Interesting. I think you need to expand on this.

All models (=equations) are imperfect, but they also serve to constrain understanding of action. For example, I have a clear (if simplistic) mind image of the difference between competitive and non-competitive inhibition. Of course, it is possible to take stochastic approaches and derive any, complex model of E"I interactions. But, would this help? Bear in mind that most kinetic or affinity constants are derived by an experiment that yields a few (5-10) data points . Also, most enzymological experiments are conducted at low uM or nM [E] whereas the intracellular concentrations of the same enzyme might be mM. Emulating this would require a very different experimental strategy. So, if we start from the premise that all such deterministic models are imperfect, the question should be: 'are they good enough' for what we want to do. If we are guilty of over-extrapolation beyond that usage, the problem is ours, not the model!

Interesting. I think you need to expand on this.

All models (=equations) are imperfect, but they also serve to constrain understanding of action. For example, I have a clear (if simplistic) mind image of the difference between competitive and non-competitive inhibition. Of course, it is possible to take stochastic approaches and derive any, complex model of E"I interactions. But, would this help? Bear in mind that most kinetic or affinity constants are derived by an experiment that yields a few (5-10) data points . Also, most enzymological experiments are conducted at low uM or nM [E] whereas the intracellular concentrations of the same enzyme might be mM. Emulating this would require a very different experimental strategy. So, if we start from the premise that all such deterministic models are imperfect, the question should be: 'are they good enough' for what we want to do. If we are guilty of over-extrapolation beyond that usage, the problem is ours, not the model!

There are many models that are utilized by enzymologists to try to study enzymes and their respective inhibitors. The simple models that are taught in introductory biochemistry are not often used by people in pharma, who deal with more complex situations, such as with tight binding inhibitors, or when the enzyme and inhibitor concentrations are above the Ki. I learned more proper ways to analyze enzyme- inhibitor interactions in pharma with different models than I was taught in grad school. And I still have a hard time understanding what models to use and how to fit complex data. I think the statement you use may be too broad. I think most people who are enzymologists, don't rely on just simple Competitive/ non competitive etc models.

Unlike myself, There are, for example, a select few, that do rely on enzyme kinetics, and following progress curves with computer modeling with specialized software and I think doing this in combination with other tools, is the way to go. I think most people, like myself, find it too complex, and thus, we try to dumb it down by relying on the Morrision equation, etc. buT don't forget, that IC50 equations for ligand binding are the same equations as what enzymologist use. The Receptor plus ligand is just exchanged with E plus I, and the IC50 is just a Ki apparent, which is not as informative as a Ki.

And most often, the data does not allow one to use simple equations. So hopefully the models that are chosen is reflective of that.

So I guess I do agree, that some try to force the data to fit certain models. I personally, ask my enzymology friends to help, when the data becomes too complex. I think every researcher needs to have the humility to be able to search for expert advice. But the other issue is also being aware that the data just doesn't fit simple models. Unfortunately, there are not many or any courses offered on enzyme inhibition as it occurs in every day settings.

And, when you think about it - whatever structural/kinetic/mechanistic/temporal model one chooses to assume, there's still a clear distinction between competitive and non/un competitive interactions. Conceptually, mechanistically, structurally...

As a further thought, Im minded to Kornberg 'never waste clean thoughts on a dirty enzyme"

There are, indeed, some flaws in the theory of enzyme kinetics. Lineweaver-Burk's classical double reciprocal plot is prone to mistakes and data distortion, due to the extrapolation of the values. Eadie-Hostee, which represents a further advancement of the previous equation, suffers from similar shortcomings.

I would have to disagree with you Marcia that IC50 is just a Ki apparent since the use of Ki implies a mechanism and not all the mechanisms are equivalent to ligand receptor interactions, which is the underlying problem. If you look at the competitive inhibition equation and the non-competitive equation the inhibition term used (1+i/Ki) is not the same in each equation, for competitive it is a multiple of the Km and for non-competitive it divides into the Vmax and when rearranged the non-competitive inhibitor term becomes Vmax-Vmax([i]/[i]+Ki) which is equivalent to the ligand receptor interactions you mention. The problem then is the competitive equation when rearranged does not result in a ligand receptor relationship such that changes in Km are not directly related to the inhibitor binding.

Maybe this is fine maybe true competitive inhibition does exist somewhere, however mixed non-competitive inhibition which then has to account for inhibition that is non-competitive but also has to produce changes to the substrate affinity now gets saddled with two binding constants, and anyone who has ever tried to use the equation can probably tell you how rare it is the two constants are the same number.

