Avidity observed between a bivalent inhibitor and an enzyme monomer with a single active site

Although myriad protein–protein interactions in nature use polyvalent binding, in which multiple ligands on one entity bind to multiple receptors on another, to date an affinity advantage of polyvalent binding has been demonstrated experimentally only in cases where the target receptor molecules are clustered prior to complex formation. Here, we demonstrate cooperativity in binding affinity (i.e., avidity) for a protein complex in which an engineered dimer of the amyloid precursor protein inhibitor (APPI), possessing two fully functional inhibitory loops, interacts with mesotrypsin, a soluble monomeric protein that does not self-associate or cluster spontaneously. We found that each inhibitory loop of the purified APPI homodimer was over three-fold more potent than the corresponding loop in the monovalent APPI inhibitor. This observation is consistent with a suggested mechanism whereby the two APPI loops in the homodimer simultaneously and reversibly bind two corresponding mesotrypsin monomers to mediate mesotrypsin dimerization. We propose a simple model for such dimerization that quantitatively explains the observed cooperativity in binding affinity. Binding cooperativity in this system reveals that the valency of ligands may affect avidity in protein–protein interactions including those of targets that are not surface-anchored and do not self-associate spontaneously. In this scenario, avidity may be explained by the enhanced concentration of ligand binding sites in proximity to the monomeric target, which may favor rebinding of the multiple ligand binding sites with the receptor molecules upon dissociation of the protein complex.

1. Part of the problem with this work is that researchers in biology/biophysics and those in (supramolecular) chemistry use a completely different language about what are essentially the same things -the (almost) synonyms of avidity and multivalency being a prime example. Usually what happens then is that researchers will go to extreme lengths to make it appear that there are some real differences between these terms and again, in the literature there are some very interesting examples of authors trying to make it so that avidity and multivalency are different things when there is little substance behind these terms. With this in mind, I would like to start to suggest to the authors that they have good look at the chemistry literature on multivalency, e.g. from authors such as Gianfranco Ercolani, George Whitesides, Pall Thordarson and Harry Anderson to mentioned a just few (see c.f. Angew Chem 1998, 37, 2754, J. Phys. Chem. B, 2007, 111, 12195, Angew. Chem. 2009, 48, 7488, Angew. Chem., 2011, 50, 1762, Chem. Soc. Rev. 2017, 46, 2622, Bioconjugate Chem. 2019. This might obviously have some impact on their introduction to the topic. 2. An often-mentioned topic by the authors/papers mentioned in 1 is that when it comes to "multivalent" binding, statistical factors need to be taken into account. As discussed also in details in Chem Soc Rev 2011, 40, 1305, the 2 to 1 interaction is often used as an archetypal example. Accordingly, care needs to be taken when discussing a 2:1 (or 1:2 -the difference really is only about which partner in the interaction is defined as the first one) interactions, do the authors mean, e.g., the microscopic (K m ) or macroscopic (K) binding constants, or do they mean the overall binding constants (which in chemistry is sometimes shown as β to avoid confusion) in their description of say, K I in Figure 5/ eq 4 which is shown there in the power of 2: K I 2 ? By the looks of it , K I is really the inverse microscopic binding constant (here it does not help that chemist usually use association constants while biologists prefer dissociation constants which are simply the inverse of the former) for each stepwise interactions and, additionally, the authors have made the assumptions to use the language from Chem Soc Rev 2011, 40, 1305 that K I = K 1m = K 2m , i.e. the stepwise interactions have no cooperativity. It does not help here that in Eq 2, K I appears to be what in chemistry would be called the overall binding constant with the units M -2 .
3. Continuing with the equations: Fig 5 / eq 4 has K I 2 = k i' /k i in which the two rate constants come from eq 3. But this does not make a lot of sense? This must be a stepwise process (here <-> equilibrium arrows: E + I <-> EI step 1, rate constants are k 1 and k -1 EI + E <-> EI step 2, rate constants are k 2 and k -2 Hence Eq 4 seems incorrect. This is also evident if one considers that for Eq 4 to be correct, k i' /k i must have the units M 2 . 4. Continuing to Eq 5, I cannot see how it was obtained from Eq 3. Whether my concerns about Eq 3 above are correct or not, the authors need to give more details on this derivation, at least in SI (write it out in full if necessary).
5. Figure 6 -which non-linear models / equations? This is really not clear at all. Again, more details, and ideally, raw data file etc should be included as SI.
6. Eq 8 on page 22 and related discussion earlier in the paper: Why does the bivalent inhibitor not bind to two trypsin (but only with mesotrypsin)? Or is this not correctly understood. 7. Eq 9 seems to be the main method to measure inhibition. But isn't this very risky? As the Graphpad manual points out this should not be used for tight binding, rather, using the Morrison equation: GraphPad But on reading about the Morrison Equation, it seems it is a quadratic question that is strongly related to those used to find free ligand concentration in a typical 1:1 equilibria. If that is so, there should be a cubic equation equivalent of the Morrison equation that would be related to the cubic one for 1:2 or 2:1 equilibria in Chem Soc Rev 2011Rev , 40, 1305 8. Somewhat related to 7 is that the authors say on page 23 that there is excess of the inhibitor that argue therefore I think that the "tight binding" models might not be necessary. But based on experience from supramolecular chemistry, even with such excess this is a dangerous assumption to make at any point for 1:2 and 2:1 equilibria.
9. And on the topic of concentration -is the concentration of the dimer inhibitor reported in various plots etc, the concentration of the molecule or the concentration of binding loops? The latter would be 2x the former. I mentioned this because IF the assumption is made that there is no cooperativity between the first and second enzyme binding to the inhibitor, then it should be possible to model the system as a simple 1:1 system provides the 2x inhibitor concentration is used in all the data analysis.
11. It would also help if the authors simply included as much as possible of their raw data and fitting program(s) as an attached (could be deposited on github or figshare).