Does configurational entropy explain why fragment linking is so hard?

Linking two weak fragments to get a potent binder is something many of us hope for. Unfortunately, as a poll taken a few years back indicates, it often doesn’t work. But why? This is the question tackled by Lingle Wang and collaborators at Schrödinger and D. E. Shaw in a recent J. Chem. Theory Comput. paper.

 

When a ligand binds to a protein it pays a thermodynamic cost in terms of lost translational and orientational entropy. By linking two fragments, this cost is paid only once instead of twice. In theory this should lead to an improvement of 3.5-4.8 kcal/mol in binding energy, resulting in a 400-3000-fold improvement in affinity over what would be expected from simple additivity. As we noted here, this is possible, though rare. Linker strain often takes the blame as a primary villain. But is there more to the story?

 

The researchers computationally examined published examples of fragment linking (most of which we’ve covered on Practical Fragments) using free energy perturbation (FEP) to try to understand why the linked molecules bound more or less tightly than expected. Impressively, they were able to computationally reproduce experimentally derived numbers, and by building a thermodynamic cycle they could extract the various components of the “connection Gibbs free energy.” These included changes in binding mode or tautomerization, linker strain or linker interactions with the protein, and the previously mentioned entropic benefits of fragment linking.

 

The analysis also identified two additional components. If two fragments favorably interact with each other, covalently linking them may not give as much of a boost. This concept had been considered decades ago, though the current work provides a more general understanding.

 

The more important factor appears to be what the researchers refer to as “configurational entropy.” The notion is that even when a fragment is bound to a protein, both the ligand and protein retain considerable flexibility, which is entropically favorable. Linking two fragments reduces the configurational entropy of each component fragment, and the linked molecule binds less tightly than would be expected. The researchers argue that this previously unrecognized “unfavorable change in the relative configurational entropy of two fragments in the protein pocket upon linkage is the primary reason most fragment linking strategies fail.” They advise that maintaining a bit of flexibility in the linker can help, as has been previously suggested.

 

This is an interesting analysis, and explicitly considering configurational entropy is likely to improve our understanding of molecular interactions. But is it really the main barrier to successful fragment linking? The researchers explore only nine different protein-ligand systems, though they did consider multiple linked molecules for three of these (pantothenate synthetase, RPA, and LDHA). Still, these represent just a fraction of the 45 examples collected in a recent review, and they only considered one somewhat contrived case (avidin) in which especially strong superadditivity was observed. It will be interesting to see whether the analysis holds true for more examples of fragment linking.

Fragment linking vs IMPDH (with a little help from the literature)

Mycobacterium tuberculosis (Mtb), the cause of its eponymous disease, is making an unwelcome comeback. Current treatments are lengthy, and highly resistant strains are emerging – and spreading. Chris Abell’s lab at the University of Cambridge has been working on multiple tuberculosis targets, and his latest results – in collaboration with Tom Blundell, David Ascher, and collaborators at the University of Cape Town and the University of Melbourne – has just published open access in J. Med. Chem.

The researchers were interested in inosine-5’-monophosphate dehydrogenase, or IMPDH, which is important for the synthesis of guanine nucleotides and is essential for every pathogen examined. They started by screening 960 fragments at 1 mM in a biochemical (spectrophotometric) assay. The IMPDH enzyme from a related organism was used due to its better expression and higher diffracting crystals; selected compounds were cross-checked with the Mtb enzyme and showed similar behavior.

This screen identified 18 molecules that gave at least 50% inhibition. IC₅₀ values were determined for the six most active, and these ranged from 325-675 µM. These molecules were soaked into crystals of IMPDH, but only compound 2 produced a structure. As if to compensate, two molecules of compound 2 bound in the active site. Moreover, these two fragments bound in the same region as a previously reported molecule, compound 1.

Initial attempts at fragment growing yielded only modest improvements in potency, so the researchers tried to link the two copies of compound 2. One linking attempt failed outright, a second gave a 58 µM inhibitor, but a breakthrough came when the linker taken from compound 1 was used. The (S) enantiomer of compound 31 is 2500 times more active than the starting fragment, and crystallography revealed that it binds as designed. Unfortunately, and in contrast to compound 1, compound 31 showed no activity against Mtb in culture. The researchers hope to figure out why.

This paper illustrates several points. First, fragment linking can be quite effective. Second, consistent with our poll from a few years ago, this is not necessarily easy. Indeed, given the reliance on the structure of compound 1, this study can be considered an example of fragment-assisted drug discovery as much as fragment linking. And finally, as we’ve said before, biochemical potency all too often does not translate to cell-based activity – let alone good pharmacokinetic properties. Potency is just the first step in the long march to a drug.

