Enzymes & enzyme kinetics

Introduction

Now we turn our attention to proteins that possess catalytic activity: enzymes. Very few biochemical reactions take place without enzymes. The key to enzyme function rests in the ability of these proteins to make otherwise slow and unfavorable reactions proceed at rates greater than 1 million-fold faster compared to no enzyme at all.

In fact, reactions that might take hours or days occur in less than one second when catalyzed by the appropriate enzyme. This lecture will focus on some of the general features of enzymes, how they are regulated, and some of the ways in which biochemists try to characterize enzyme kinetic properties.

The range of enzyme-driven events that take place in an organism is enormous. Enzymes can catalyze reactions as simple as adding a phosphate group to its substrate (the biological "target" of an enzyme) to replication of the entire genome.

Enzymes control cellular metabolism and cell division. As such, normal cell physiology is highly dependent on the proper function of enzymes. As an example, the molecular basis of many cancers can be traced to inappropriate actions of particular classes of enzymes, including kinases and GTPases, that can induce uncontrolled cell growth signals and lead to loss of regulated proliferation.

Given the central role that these proteins play in biology, then, we as scientists can't help but be intensely interested in how they work and what their place is in cell biology. In this lecture, I will attempt to present the nuts-and-bolts of enzyme function. However, as our discussions during the course expand into larger systems within the cell our view of these proteins will, hopefully, be more holistic in terms of their relevance to cell function.

Catalytic power & specificity of enzymes

As I mentioned above, enzymes derive tremendous catalytic power from dramatic acceleration of normally slow biochemical reactions. Enzymes are also usually highly selective in terms of their substrates, be it another protein or other compound such as lipids, sugars, or nucleic acids.

However, degrees of specificity exist within particular classes of enzymes. Let's consider proteolytic enzymes. These are enzymes that cleave peptide bonds and, thus, function by breaking down proteins.

Some of these enzymes, such as subtilisin, will cleave peptide bonds regardless of the specific amino acids that are joined by that particular bond. Trypsin, on the other hand, only cleaves peptide bonds on the carboxyl-side of lysine and arginine residues.


trypcleav

Thrombin, an enzyme involved in blood clotting, is even more specific since it cleaves peptide bonds between arginine and glycine when these residues are found within a certain, larger peptide sequence.

thromcleav

Another example of a highly specific enzyme is DNA polymerase I which synthesizes DNA from a single stranded DNA template. This enzyme is very good in generating an accurate nucleotide sequence because it contains an editing function that corrects any misincorporated base into the sequence. Thus, the wrong nucleotide is inserted into the newly synthesized strand less than once in a million times (nucleotides).

Enzyme regulation

Regulation of enzyme systems provides the basis for higher order control of biological responsiveness (i.e., cell growth, differentiation, movement, etc.). There are several ways in which enzyme activity is regulated and these include:

Good examples of this are some of the amino acid biosynthetic pathways found in bacteria. Threonine is converted into isoleucine in several steps; the first enzyme in the pathway is threonine deaminase.

The enzyme is inhibited when the intracellular concentration of isoleucine reaches a sufficiently high level. Isoleucine inhibits by binding to a regulatory site that is distinct from the catalytic site of the enzyme.

This inhibition is mediated by an allosteric interaction that is reversible. When isoleucine levels drop, threonine deaminase is active once more and initiates new synthesis of isoleucine.

One example of a regulatory protein is the calcium binding protein, calmodulin. Calmodulin contains four calcium binding sites that, when occupied, alter its conformation.

This change in shape imparts regulatory activity upon calmodulin such that it can modulate the activities of kinases, adenylate cyclase (which produces cyclic-AMP), and many other proteins within the cell.

This is a theme that you will see time and time again during this course.

Perhaps one of the most classic examples of enzyme regulation through covalent modification is found in the metabolism of glycogen.

The activities of several enzymes are controlled via protein phosphorylation. The hormone, epinephrine (adrenaline), simultaneously promotes the breakdown of glycogen into glucose while inhibiting glycogen synthesis.

Epinephrine binds to cell surface b-adrenergic receptors that activate adenylate cyclase (through a G protein, called Gs) and results in increased cyclic-AMP (cAMP) production.

Cyclic-AMP binds to and turns on a serine/threonine kinase, called cAMP-dependent protein kinase (or PKA), that phosphorylates glycogen phosphorylase kinase (activates) and glycogen synthase (inactivates).

