Where in this PhD thesis? I checked the text and could not find (it might be my fault). Would you please point to the experiment.

Many years ago, my very first published paper was on the equilibrium of the glutamate dehydrogenase reaction (Biochem. J. 105, 691-695 (1967)). I realise now in retrospect that I designed the experiment in a way that maximised its sensitivity to small errors, so it took me a while to achieve reliable results, but eventually the Keq was demonstrably the same at pH 7, pH 6.5, pH 8.5 (taking account of the proton that is released in the reaction and the very accurately measured pH). So violations of thermodynamics. However, as soon as I went to pH 8 or also down to 6, immediately there was a big change, and this certainly would have been dependent on enzyme concentration, because it was an artifact. At low pH NADH is unstable and at high pH NAD+ is unstable, so that the total cofactor went down with time. The time in my experiments was roughly 40 minutes, but of course with more enzyme it would have been faster and vice versa with accordingly less or more departure from the true Keq value.

Is there any scope for something similar in your experiments?

Apart from my own experiments mentioned K. Burton was responsible for a huge compilation of equilibrium data on metabolic enzymes in order to obtain the relevant free energy values. There is considerable detail in some of those papers. 

Thank you, I am checking your paper from 1967 and will back to you.

I don't think the paper explicitly deals with the question of whether it was dependent on enzyme concentration. We ensured it wasn't but then, as mentioned, encountered a situation once we moved to pH values where there was small but significant coenzyme loss over 40 min where it undoubtedly appeared (falsely) pH-dependent.

Commonly the reactions catalyzed by enzymes are very favorable thermodynamically. This means that the equilibrium is significantly shifted to the products. If K> 100, than the substrate conversion is >99%. In this case it's experimentally impossible to quantify the remaining concentration of a substrate. If the addition of the reaction product in the beginning of the reaction affects the conversion, then the reaction is probably close to equilibrium. In your case add the reaction products to the system and see what happens. 

First of all,  a correction to my first answer, which meant to say 'So NO violations of thermodynamics.

Second, a clarification to my second answer to emphasise that under the artifactual conditions, where coenzyme is actually being destroyed, the apparent measured Keq WOULD depend on time taken and therefore on the enzyme concentration.

Finally, I don't entirely agree with Yurii. Even in vivo many reactions are expected to go in both directions according to the location and the conditions e.g. we both reduce pyruvate to lactate under anaerobic conditions and oxidise lactate to pyruvate under aerobic conditions. But further, once we are dealing with a purified enzyme in vitro the control of individual substrate concentration and of pH allows us to play all sorts of games and drive a reaction whichever way we want. Thus alcohol dehydrogenase, for example can be used for quantitative assay of ethanol, of acetaldehyde, of NAD+ or of NADH, in every case driving the reaction to 99%+ conversion. Those, of course, are precisely the conditions you would NOT choose for measuring Keq, for the reason Yurii mentioned, but we can just as easily rig the conditions to have the reaction more evenly poised so that you can estimate all concentrations with reasonable reliability.

Paul, 

there is some misunderstanding of my answer. When I wrote "If K> 100, than the substrate conversion is >99%." I meant that the reaction starts from 100% of substrate and 0% of products. If you start from 100% of product and 0% of substrate, the reaction will proceed in opposite direction. I absolutely agree with you that "the control of individual substrate concentration and of pH allows us to play all sorts of games and drive a reaction whichever way we want." These are basics of chemical thermodynamics. The position of equilibrium depends on initial conditions. If you want to determine Keq experimentally, you have to from right initial concentrations. 

Dear Yurii,

Since my original post I had some suggestions where to find such experiments, and really equilibrium constants are quite high, but not always as high as 100. 

In our case not the "addition of the reaction product in the beginning of the reaction affects the conversion". It is the change of the enzyme concentration what affects the (apparent) equilibrium constant. If we add more enzyme, we got more products. (It is published in BBA Proteins and Proteomics 1834 (2013) 658-664.). We did not determine the Keq, sorry about it, but in usual cases (at concentrations where almost all people are measuring) around 20% of substrate is converted (it depends on initial substrate concentration as well).

It is funny, anyway, and I am wondering if other enzymes show this phenomenon. 

Thanks.

Dear Gyuri,

Thanks for the link. It was useful to check it. I can say that amilases are "normal" enzymes, nothing similar to our experiment I could find in that book.

Thank you.

Dear Paul,

I agree that one should be very careful when investigating the final equlibrium state. It can be affected by many side reactions, destroying the enzyme is just one of them. Also the substrate and the product might have such side reactions. People readily explain the unusual behaviour with such side effects. In the case of hydrogenase it was the very first objection.

Therefore it might be that a phenomenon similar to ours was just simply overlooked or explained with such a side effect, as "enzyme degradation", although it really was not. 

We were quite careful, in our case we can run the reaction back and forth several times just by changing the gas in the reaction (H2 is one of the substrates/products of the reaction). 

Dear Csaba, 

I had a quick look at your paper. I absolutely agree with your conclusion that "the reaction is not in chemical equilibrium." The products yield is controlled by kinetics

Enzymes catalyse a variety of biochemical reactions. Enzyme catalysed reactions follows Michaelis-Menten reaction mechanism : 1) a reversible 9equilibrium)step in which the substrate (S) and the enzyme (E) react  to form a transient complex [ES]  and 2) decomposition of the unstable complex to give the product (P)and releasing the enzyme.

Steady state treatment is applied to the complex ie rate of formation of [ES] =rate of removal of [ES] so that there is no buildup of the complex in the reaction system.

The rate of the reaction depends on step 2 where the product is formed . At low concentrations of the substrate , the rate is given by the equation, rate =k [S][Eo] where Eo is the amount of enzyme added initially at the start of the reaction.Thus the order of reaction is 1 with respect to the substrate.

At high concentrations of the enzyme, rate =k [Eo] .k is the rate constant for step 2.Thus the order becomes zero with respect to the substrate .

Dear Prabhu,

Thank you for your contribution.

What you described here, that is the theory. But the life is more complicated. I was asking for experimental data where this theory was checked. Can you please cite me experiments where the dependence of final equilibrium on enzyme concentration was actually measured? I would appreciate the confirmation of this theory also (I got this kind of citations too).

Dear Csaba,

I agree with you . I will be in search of some experiments where the rates have been measured and shown to obey the kinetic  equations.

With regards

Damodar Prabhu