Chapter 8 Enzyme Catalysis

Homework II (cont’d): Chapter 8, Problems 4, 5, 7, 8, 9, 11 (the diagonal line with “Slope” is the blue line), 12, 16, 17Due October 25 (Wed).

1. Enzymes were among the first biological macromolecules to be studied chemically

1.1 Much of the early history of biochemistry is the history of enzyme research.

1.1.1 Biological catalysts were first recognized in studying animal food digestion and sugar fermentation with yeast (brewing and wine making).

1.1.2 Ferments (i.e., enzymes, meaning in “in yeast”) were thought (wrongly) to be inseparable from living yeast cells for quite some time (Louis Pasteur)

1.1.3 Yeast extracts were found to be able to ferment sugar to alcohol (Eduard Buchner, 1897, who won the Nobel Prize in Chemistry in 1907 for this discovery).

1.1.4 Enzymes were found to be proteins (1920s to 1930s, James Sumner on urease and catalase, “all enzymes are proteins”, John Northrop on pepsin and trypsin, both shared the 1946 Nobel Prize in Chemistry).

1.1.5 Almost every chemical reaction in a cell is catalyzed by an enzyme (thousands have been purified and studied, many more are still to be discovered!)

1.1.6 Proteins do not have the absolute monopoly on catalysis in cells. Catalytic RNA were found in the 1980s (Thomas Cech, Nobel Prize in Chemistry in 1989).

2. The most striking characteristics of enzymes are their immense catalytic power and high specificity.

2.1 Enzymes accelerate reactions by factors of at least a million.

2.1.1 Most reactions in biological systems do not occur at perceptible rates in the absence of enzymes.

2.1.2 The rate enhancements (rate with enzyme catalysis divided by rate without enzyme catalysis) brought about by enzymes are often in the range of 107 to 1014)

2.1.3 For carbonic anhydrase, an enzyme catalyzing the hydration of CO2 (H2O + CO2 HCO3

- + H+), the rate enhancement is 107 (each enzyme molecule can hydrate 105 molecules of CO2 per second!)

2.2 Enzymes are highly specific both in the reaction catalyzed and in their choice of substrates (i.e., reactants).

2.2.1 An enzyme usually catalyzes a single chemical reaction or a set of closely related reactions (side reactions leading to the wasteful formation of by-products rarely occur).

2.2.2 Enzymes exhibit various degrees of specificity in accord with their physiological functions (what of the following?):

Low specificity: some peptidases, esterases, and phosphatases.

Intermediate specificity: hexokinase, alcohol dehydrogenases, trypsin.

Absolute or near absolute specificity: Many enzymes belong to this group, and in extreme cases, stereochemical specificity is exhibited (i.e., enantiomers are distinguished as substrates or products).

2.3 Most enzymes are proteins.

2.3.1 Some enzymes require no other chemical groups other than their amino acid residues for activity. (e.g.)

2.3.2 Other enzymes require additional chemical components called prosthetic groups (covalently bound) (or cofactors).

2.3.3 Prosthetic groups could be inorganic metal ions (e.g., Fe2+, Mg2+, Mn2+, Zn2+) or complex organic or metalloorganic molecules called coenzymes.

2.3.4 A complete catalytically active enzyme (including its prosthetic group) is called a holoenzyme.

2.3.5 The protein part of an enzyme (without its prosthetic group) is called the apoenzyme.

2.3.6 Coenzymes often function as transient carriers of specific (functional) groups during catalysis.

2.3.7 Many vitamins, organic nutrients required in small amounts in the diet, are precursors of coenzymes.

3. Enzymes are classified by the reactions they catalyze

3.1 Trivial names are usually given to enzymes.

3.1.1 Many enzymes have been named by adding the suffix “-ase” to the name of their substrate or to a word or phrase describing their activity (type of reaction).

3.2 Enzymes are categorized into six major classes by international agreement.

3.2.1 The six major classes include

Oxidoreductases: catalyzing oxidation-reduction reactions.

Transferases: catalyzing the transfer of a molecular group from one molecule to another.

