Dear Rossana,

explaining protein ligand binding in detail is still the "holy grail" , so a detailed analysis is very difficult. Either keep it simple (residue X may contribute by hydrophobic/aromatic/H-bond/charged interaction to orient/bind ) or go for a full computational free energy prediction including solvation and entropic contributions.

Specific protein and inhibitor classes have different driving forces, so you have to compare your inhibitor/protein complex with similar ones first.

You will find numerous reviews on this with different Points of View. , e.g.

Thermodynamics of Ligand Binding and Efficiency

Charles H. Reynolds *† and M. Katharine Holloway ‡

ACS Med. Chem. Lett., 2011, 2 (6), pp 433–437

DOI: 10.1021/ml200010k

or

Binding of Small-Molecule Ligands to Proteins: “What You See” Is Not Always “What You Get”

David L. Mobley1, and Ken A. Dill2

Structure, Volume 17, Issue 4, 489-498, 15 April 2009

doi:10.1016/j.str.2009.02.010

or

Ladbury, J. E.; Klebe G.; Freire, E.

Adding calorimetric data to decision making in lead discovery: a hot tip

Nat Rev Drug Discov.

9 (1) , 23-27

This is somewhat a hand waving argument. If you have close analogues, that is, similar inhibitors then one can draw empirical conclusions (ie this group is better than that etc). The problem without this is that whilst you can quantify interactions from a structure, structural analysis of complex is not good at pulling out entropic contributions. These are all bound up in Ki. if you have an ITC machine you could measure the the H and S, in some ways this might be more helpful for you in the interpretation. There are free modelling programs GOLD etc that can estimate binding affinity. Single H-bonds rarely give much actual binding energy, if you have bidentate ones they will. VDW tends to always to help binding so those are worth looking focussing on. However immobilising a loop or expelling a water, could give a huge entropy shift, that would outweigh the energy change in interactions. This may underlie why a compound with more interactions binds more weakly. If the result is obvious more interactions = more binding, most people leave it at that. If it is not, then if you really want to understand or explain it, you will need more data.

Hi Rossana,

if you want to make it simple just consider the nature of interactions (h-bonds 2-5 kcal/mol, CH-pi and pi-stacking 1-4 kcal/mol, Van der Waals 0.5-1.5 kcal/mol as average energetic contribution values).

Otherwise you could take advantage from tools like AMBERTools (MM-GBSA and energy decomposition methods). Although the results you get from these tools are still an approximation they will give you more quantitative data that can corroborate your discussion.

However, in order to give you a more precise advice it would be nice to have more informations on the system you are working on. Which enzyme? Is it a docking study? Are you working aith crystal structures? etc..

Hope these suggestions can help you.

Regards,

Matthias

Dear Rossana,

explaining protein ligand binding in detail is still the "holy grail" , so a detailed analysis is very difficult. Either keep it simple (residue X may contribute by hydrophobic/aromatic/H-bond/charged interaction to orient/bind ) or go for a full computational free energy prediction including solvation and entropic contributions.

Specific protein and inhibitor classes have different driving forces, so you have to compare your inhibitor/protein complex with similar ones first.

You will find numerous reviews on this with different Points of View. , e.g.

Thermodynamics of Ligand Binding and Efficiency

Charles H. Reynolds *† and M. Katharine Holloway ‡

ACS Med. Chem. Lett., 2011, 2 (6), pp 433–437

DOI: 10.1021/ml200010k

or

Binding of Small-Molecule Ligands to Proteins: “What You See” Is Not Always “What You Get”

David L. Mobley1, and Ken A. Dill2

Structure, Volume 17, Issue 4, 489-498, 15 April 2009

doi:10.1016/j.str.2009.02.010

or

Ladbury, J. E.; Klebe G.; Freire, E.

Adding calorimetric data to decision making in lead discovery: a hot tip

Nat Rev Drug Discov.

9 (1) , 23-27

For an assessment of the most relevant interactions of a protein with a ligand you may try the LPC-CSU (http://bip.weizmann.ac.il/oca-bin/lpccsu) or PLATINUM servers (see http://www.geneinfinity.org/sp/sp_structanalysis.html#ligands). The results should allow you to estimate which residues or functional groups are the critical ones. Accordingly, you may start a mutational analysis or measure kinetics with varying ligands.

