Enzyme Kinetics

Enzymes lower the activation energy for a specific chemical reaction

The active site of an enzyme is formed in such a way that it is highly specific as to the molecule that can enter and bind to the active site. This feature explains the specificity of an enzyme-catalyzed reaction. But the induced fit of the substrate and enzyme results in placing stress on certain bonds in the substrate. These stresses actually increase the potential energy of the enzyme-substrate complex. The increase in this potential energy means that the amount of energy required to break that particular bond...the activation energy...is reduced. The reaction proceeds and the products are released.

E + S ↔ ES* ↔ E + P

One would easily notice that this scenario means that the enzyme is not used up in the reaction, that only a small amount of any one enzyme is therefore all that is needed to produce much product, and that the ES complex formation means the enzyme will be specific as to what substrate binds, what reaction is catalyzed, and what product is made!

Because of this, enzymes are given names by the International Union of Biochemistry. Enzyme names indicate the substrate, the reaction carried out on that substrate, and an "-ase" ending. An example of an enzyme name is:

D-ribulose-1,5-bisphosphate carboxylase/oxygenase

In this case, D-ribulose-1,5,-bisphosphate is the substrate
carboxyl/oxygen refers to what kind of reaction can take place
(it can have a carbon or an oxygen added to its structure)
the -ase endings mean these are enzymes.

This example happens to be the most abundant enzyme on earth! It is the enzyme initiating the Calvin cycle of photosynthesis. It draws atmospheric carbon into the food chain for virtually all terrestrial and aquatic organisms on the planet. It is sometimes abbreviated RuBisCO.

An energy diagram helps to understand what is meant by "lowering the activation energy" (shown below). The "transition state" is the energy usually needed to break the bond for a particular reaction without enzymes. There is also a small energy yield (the difference between substrate and product). In the line showing the same reaction...but with an enzyme acting as a catalyst...an "activation energy" is shown. It is much less than the energy required for achieving the uncatalyzed transition state. Notice how the energy yield, however, is the same for both the catalyzed and uncatalyzed reactions!

What is more...the enzyme only accelerates the reaction this way. It does not determine how much product may be made in a particular system! The enzyme only increases the rate of the reaction...not the yield of the reaction.

The criticism I would level about the diagram above is that the catalyzed line in light green does not show it resulting in product yield or energy production. I will put a better diagram on the board in class.

Enzyme Kinetics

A typical enzyme accelerates the reaction in a kinetic way that can be given by what is called the Michaelis-Menten equation. If one plots the rate of an enzyme-catalyzed reaction as a function of substrate concentration, the curve has a hyperbolic shape. This shape fits the Michaelis-Menten function shown below.

In this figure, the initial velocity might be measured in moles per liter per second. The substrate concentration might be given in moles per liter. The curve is hyperbolic to a horizontal line that crosses the rate axis at a value known as Vmax...the maximum rate of the reaction. The other parameter needed for the function is the Km...the substrate concentration at 1/2 the maximum rate. The Km is typically between 10-6 and 10-3 moles per liter (M)...that is generally close to the concentration of substrates found inside cells!

Another value commonly mentioned for enzymes is the enzyme affinity for a substrate. This is basically 1/Km.

Determining Vmax and Km

Back in the old days, people made Michaelis-Menten plots and used their eye-brain combination to "fit" a curve to the plotted points. The parameters were then determined by inspection of the fitted curve. There were no "statistical" ways to do this known to biologists. Of course this had a subjective component that was not acceptable for long.

In the not-so-old days, people learned how to obtain the parameters by data transformation. A little algebra on the Michaelis-Menten function gives you:

1/V = Km/Vmax1/[S] + 1/Vmax

which can be thought of as a form of:

y = m • x + b

where 1/V is y and 1/[S] is x

This Lineweaver-Burk transformation converts the Michaelis-Menten curve into a straight line. Rather than plotting rate as a function of substrate concentration, their inverses were plotted as shown here.

You can see that the hyperbolic curve becomes a straight line. What is even more helpful is that the absolute value of the x-intercept of this line is the affinity (1/Km) of the enzyme for the substrate. The y-intercept is 1/Vmax (note the sign-error in the pdf file!). The slope of the line is Km/Vmax. Again, originally this was done subjectively. Later, computers permitted least-squares fit of linear models to data (linear regression); this statistical process removed the subjective component.

Today, people use either linear regressions on Lineweaver-Burk transformed data or they do non-linear regression of raw data to fit to the Michaelis-Menten function. In our laboratory exercise, we will use this much finer method for finding the best-fit parameters for the untransformed Michaelis-Menten relationship.