Glycogen phosphorylase kinase activates yet another kinase, glycogen phosphorylase, that in turn initiates the breakdown of glycogen into glucose.

glycogenolysis

Examples of this type of regulation can be found with the digestive enzymes, such as chymotrypsinogen (the zymogen).

This active form of chymotrypsinogen is called chymotrypsin.  Interestingly, the 3 chains that are eventually produced can be assembled to form the active enzyme.



proactchym


Another example of proteolytic activation is the well-characterized blood clotting cascade. This pathway involves cleavage of precursor proteins with the cleaved products catalyzing the activation/cleavage of other factors "downstream" in the cascade.

bloodclottingcasc



Kinetic properties of enzymes

 

The kinetic properties of many enzymes have been extensively characterized. Understanding these properties has enabled those interested in them to better understand the catalytic nature of these proteins and, in some cases, devise therapeutic strategies aimed at regulating enzyme function for the purpose of treating certain diseases. The following points regarding enzyme function will be addressed in this lecture:

Equilibria can be described in terms of equilibrium constants that define the rates of the forward and reverse reactions.

As we said earlier, enzymes can accelerate the rate of a reaction. However, enzymes do not alter the equilibrium of the reaction. In other words, an enzyme accelerates the forward and reverse reactions by precisely the same factor.

In the example below, interconversion of A and B occurs with defined forward and reverse rate constants with the equilibrium constant of B 100 times that of A whether enzyme is present or not.

However, it may take a long time (hours or days) to approach this equilibrium in the absence of enzyme, while equilibrium is attained rapidly (less than a second in many cases) when the enzyme is present.

Put another way, enzymes accelerate the attainment of equilibria but do not shift their position.

 

Think of it as an activation barrier or the "hump" a chemical reaction needs to get over in order to form P. The term, DG+, refers to the difference in free energy between the transition state and the substrate. Basically, enzymes work by decreasing DG+, the activation barrier, facilitating more rapid formation of P. The combination of enzyme and substrate creates a new reaction pathway whose transition state energy is lower than that of the reaction in the absence of enzyme.

 

Enzymes get much of their catalytic power by bringing in a substrate molecule at a "favorable" orientation.

In other words, enzymes can (as mentioned above) form an ES complex leading to reduction in the free energy required to convert S into P by way of the transition state.

At constant enzyme concentration, the reaction rate increases with increasing substrate concentration until a maximal velocity (Vmax) is achieved.

This is an important distinction versus uncatalyzed reactions, which do not exhibit this saturation effect.

Leonor Michaelis (1913) interpreted this effect to mean that ES complexes are formed until substrate saturation occurs and the increasing velocity ultimately reaches a plateau or maximum.

A number of general features have been described for catalytic sites:

The catalytic site is relatively small compared with the rest of the enzyme. Why are enzymes so big, then?

The catalytic site is a three-dimensional entity: enzyme active sites are made up of amino acids that, in the linear sequence, can be far away from one another. Remember that proteins exist in a folded, three-dimensional conformation and as such amino acids that are far from one another in the primary (linear) sequence can be close to one another in the folded protein. The same holds true for enzymes and there are often key amino acids that participate in catalysis that reside at quite a distance from one another in the linear sequence but are spatially close together in the 3-D version of the enzyme. The example , below, that illustrates this is seen with  the hydrolytic enzyme, lysozyme.

asolys 

Related to this first point is the idea that particular amino acids that participate in catalysis are arranged spatially in such a way that catalysis can occur. Furthermore, because the active site is often exclusive to the outside environment (see below) this allows for these critical amino acids within the active site to assume special properties (i.e., catalytic) that they might not, otherwise (in a different local environment) have. The example below shows a ribbon diagram of the enzyme, cytochrome P-450, with a blow-up view of the catalytically relevant amino acids spatially arrayed about the substrate (camphor). Note that the active site resides deep within the enzyme and that the 3-D conformation of the active site is reflected in the specific positions of the amino acids shown.

ascytop450

Substrates are bound to enzymes by multiple weak interactions: interactions between an enzyme and its substrate involve relatively weak, non-covalent bonding. These interactions typically include electrostatic bonds, hydrogen bonds, van der Waals forces, and hydrophobic interactions. The enzyme and the substrate often have complementary shapes that allow for these interactions to take place.

HBribo

However, the cleft can also contain polar residues that create a microenvironment with these amino acids taking on catalytic properties. This is an important exception to the rule that the core of a protein is primarily made up of hydrophobic residues.