Otherwise, if you still consider to calculate and predict Ki values from structures some of the following approaches concerning protein inhibitors might be interesting to you:

Mlinsek et al. (2001) Prediction of enzyme binding: human thrombin inhibition study by quantum chemical and artificial intelligence methods based on X-ray structures. J Chem Inf Comput Sci. 41, 1286-94.

Laskowski M Jr et al. (2003) Additivity-based prediction of equilibrium constants for some protein-protein associations. Curr Opin Struct Biol13, 130-9.

Mozzicafreddo et al. (2009) Homology modeling and docking analysis of the interaction between polyphenols and mammalian 20S proteasomes. J Chem Inf Model. 49, 401-9.

Thanks everybody for your answers.

I am working with a BPTI-Kunitz domain in complexes with trypsin, chymotrypsin and pancreatic elastase. I have the Ki values determined thought enzyme kinetics. In the discussion of my phD thesis I just want to correlate or suggest, for example, why the Ki values are different (or similar) to another inhibitor by mapping/comparing the interactions in both structures. If I do it it will be of course as suggestions and then maybe the way of writing should be careful. "residues that are potentially important for the affinity". Of course the best way is to continue with mutational analysis, calorimetric studies, or estimating the energies of interacting residues.

I recommend that you determine Ki value through Dixon plot and the lower value of Ki is, the more binding of inhjbitor will be for the enzyme. This is observed in the magnitude of Ki value. Also, you can study CD spectra for the protease with the inhibitor and compare it to the enzyme without inhibitor.

Hey,

I just have a master's degree yet, so my suggestion might not hold much weight, but i would like to throw my idea out here as well to be critically evaluated.

From the little time that i have spent in this area of Molecular Dynamic simulations I have come across one observation. No approach so far has been able to fully correlate the two entities you are trying to relate, it may appear to be work for one system but you take the same protocol to the next system and the protocol breaks down. This is the main reason why new methods keep emerging especially ones that now include effect of water molecules in the vicinity.

I am working on something along similar lines. My work involves calculation of energies (GBSA) method from molecular dynamic trajectories. I have tested various other methods as well along similar lines.

As to your first part, No you cant say that contacting residues are potentially important without looking at the context, This can include the neighboring residues in case of peptide or the orientation of the inhibitor, if a ligand . This should in theory include detail workout of the binding site, possible dispalcement of water form that site since the inhibitor effects the system entropically so the net effect has to be balanced in terms of stability being achieved. You can develop parameters on your own which are computable without working out energies e.g. surface area exposed in the binding site and how much of that is from non-polar residues. This can then act as a relative parameter to the energy values.

As to the second part about the nature of interactions, well you can try but from my work on a few systems one usually doesnt find significant correlation amongst such interactions and a lot of decomposition of energy values is required. Again here you can coarse grain the parameters.

I am not sure if this is going to be much help compared to the answers you have already received however, this might point to other areas that might be of interest.

Good luck :)

Best,

/A

Probably a good approach to review the structural elements behind your data is use a protein-protein docking program to produce a complex of your protein and your receptor (such as cluspro 2.0: http://cluspro.bu.edu/login.php ; or rosetta software : http://www.rosettacommons.org/; for rosetta you need to download it and install locally). Then revise the many docking conformations to find one correlating with other known experimental structures for similar enzyme-inhibitor complexes. You may need to do a full geometry minimization of the complex using a suitable molecular mechanics software (if you downloaded and installed rosetta, you may take advantage of the relax-fast protocol, check in the documentation in the demos folder of rosetta software distribution ). Then, you may proceed to the calculation of the change accessible surface area (ASA) of polar residues and non-polar residues, of both the enzyme and the ligand in complex, and the enzyme and the inhibitor alone. Then you can calculate an estimate of the ∆G of binding with Ernesto Freire's equations (for a general quick review see under "structure/energy correlations" in Leavitt S & Freire E (2001) Direct measurement of protein binding energetics by isothermal titration calorimetry. Current Opinion in Structural Biology 11(5):560 - 566. For a detailed review see Freire E: The thermodynamic linkage between protein structure, stability and function. In Methods in Molecular Biology. Edited by Murphy KP. Totowa, New Jersey: Humana Press; 2001:37-68; and references therein ).