However by making the change in substrate affinity directly dependent on the binding of the inhibitor like all the other ligand receptor interactions only one constant for binding is required although where the new Km shifts to must be experimentally determined.

Unfortunately the pervasiveness of the 1+i/Ki term, which obscures the ligand receptor interaction, has resulted in the production of overly complex equations which are rarely useful.

Sorry Ryan, I am not sure if I understand your response. For enzymes, inhibition studies with competitive inhibitors are done with substrate concentrations way below the Km, and so V/K becomes very small. For enzymes, the Ki may not be the real KI and is just an IC50 when the enzyme concentration is at or above the real Ki. So I used the term apparent Ki. For ligand binding and for Enzyme binding to inhibitor, when it is competitive, the same equations are used. The Morrison equation is the same quadratic equation that is used in receptor binding when the concentrations of receptor and ligand are above the KD. And this is true for competitive binding only.

There are many models for receptor- ligand interactions where allosteric interactions are occurring and there are more than one binding constant. The same is true in enzymology for multimeric enzymes. I was referring to the simple equation R + L goes to RL, and E + I goes to EI. Obviously, things in reality, are usually not this simple.

But this is part of the problem. Very few people, are able to analyze complex situations. The real enzyme inhibitor theory, to me is the complex scenario, which is not a farce. But I often don't express myself in a clear fashion.

Equations for basic enzyme inhibition mechanisms are not flawed; in fact they are infinitely accurate descriptions of their corresponding models.

Enzyme Inhibition Theory is not a farce either. It is based on Thermodynamic Principles and Chemical Equilibrium Theory, combined with Linear Algebra and the Theory of Systems of Linear Differential Equations.

Having said that, if you encounter a real-world problem which cannot be explained by (a combination of) basic models, then postulate your own model and solve the corresponding equations, or use a numerical approach if the equations get too complicated.

It all depends on what level of understanding of the process under study you want to achieve. If you are happy using empirical parameters to describe complex phenomena, then go ahead and do it, but don't assume that the more rigorous approaches to are flawed.

And for Nicola, again, there are no flaws in the Theory. Linearized forms of the basic inhibition equations were used back in the day when the only way of fitting data to a curve was by using a ruler and data points on a piece of paper. The exact same equations of the Theory can be approached today with modern nonlinear fitting algorithms, and all the power of Enzyme Kinetics Theory can be readily appreciated. Check out, for instance, the program DYNAFIT (http://www.biokin.com/dynafit/), one of my favorite to perform such tasks.

You will have to clarify your arguments Marcia

Why would competitive inhibition studies need to be done at concentrations way below the Km of the substrate, since you are looking at an inhibitor that disrupts the binding between the substrate and the enzyme, so analyzing the inhibitory properties along the full binding curve would be needed. Since the competitive inhibition equation is supposed to describe a linear decrease in substrate affinity (increase in the Km) with the addition of inhibitor, why would you want to look at data that excluded the principle definition of competitive inhibition?

I don’t understand what you mean when you say the enzyme is at or above the apparent Ki since the Ki is defined by the concentration of the inhibitor.

I agree that there are many different ways inhibitors can interact with enzymes but the problems associated with describing them are rooted in the generation of the initial inhibitory equations which produced a mechanistic approach that does not link change in kinetic parameters to inhibitor binding.

Let’s suppose you find an inhibitor that only changes the substrate affinity so decide it’s competitive and do your study below the km value. By observing that the Km changed and not the Vmax you assume its competitive but changes in substrate affinity are much more likely to result from changes in the conformation of the substrate binding site, there is all sorts of evidence for this just by looking at mutant enzymes or enzymes from different species. So by not looking at the possible shift in Km between the unbound and the inhibitor bound enzyme you assume the Km increases to infinity with increasing inhibitor concentration. Competitive inhibition does not allow for changes in Km that do not result from competition between substrate and inhibitor at the active site. The basic equations are missing this relationship because while multiplying the Km by 1+i/ki may be applicable to to the very specific case of true competitive inhibition, in all other cases it is wrong and has produced terrible problems for understanding and modeling more complex inhibitory systems.

Javier stating that everything is perfect without even addressing any of the issues raised is a terrible approach to science, addressing problems brings progress, and I have postulated my own models to address these problems (check out wikepedia they have been up there for about 2 years now, or you could check out my book chapter as well) but if you would rather stick to the everything is fine approach and all answers can be found in old text books approach please disregard my comments.