 

The "lock and key" hypothesis, described over 100 years ago by Emil Fischer, is amazingly close to the actual mechanism of enzyme-substrate interaction.

l&k

A more refined model has been proposed, called the "induced fit" model. Essentially, an enzyme assumes a complementary shape to that of its substrate only after the substrate binds to the enzyme. This is a more dynamic scenario compared to the lock and key hypothesis.

 if

When enzyme concentrations are constant, V is linearly proportional to [S] WHEN [S] IS SMALL. At high [S] (i.e., when S is in vast excess of the enzyme concentration), V is nearly independent of [S].

The key element of their interpretation is the existence of the ES complex described earlier and is described in the equation below:

In the equation, ES is formed from E and S at a certain rate (k1) and this reaction is reversible (k2). So, the ES complex has two possible fates, it can dissociate to form E and S or it can proceed to form product at a certain rate (k3). This assumption is valid in the initial stages of a reaction, when [P] is still relatively low.

Combining experimental observation with mathematical principles, the so-called Michaelis-Menten equation was derived (for this class, I do not expect you to know how to derive the equation nor memorize it). However, I do want you to know what Vmax and Km mean (described below).

From the Michaelis-Menten equation, two terms (Vmax and Km) have been described.

Km is the Michaelis constant and can be defined as the substrate concentration at which the reaction rate is half of its maximal value. In practical terms, Km has often been used to define the relative affinity of an enzyme for its substrate. Thus, the higher the Km value the lower the affinity and vice versa. Km values can vary significantly.

 Vmax is a value that essentially describes the maximal rate of product formation when [S] is high (i.e., in vast excess of enzyme). Under these conditions, all of the active sites of an enzyme are occupied.

If one looks at enzyme catalysis under conditions in which the [S] is varied, the Vmax and Km values can be determined. By varying the concentration of S and looking at the amount of product formed, the data can be expressed as 1/V versus 1/[S] in a double-reciprocal plot (sometimes called a Lineweaver-Burk plot).

Plotting the data like this gives a straight line with a Y intercept of 1/Vmax and a slope of Km/Vmax. Where the line intercepts the X axis is 1/km. Use of the double-reciprocal plot can also help characterize the mechanisms of enzyme inhibition by specific compounds (see below).

 drp

ckv
Our discussion of Michaelis-Menten kinetics does not extend to all enzymes in nature. For instance, allosteric enzymes do not conform to these kinetic properties. Instead of seeing a hyperbolic curve in a V versus S plot (as you would under Michaelis-Menten conditions), allosteric enzymes yield a sigmoidal plot (which is also seen with non-catalytic allosteric proteins, like hemoglobin).

This type of curve may sometimes (but not always) be indicative of cooperative binding of substrate to enzyme. Thus, binding of one molecule of S can affect the affinity (usually increased) and binding kinetics of additional S molecules. Additionally, regulatory molecules can further alter the activity of allosteric enzymes.

 alloenz


cvnc

What this means is that competitive inhibitors do not alter Vmax, but they increase Km. Thus, competitive inhibitors block substrate binding to the active site of the enzyme. Furthermore, competitive inhibition can be overcome by increasing substrate concentration.
ci

Some examples of competitive inhibitors:

1.) Alcohol and inhibition of alcohol dehydrogenase in automobile antifreeze poisoning:

A practical application of competitive inhibitors of enzymes involves treatment of ethylene glycol (EG) poisoning. EG is a constituent of automobile antifreeze. Although not toxic itself, EG is converted to oxalic acid which forms crystals in the kidneys leading to extensive tissue damage.

The first step of conversion of EG to oxalic acid is its oxidation to an aldehyde by alcohol dehydrogenase. This reaction can be inhibited by administering a dose of ethanol which competes with EG for binding to the alcohol dehydrogenase.

 2.) Inhibition of RNase using a uricil analogue, UpCA:

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3.) Use of metabolic compounds as anti-cancer drugs; aminopterin & amethopterin:

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4.) Use of sulfa drugs to block metabolic pathways of  pathogenic bacteria:

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5.) Physiological use of competitive inhibitors: feedback inhibition of biosynthetic pathways by endproduct:

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6.) Pancreatic trypsin inhibitor: another example of physiological competitive inhibition.  

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Noncompetitive inhibitors: contrary to competitive inhibitors, noncompetitive inhibitors do not alter Km, but they decrease Vmax instead. This type of inhibition cannot be overcome by adding excess substrate. Thus, noncompetitive inhibitors inhibit an enzyme by binding to a site outside of the catalytic site and act by decreasing the turnover number of an enzyme.

nci

Irreversible inhibitors:


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