3.2.1 (cont’d)

Hydrolases: catalyzing the cleavage by the introduction of water.

Lyases: catalyzing reactions involving removal of a group to form a double bond or addition of groups to double bonds. (e.g.?).

Isomerases: catalyzing reactions involving intramolecular rearrangements.

Ligases: catalyzing reactions joining together two molecules.

3.3 Each enzyme is given a systematic name which identifies the reaction catalyzed (e.g., hexokinase is named as ATP:glucose phosphotrasferase).

3.4 Each enzyme is assigned a four-digit number with the first digit denoting the class it belongs, the other three further clarifications on the reaction catalyzed.

4. Enzymes, like all other catalysts, does not affect reaction equilibria, only accelerate reactions.

4.1 Equilibrium constant (Keq’) of a reaction is related to the free energy difference between the ground states of the substrates and products (Go’)

Go’ = -RTlnKeq’

Enzyme catalysis does not affect Go’, thus not Keq’.

4.2 The rate constant of a reaction (k) is related to the free energy difference between the transition state and the ground state of the substrate (G‡)

4.2.1 Transition state is a fleeting molecular moment (not a chemical species with any significant stability) that has the highest free energy during a reaction.

4.2.2 An enzyme increases the rate constant of a reaction (k) by lowering its G‡.

4.2.3 The combination of a substrate and an enzyme creates a new reaction pathway whose transition state energy is lower than that of the reaction in the absence of energy.

5. Formation of an enzyme-substrate complex is the first step in enzyme catalysis.5.1 Substrates are bound to a specific region of an enzyme called the active site.

5.1.1 Much of the catalytic power of enzymes comes from their bringing substrates together in favorable orientations in enzyme-substrate (ES) complexes. (mutations that affect the on-rate, the off-rate, kcat, …etc).

5.1.2 Most enzymes are highly selective in their binding of substrates.

5.1.3 The active site usually takes up a relatively small part of the total volume of an enzyme.

5.1.4 The active site is a three-dimensional entity formed by groups that come from different parts of the linear amino acid sequence.

5.1.5 Substrates are bound to enzymes by multiple weak (noncovalent) attractions.

5.1.6 Active sites are clefts or crevices with a generally nonpolar character (polar residues, when present in the active site, usually participate in the catalytic processes, thus called catalytic groups) (or specificity of binding).

5.1.7 The active sites of some unbound enzymes are complementary in shape to those of their substrates (the lock-and-key metaphor, Emil Fisher).

5.1.8 In many enzymes, the active sites have shapes complementary to those of their substrates only after the substrates are bound (the induced fit, Daniel Koshland).

5.2 The existence of ES complexes has been shown in a variety of ways.

5.2.1 The saturation effect: at a constant concentration of an enzyme, the reaction rate increases with increasing substrate concentrations until a Vmax is reached.

5.2.2 ES complexes have been directly observed by electron microscopy and X-ray crystallography.

Dihydrofolate reductase, NADP+ (red), tetrahydrofolate (yellow)

The lack of perfect complementarity is important to enzymaticcatalysis (induced fit) (not evident in this figure).

6. Binding energy is the major source of free energy used by enzymes to lower the activation energies of reactions. 6.1 Binding energy (Gb) is the energy derived from enzyme-substrate interaction.

6.1.1 Formation of each weak interaction in the ES complex is accompanied by a small release of free energy.

6.1.2 Weak interactions are maximized when the substrate is converted to the transition state.

6.1.3 The weak interactions that are formed only in the transition state are those that make the primary contribution to catalysis: Transition state theory. In another words, the enzyme is evolved (“designed”) to bind the transition state structure.

6.1.4 Catalytic antibodies can be formed by using transition state analogs as immunogens (predicted by William Jencks in 1969 and confirmed by Richard Lerner and Peter Schultz in 1986). Problems: specific chemical reaction, lack of substrate specificity. E.g. Cutting DNA independent of or relative insensitive to the flanking sequence.

6.2 The summation of the unfavorable (positive) G‡ and the favorable (negative) Gb results in a lower net activation energy.