Group efficiency

Ligand efficiency (LE) is one of the more controversial topics we cover at Practical Fragments. One critic asserted – incorrectly – that it is mathematically invalid. Another has stated that it is “not even wrong,” because the metric is predicated on standard state conditions and thus "arbitrary". (As he acknowledges, this also applies to the value and even the sign of the Gibbs free energy for a reaction.) A related metric that has received less attention is group efficiency (GE). In a paper just published in ChemMedChem, Chris Abell and colleagues at the University of Cambridge use this to help them optimize pantothenate synthetase (Pts) inhibitors.

Ligand efficiency is defined simply as the free energy of binding divided by the number of non-hydrogen, or “heavy” atoms (often abbreviated as HAC for heavy atom count) in the ligand. (Geek notes: although the binding energy is negative, LE is expressed as a positive number, so LE = - ΔG / HAC. Also, on Practical Fragments, units are assumed to be kcal mol^-1 per heavy atom unless otherwise stated.)

Instead of focusing on a single ligand, group efficiency compares two ligands that differ by the presence or absence of a given group of atoms. To calculate GE, you simply subtract the ΔG values for the two ligands and divide by the number of heavy atoms in the group. For example, if you add a methyl group to your molecule and are lucky enough to get a 100-fold pop in potency, the methyl group has a group efficiency of 2.7 kcal mol^-1 per heavy atom.

The current paper chronicles lead discovery for Pts, a potential target for tuberculosis. Previous screening efforts followed by fragment growing and fragment linking had generated low micromolar and high nanomolar inhibitors. The researchers turned to group efficiency to improve their molecules further.

As expected from ligand deconstruction studies (see for example here, here, and here), different portions of a molecule are likely to have vastly different group efficiencies. Indeed, this turned out to be the case here: the acetate moiety had high group efficiency, whereas the pyridyl moiety had lower group efficiency. Thus, the researchers set out to replace the pyridyl with ten diverse substituents. Happily, one of these improved the dissociation constant to 200 nM as assessed by isothermal titration calorimetry of the fully elaborated molecule. Compound 11 also showed reasonable enzyme inhibition in a functional assay.

One potential problem with group efficiency is that it assumes the molecules being compared bind in a similar fashion, which is not always a safe assumption. In this case, the researchers obtained a crystal structure of compound 11 bound to the enzyme, which not only revealed that it binds similarly to compound 5, but also suggested that inserting a methylene may improve binding. The resulting compound 20 showed better activity in the inhibition assay, as well as activity against M. tuberculosis in a cell assay (though unfortunately the dissociation constant was not reported).

This paper offers a clear illustration of how group efficiency can be useful for prioritizing which portions of a molecule to change. In some cases, such as the example here, it makes sense to try to replace groups with low group efficiency. On the other hand, the core fragment may bind in a hot spot, and so just a slight tweak can dramatically boost potency. As with lead optimization in general, there are many paths – both to enlightenment and to perdition.

Deconstruction, superadditivity, and selectivity

One of the more exciting phenomena in fragment-based approaches is synergy (or superadditivity), in which the binding energy of linked fragments is greater than the sum of the binding energies of the individual fragments. Extreme cases are relatively rare, and the underlying thermodynamics can be counterintuitive, so it is always fun to see new examples. Cosimo Altomare and collaborators at the University of Bari and Consiglio Nazionale delle Ricerche (Italy) describe one in a recent paper in J. Med. Chem.

The proteases factor Xa (fXa) and thrombin (fIIa) are two heavily-studied anticoagulant targets. The paper characterizes a previously described molecule (compound 3) that is selective for fXa but still potent against fIIa, leading to good anticoagulant activity in human plasma as well as profibrinolytic activity. The researchers took a fragment deconstruction approach to better understand the binding to both targets.

As seen previously for fXa, the chlorothiophene moiety (red) is essential for binding, and removing it (compound 14) obliterates any detectable activity on both enzymes. However, while removing the glucose moiety (green) to give compound 1 reduced affinity for fXa by less than ten-fold, it reduced affinity for fIIa by more than two orders of magnitude. In contrast, removing the piperidine moiety (blue) to give compound 6a reduced affinity to both enzymes by several orders of magnitude.

However, these results are context-dependent. Removing both the piperidine moiety and the glucose moiety gives compound 4a, which has similar activity against fIIa as compounds 1 and 6a, where only a single moiety has been removed. In fact, compound 4a (without the glucose) is actually slightly more potent than compound 6a (with the glucose) against fIIa. But, as mentioned above, adding the glucose to compound 1 gives an impressive 110-fold boost in affinity for fIIa. In comparison, a famous early example of cooperativity in an NMR by SAR study gave only a 14-fold boost.

