The Theory of Single Domain Allostery

There are times when you need to flog your own work. I recently published a paper [1] that provides a concrete model of single-domain allostery. It also provides a clean computational model of interior sidechain-sidechain interactions. I think it's my best work yet, and I will now flog the shit out of it for you.

1: Bosco K. Ho and David A. Agard. 2010. Conserved Tertiary Couplings Stabilize Elements in the PDZ fold, leading to Characteristic Patterns of Domain Conformational Flexibility. Protein Science 19:398-411.

What is allostery and why should you care about it?

From the greek word for other (allo), allostery refers to how events occurring at one site on a protein induces changes at another site, far, far away. Allostery was originally conceived to explain cooperative binding in oligomeric proteins made up of identical subunits. Binding sites are typically found at domain interfaces, where the binding of ligand at one site forces changes in the domain interface that lead to quaternary structure rearrangements. The rearrangements propagate to the empty binding sites on the other domain interfaces, resulting in better (cooperative) binding and hence, allostery. The concept of allostery now means any long-distance effect in a protein system.

As such, allostery is the foundation stone of information processing in the cell. Let's say we have two pathways, pathway A and pathway B, which are at first separate. We then select protein A from pathway A, and protein B from pathway B. Then we design an allosteric adaptor protein C where binding protein A to protein C will induce better binding for protein B at another site on protein C. The allostery in the adaptor protein C now intermingles pathway A to pathway B.

Allostery is thus the key to identifying pathway interactions in protein structures and finding a theory of allostery in protein systems is one of the major challenges in computational structural biology. The problem has split in all sorts of sub-problems such as oligomeric proteins and nucleotide-protein systems. But for me, the most challenging sub-problem is the allostery of single domains.

Singe domain allostery: allostery through dynamics

The surprising thing is that even a single domain can undergo allostery. What makes this difficult to understand? Well, if binding a ligand transmit changes to another site, then, in the absence of quaternary structure, these changes must tunnel through the body of the protein. Here is the rub: how do you model dynamics through the body of a protein?

One hypothesis for how single domain allostery might work is the Cooper-Dryden model [2], which argues that allostery occurs through flexibility in a protein. The idea is that large pieces of a single domain, including the binding site, are intrinsically flexible. Subsequent binding of a ligand will rigidify, not just the binding site, but other parts of the protein. These newly rigidified sites can serve as allosteric binding site.

2: Cooper A, Dryden DTF (1984) Allostery without conformational change—a plausible model. Eur Biophys J Biophys Lett 11:103–109.

However, the Cooper-Dryden model is only a generic thermodynamic argument. What is lacking is a way of calculating the intrinsic flexibility of a protein from the crystal structure, and showing that this explains allostery in a real protein system.

The same PDZ fold gives rise to different dynamics

The poster child of single-domain allostery is the PDZ domain. A shockingly small domain of ~60 amino acids, PDZ domains are ubiquitous scaffolding proteins. The PDZ domains have a well-defined binding groove that mainly binds C-terminii of other proteins or short peptides. However, there are at least 2 or three other binding sites in the PDZ fold. A quick survey of these interactions show that indeed, these little buggers act as allosteric adaptors.

Nevertheless, no one had actually catalogued the differences in allosteric changes across the PDZ domains. I found 5 PDZ domains with crystal structures that show distinctly different allosteric response. The differences can be seen in the mobility of the α-helices in the different PDZ domains upon ligand-binding, apo structures in magenta, ligand in blue, and ligand-bound structure in light blue:

As per the Cooper-Dryden model, we can attribute allostery in the PDZ domain to the intrinsic dynamics of the α-helices. Upon binding, the α-helices rigidifies creating new rigid surfaces, which are available for binding to other ligands, leading to allostery.

Here's the challenge: we have five PDZ domains (all with the same fold) with different dynamics in the α-helices. Is there a way to calculate the conformational flexibility from the apo crystal structures of the PDZ domains?

A computational model of sidechain-sidechain interactions

Well, of course there is a solution to the computational problem of single domain flexibility, otherwise I would be leading you down the garden path. Clearly, all 5 PDZ domains have the same fold, so major differences must lie in the sidechain-sidechain interactions. Now one might argue that long-time molecular-dynamic (MD) simulations of the 5 structures will tell you about the flexibility, but there are problems with this. First, it's expensive to run these simulations, but second, even if you could identify the flexible regions, there is currently no trajectory analysis method that allows you to clearly deduce sidechain-sidechain interactions.

The solution is the Rotamerically Induced Perturbation (RIP) method that I developed for large conformational changes. Simply put: RIP applies a local perturbation to a sidechain by only heating the rotamer degrees of freedom. Here, we apply RIP at a much lower temperature. I take each PDZ domain, freeze them to a near-zero temperature, then apply RIP to every single residue. Simply by studying which other residue gets heated up, I can construct the sidechain-sidechain coupling maps from the heat maps of RIP simulations across all the residues of a PDZ domain:

How sidechain couplings differ

The results from the heat maps of different PDZ domains are striking: at the same tertiary contact in the PDZ fold but in different PDZ domains, different sidechain-sidechain have different interaction strengths. Here are two examples of the same contact position in two different PDZ domains. On the left they interact strongly. On the right they do not.

The usual definitions of good interaction strength – being in contact and being buried – is insufficient. Sidechain interaction depends on how they interlock, which depends on the sidechain degrees of freedom and their orientation with respect to each other. The RIP method provides a straightforward computational method to explore all these factors, and identify the couplings in a structure.

Tertiary couplings explain α-helix flexibility

However, not all couplings are interesting: couplings between residues in the same piece of secondary structure (β-sheet and α-helicx) don't tell us very much. After all these residues are already coupled by the backbone hydrogen bonds. What turns out to be extremely informative are the sidechain-sidechain couplings of tertiary contacts. On the left are the apo structures overlaid over the ligand-bound structures (red indicates of large RMSD difference). On the right are the residues involved in major tertiary couplings (red):

By comparing the tertiary coupling maps of the apo structures to the conformational freedom in the ligand-bond structures, I found a rather simple relationship: PDZ domains with tertiary RIP couplings between the α-helices and the body of the protein have rigid α-helices; the PDZ structures without couplings have dynamic α-helices.

The theory of single domain allostery

Although one shouldn't generally generalize from a single case study, I'm going to anyway since there are few examples known to me of single-domain families with diverse allostery and crystal structures.

Single domain allostery arises from the intrinsic dynamics of a protein fold. A piece of secondary structure (α-helix or loop) is flexible or rigid depending on the strength of the tertiary contacts to the body of the protein. The strength of these contacts depend on how well the sidechain-sidechains interlock, which (surprise! surprise!) can be adequately explored with the RIP method.

So, depending on the specific sidechain interactions, the same fold will have different surface flexibilities. Binding a ligand at one of these regions will rigidify all connected pieces of flexible regions. The newly rigidified portions of the surfaces provide new allosteric binding sites, thereby transmitting information through the body of the protein.