Michaelis-Menten Constant

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Michaelis-Menten Constant

Introduction

We all know that enzymes are the natural catalysts that are present in all the living cells. They are necessary for all the metabolic reactions. Specific substrate molecules bind the enzyme at the active site and get converted into the products.

Several models have been put forward to explain the enzyme kinetics. One of such models is called Michaelis-Menten enzyme kinetics. This model was put forward by two scientists: Leonor Michaelis from Germany and Maud Menten from Canada. This enzyme kinetic model explains the rate of enzyme action as a function of substrate concentration. The equation of rate of reaction uses a constant called Michaelis-Menten constant.

In this article, we will study Michaelis-Menten constant in detail. We will discuss its definition, derivation, factors affecting Michaelis-Menten constant, and various examples from metabolic reactions taking place in living organisms.

Definition

Michaelis-Menten constant is defined as a substrate concentration at which the rate of reaction is half than the maximum rate that can be achieved under the given conditions. It is denoted by symbol Km. In other words, it is a substrate concentration at which the rate of reaction is half than the Vmax.

It is a substrate concentration at which half of all the active sites of enzyme are covered by substrate molecules. Michaelis-Menten constant represents that affinity of enzyme for the substrate molecules.

If the enzyme has high affinity for substrate, less substrate concentration will be needed to occupy half of the active sites of enzymes and thus, the value of Km will be low.  Contrary to this, if the enzyme has less affinity for its substrate, more substrate concentration will be needed to occupy half of the active sites and the value of Michaelis-Menten constant will be high.

Different factors affecting the value of Km will be discussed later.

Derivation

The value of Michaelis-Menten constant (Km) can be obtained by plotting double reciprocal graph of substrate concentration against the rate of reactions. In this graph, the reciprocal of substrate concentration is plotted along x-axis and the reciprocal of rate of reaction is plotted against y-axis. The graph is extrapolated to meet the x-axis.

The intercept on x-axis gives the reciprocal of Km. Thus, the value of Km can be calculated using this graph. This plot is known as Lineweaver-Burke plot.

It should be kept in mind that the value of Km is different for different enzyme. Each enzyme has different affinity for its substrate and thus have a different Km value. Moreover, the value of Km is also different for different isozymes of the same enzyme. This is seen in the case of enzymes like hexokinase. The example of hexokinase will be discussed later.

Characteristics

Michaelis-Menten constant is very important to understand the kinetics of various enzyme catalysed reactions. Some of the important characteristics of this constant are mentioned below.

Signature of Enzyme

Michaelis-Menten constant is specific for each enzyme. In cases where one enzyme has more than one substrate, each substrate has its own specific Km value. The value of Km is specific and constant for each enzyme keeping the other factors neutral.

Independent of Enzyme Concentration

It should be noted that the value of Km is independent of the concentration of enzyme. Its value does not increase or decrease with changing the enzyme concentration.

It is because an enzyme will have same affinity for its substrate under the given conditions, no matter the enzyme is present in low or high concentration. Thus, the value of Km remains unaffected.

Factors affecting the Value of Km

The value of Michaelis-Menten constant depends on a number of factors such as pH, temperature, etc. A brief detail of these factors is given below.

Effect of pH

Enzymes are very sensitive to the pH of the working environment. Any change in pH drastically affects the activity of enzymes. Any change in pH affects the ionization state of amino acids at the active site of enzyme.

Enzymes have maximum affinity for substrates at the optimum pH. Thus, the value of Michaelis-Menten constant for each enzyme will be lowest at its optimum pH. Any change in pH will decreases the enzyme affinity and thus the Km value will increase.

The exact pattern of change in the value of Km with changing pH is still unknown. It is different for different enzymes.

Let us study pepsin as an example. Pepsin is a protein digesting enzyme found in the gastric juice. This enzyme works only in the acidic environment. It has optimum pH between 1.0-2.0. Thus, it will have lowest Km value in this pH range, indicating the maximum affinity of enzyme. If the pH increases to 3.0, pepsin becomes inactive and the value of Km drastically increases, indicating decreased affinity for substrate.

