Showing posts with label synergy. Show all posts
Showing posts with label synergy. Show all posts

16 October 2012

Fragment linking, enthalpy, and entropy: not quite so simple

The strategy of fragment linking dates to the origins of fragment-based lead discovery. The idea that two low affinity binders can be linked to produce a more potent molecule is based on the theory that the binding energies of linked fragments will at least be additive. Indeed, sometimes superadditivity can be observed; in those cases, the binding energy of the linked molecule is considerably better than the sum of the binding energies of the separate fragments. The most common explanation for this is that linking two fragments “pre-pays” the entropic cost of binding to the protein; rather than two fragments locking into fixed binding modes, only a single linked ligand pays this entropic penalty. This makes sense intuitively, but is it correct?

An early example of fragment linking was reported by Abbott researchers in 1997: two fragments that bound to the matrix metalloproteinase stromelysin were linked together to give a molecule that bound about 14-fold more tightly than the product of the affinities of the two fragments. Thermodynamic analyses were conducted to explore the roles of entropy and enthalpy, but these were complicated by the fact that one of the fragments contained an acidic phenol that was removed in the course of linking. In a new paper published in Bioorg. Med. Chem. Lett., Eric Toone and colleagues at Duke University have re-examined this system.

The researchers dissected several of the originally reported linked molecules into component fragments and examined their thermodynamics of binding using isothermal titration calorimetry. All of the experiments produced similar results; a particularly illustrative example is shown in the figure, in which a single bond in compound 1 was conceptually broken to yield component fragments 5 and 8.

As the researchers note, weirdly, the “favorable additivity in ligand binding – that is a free energy of binding greater than the sum of those for the constituent ligand fragments – is enthalpic in origin,” not entropic. It is not clear why this is the case, but what is clear is that the results are completely different from those obtained by Claudio Luchinat and colleagues on another matrix metalloproteinase. In that report, the enhanced affinity of the linked molecule was entirely entropic in origin, as might be expected. So what’s going on here?

One clue is provided by Fesik and colleagues in their original analysis of their stromelysin inhibitors. They noted that, when fragment 8 (acetohydroxamic acid) was added to the protein, biphenyl ligands similar to fragment 5 bound considerably more tightly than when fragment 8 was not present. In other words, the ligands displayed cooperative binding even when they were not covalently linked, probably due to non-covalent interactions between the two bound ligands or possibly to changes in protein structure and dynamics.

It is easy to assume that two ligands bind independently to two sites on a rigid protein, when in fact proteins are anything but rigid, and the addition of one ligand to a protein can dramatically change its properties. Thermodynamics measures changes in the entire system, not just the ligands, and if the protein changes upon ligand binding things can quickly get complicated. As Fesik and coworkers noted:

The observed cooperativity between the two ligands is a factor that should be considered when optimizing compounds for binding to nearby sites, since a portion of the binding energy is due to the cooperativity rather than interactions between the ligands and the protein.

All of which is to say that we remain woefully ignorant of the forces driving ligand binding, let alone fragment linking. But assessing how much better (or worse) a linked molecule binds than its component fragments can still be a useful exercise to guide optimization, even if the thermodynamic origins of the effects are unclear.

30 January 2012

Fragment linking: flexible rules

Linking two fragments together to achieve a boost in potency has been done a number of times (see here, here, here, and here), though it often doesn’t work as well as might be hoped (see here). To better understand the energetics of fragment-linking, Marc Nazaré, Hans Matter, and colleagues at Sanofi-Aventis Deutschland have analyzed ligands for the blood coagulation enzyme factor Xa (fXa) and published their results in a recent issue of Angew. Chem. Int. Ed.

The researchers “deconstructed” potent fXa inhibitors into component fragments, measured their inhibition constants (and thereby inferred their binding energies), and compared these binding energies with those of the original linked molecules. One of the first observations was that many of the component fragments bound so weakly as to show no measurable activity, a phenomenon that has been observed previously.