6.2.1 The requirement for multiple weak interactions to drive catalysis is one reason why enzymes (and some coenzymes) are so large. Therefore, larger Gb.

6.3 Catalysis and specificity arise from the same phenomenon.

6.3.1 Catalysis refers to the acceleration of the reaction due to the involvement of enzymes.

6.3.2 Specificity refers to the ability of an enzyme to discriminate between two competing substrates.

6.3.3 The same binding energy that provides energy for catalysis also makes the enzyme specific. (Gb-transitio

n-state + Gb-substrate-general + Gb-substrate-specific)

But they are not always separable. It is intellectually useful to make distinctions among these binding energies, attributable to a particular group of atomic interactions. They are often used in the combined interpretation of kinetic, biochemical, genetic, and structural data.

6.4 Binding energies can be used to overcome various energy barriers that exist during catalysis.

6.4.1 Binding energy holds the substrates in the proper orientation to react, thus overcome entropy reduction (substrate recognition and complex formation).

6.4.2 Formation of weak bonds between substrate and enzyme also results in the unfavorable desolvation of the substrate (requiring a binding energy of what form? Nonspecific?).

6.4.3 Binding energy involving weak interactions formed only in the reaction transition state helps to compensate thermodynamically for any strain or distortion that substrate must undergo to react (to break or form a bond).

The interactions from the added groups contribute largely to the stabilization of the transition state. Moreover, the rate can beaffected greatly by the interactions physically remote from thecovalent bond broken.

6.4.4 Weak interactions between substrates and enzymes may generate conformational changes on the enzyme, a phenomenon called induced fit.

6.4.5 Induced fit may serve to bring specific functional groups on the enzyme into the proper orientation and position (alignment) to catalysis (need to overcome the entropy increase).

6.4.6 Modern approaches combine multiple theoretical (e.g., computational) and experimental (e.g., mutagensis) approaches to the studies of enzymes.

Reactions of an ester with a carboxylate group to form an anhydride

7. Properly positioned catalytic functional groups aid bond cleavage and formation during enzyme catalysis.

7.1 The active sites of some enzymes contain amino acid functional groups that can participate in the catalytic process as proton donors or proton acceptors--general acid-base catalysis.

7.1.1 Many biochemical reactions involve the formation of unstable charged intermediates that tend to break down rapidly to their constituent reactant species.

7.1.2 Charged intermediates can often be stabilized by transferring protons to or from the substrate or intermediate to form a species that breaks down to products more readily than to reactants. Catalysis here means the facilitated (coordinated, aligned) proton transfer.

7.1.3 General acid-base catalysis can provide a rate enhancement on the order of 102 to 105.

7.2 Some enzymes accelerate reactions by forming transient covalent intermediates with the substrates--covalent catalysis.

7.2.1 Amino acid side chains (e.g., Ser) and prosthetic groups can function as nucleophiles in forming covalent intermediates with substrates. ( leading to enzyme conformational changes)

7.2.2 The new pathway of reaction must have a lower activation energy than the uncatalyzed one.

7.2.3 Free enzyme is always regenerated at the end of the reaction.

7.3 Metal ions can participate in catalysis in several ways.

7.3.1 Metal ions can be tightly bound to the enzyme or taken up from the solution along with the substrate.

7.3.2 Metal ions (bound to the enzymes) can help orient a substrate or stabilize charged reaction transition states.

7.3.3 Metal ions can help activate substrates (how? By polarizing the bond or creating a better nucleophile?)

7.3.4 Metal ions can mediate oxidation-reduction reactions by reversibly change their oxidation states (electron donor and acceptor).

7.3.5 Many enzymes have metal ions in their active centers playing important roles in catalysis.

7.3.6 (Noncatalytic function) Metal ions can also have structural purposes (e.g., Ca2+ binding leads to conformational changes of calmodulin, EF-hand, etc.). Regulation of enzymes is done through regulation of their structures (conformations).

7.4 An enzyme may use a combination of several catalytic strategies to bring about a rate enhancement.

7.4.1 Chymotrypsin uses both covalent catalysis and general acid-base catalysis (details?)

8. Michaelis-Menton equation reflects the kinetic behavior of many enzymes

8.1 Saturation effect was observed in enzyme catalysis when plotting the initial velocity (Vo) against the substrate concentration([S]).