Effect of Temperature

Enzyme also require optimum temperature for their optimum function. Contrary to optimum pH that is different for each enzyme, all the enzyme in an organism has one optimum temperature. For example, the enzymes in human body work best at 37 degrees Celsius.

An enzyme has maximum affinity for its substrate at the optimum temperature. Thus, the value of Michaelis-Menten constant will be lowest. However, change in temperature has different affects on the value of Km.

If the initial temperature is less than the optimum temperature, increase in temperature will decrease the value of Km. It is because the reaction medium becomes closer to the optimum temperature and the affinity of all enzymes increases. The opposite is true for decrease in temperature.

However, if the temperature is increased above the value of optimum pH, the value of Km increases. It is because the increasing temperature decreases the enzyme affinity. A very sharp increase in Km value has been noticed as the temperature approaches the denaturation temperature. It is the temperature at which the enzyme loses its structure and becomes denatured.

Effect of Ionic Strength

The presence of certain types of ions or salts in the working medium also affects the enzyme affinity and thus, the value of Michaelis-Menten constant. It has been demonstrated in a study where scientists compared the proteolytic activity of a protease enzyme found in HIV. The study concluded that the Km value becomes drastically changes by increasing or decreasing the ionic strength of different salts present in the reaction medium. Any more details will be unnecessary at this level.

Nature of Substrate

This factor is important to consider if one enzyme is shared by two or more substrates. An important example can be seen in enzyme called hexokinase. It is an enzyme that causes phosphorylation of hexose sugars including glucose, galactose, fructose etc.

In this case, enzyme will have more affinity to one of the substrates and thus, the value of Km will be low for that specific substrate. Taking the example of hexokinase, this enzyme has maximum affinity for glucose and thus low Km for this substrate as compared to others.

Many such examples of nature of substrate affecting the value of Km can be seen in metabolic reactions taking place in the human body.

Study of Hexokinase Isozymes

The hexokinase isozymes can be studied as an example, in order to understand the concept of Michaelis-Menten constant.

As we already know, hexokinase causes phosphorylation of hexose sugars like glucose, fructose, galactose, etc. This enzyme is used in the reactions of glycolysis. It has four isozymes. Hexokinases I-III are similar in action while hexokinase IV is different to some extent. Both these types are briefly discussed below.

Hexokinases I-III

In most of the tissues, the hexokinases I-III cause the phosphorylation of glucose. These isozymes have broad substrate specificity and thus can also phosphorylate other hexoses.

As compared to other hexose sugars, hexokinase I-III have low Km value for glucose. It shows that these isozymes have very high affinity for glucose. They can cause phosphorylation of glucose even at very low concentrations. It is because only a small amount of glucose molecule is needed to cause saturation of half of the active sites of enzymes.

Thus, these isozymes are able to cause phosphorylation even at low glucose concentration within the tissues. They permit the glycolytic process to occur even at low concentrations of glucose.

Hexokinase IV or Glucokinase

This isozyme is also called glucokinase. It is predominantly present in the liver parenchymal cells as well as in the beta cells of pancreas. This enzyme also has same broad substrate specificity for other hexose sugars as the other three isozymes.

Glucokinase differs greatly from hexokinases I-III in terms of kinetic properties. It has a high Km value for glucose. It indicates that the enzyme has low affinity for glucose at lower concentrations. It needs very high concentrations of glucose to cause phosphorylation.

Because of this property, glucokinase performs following important roles:

  • It causes glycolysis to occur in the hepatocytes even in the state of hyperglycaemia. It is because the enzyme can work only when the concentration of glucose within the hepatocytes is very high. Under low concentrations, the active sites of enzyme will not be saturated.
  • It acts as a glucose sensor in the beta cells of pancreas for the release of insulin. The enzyme is activated by high glucose concentrations and triggers the release of insulin from pancreas.
  • It also serves as a glucose sensor in cells of hypothalamus, causing an inhibiting effect on the adrenergic response to a hypoglycaemic event.

Inhibitors and Michaelis-Menten Constant

An inhibitor is a substance that can decrease the rate of an enzyme catalysed reaction. The inhibitors may be reversible or irreversible.