I suggest reading R.A. Copeland's book on enzyme inhibitors in Drug Discovery.

1.

Determination of Ki is done at low substrate concentrations for competitive inhibitors, if you know they are competitive. So when one does high throughput screening, the assays are set up using substrate concentrations below the Km.

2. The Ki is called an apparent Ki, or IC50 until you know that your enzyme concentration is way below the Ki. Otherwise you are just titrating the enzyme, and get an artificially large number for the Ki. The same is true for receptor ligand interactions and the Kd.

I hope this helps.

From what I have heard, and seen, Dynafit is a great program. The program was used in some of the papers I co-authored with the person who wrote the program, Petr Kuzmic.

I need to re-read the copeland book myself. So I think at low S, the equation reduces to vi/vo = V/K inhibited over V/K uninhibited, and a plot of 1-vi/vo vs. inhibitor concentration gives something close to a Ki.

Marcia the problem once again is the presumed mechanism you are saying that if you know the inhibitors are competitive you analyze them in a particular way, what is the point of high throughput determination of competitive inhibitory constants if you already think they are competitive and are forcing them to that model? Why not do a single substrate concentration and stick with your ic50?

That is pretty much what we did for most situations. But I like your universal solution.

I don't work in pharma now, but sometimes things don't fit to a simple solution, especially for tight binding inhibitors.

Ryan, I was misled by the rather harsh description of your question. I agree current models describing Enzyme Inhibition can be improved, but that doesn't mean they are flawed or a farce, they may just be incomplete or inadequate to describe specific situations. Instead, I would say many researchers make use of the basic inhibition models disregarding all their implicit assumptions, leading to meaningless results that appear to indicate that the basic models are flawed.

Ryan, also now I have questions concerning your answer about a fixed concentration of substrate. If one works in a certain inhibitor series, and one knows that the substrate competes with the inhibitor for binding to enzyme, and the chemists are just interested in relative numbers, then I see how your solution is fine and perhaps advantageous. What happens when you are dealing with HTS, and you are looking for hits, and the interactions are weak. You may end up missing certain pure competitive inhibitors if your substrate concentrations are too high. So what do you suggest for a substrate concentration? Maybe something near the Km?

Also, from your comments, if researchers report data, do you think an IC50 should always be reported rather than a Ki? And under what circumstances would you yourself use a Ki?

Thanks, Marcia

At high [S]. the system becomes insensitive to competitive inhibition, unless the inhibitor is phenomenal. Arguably, a two [S] experiment (one as ~Km, the other a lot higher) might be a useful way to discern mechanisms. But aren't all these experiments just screen, leading to detailed characterisation later for the few that tick the right boxes?

Also, there is nothing flawed about Lineweaver Burk, Eadie Hofstee or any other method (e.g. the direct linear plot of Athel Cornish-Bowden) until you invoke error in the measurement of V. It then becomes an argument about the best way to handle error. At this point, linearisation methods distort the error structure of the data (e.g. in simple MM kinetics,the equation is linear in Vmax, non linear in Km) and thus, any non-linear curve fitting methods are superior. I once used direct search algorithms and made a movie of the algorithm moving over the error surface in pursuit of the local minimum - very illuminating.

The main problem with the base equations in not fitting its that they don't distinguish between binding constant and effect on enzymatic activity. The use of ki as the sole descriptor for the inhibition effect is incorrect. Just as if you had a receptor agonist and you found its binding affinity you could not assume that the effect on the receptor was the same as the receptors natural agonist you can't assume that all inhibitors completely inhibit enzymatic activity.

The use of the term 1+ I/ki obscure the distinction between binding constant and effect. When expanded in the non-competitive equation That term shows that the equation for non-competitive inhibition only describes complete inhibition of enzymatic activity.

Vmax - Vmax([I]/[I]+Ki)

By changing the second Vmax to a delta you can describe minimal inhibition to complete inhibition. It can also be used to describe activation.

Vmax - ΔVmax([I]/[I]+Ki)

The same term can be used to describe changes in substrate affinity

Km - ΔKm ([I]/[I]+Ki)

However derivations of complex kinetic equations which produced in the same way the base equations were, all containing 1+I/ki terms which do not separate effect from ki. This has resulted in more and more complex equations that are seldom compared if they are comparable at all.