8.1.1 Initial velocity (Vo) was measured at the beginning of the enzyme-catalyzed reaction, when substrate concentration can be considered constant ([S] will decrease as the reaction progresses).

8.1.2 At relatively low concentrations of substrate, Vo increases almost linearly with an increase in [S].

If [S]<<Km,

8.1.3 At higher [S], Vo increases by smaller and smaller amounts in response to the increase in [S].

8.1.4 Finally, a point (a plateau of maximum velocity, Vmax) is reached beyond which there are only vanishingly small increases in Vo with the increasing [S].

8.1.5 The ES complex was proposed to be a necessary step in enzyme catalysis based on this kinetic pattern.

8.2 The Michaelis-Menton equation was established to account for the observed relationship between Vo and [S].

8.2.1 A single-substrate, single-product reaction is considered for simplicity.

8.2.2 At early times in the reaction, the concentration of the product ([P]) is negligible and the overall reaction can be written as (no reverse reaction) k1 k2

E + S ES E + P k-1

8.2.3 It is hypothesized (unnecessary unless in a sequence of reactions) that the rate-limiting step (M-M mechanism) in enzymatic reactions is the breakdown of the ES complex to form the product and the free enzyme:

Vo = k2[ES]

8.2.4 The free enzyme concentration [E]=[Et]-[ES] ([Et] is the total enzyme concentration).

8.2.5 The amount of substrate bound by the enzyme at any given time is negligible compared with the total [S], because [S] is usually far greater than [Et] ([S]>>[Et], still true for low [S]); therefore, the free substrate concentration is [S].

8.2.6 The rate of ES formation = k1([Et]-[ES])[S],

the rate of ES breakdown = k-1[ES]+k2[ES].

k1 is the substrate on-rate or the forward rate. k-1 is the off-rate or the backward rate.

8.2.7 It is assumed that Vo reflects a steady state in which [ES] is constant (steady-state kinetics),

k1([Et]-[ES])[S]= k-1[ES]+k2[ES]

k1[Et][S][ES]=-----------------------

k1[S]+k-1+k2

Because Vo = k2[ES],

k2k1[Et][S] k2[Et][S] Vmax[S] Vo=------------------=-----------------------=--------------- k1[S]+k-1+k2 [S]+(k-1+k2)/k1 [S]+Km

8.2.8 This is the Michaelis-Menton equation, and Km =(k-1+k2)/k1, is the Michaelis-Menton constant.

8.2.9 The equation fits the observed curve very well.

When [S] is very low (<<Km), Vo=Vmax[S]/Km

when [S] is very high (>>Km), Vo=Vmax

8.3 Km equals to the substrate concentration at which the reaction rate is half its maximal value (Vo=Vmax/2).

8.3.1 This represents a practical (operational) definition of Km.8.4 Km and Vmax can be determined by varying the substrate concentrations--The Michaelis-Menton equation can be transformed by taking double reciprocal of both sides into the following form:

1 Km 1------ = ------------ + --------

Vo Vmax[S] Vmax

8.4.1 A plot of 1/Vo versus 1/[S] yields a straight line, which has an intercept of 1/Vmax on the 1/Vo axis, -1/Km on the 1/[S] axis, and a slope of Km/Vmax. The double reciprocal plot is called the Lineweaver-Burk plot.

8.4.2 Alternatively, Km and Vmax can be obtained by fitting the data into the Michaelis-Menton equation using a computer program (software installed in modern photospectrometers).8.5 The real meaning of Km can change from one enzyme to another.

8.5.1 A great many enzymes that may have quite different reaction mechanisms (from what assumed when establishing the equation, which is called Micahelis-Menton mechanism, a single-substrate single-product two-step reaction, k2 is rate-limiting) follow Michaelis-Menton kinetics: that is, exhibiting a hyperbolic dependence of Vo on [S].

8.5.2 The actual meaning of Km depends on the number and relative rates of the individual steps of the reaction. (the non Michaelis-Menton mechanism).

