The measurement of Km should not be affected by error in the protein concentration, but the measurement of kcat will be. If it is a soluble protein, one of the standard protein assays (Bradford, BCA, Lowry) should produce a concentration within about 2-fold of the actual concentration if a suitable standard is used (BSA, IgG). Another source of error in protein concentration could be due to an impure sample, if the protein sample is not predominantly the protein of interest. People often overestimate the purity of proteins based on SDS-PAGE. A further source of error can arise if not all of the enzyme in a sample is active. The concentration of active protein can sometimes be determined, if there is a very potent inhibitor available, by an active site titration. If the protein is meant to contain a prosthetic group but some of the protein lacks it, that will reduce the measured kcat.

The experimental conditions can have a substantial effect on kcat and Km. These conditions include temperature, pH, concentration and identity of salts, and the concentration of activators such as divalent metal ions.

If the reaction involves more than one substrate, the measurement of Km for each substrate should be done by varying the concentrations of both substrates in a matrix, and fitting the data by nonlinear regression to the appropriate rate equation. People often take a shortcut and fix the concentration of one substrate while varying the concentration of the other. This can sometimes lead to an erroneous value if there is substrate inhibition or if the concentration of the fixed substrate is not saturating. A Km measurement for one substrate made at a fixed concentration of the other substrate should be referred to as Km,apparent if it is not certain that it is the true value.

Determining the substrate concentration based on the amount of product formed can result in error if the reaction does not go to completion. This may happen if there is product inhibition or if the reverse reaction rate is favorable. To prevent these problems, it is sometimes possible to couple the formation of the product to a second reaction that consumes the product.

The measurement of Km should not be affected by error in the protein concentration, but the measurement of kcat will be. If it is a soluble protein, one of the standard protein assays (Bradford, BCA, Lowry) should produce a concentration within about 2-fold of the actual concentration if a suitable standard is used (BSA, IgG). Another source of error in protein concentration could be due to an impure sample, if the protein sample is not predominantly the protein of interest. People often overestimate the purity of proteins based on SDS-PAGE. A further source of error can arise if not all of the enzyme in a sample is active. The concentration of active protein can sometimes be determined, if there is a very potent inhibitor available, by an active site titration. If the protein is meant to contain a prosthetic group but some of the protein lacks it, that will reduce the measured kcat.

The experimental conditions can have a substantial effect on kcat and Km. These conditions include temperature, pH, concentration and identity of salts, and the concentration of activators such as divalent metal ions.

If the reaction involves more than one substrate, the measurement of Km for each substrate should be done by varying the concentrations of both substrates in a matrix, and fitting the data by nonlinear regression to the appropriate rate equation. People often take a shortcut and fix the concentration of one substrate while varying the concentration of the other. This can sometimes lead to an erroneous value if there is substrate inhibition or if the concentration of the fixed substrate is not saturating. A Km measurement for one substrate made at a fixed concentration of the other substrate should be referred to as Km,apparent if it is not certain that it is the true value.

Determining the substrate concentration based on the amount of product formed can result in error if the reaction does not go to completion. This may happen if there is product inhibition or if the reverse reaction rate is favorable. To prevent these problems, it is sometimes possible to couple the formation of the product to a second reaction that consumes the product.

Dear Dr,

beside all what Dr Shapiro has written to you, i have found such situation in my work.

My constants were different over a broad ENZYME concentration and also on other values published before.

I attach my papers and I wait when you will ready do discuss the problem.

Hi Ramesh,

I had a look at the first of your papers.

It is unusual for an unspecific hydrolase to exhibit positive cooperativity. It is even complicated to figure how this cooperative is generated because it is inconsistent. 5'AMP is degraded following MM kinetics (h~1), while 3'AMP is degraded with detectable cooperativity (h~2).

The hill coefficient has an important effect on S0.5 and is overlooked can have significant effects on the Km estimate. But the real question is what is the mechanism behind cooperativity?

One possibility is enzyme instability during assay. If the enzyme is unstable, and your assay is not performed with a continuous monitoring assay, it is frequent to overlook deviations from linearity of the [P] vs t and underestimate activity at low substrate concentrations. At higher substrate concentrations, the ligand binding will increase enzyme stability (which is the basis for temperature-shift binding assays) and will reduce the uncertainty in activity estimates.

Do careful evaluations of your activity at low enzyme concentrations following the progress curve ([P] ve t).

In particular, if we consider the linear phase of the progress curve we have:

[P]/t=ET f([S]), regardless of what form has f([S]) (Hyperbolic or not), we may write:

[P] = (f([S])) (ET) (t) ; (t>0)

If you follow the progress curve at several enzyme concentrations and then plot all the curves together in a plot of [P] against ET · t all th epoints in your plot should fall on a single line of linear shape. If it does not, this indicates your enzyme is unstable in the assay.

You can read chapter 2 of Segel, Enzyme Kinetics for other sources of non-hyperbolic v vs [S] plots.

Best wishes,

Rogelio

Dear all,

I attach an abstract of one of ny papers (2001) showing that unspecific prostatic phosphatase exhibits positive cooperativity and all kinetic constants are dependent on enzyme concentration, for each studied substrate in other manner, depending on the chemical chracter of the substrate.