Marcia

I think an initial screen is completely fine when looking for potential drug candidates but most are never characterized properly since regulatory committees are willing to accept ic50s if they perform well in clinical trials. So theses drugs get screened in animals and clinically since all he pharmaceutical parameters have to be assessed and years are wasted because the initial full characterization was not done properly. Take the gamma-secretase inhibitor DAPT, which was initially described with an ic50 over a decade ago by the company that made it and is still being researched today, probably because it took almost a decade to get groups to analyse the data and produce better models of what it does which is activate gama-secretase production of beta-amyloid at concentrations below the effective inhibition concentrations.

This failure of the industry to require more thorough drug kinetic characterization stems from the over complication of kinetic models which has resulted from the way these equations are derived.

I agree, based on what I have seen that everything you have said is true. But I think it is a failure of the companies, to not require drug characterization. I don't know what the current environment is, but when research was allowed in big pharma, 20 years ago, potential drugs and drugs were characterized by some companies.

But sometimes, it may not be good to know how they act or they never would have become drugs. Look at aspirin, for example and cyclosporine A.

The tools that are available today, ie the signalling and protein arrays, etc, allow for a better understanding of how potential drugs work at the cellular level. And sometimes, the target isn't even known. But I agree completely, that if the target is known, in order to approve a drug, in this day and age, there should be a requirement to know as much as possible about how it works. So The enzymological studies are critical, but I would take your thoughts a step further, and say even understanding how it affects cellular function is critical as well. This is important not only for efficacy, but for its safety profile as well.

I don't know the story behind DAPT, even though I was a chair for a GRC conference on regulated proteolysis at the cell surface. So I will research the story. I may use this in the introduction I will be giving for the keynote speakers.

Hi Dr Moss

I agree that taking thing further and understanding how drugs regulate things in the bigger picture sort of way is also very important but I feel that characterization at the kinetic level has been overlooked for far too long and has to be reexamined so it can be the useful tool it should be.

Sorry to make such a late addition to this discussion, but I wanted to amplify an earlier comment regarding inhibitors that are not in rapid equilibrium with the enzyme. It is quite common among drugs that inhibit enzymes that they are either covalent and irreversible or slow tight binders. As a result, steady-state kinetics, assuming rapid equilibration of ligands with enzyme on the time scale of the reaction, does not provide an adequate description of the inhibitory mechanisms of such compounds. Moreover, the IC50 decreases with exposure time and is therefore not the best way to compare the potencies of a set of related inhibitors. In such cases, the second order rate constant of inactivation (or kinact/Ki) can be used.

Adam, your statement is very true. Most of the inhibitors we tested that became drugs were slow binding. That is why the screeners often did preincubations, once they knew this, but full mechanisms were done on ones that were considered potential drug candidates. By doing this type of screening, an awful lot of info about the class of inhibitor was not obtained. For Proscar, the mechanism of inhibition wasn't figured out till after it became a drug. But understanding the slow tight binding part of the mechanism helped the enzymolgists and chemists to make a better second drug, IMO. Given now, the computers that are available, and equipment, progress curve analysis provides far more useful info, and should be done. It kinda depends now on what type of assay can be done. For 5 alpha reductase, the assay was with HPLC separation, with end points. It was extremely cumbersome to get progress curves.

In defense of preincubations, if the inhibitor doesn't inhibit well after a certain period of time, then it is probably not a good drug candidate, and would be weeded out.

Reproducibility of biological data is a significant problem in research today. One of the potential contributors to this, which has received little attention, is the over complication of enzyme kinetic inhibitory models. This stems from the way inhibition equations are generated which has followed the methods used to generate the initial flawed inhibition equations.

The main problem with the basic inhibitory equations is that they don't distinguish between binding constant and effect on enzymatic activity. The use of ki as the sole descriptor for the inhibitory effect is incorrect.

For example, in the closely related field of receptor binding kinetics, if you had a receptor agonist and you determined its binding affinity you could not assume that the effect on the receptor was the same as the receptors natural agonist, you would have to determine the effect and report it.

Following the same logic you can't assume that all inhibitors completely inhibit enzymatic activity.

However the use of the term inhibitory term (1+ I/ki) obscures the distinction between binding constant and effect.

The effect of an inhibitor on an enzyme is not linked to the equilibrium binding constant used to describe the association of the inhibitor with the population of enzymes being studied.

While changes in enzymatic activity do result from enzyme inhibitor binding, like receptor agonists the change in activity produced by the binding has to be determined.