8.5.3 In the two-step (Michaelis-Menton mechanism) reaction, k2 is assumed rate-limiting, i.e., k2<<k-1, and Km reduces to k-1/k1, being the dissociation constant (Ks) for the ES complex (the inverse of the association or equilibrium constant, the exchange rate of the substrate is so fast, ES is in transitional equilibrium).

8.5.4 When Km=Ks, Km does reflects the affinity between the substrate and enzyme in the ES complex.

8.5.5 k-1<<k2, Km=k2/k1. In this case, Km does not reflect affinity between substrate and enzyme! (Briggs-Haldane mechanism, k2/Km=(kcat/Km)=k1, diffusion-controlled on-rate, ~108s-1M-1).

8.5.6 When k2 and k-1 are comparable, Km=(k2+k-1)/k1, Km does not reflect the affinity between substrate and enzyme!

8.5.7 When the reaction goes through multiple steps after the formation of the ES complex, Km then becomes a very complex function of many rate constants! (Km does not reflect substrate affinity in many cases) (What’s the definitions of Kapp and kapp, Km and kcat? Same! There are cases when no real single ES exists, simply Michaelis-Menton-like steady state kinetics).

app=apparent

8.6 The actual meaning of Vmax also varies from enzyme to enzyme.

8.6.1 In the two-step (Michaelis-Menton) reaction, k2 is assumed to be rate-limiting, Vmax=k2[Et]

8.6.2 The number of reaction steps and the identity of the rate-limiting step(s) can vary from enzyme to enzyme (thus Vmax varies).8.7 A more general term kcat, instead of Vmax is usually used.

8.7.1 kcat is defined as the limiting rate of any enzyme-catalyzed reaction at saturating substrate concentrations.

8.7.2 In a multiple reaction, kcat equals to (or less than, upper bound) the rate constant of the clearly rate-limiting step if any (e.g., kcat=k2 in the ‘two-step’ Michaelis-Menton reaction)

8.7.3 When several steps are partially rate limiting, kcat is a complex function of them all.

8.7.4 kcat is also called the turnover number, equivalent to the number of substrate molecules converted to product in a given unit of time on a single enzyme molecule (at saturating substrate concentration).8.8 The factor kcat/Km is generally the best kinetic parameter to use in comparisons of catalytic efficiencies of enzymes.

8.8.1 kcat is not satisfactory because two enzymes having the same kcat may have very different rate enhancements (catalyzed versus uncatalyzed, thus different efficiencies). Also kcat reflects situations when substrate concentration is saturating (most enzymes are not normally saturated with substrates; under physiological conditions the [S]/Km ratio is typically between 0.01 and 1.0).

8.8.2 When [S]<<Km, Vo=(kcat/Km)[Et][S]the ratio of the products of two reactions =(kcat1/Km1)/(kcat2/Km2), others being equal, i.e., [Et] and [S] are the same for the two reactions.

8.8.3 kcat/Km relates the reaction rate to the total enzyme concentration and substrate concentration.

8.8.4 kcat/Km=k2/Km=k2k1/(k2+k-1) 8.8.5 Suppose the rate of formation of product (k2)

is much faster than the rate of dissociation of the ES complex (k-1), then kcat/Km approaches k1 (Haldane).

8.8.6 The ultimate limit on the value of kcat/Km is set by the rate of formation of the ES complex (k1, the on-rate), which can not be faster than the diffusion-controlled encounter of an enzyme and its substrate, which is between 108 to 109 M-1s-1.

8.8.7 Many enzymes have a value of kcat/Km near this range, attaining kinetic perfection.

8.8.8 Any further gain in catalytic rate can come only by decreasing the time for diffusion (How could this be realized? Directed kinetic binding through electrostic field)8.9 Many of the principles developed for the single-substrate systems may be extended to multisubstrate systems.

8.9.1 The majority of enzymes involve two substrates.

8.9.2 Most reactions obey Michaelis-Menton kinetics when the concentration of one substrate is held constant and the other is varied.