An inhibitor is said to be reversible if its affect on the enzyme can be reversed. Such inhibitors bind to enzyme via non-covalent bonds that can be overcome easily.

An irreversible inhibitor is one whose effect cannot be reversed. Such an inhibitor binds to the enzyme via strong covalent interactions.

Different types of inhibitors have different affect on the value of Km. It is important to understand the following two types of inhibitors while studying the Michaelis-Menten constant.

Competitive Inhibitor

Such inhibitors have structural similarities to the original substrate. Thus, they bind to the same site on enzyme as the original substrate i.e. the active site. In this way, the inhibitor molecules compete with the original substrate molecules to bind the active site.

The effect of a competitive inhibitor can be overcome by increasing the concentration of substrate.

Effect on Km

Competitive inhibitors block the access of substrate molecules to the active site. These inhibitors increase the Km value of the enzyme for the substrate. It means that in the presence of a competitive inhibitor, more substrate molecules are needed to reach half Vmax.

Effect on Lineweaver-Burk plot

As mentioned earlier, Lineweaver-Burk plot is used to obtain the value of Km. In the presence of a competitive inhibitor, the shape of this plot also changes. If we compare the plots in the presence and absence of competitive inhibitor, both of them would be seen intersecting at the y-axis. However, the inhibited and uninhibited reactions show different x-intercepts.

In the presence of a competitive inhibitor, the x-axis intercept moves close to zero.

Example

Succinate dehydrogenase is an enzyme that catalyses oxidation of succinate to form fumarate. The active site of this enzyme can be occupied by malonate, that have a structure similar to succinate. The binding of malonate results in the formation of an enzyme inhibitor complex. The succinate molecules do not find any site to get attached to the enzyme and thus, the reaction is stopped.

Non-Competitive Inhibitors

These inhibitors bind to the enzyme at a site other than the active site. The active site is free for the substrate molecules to attach. The binding of inhibitor causes some structural changes in the enzyme and the reaction stops.

The non-competitive inhibitors can bind to a free enzyme or an enzyme-substrate complex. The effect of such inhibitors cannot be overcome by increasing the substrate concentration.

Effect on Km

As the non-competitive inhibitors bind the enzymes at a site other than the active site, they do not affect the binding of substrate molecule. Thus, the affinity to enzyme for the substrate remains the same in the presence or absence of such an inhibitor. They have no effect on the value of Km.

Effect on Lineweaver-Burk Plot

Although these inhibitors do not affect the value of Km, they decrease the Vmax of the reaction. Therefore, some changes are seen in the Lineweaver-Burk plot.

If the plots of inhibited and non-inhibited reactions are compared, the reaction occurring in the presence of inhibitor has a y-intercept away from the zero value.

Example

Inhibition of ferrochelatase enzyme by lead is an example of non-competitive inhibition. It is an enzyme used in the synthesis of heme portion of haemoglobin. It causes transfer of iron to the porphyrin ring to finally form heme.

Lead binds to ferrochelatase at a site other than the active site and stops the reaction. The affinity of enzyme for its substrates remains the same. The effect of lead cannot be overcome by increasing the concentration of substrate molecules.

Significance

Michaelis-Menten constant has various applications in the study of metabolic reactions in the living systems. Here, we will discuss how knowing the value of Km will help us in better understanding the metabolism.

Designing Computerised Models

The value of Km helps us understand the behaviour of enzyme in the presence of various substrates. Using this knowledge, the scientists might be able to design the computerised models of metabolic reactions or even an entire cell with the technological advancements. These models can then be used to assess the consequences of changing conditions like temperature, pH, ionization, substrate saturation, etc. This will provide a better understanding of cells from a metabolic point of view.

Comparison of Substrate Preference

As we know, the value of Km indicates the affinity of enzyme for its substrates. If more than one types of substrate are available, it will provide us a clue about the substrate that is going to be consumed earlier in a reaction due to its high affinity. An example of this has been demonstrated in relation to the isozymes of hexokinase.

This information can prove much beneficial in biotech industries where different enzymes are used for various purposes that will benefit the mankind.

Making Better Catalysts and Inhibitors

The information regarding the affinities of enzymes for a substrate and the factors affecting them can help in making better catalysts to be used in biotech industry. Different types of inhibitors can also be made as per need of the hour.