Enzyme catalyzed reactions can be inhibited competitively

Enzymes can be altered in various ways. One way, is by competition between the substrate and a molecular analog called a competitive inhibitor. The competitive inhibitor is so similar to the substrate that it binds at the active site and accomplishes some kind of induced fit with the enzyme. However, the competitive inhibitor is different enough that it cannot react in the same way as the substrate. So no chemical reaction occurs, no product is formed, the inhibitor is released unchanged, as is the enzyme. This relationship can be depicted as:

E + I ↔ EI

Be sure to take special note of the bidirectional arrow. The enzyme-inhibitor complex falls apart without forming a product.

This competitive inhibition does not occur in isolation. Generally the reaction system looks more like this:

E + S + E + I + S + E + I + E ↔ ES* ↔ E + P

Obviously there is a mixture of substrate and inhibitor present in the cell and these compete for a position in the active site of the enzyme. Obviously the frequency that the substrate occupies the site will be determined by how abundant the substrate is compared to the inhibitor. If the substrate is present in relative abundance then the rate of the reaction will be the same as if the inhibitor were absent. In other words, the presence of a competitive inhibitor does not change the Vmax. The presence of the competitive inhibitor does, however, reduce the affinity (1/Km)of the enzyme for the substrate...and thus the Km is increased. It takes more substrate to reach half of Vmax. This increase in Km will also increase the slope (Km/Vmax) of the line in a Lineweaver-Burk plot.

Again, if one measures the rates of reaction systems with various substrate concentrations and repeats those in the presence of the inhibitor, then a plot like the one above can be made. Linear regression software can produce the least-squares best-fit line for you, and present you with the y = mx + b form of that line. Solving that for x=0 and y=0 can give you the intercepts from which the Vmax and Km can be determined. If the Vmax is the same in the presence and absence of the inhibitor, and the Km increases in the presence of the inhibitor, then you have great evidence for a competitive inhibitor.

An example of an enzyme regulated by competitive inhibition in plants (perhaps to the benefit of people) is 5-enolpyruvylshikimate-3-phosphate (EPSP) synthase. This enzyme is critical in the synthesis of aromatic amino acids (phenylalanine and tyrosine). Without these amino acids, a plant cannot translate complete proteins. Severe symptoms of yellowing, wilting, and death follow. People can spray plants with glyphosate (Roundup™: HOOC-CH2-NH-CH2-PH2O3) which competitively inhibits this enzyme activity and brings on the symptoms of aromatic amino acid deficiency and death. Thus glyphosate can be used as an herbicide (vegetation killer). Because humans do not have EPSP synthase, it is "safe" to use compared to most other herbicides. Biologists have inserted extra copies of EPSP synthase genes into the genome of crop plants behind a constitutive promoter. This causes the transformed plants to over-produce EPSP synthase, swamping out the effect of any glyphosate sprayed on them. This way the engineered crop plants can be grown in a weed-free field using a relatively safe herbicide. Of course if the crop plant has wild relatives nearby, the genes for this herbicide resistance could be passed to the wild relatives producing herbicide resistant weeds.

Enzyme catalyzed reactions can be inhibited non-competitively

Another way to inhibit a enzyme-catalyzed reaction is by use of a non-competitive inhibitor. This kind of molecule binds to the enzyme somewhere besides at the active site. This binding therefore does not interfere with the affinity (and therefore Km) of the enzyme for the substrate. What inhibitor binding does is to alter the effectiveness of the other functional groups of the enzyme in catalyzing the reaction through poorer induced fit. This will, of course, reduce the Vmax possible. This kind of relationship is depicted below.

Enzymes that are allosterically regulated often work in this non-competitive way. Once an enzyme has been "deactivated" this way, no amount of substrate will increase the rate of reaction back to normal. The only solution is to metabolize the inhibitor, thereby restoring normal conformation of the enzyme and normal rates of reaction.

Enzyme activity is pH sensitive

As a protein, made of some 20 different amino acids in primary structure that end up producing the secondary, tertiary and quaternary structure, its conformation is pH dependent. Some of the amino acids have R groups with imidazole (his), carboxyl (asp, glu) or amino (lys, arg).

These groups can gain or lose a proton (H+) with changes in pH, and thereby change in charge. This change in charge will, very likely, alter the conformation and thereby activity. This is demonstrated above. The equilibrium is shifted to the left when acids are increased (low pH)
It is shifted to the right when acids are decreased (high pH)

Thus conformational changes induced by pH will of course change the reaction rate as exemplefied below.