8.9.3 Reactions in which all the substrates bind to the enzyme (to form a ternary complex) before the first product is formed are called sequential mechanisms.

8.9.4 Sequential mechanisms are called ordered if the substrates combine with the enzyme and the products dissociate in an obligatory order.

8.9.5 A random mechanism implies no obligatory order of combination or release.

8.9.6 Reactions in which one or more products are released before all the substrates are added are called ping-pong mechanisms.

8.9.7 Steady-state kinetics can be used to distinguish the sequential and ping-pong mechanisms (how?)

Sequential mechanism

Ping-pong mechanism

Sequential pathway

Ping-pong pathway

9. It is during the pre-steady state that the individual rate constants may be observed.

9.1 A complete description of an enzyme-catalyzed reaction requires direct measurement of the rates of individual reaction steps.

9.1.1 Pre-steady state phase of a reaction is generally very short: values of kcat usually lie between 1 and 107s-1, thus measurement must be made in a time range of 1 to 10-7s (rapid mixing and sampling are needed).

9.1.2 Rapid mixing and sampling techniques are available (e.g., the stopped-flow method).

Fast acylationstep

Slow deacylationstep

10. Enzymes are subject to reversible and irreversible inhibition

10.1 The inhibition of enzymatic activity by specific small molecules and ions is important.

10.1.1 It serves as a major control mechanism in biological systems.

10.1.2 Many drugs and toxic agents act by inhibiting enzymes.

10.1.3 Inhibition can be a source of insight into the mechanism of enzyme action: residues critical for catalysis can often be identified by using specific (irreversible) inhibitors.

10.2 Reversible inhibition can usually be divided into different types.

10.2.1 Reversible inhibitors bind to enzyme noncovalently.

10.2.2 In competitive inhibition, the inhibitor competes with the substrate for the active site (binding of one prevents binding of the other, forming ES or EI complexes but no ESI complexes, fig.).

10.2.3 Competitive inhibitors are often compounds that resemble the substrates.

10.2.4 Vmax is not affected by the presence of a competitive inhibitor (There is always some high substrate concentration that will replace the inhibitor from the enzyme’s active site).

10.2.5 Km is increased due to the presence of a competitive inhibitor. Higher substrate concentration is needed to achieve Vmax/2.

10.2.6 In noncompetitive inhibition, the inhibitor binds to a site distinct from that (the active site) which binds the substrate. (fig.)

10.2.7 Inhibitor binding does not affect substrate binding and vice versa (i.e., inhibitor can bind to ES complex, substrate can bind to EI complex).

10.2.8 The enzyme is inactivated when inhibitor is bound (whether or not substrate is also present). (e.g.)

10.2.9 The apparent Vmax is lowered (due to the concentration decrease of active enzymes)

10.2.10 Noncompetitive inhibition are only observed with enzymes having two or more substrates.

10.2.11 In uncompetitive inhibition, the inhibitor binds only to the ES complex (unable to bind to free enzyme). (fig.)

10.2.12 In an enzyme-catalyzed bisubstrate reaction, an inhibition can be competitive, noncompetitive, and uncompetitive at the same time depending on the inhibitor used. (Lineweaver-Burk plots).

Noncompetitive inhibition

=1+[I]/KI

Uncompetitive inhibition

’=1+[I]/K’I, K’I=[ES][I]/[ESI]

Mixed or noncompetitive inhibition, plots similar tothe sequential binding in ternary complexes

10.3 Irreversible inhibitors bind very tightly (covalently or noncovalently) to the enzymes.

10.3.1 Many irreversible inhibitors modify critical catalytic residues covalently, thus inactivating the enzymes.

10.3.2 Diisopropylphosphofluoridate (DIPF, one component of the toxic nerve gases) reacts with a critical Ser residue on acetylcholineesterase.

10.3.3 Critical catalytic residues in the active site can sometimes be identified using irreversible inhibitors (DIPF on chymotrypsin).

10.3.4 A suicide inhibitor binds to the active site of a specific enzyme, being converted to a very reactive compound by the enzyme catalysis (mechanism-based), then covalently modifies the enzyme, thus irreversibly inhibits the enzyme activity. (e.g., after forming the covalent intermediate, but lack of the ability to complete the reaction.)