In an exemplary case, cleaving a single bond connecting the two component fragments of a 2 nM ligand (1a, below) yielded one fragment (1g) with 58 micromolar activity and another (1d) whose activity was worse than 10 millimolar. Because the second fragment has such low affinity, the binding energy of linking is really just a lower estimate, but it seems to be at least 3.3 kcal/mol, which is greater than the binding energy of fragment 1d itself. In other words, the affinity brought about by linking is greater than the affinity of the weakly binding fragment. The superadditivity provided by the linker in this case is about 300-fold, a similar value to that observed in the unrelated MMP-12 system. This is perhaps all the more remarkable given the fact that the fragments are connected by a linker containing several rotatable bonds, the entropy of which should partially counter the advantages of linking.

In fact, a common strategy to improve the potency of two linked fragments is to rigidify the linker. Often this doesn’t work: in a second case, the Sanofi-Aventis researchers cleaved one bond of a 3 nM ligand (2a, below) to yield two fragments with roughly equal potency. However, even though the linker is more rigid than in the previous example, the binding energy due to linking is less – just 2.0 kcal/mol, representing a boost of about 30-fold.

As the authors note:
The introduction of rigid aromatic moieties as a common approach to increase affinity does not necessarily maximize the benefit from the linker effect as detrimental affinity contributions might originate from suboptimal orientation and accommodation of specific binding elements.
There are many more examples in this paper than can be covered in a blog post; the authors dissect compounds 1a and 2a at a number of different points, and while the component fragments typically bind less tightly than simple additivity would suggest, there are lots of interesting details.

Finally, it is interesting to note that ligands 1a and 2a consist of a relatively hydrophobic fragment (1g or 2g) connected to a more polar fragment (1d or 2h). The fact that these show superadditivity is consistent with Mark Whittaker and colleagues' proposal last year that linking such fragments is likely to maximize additivity, although given the precise interactions made by both parts of the molecules the details get a bit messy. We’re not yet at the point where the universe of molecular interactions can be distilled to rigid rules.

25 July 2011

Fragment linking: oil and water do mix

Fragment linking is one of the most seductive forms of fragment-based lead discovery: take two low-affinity binders, link them together, and get a huge boost in potency. But what’s appealing in theory is difficult in practice: the linked molecule rarely binds more tightly than the product of the fragment affinities, and sometimes there is not even an improvement over the starting fragments. In a recent paper in Molecular Informatics, Mark Whittaker and colleagues at Evotec suggest a strategy to maximize the chance of success.

The researchers start by briefly reviewing nine published examples of fragment linking where affinities for both fragments as well the linked molecule are provided (some of these have been discussed previously here, here, and here). Of these, only three examples showed clear superadditivity (in which the linked molecule has a significantly higher affinity than the product of the affinities of the individual fragments), and two of these examples are rigged systems in which a molecule already known for its potency (such as biotin) is dissected into fragments. The challenges of linking are succinctly summarized:
The keys to achieving superadditivity upon linking are to maintain the binding modes of the parent fragments, not introduce both entropy and solvation penalties while designing the linker, and also make any interactions with the intervening protein surface that need to be made.
Also, of course, the resulting molecule needs to be synthetically accessible. Having a certain amount of flexibility in the linker can be useful, as this will allow the fragments some room to shift around, but too much flexibility introduces an entropic cost that defeats the purpose of linking in the first place. Software tools such as those by BioSolveIT can help design the linker, but what if some fragments themselves are inherently better suited for linking?

All three of the examples that show superadditivity start with one fragment that is highly polar and makes hydrogen bonds or metal-mediated bonds with the protein. The researchers suggest that such fragments are likely to pay a heavy thermodynamic penalty when they are desolvated, and that this cost can be reduced by linking them to a hydrophobic fragment. Thus, to maximize your chances of successful linking, the authors suggest you should choose
a fragment pair that consists of one fragment that binds by strong H-bonds (or non-classical equivalents) and a second fragment that is more tolerant of changes in binding mode (hydrophobic or vdW binders).

This is an interesting proposal, though because there are so few examples it is hard to assess. Indeed, the only other case of clear superadditivity I found involves dimerizing a fragment that is reasonably hydrophobic (ClogP = 2.4), albeit negatively charged. Hopefully we’ll see more examples in the coming years, but in the meantime, linking a water-loving fragment to an oily one is worth a shot.

11 June 2010

Fragment linking: how much is it worth?