The inflection points on each side of the curve represent the pKa of the critical R-groups in the enzyme. The pH that gives the maximum rate (at the peak of the curve) is called the optimum pH.

Enzyme activity is temperature-sensitive

As with all proteins, the conformation is sensitive to temperature. As with all chemical reactions, the enzymem catalyzed reactions are temperature sensitive. This relationship is shown below.

This bell-shaped curve is superficially similar in overall shape to that induced by changes in pH. Close examination of the left side of the curve shows that it is exponential. Higher temperatures accelerate the catalytic effect. This relationship continues up to the optimum temperature. However, increasing the temperature beyond this optimum (usually by about 10° C) denatures the conformation of the enzyme. The activity at these super-optimal temperatures falls precipitously to 0. For typical plant enzymes, the optimum is between 40 and 50 °C and denaturation is complete between 50 and 60 °C.

Substrate concentration is not a likely regulatory factor in cells

In most plant cells, it is impossible to control the reaction rate by regulating the concentration of the substrate. It takes an 81-fold increase in the substrate concentration to change the rate of an enzyme-catalyzed reaction from 0.1 x Vmax to 0.9 x Vmax. I will try to explain that here.

If you do some algebra on the Michaelis-Menten function you get:

0.1 Vmax = Vmax[S]/Km + [S]       0.9 Vmax = Vmax[S']/Km + [S']

Now multiply both sides by the denominator and by 1/Vmax:

0.1 (Km + [S]) = [S]       0.9 (Km + [S']) = [S']

Now distribute the decimal and subtract the resulting substrate concentration from both sides:

0.1 Km = 0.9 [S]       0.9 Km = 0.1 [S']

Now combine the two equations as a ratio:

0.1 Km/0.9 Km = 0.9 [S]/0.1 [S']

The Km cancels out on the left side. You can then multiply both sides by [S'] and simplify:

[S'] = 81 [S]

It takes 81 times as much substrate to get from a rate of 0.1 to 0.9 times Vmax. This kind of range is not expected physiologically for very many natural substrates. Obviously enzyme-catalyzed reactions are not sensitive to small changes in substrate concentration.

Most enzyme systems are allosterically regulated

Typical enzymes then must be regulated by the presence and absence of allosteric regulators that either activate or inhibit the reaction. This relationship is shown below.

In the case of an activator, the binding of the activator increases the chance of binding of the substrate. In the case of an inhibitor, the binding of the inhibitor decreases the chance of binding of the substrate.

Great examples of allosteric regulation are described throughout plant physiology. Perhaps the best-know examples are phosphofructokinase (fructose-6-phosphate-2-kinase in glycolysis) and fructosephosphatase (fructose-1,6-bisphosphatease in gluconeogenesis). This case is shown below:

In this system of two enzymes, Fructose-6-phosphate and Fructose-1,6-bisphosphate are interconverted. The relative rates of the forward and reverse reactions are allosterically regulated by feedback inhibition by: either substrate, ATP, AMP, and Pi. The enzymes are also regulated by dihydroxyacetonephosphate and 3-phosphoglycerate and even citrate. WOW! This is obviously a control point in both biochemical pathways.

Enzyme systems can be regulated by enzyme concentration

Obviously transcription and translation can increase the enzyme concentration and because these catalysts are efficient at very low concentration, the rate of reaction is very sensitive to enzyme concentration. The degradation of enzymes by proteases is the back-side of this regulation.

Enzymes can be modified or phosphorylated

Enzymes are sometimes inactive right after translation. To become activated these must be either modifed (some peptide bonds cleaved or covalent ligands added) or phosphorylated by reaction with ATP, GTP or other triphosphates.

Enzyme systems can be regulated by compartmentalization

In many cases the enzyme is in an active conformation but no reaction occurs...that is because the substrate is in one membrane-bound compartment in the cell and the enzyme is found in the another compartment.

A great example of this is kind of control is found in the case of polyphenoloxidase. This reaction converts polyphenols into brightly colored products. Normally the polyphenols are found in the vacuole with other phenolic compounds (toxic to most cytosolic functions). Polyphenoloxidase is found in the cytosol. Thus the substrate and the enzyme never meet unless the cell is wounded. Upon wounding, the vacuole is ruptured, the polyphenol is mixed into the cytosol, the polyphenoloxidase catalyzes the reaction of the polyphenol with oxygen to produce a quinone. The quinones polymerize into brightly colored products. This was the basis for our lab exercise.