The ki is an equilibrium binding constant just like the substrate affinity constant (Km) of the Michaelis-Menten equation

[S]/[S]+Km

And the receptor binding constant of the hill equation

[L]/[L]+Kr

And like both of those terms the description of an Inhibitor binding to an enzyme population using the ki should be represented in exactly the same way

[I]/[I]+ki

This remarkably new way of representing the inhibitory term can easily be adapted to describe the effect of the inhibitor on the enzymes reaction rate or substrate binding affinity.

Vmax - delta Vmax ([I]/[I]+ki)

Km - delta Km ([I]/[I]+ki)

It can also be easily adapted to describe activation of enzymatic activity.

However due to the fact that inhibitor theory has overlooked this relationship enzyme kinetic modeling has become a field where new equations are constantly derived using the same assumptions which disregard the distinction between a binding constant (ki) and the affect on the enzyme. These equations are overcomplicated and not useful and have been abandoned by most biological research, pharmacological studies and regulatory bodies in favor of simplified descriptors such as ic50s.

With such apathy towards understanding the way things actually work it is surprising there isn’t more of a problem with reproducibility of biological studies.

For competitive inhibitors that are in equilibrium with the target enzyme during the catalytic reaction (excluding slow-binding inhibitors and covalent inhibitors), the ratio IC50/Ki between IC50 (the concentration of inhibitor that causes 50% inhibition in a particular set of assay conditions) and Ki (which is the dissociation constant of the inhibitor for the enzyme form, e.g. E, EA, etc., to which it binds during the catalytic cycle) is described by the Cheng-Prusoff relationship. The derivation of this ratio requires knowing the kinetic rate equations for the reaction with (Vi) and without (Vo) the inhibitor, then substituting them into the relationship Vo/Vi = 2, where [I] = IC50. and solving for IC50/Ki. The result is an equation with IC50/Ki on one side and a combination of kinetic constants and substrate concentrations on the other. This works nicely even for multi-substrate enzymes, as long as the inhibitor is competitive and there is only one Ki. It doesn't work if the inhibitor binds with different affinities to different enzyme forms, of if the inhibitor is non-competitive, or if it is non-specific (e.g. denaturing). In those cases where it is applicable, however, if you know the kinetic constants and substrate concentrations, you can state by what factor the IC50 is greater than the Ki, and you can also be sure that as long as the mode of inhibition for a set of compounds is the same, the IC50s will reflect the relative affinities of the compounds.

I'd like to emphasize again that the Ki of a competitive inhibitor is the dissociation constant of the inhibitor for the enzyme form to which it binds, which may be only one of several enzyme forms present at steady-state for multi-substrate enzymes.

There were a lot of caveats in the above, but I have been involved in early-stage drug discovery projects where this sort of analysis has been very useful.

It would be difficult to apply this analysis to an the enzyme that has allosteric modulators or a complex, cooperative mechanism. That may be a reason why some people prefer to keep things simple and use IC50, but they hopefully have other readouts, such as inhibition of cell growth to drive their programs.

I would additionally like to point out that Km is not always, or even usually, a substrate dissociation constant, not even for a single-substrate enzyme in the steady-state model. It can be equal to a complicated arrangement of on- and off-rate constants in a multi-substrate enzyme, but it can be measured if the steady-state rate equation is known.

One possible reason for the perceived lack of reproducibility of results could be that assays are run differently by different labs. Changing the temperature, pH, ionic strength, cosubstrate (e.g. Mg2+) concentration, and/or substrate concentrations could have large effects on IC50s and Kis. This would be a problem no matter what parameter were used to measure inhibitor potency.

Another reason for lack of reproducibility could be (and is) variation in the purity of the inhibitor. Compound samples are often impure, degraded, and contaminated. The contaminants could be causing the inhibition rather than the compound on the label. Quality control is therefore hugely important in drug discovery programs.

The final point I'll make regarding lack of reproducibility is that inhibitors sometimes are non-specific, e.g. aggregators or denaturants. These non-specific effects can be very sensitive to conditions such as temperature and buffer composition. This is a huge problem for hit followup in screening campaigns, and methods have been developed to identify such situations.

HI Adam thanks for your response,

You raise a lot of points however the caveats and amount of information is hard for me to follow let alone everyone else

But I am eager to learn as null hypothesis always make theories stronger so how about you treat my ideas as the null hypothesis and I will do the same with yours

So please have a look at my book chapter as it covers most of my views

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

But let’s start with the basics since I think that will let everyone contribute

Do you believe that inhibitors are special or that they follow the same mass action principles that govern all chemical equilibriums and are used and are used to define the Hill-Langmuir equation and Michaelis-Menten equation?