10.3.5 Suicide inhibitors could be very effective drugs (rational drug design).

10.3.6 Transition state analogs act as potent inhibitors for enzymes: transition-state analogs usually bind to enzymes 102 to 106 times more tightly than the normal substrates (strongly supporting the transition-state theory for catalysis). They are often a intermediate with a tetrahedral structure.

F is a much better leaving group.

11. Enzyme activity is affected by pH

11.1 Each enzyme has an optimal pH or pH range (where the enzyme has maximal activity).

11.1.1 Requirements for the catalytic groups in the active site in appropriate ionization state is a common reason for this phenomenon.

11.1.2 Change of ionization state of surface groups (which may affect the protein structure) sometimes is responsible for this phenomenon.

11.1.3 In rare cases, it is the change of ionization state of substrate that is responsible for this phenomenon.

11.2 The pH range over which activity changes can provide a clue to what amino acid residues are involved.

11.2.1 This has to be treated with great caution, because in a closely packed environment of a protein, the pK values of amino acid side chains can change significantly (e.g., a nearby positive charge will increase the pK value of a Lys residue, and a negative one will decrease the pK!).

12. The molecular mechanisms of enzyme catalysis is not easy to study.12.1 A complete understanding of the catalytic mechanism of an enzyme includes many aspects including

12.1.1 Temporal sequence in which enzyme-bound reaction intermediates occur.

12.1.2 Structure of each intermediate and transition state.

12.1.3 The rates of interconversion between all intermediates.

12.1.4 The structural relationship of the enzyme with each intermediate. (conformational and chemical states of the enzyme).

11.1.5 The energetic contribution of all reacting and interacting groups with respect to the intermediate complexes and transition states (utilization of binding energies).

11.1.6 There is probably no enzyme for which the current understanding meets all these requirements.

11.2 The catalytic mechanisms of chymotrypsin is partially understood using a comprehensive approach.

11.2.1 Pre-steady state kinetics studies revealed that the hydrolysis of p-nitrophenylacetate by chymotrypsin, as measured by release of p-nitrophenol (a colored product) consists of a fast phase (acylation--covalent catalysis) and a slow phase (deacylation). In hydrolysis of proteins, the deacylation step is rate-limiting!

11.2.2 Two catalytic residues (Ser195 and His57) were identified by chemical modifications (using DIPF and TPCK respectively).

11.2.3 X-ray structure determination of the enzyme revealed the presence of Ser195 (function as a nucleophile to attack the carbonyl carbon) and His57 (function as proton acceptor first and then as proton donor in the catalytic process--general acid-base catalysis) at the active site of the chymotrypsin.

11.2.4 Ser195 and His57 form a catalytic triad with the buried Asp102 residue (which stabilizes the positive charge formed on the His57 residue, that in turn prevents the development of a very unstable positive charge on Ser195 hydroxyl, thus making Ser195 a more effective nucleophile).

11.2.5 At the transition state, the carbonyl oxygen acquires a negative charge, which is stabilized by hydrogen bonds formed from groups (which residues?) in an oxyanion hole at the active site.

11.3 Reasons for the markedly different specificity of chymotrypsin, trypsin, and elastase were revealed by structure determination of the three enzymes.

11.3.1 Chymotrypsin has a nonpolar pocket serving as the binding site for the aromatic or bulky nonpolar side chains.

11.3.2 Trypsin has an Asp residue replacing a Ser residue in the binding site, and so, recognize only residues with positively charged side chains (Lys and Arg).

11.3.3 Elastase has two much bulkier Val and Thr replacing two Gly residues at the entrance of the pocket, and so, only smaller side chains can bind.

木糖

Glycolysis: 糖原酵解

13. The enzymatic activity of some enzymes are precisely and tightly regulated in living organisms to meet physiological requirements.13.1 Allosteric enzymes (similar to hemoglobin) are regulated by reversible, noncovalent binding of modulators (often being metabolites).