This is specifically important for the pharmaceutical industry where various drugs are made that work by altering the affinities of enzymes catalysing reactions in the human body.

Comparing the Enzyme Efficiency

The Km value helps us to compare the efficiency of two or more enzyme for the same substrate. This information can prove useful in the case of commercially used enzymes. One would be able to choose an enzyme with better and early results by comparing the Km values.

Application to other Reactions

The use of Michaelis-Menten constant is not limited to enzyme catalysed reactions only. Its use can be extended to other reactions such as binding of an antigen to its antibody, etc. Thus, it can be used to study several other important reactions.

Calculating the Active Sites

Recall that Km is the substrate concentration at which half of the active sites are occupied by the substrate molecules. This information can be used to calculate the state of active sites at any substrate concentration using simple mathematical techniques.

Clinical Significance

Mutation in pyruvate dehydrogenase enzyme changes its Km value in some cases. Pyruvate dehydrogenase is an enzyme complex consisting of multiple copies of three enzymes. These enzymes are involved in causing oxidative decarboxylation of pyruvate molecules and incorporation of CoA converting them into acetyl CoA molecules.

One type of mutation in pyruvate dehydrogenase complex decreases its affinity for coenzyme, thus increasing the Km value. It has been noted in some but not all the cases of mutation. This mutation also causes the deficiency of enzyme complex. The aerobic oxidation of glucose in such individuals is highly affected as they cannot covert all the pyruvate molecules into acetyl CoA for entering into the citric acid cycle.

Summary

  • Michaelis-Menten constant is substrate concentration at which half of the active sites are occupied by substrate molecules.
  • It represents the affinity of enzyme for its substrates. Higher the value of Km, lower is the affinity and vice versa.
  • The values of Km can be obtained by double reciprocal plot of substrate concentration against the rate of reaction, also called the Lineweaver-Burk plot.
  • Each enzyme has its specific Km value that is independent of the concentration of enzyme.
  • The value of Km is minimum at the optimum pH of an enzyme. It increases with changes in the pH of environment.
  • Michaelis-Menten constant value decreases if the temperature is increased till the optimum temperature. Any further rise in temperature will decrease the enzyme affinity, increasing the value of Km.
  • The presence of different ions also affects the value of Km.
  • In some cases, the value of Km varies with the nature of substrate.
  • Hexokinase has four isozymes. Hexokinase I-III have low Km value for glucose while hexokinase IV has high Km value.
  • Hexokinase IV functions as glucose sensor in beta cells of pancreas as well as cells of hypothalamus.
  • Competitive inhibitors increase the Km value of enzyme and cause the x-intercept in Lineweaver-Berk plot to move closer to zero. It is because they decrease the affinity of enzyme.
  • Non-competitive inhibitors cause no effect on the Km value. However, they decrease the Vmax and cause the y-intercept in Lineweaver-Berk plot to move away from zero.
  • The value of Km has various industrial significance. It can be used to design computerised models, compare substrate preferences, compare enzyme efficiencies, make better drugs, etc.
  • Mutation in PDH complex causes a decrease in the affinity of pyruvate dehydrogenase for one of its coenzymes.

References

  1. Srinivasan, Bharath (2020-09-27). “Words of advice: teaching enzyme kinetics”. The FEBS Journal. doi:10.1111/febs.15537ISSN 1742-464X.
  2. “Substrate Concentration (Introduction to Enzymes)”www.worthington-biochem.com.
  3. Chen, W.W.; Neipel, M.; Sorger, P.K. (2010). “Classic and contemporary approaches to modeling biochemical reactions”. Genes Dev. 24 (17): 1861–1875. doi:10.1101/gad.1945410PMC 2932968PMID 20810646.
  4. Laidler K.J. and Meiser J.H. Physical Chemistry(Benjamin/Cummings 1982) p.430 ISBN 0-8053-5682-7
  5. Lehninger, A.L.; Nelson, D.L.; Cox, M.M. (2005). Lehninger principles of biochemistry. New York: W.H. Freeman. ISBN 978-0-7167-4339-2.