Fragment linking is a topic we’ve discussed a few times. One of its great appeals is that, all other things being equal, the entropic cost of binding one linked molecule is less than the cost of binding two separate molecules. Thus, linking two fragments should give more than an additive increase in binding energy. As the late William Jencks noted, for two fragments A and B:
Kd(AB) = Kd(A) * Kd(B) * E
Kd(AB) is the dissociation constant for the linked molecule AB
Kd(A) is the dissociation constant for fragment A
Kd(B) is the dissociation constant for fragment B
E is a “linking coefficient”, reflecting the costs and benefits of linking

The lower the Kd the better, so ideally E < 1, though in practice finding a suitable linker can be tricky and all too often E > 1 (sometimes >> 1). But how low can E go? How much of a boost can you get by linking two fragments? Claudio Luchinat and colleagues at the University of Florence looked at this question experimentally in a recent paper in J. Med. Chem.

The researchers took PMAHA, a known inhibitor of the matrix metalloproteinase MMP-12, and dissected it into two fragments, AHA and PMS, by conceptually “cleaving” the bond connecting them (see figure). This simplifies analysis: since the two fragments are almost identical to the linked molecule, there are no concerns that atoms in the linker interact with the protein.

The crystal structure of PMAHA bound to MMP-12 had been previously reported, but Luchinat and co-workers solved the co-crystal structure of AHA and PMS bound simultaneously to MMP-12. The two fragments overlay fairly well with the parent molecule: AHA binds to the catalytic zinc, while PMS binds in the S1’ pocket. The AHA fragment is rotated with respect to its position in PMAHA, though it makes the same interactions in both structures.

Thermodynamic binding parameters for the three molecules were determined (see figure). As expected, PMAHA binds considerably more tightly than the product of the affinities of the two fragments: E << 1 (in fact, about 0.0021). And in nice accord with theory, this enhanced affinity is entropic: both fragments bind with favorable enthalpy and unfavorable entropy, while the linked molecule has both favorable enthalpy and entropy. In other words, the salutary effect of linking these two fragments does seem to come entirely from entropic effects.

One of the more interesting lessons from this paper is a sense of how much of a boost in potency you can expect if fragment linking goes well: about 500-fold. In theory you could do better, but in practice you should expect much more modest benefits: a prominent success of SAR by NMR on a different metalloproteinase reported a 14-fold boost in affinity. But just like the lottery, the hope of a big payout will continue to attract people to the linking game.

17 December 2008

50% ain’t half-bad

In the world of fragment-based ligand discovery, researchers hope that two fragments, when linked together, will behave at least additively: the free energies of binding for each fragment will sum together, with a multiplicative effect on affinity. In ideal cases, linked fragments will behave synergistically (see for example the post from 18 August, below). But all too often, linking two fragments produces disruptive behavior, and the resulting molecule actually binds less tightly than would be predicted based on the binding energies of the individual fragments. This occurs not just when linking fragments, but in fragment merging and growing as well. Can such phenomena be modeled?

The mathematical groundwork was described more than forty years ago by Spencer Free and James Wilson at the old Smith Kline and French company, and came to be known as a Free-Wilson analysis. In a nice update of this work, Julen Oyarzabal and co-workers have applied this technique to the screening results of eight libraries consisting of several hundred compounds total. The molecules belong to five diverse chemical scaffolds (shown), and were tested against a variety of different targets, including a kinase, GPCRs, ion channels, and P450s.

For each library tested against each target, the authors asked whether the binding contribution due to a substituent Rx was additive, partially additive, or non-additive with the binding contribution of a substituent Ry. The mathematics get pretty intense, and the paper goes far beyond what I can summarize in a blog post, but the main conclusion is surprisingly encouraging: roughly half of all the data sets (10 of 19) show clear additive behavior, while another quarter (5 of 19) show partially additive effects. Only 4 data sets show non-additive behavior.

In many fields, a 50% success rate wouldn’t look too impressive, but in medicinal chemistry (in fact in much of chemistry in general), half-right sounds pretty good. The authors don’t further divide the non-additive data sets into sub-additive versus super-additive categories. In other words, the non-additive effects could well be due to synergy, the quality those of us pursuing FBLD ardently desire. But even if synergy is elusive, the paper suggests that you’ve got a better than even shot of producing a whole that is at least equal to the sum of its parts.