The researchers solved the crystal structure of compound 3 bound to fIIa, which reveals several hydrogen bond interactions between the glucose moiety and amino acid residues that have been previously implicated in allosteric activation of the protein. Perhaps compound 3 is exploiting this allosteric mechanism to bind more tightly.

This is a careful, thorough study and serves as a useful reminder that cooperativity can be huge, but it is still difficult to explain, much less predict.

From substrates to fragments – or not

Recently we highlighted a paper in which enzyme substrates were deconstructed into component fragments and tested against an enzyme with unknown specificity. In a new paper in J. Am. Chem. Soc. a collaboration led by Karen Allen (Boston University), Frank Raushel (Texas A&M), and Brian Shoichet (UCSF) has performed a similar experiment to ask whether fragments could be used to identify substrates.

The researchers chose six enzymes from three different classes and collected various-sized fragments based on known substrates. These were then tested in functional assays to see whether they could be substrates or inhibitors. Stunningly, in most cases the fragments showed no activity against the enzymes; when activity was detectable, it was usually at least 100,000-fold lower than the natural substrate. Even subtle tweaks, such as removing a hydroxyl group, were enough to mess things up, as illustrated for adenosine deaminase (compare compounds 1 and 4). Breaking the substrate in two was sometimes better: compound 8 was turned over slowly by the enzyme, though its complementary fragment 9 had no effect on activity – positive or negative – when added to the assay along with compound 8 or the natural substrate.

Of course, functional assays are less sensitive than biophysical assays, but in the one case where the researchers tried soaking fragments into crystals of the enzyme they found that the fragments bound in a different manner than the substrate – echoing previous work deconstructing synthetic inhibitors of protein-protein interactions.

As the authors note, the remarkably sharp structure-activity-relationships (SAR) observed here could reflect a fact of nature: most enzymes need to be highly selective for their substrates to avoid mucking up cellular metabolism.

Moreover, the notion that two fragments, when properly linked together, can bind more tightly than the sum of their individual binding energies has been a primary motivator behind fragment-based lead discovery for more than 30 years. In a sense, this paper illustrates this principle in reverse. Indeed, it is possible for the energy gained by linking two fragments to exceed the binding energy of an individual fragment.

This is a nice study from which we can draw two lessons, one pessimistic, the other optimistic. On the down side, we are unlikely to be able to use fragments to predict the natural substrates of uncharacterized enzymes, at least on a general basis. As noted previously, this is not surprising: the concept of molecular complexity predicts that fragments should be fairly promiscuous, and we’ve seen time and again that fragment selectivity is not necessarily maintained during optimization.

On the positive side, this study beautifully illustrates that it is possible to achieve massive enhancements in affinity with relatively small changes. Beyond just the magic methyl effect, we’ve got the magic hydroxyl effect, the magic thiophene effect – heck – the magic fragment effect. Of course, these are retrospective analyses, and it’s easier to break things than make them. That said, folks at Astex demonstrated that it is possible to improve the affinity of a millimolar fragment a million-fold by adding just six atoms. Perhaps such opportunities are more general than we have previously dared to dream.

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.

Hsp90 and fragment linking

There has been no shortage of fragment-based approaches directed toward the anti-cancer target Hsp90, most of which have relied on growing fragments (see here for some impressive recent examples). Researchers from Abbott published a report providing a couple examples of linking fragments against this target a few years back, but in those cases the ligand efficiencies of the linked molecules were dramatically lower than those of the initial fragments. In a recent paper in ChemMedChem, researchers from Evotec describe an example that maintains the ligand efficiency.

The research group had previously conducted a fragment screen against Hsp90, resulting in a number of hits. In the new paper, fragment hits 1 and 2 (see figure) were both found to have fairly low affinities, but were characterized crystallographically. Interestingly, fragment 2 could adopt at least two very different conformations, depending on whether it was co-crystallized in the presence of fragment 1. In the ternary structure, the two fragments come within about 3 Å of each other, and molecular modeling suggested that four atoms should be able to link them.

Gratifyingly, when such a compound was made and tested, it inhibited the enzyme several hundred-fold more tightly than either of the initial fragments. The crystal structure revealed that the compound binds similarly to the ternary structure of Hsp90 and fragments 1 and 2.

The authors note that “the binding free energy of the linked fragment 3c was found to be exactly the sum of those of the original two fragments.” Of course, this is still a long way from an ideal linking situation: as noted earlier this year a good linker should lead to super-additivity (an improvement of ligand efficiency), not just additivity (maintenance of ligand efficiency). Nonetheless, this example is still better than many attempts at linking, which often are less than additive.

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.