Probably the simplest approach I can foresee right now, though it is still though work. Specially if you are a newcomer to this field.

Best wishes,

Rogelio

I would start from evaluation of the interaction interfaces in your complexes. For this purpose it is convenient to use web-server based programs, e.g. PLATINUM (http://model.nmr.ru/platinum/). The abbreviation means Protein Ligand Attraction Investigated Numerically. The program is described in the work:

http://www.ncbi.nlm.nih.gov/pubmed/19244385

(Pyrkov et al., PLATINUM: a web tool for analysis of hydrophobic/hydrophilic organization of biomolecular complexes. Bioinformatics. 2009 May 1;25(9):1201-2).

This is very easy to use and useful for your purposes program.

In addition to all the suggestions above, be aware of your conditions. It is not just protein and inhibitor, you have buffers and salts and substrates and stuff. Hofmeister effects everywhere, Usually it is not easy to know what the "real" physiological conditions would be, but they are for sure not what you have in the crystal or in the NMR tube. Although I don't have any experience with it, clever mutlidimensional spectrometry in "representative" conditions might be a suitable method, especially if the inhibitor has chemistry (and therefore a spectrum) that stands out.

Dear Rossana,

James is right and wrong at the same time in what he writes. I would rather support Marco.

My experience is quite simple. The analysis of one class of the proteases against the other does not support generalizations. Several things are certain:

1) Not only the residues in the binding pocket are important, usually there are some other that are important (for tiny bit more info look at: Protein sectors: evolutionary units of three-dimensional structure. Halabi N, Rivoire O, Leibler S, Ranganathan R.

Cell. 2009 Aug 21;138(4):774-86)

2) Different structural elements optimize different kinetic parameters and never they are optimal on their own. They are optimized as an ensemble. What it means that sometimes Km is lower (weaker binding) to have higher kcat (faster turnover).

3) If you optimize Km you would get very bad enzyme as the release would be impeded.

4) There is always a competition between ON and OFF rates so the binding for the transition state has to be optimized but not perfect. What it means practically is that a precut and post cut fragments binding always can be improved.

5) Many proteases use ingenious mechanisms for a release. One of these was described in (Autocatalytic activation of the furin zymogen requires removal of the emerging enzyme's N-terminus from the active site. Gawlik K, Shiryaev SA, Zhu W, Motamedchaboki K, Desjardins R, Day R, Remacle AG, Stec B, Strongin AY. PLoS One. 2009;4(4):e5031).

6) So, the prediction of inhibitor power might be just simply a strong binding but also a subtle change in electrostatics so the reactive group stops functioning.

7) In enzyme's function the dynamics is equally important as the placement of individual groups and this element of extinguishing the necessary motion by inhibition is not well studied at all.

8) In your particular case one of the most neglected elements of the protein-protein interaction is the mass action. It is very difficult to dislodge a large molecule with a small molecule. What it practically means is the two molecules with identical sets of interaction but different masses would have different Ki values.

9) If I remember correctly your system, the Kunitz inhibitor is cut therefore the element of protein folding and complementarity is involved in the process.

Build models, of course

I agree with Lan Zhao. By modeling the complexes/interactions you may get ideas about differences in Ki. In any case, your explanations would be hypothetical.