Hi Ryan,

Sorry if I got a little carried away and covered too many topics. One thing I was trying to do was point out various pitfalls that could cause enzyme inhibitors to appear to behave oddly in the ways you describe. This perspective comes from my experience with high-throughput screening with enzyme assays for inhibitors, where most or all of the positives (i.e. inhibitory compounds) are non-specific, or artifactual, or interfere with the detection of product, or bind to the substrate or the activating metal ion rather than the enzyme, etc. It's a long list. The again, some "real" inhibitors don't follow steady-state kinetics because they are slow-tight binders, or covalent, or inhibit enzymes with cooperative properties.

Of course I believe that inhibitors "follow the same mass action principles that govern all chemical equilibriums..." since they are chemical substances. However, there are lots of phenomena that may confuse the interpretation of inhibition, which should make one cautious about questioning the theory of enzyme inhibition when an inhibitor behaves oddly.

I don't disagree that there can be a discrepancy between inhibitor binding stoichiometry and inhibitory effect. I just think that in some cases this is caused by any of a number of effects that have more to do with the physical or chemical or optical properties of the inhibitor than with the specific interaction between the inhibitor and the enzyme.

Having said all that, I think it's perfectly reasonable to try to reformulate the existing theory as you are doing in order to cover situations that aren't currently covered (assuming they actually aren't). But there are certainly many enzyme inhibitors that follow steady-state kinetics theory perfectly well. So to answer your original question, I don't think enzyme inhibitory theory is a farce, but the Michaelis-Menten-based equations aren't the whole story.

The last point I want to make is that your formulae only cover enzymes with one substrate. That leaves out a lot of enzymes. Do you plan to try to extend the theory to multi-substrate enzymes?

Hi Adam

Okay let’s try this again neglecting all the interference and background noise that may interfere with acquisition of your experimental results you agree that a population of inhibitor binding to a population of enzymes is subject to mass action principles.

Although you suggest I am making too much out of discrepancies between binding stoichiometry and inhibitory effect you make it seem as if there aren’t thousands of papers that have been generated to explain just that using the same principles and inhibitory terms (1+i/Ki), that disregard the difference between binding stoichiometry and inhibitory effect, used to derive the competitive non-competitive and mixed non-competitive equations.

A clear example is Segel’s extensive coverage of almost every conceivable inhibitory situation back in 1975, his book (Enzyme Kinetics) is a classic but I think it is as widely ignored as Fontes at al., who attempt to redefine all the equations in 2000..Do you think researchers really should feel the need to have to be redefining the field still?

So yes I am covering situations that have already been described but with one equation rather than hundreds.

Currently I haven’t looked into expanding these ideas into multi-substrate systems as the equations I have generated were all based on need and I don’t have any data pertaining to multi-substrate systems. If someday I get my own lab or find a collaborator who wants to share their data with me I may look into it.

Fontes, R., Ribeiro, J. M., and Sillero, A. (2000). Inhibition and activation of enzymes. The effect of a modifier on the reaction rate and on kinetic parameters. Acta Biochim. Pol. 47:233–257.

So I have been asked to be a guest editor at frontiers and I would like to know if this group has any suggestions or if any of you would like to contribute articles.

While I am sorry if come across as a little defensive here I would definitely encourage submission of articles that argue against my ideas.

So please let me know if you are interested

Thanks

I am agree, some changes should be made if you want to use classical kinetic model for not simple enzymes. For example, gamma scretase should harbour distinct places for docking and for catalytic site. It also should hold two substrate molecule at the same time but at different places. The clasical approach should work if you consider the first docked substrate plus enzyme as one and then attaching of the next substrate.

Article Are γ-secretase and its associated Alzheimer's disease γ problems?

I agree there has to be a clear distinction between enzyme forms containing 1 and 2 or more substrate molecules.  The old way of just adding 2 michaelis menten equations together does not work because modifiers can't affect each form separately using this notation. ie. an inhibitor affecting the form bound by 2 substrate molecules can only reduce the reaction rate of V2 to V1. 

v= V1([S]/([S]+K1)) + V2([S]/([S]+K2))

The distinct forms present in each substrate range have to be clearly defined. this can be achieved by adding a single term making each substrate derived form distinct 

"-V1([S]/([S]+K2))"

v= V1([S]/([S]+K1)) -V1([S]/([S]+K2)) + V2([S]/([S]+K2))

This term allows for the disappearance of the single substrate form at higher concentrations where the double bound substrate form prevails.