Cooperative kinetics of human prostatic acid phosphatase

Abstract

The steady-state kinetics of hydrolysis reaction catalysed by human prostatic acid phosphatase (PAP) by using 1-naphthyl

phosphate, phenyl phosphate and phosphotyrosine as substrates has been studied at pH 5.5. The substrate binding curves

were sigmoidal and Hill cooperation coefficient h was higher than 1 for each of the examined compounds. Thus, human

prostatic acid phosphatase kinetics exhibits positive cooperativity towards the studied substrates. The extent of cooperativity

was found to depend on the substrate used and on enzyme concentration. The highest cooperativity of PAP was observed for

1-naphthyl phosphate and the lowest for phosphotyrosine. When prostatic phosphatase concentration increased, Hill

cooperation coefficient (h) and half saturation constant (K0:5) both grew, but the catalytic constant (kcat) remained constant,

for each of the substrates studied. Ligand-induced association^dissociation equilibrium of the active oligomeric species

(monomer-dimer-tetramer-oligomers) is suggested.

in next paapers, listed above there are another aspects of that problem.

Dear Ewa,

When I said it is unusual, I did not mean it does not happen, animal fructose-1,6-biphosphatase is one well know exception, it does exhibits a Hill coefficient of ~2 in the presence of its allosteric inhibitor AMP, and this has been widely recognized as a physiological regulatory trait.

Nevertheless, extensive characterization was required to ensure that an observed behaviour is not a side-effect of some experimental artefact.

I hope your work was carefully done, though you forgot to include the references or links to your papers.

Best wishes,

Rogelio

Dear Rogelio,

I attached the references above in my answer 12 days ago.

• 2016_Homotropic allostery of nucleotidase activity of human prostatic acid phosphatase.pdf606.69 KB
• CoopPAP.pdf223.05 KB
• JProtChem2003-01.pdf73.04 KB
• PAP2004.pdf191.84 KB

please look. i will discuss it.

if it will be needed i will attach once more

sincerely ewa

This week I will be busy, I'll take a look afterwards.

Best wishes

Rogelio

When the activity of an enzyme is determined as function of substrate concentration, Vmax is usually determined fairly accurately, but Km has a much larger standard deviation. Thus relatively large differences in Km values may not be statistically significant. If there are several substrates, this effect will be compounded.

In addition, Km is quite dependent on experimental conditions. For example, when a buffer is diluted from a stock solution without taking into account how this affects the pH, the Km may well be quite different from what one would observe with more careful experimentation.

As a colleague once said: "There are lies, dam lies and Km-values. "

While I can agree with Engelbert about uncertainty in estimates, and I could laugh at the last comment, I would not agree in equating experimental uncertainty to falsehood.

Best wishes,

Rogelio

Not if the uncertainty is acknowledged. But then it is also easy to calculate the significance of differences.

I attach a piece of my new paper (in preparation):

The values of the Michaelis constant (Km) at pH 5.0 published so far unfortunately cannot be compared because they are very scattered. They are between 0.16 mM, 0.20 mM, 0.28 mM, and 0.81 mM in acetate buffer as well as between 0.18 mM, 0.31 mM and 0.50 mM in citrate buffer.

The scattering of the previously determined enzyme-substrate affinity constant (Km) may have several various reasons. The first one may be the small differences in the experimental conditions used (composition of buffer or/and additives). The second reason of the Km variation may be the inaccurate determination of the initial reaction rate (vo) by using the one-point (discontinuous) procedures and therefore the erroneous calculation of the kinetic constants. The third reason for Km scattering can be the application of the Michaelis-Menten rate equation, describing only the hyperbolic kinetics, to fit to the experimental results of the reaction catalysed by enzyme, showing the sigmoidal enzyme-substrate saturation curves, described by the general Hill rate equation when Hill cooperativity coefficient is higher than 1. The successive fourth reason of the variations of the Km value may be the usage of the various concentration of the enzyme in the reaction mixtures, even not mentioned in most of the paper, shifting the enzyme-substrate affinity constant, as we have previously established for hydrolysis of three other phosphomonoesters [2001].

Therefore I suggest to all in such situation to start calculation only with Hill equation, because the Michaelis equation is a special case when h=1.

I have experienced this several times with very common enzymes like L-asperginase. The best and the very simplest way to find out the reason is to sequence the amino acid of the enzyme and then run BLAST-P and see the phylogenetic tree. This more than often serves as an wake up alarm (I mean how far we are from the real objective of our work or not).

I must sadly and repeatedly say that HPLC-photometric enzyme assay, which is quantitative, reliable and sensitive, should be utilized (please see file; J Chrom B rat BIN LIP Km). Direct utilization of photometer without purificatio is very dangerous due to violence against the Lambert-Beer's law. Thus, notorious ELISA method gives only the false values.

Quantitative protein determination also is surely an important issue, and please use quantitative, sensitive and quick HPLC-Surf-SEC-photometric protein determination method (please see file; HPLC-Surf-SEC protein determination method).