You've got lots of good suggestions for the general problem, and basically I'd suggest wording your ideas as hypothesis rather than "proof" unless you get further experimental data with mutants, or determine thermodynamics by ITC or similar. In your specific case, I'd venture to speculate in your thesis if you are comparing Kunitz domains to other Kunitz domains, or possibly other canonical serine protease inhibitors for which there are structures and the conserved active site loop residues take on identical conformations (the Laskowski lab had a few nice papers looking at the concept of "interscaffolding additivity" under limited circumstances that you should look at). Jim Naismith is correct that the entropic contributions in binding of canonical inhibitors to serine proteases is huge. In an early paper of mine comparing CI2 to a linear and cyclic peptide with same loop sequence, CI2 bound 6 orders of magnitude more tightly to subtilisin than the linear peptide, and 4 orders of magnitude more tightly than the cyclized peptide despite direct contacts that were presumed to be identical. I think a few other groups have had similar findings in other canonical SPI systems. For Kunitz domains specifically, my group has done a lot of work recently with mutants of BPTI and APPI binding to different trypsin isoforms. Although our sample size is limited, our results would suggest that differences in affinity of different Kunitz inhibitors binding to a single protease can be largely attributed to the sequence of the reactive site loop contact residues, whereas different scaffolds within the Kunitz family have a larger impact in determining the relative resistance to proteolysis of the inhibitors (see Salameh et al, Biochem J, 2011 and maybe some of our other recent papers). Hope this helps. If you need help finding the specific refs maybe I can help with that next week-- currently I'm on a plane typing on my iPad :)

Correction: the most relevant paper from my group that I intended to list is: Salameh MA, Soares AS, Navaneetham D, Sinha D, Walsh PN, Radisky ES. Determinants of affinity and proteolytic stability in interactions of Kunitz family protease inhibitors with mesotrypsin. J Biol Chem. 2010 Nov 19;285(47):36884-96. PubMed PMID: 20861008; PubMed Central PMCID: PMC2978618.

Correlating protein-ligand structures with thermodynamics of binding is difficult. I spent my PhD assembling a database of protein-ligand complexes that had structural data in the PDB and had had their binding event characterised using isothermal titration calorimetry (ITC). The findings of this work are summarised in the paper below.

The Thermodynamics of Protein–Ligand Interaction and Solvation: Insights for Ligand Design, Olsson et al, JMB, 2008, 384, 1002-17

http://dx.doi.org/10.1016/j.jmb.2008.09.073

This study gives a global view of the thermodynamics of protein-ligand binding rather than focussing on specific interactions. For a review of methods for understanding the importance of specific interactions I would recommend the paper below.

A Medicinal Chemist’s Guide to Molecular Interactions, Bissantz et al, J Med Chem, 2010, 53, 5061–84

http://dx.crossref.org/10.1021%2Fjm100112j

I would have to disagree with Andrew

"If you are determining Ki from enzyme kinetics, then it is very important to know the mechanism (e.g. pure competitive- binding to the free enzyme, or uncompetive/non-competitive, in whcih case teh interaction is with the enzyme-substrate complex). In so far as Ki is a thermodynamic dissociation constant"

The Ki values generated with these sorts of traditional notions of binding kinetics are flawed as they do not distinguish between binding and the amount of inhibition produced.

Specifically with proteases you can have an excellent binding affinity for say r group binding pockets but poor inhibition as the active site is still available for hydrolysis of amide bonds of the protein backbone. A specific example of this is the enzyme Kallikrein which is believed to be competitively inhibited by by benzamdine, but crystal structures clearly show the molecule bound in the side chain binding site which provides kallikrein its specificity. Examination of the supposed competitive inhibition data shows that the change in km is a hyperbolic one not linear and the change in catalytic activity reflects the population of enzymes shifting from enzymes with good affinity for the substrate to enzymes with bad affinity. This is akin to enzymes from different animal species with different binding affinities for a substrate due to slight differences in the binding surfaces they present.

Walsh R, Martin E, Darvesh S. Limitations of conventional inhibitor classifications. Integr Biol (Camb). 2011 Dec;3(12):1197-201.

Non-competitive inhibition is also flawed in that it assumes exclusively 100% inhibition with binding of the enzyme so trying to graft that model onto inhibition patterns has probably added additional difficulty to models for inhibitor binding. So as your tittle suggests there is a distinction between affinity and Ki values, Ki values assume inhibition is complete and are flawed so should not be trusted for models of molecular interaction in a protease/inhibitor complex

Ryan Walsh. Alternative Perspectives of Enzyme Kinetic Modeling

http://www.intechopen.com/books/medicinal-chemistry-and-drug-design/alternative-perspectives-of-enzyme-kinetic-modeling