’t in the amino acid sequence.  It isn’t the conformations adopted in space.  The structure is  in the net charge.  Many intrinsically disordered proteins have levels of net charge similar to those of prothymosin alpha and histone H1.  In the human proteome alone, several hundred proteins that are predicted to be intrinsically disordered contain contiguous stretches of at least 50 residues with a fractional net charge similar to that of H1 or proThymosin alpha (Bioinformatics 21, 3433–3434 2005) — hopefully there’s something newer.

The amino-acid sequences of disordered regions in proteins evolve rapidly, yet (Proc. Natl. Acad. Sci vol. 114 pp. E1450–E1459 2017) showed that the net charge is conserved despite a high degree of sequence diversity .  This should be a current enough reference.

Why in the world would the cell have something like this?  Most readers probably know what histones are.  If so, stop and think how the binding of the two proteins could be used by the cell before reading what the authors say about it.

“The interaction mechanism of proThymosin alpha and Histone H1 probably aids their biological function.  proThymosin alpha assists with the assembly and disassembly of chromatin, the material in which DNA is packaged with histone proteins (such as H1) in cells. To perform its function, proThymosin alpha must recognize its histone substrates rapidly and with sufficient affinity to compete with the high affinity of histone–DNA interactions (a similar high positive charge high negative charge interaction). The high binding affinity of Pro-Tα for H1 and the association rate of the two pro-teins imply that the dissociation of proThymosin alpha–H1 complexes is slow enough to allow functional outcomes, but fast enough not to slow down biological turnover.”

Why don’t they form a coacervate — a bunch of molecules held together by hydrophobic forces? Why don’t they show liquid liquid phase separations? The authors speculate that it might be due to the complementarity of the two proteins in terms of effective length and opposite net charge. Also they don’t have hydrophobic and aromatic side chains and cation pi interations which are said to favor phase separation mediated by proteins.

Addendum 20 March’18 — from my comment and a response on Derek’s blog


Another way to look at these very charge imbalanced proteins, is that they are being strongly (and positively) selected for. They are incredibly improbable on a purely statistical basis. Prothymosin alpha has 111 amino acids of which 44 are negatively charged. There are 20 amino acids of which only 2 (glutamic acid and aspartic acid) have negative charges at physiologic pH — cysteine and tyrosine can form anions but under much more basic conditions. So, assuming a random assortment of amino acids, the idea that 10% of the amino acids could fight for space with 90% of the rest and win around 40% of the time in 111 battles is extremely improbable. You’d have to use Stirling’s approximation for factorials to figure out exactly how improbable this is. Any takers?

DCRogers says:
March 20, 2018 at 2:35 pm
CDF(N=111, X=44, p=0.1) = 1.87 * 10^-16

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