13.1.1 Feedback inhibition, i.e., building up of a pathway’s end product ultimately slows the entire pathway, is often realized through allosteric enzymes.

13.1.2 The enzyme catalyzing the first step of a synthetic pathway is often an allosteric enzyme.

13.1.3 For example, threonine dehydratase in the Ile synthesis pathway, and aspartate transcarbamoylase (ATCase, the best understood allosteric enzyme) in the pyrimidine nucleotide synthesis pathway.

13.1.4 The modulators usually bind not to the active site but to another specific regulatory site.

13.1.5 The enzyme activity varies when the concentration of the modulators vary, hence the synthesis pathway is open only when the end product is lacking (closed when the end product is abundant).

13.2 Allosteric enzymes do not follow the Michaelis-Menton kinetics.

13.2.1 They do exhibit saturation effect, but do not show a hyperbolic curve when plotting Vo against [S].

13.2.2 The substrate concentration at which Vo is half maximal is referred as K0.5 (which is not Km!)

13.2.3 Homotropic enzymes show sigmoidal saturation curve when plotting Vo against [S], where the substrate itself is a positive (stimulatory) modulator for a multiple-subunit cooperative enzyme system.

13.2.4 Heterotropic enzymes have substrate-saturation curves in various shapes, where the modulator is a metabolite other than the substrate.

13.2.5 A positive modulator may make the curve more hyperbolic-like (still sigmoidal) (with a decreased K0.5, but no change on Vmax).

13.2.6 A negative modulator may make the curve more sigmoidal (with increased K0.5 and unchanged Vmax).

13.2.7 In a less common type of modulation, Vmax is changed with K0.5 almost constant.

13.3 Two models have been proposed to explain the cooperativity phenomenon of some homotropic allosteric enzymes.

13.3.1 They are the same as the two models proposed to explain the cooperative oxygen binding process of hemoglobin: the sequential model and the concerted model.

13.4 The activity of many enzymes are regulated by reversible covalent modifications.

13.4.1 Phosphorylation, the most common reversible covalent modification, is a highly effective means of switching the activity of target enzymes.

13.4.2 Protein kinases catalyze the transfer of a phosphate group from an ATP molecule to the side chains of Ser, Thr, or Tyr residues in proteins.

13.4.3 Protein phosphatases catalyze the hydrolysis of phosphoryl groups attached to proteins, thus reversing the effects of kinases.

13.4.4 The degree of specificity of protein kinases varies. Some catalyze the phosphorylation of many different target proteins (at sites of conserved sequences, e.g., protein kinase A recognizes a conserved sequence made of Arg-Arg-X-Ser-Z or Arg-Arg-X-Thr-Z). Some phosphorylate a single protein or several closely related ones.

13.4.5 Phosphorylation is a highly effective means of controlling the activity of proteins for structural, thermodynamic, and kinetic reasons. (elaborate please).

Glucose (red), AMP (dark blue, allosteric activator), pyridoxal phosphate (PLP, B6 derivative, light blue), and ser14 (yellow)

Glycogen phosphorylase

13.5 Stimulatory or inhibitory proteins, as well as small molecules, regulate the activity of enzymes.

13.5.1 Most effects of cyclic AMP (formed when many hormones interact with their receptors on the cell surface, G-protein signal transduction pathway) in eukaryotic cells are mediated by the activation of a single protein kinase, called protein kinase A (PKA).

13.5.2 Cyclic AMP activates PKA by binding to its two regulatory subunits, thus relieving the two catalytic subunits, which then become active.

13.5.3 A pseudosubstrate sequence (a segment of peptide) on the regulatory subunits occupies the active site of the two catalytic subunits, thus inhibiting their activity.

13.5.4 Calmodulin activates many proteins inside a cell when calcium levels rise.

13.5.5 Blood clotting is markedly accelerated by antihemophilic factor, a protein that enhances the activity of a serine protease.

13.6 Many enzymes are activated by specific proteolytic cleavage.

13.6.1 These enzymes are synthesized as inactive precursors called zymogens.

13.6.2 They are activated by cleavage of one or several specific peptide bonds.

13.6.3 Proteolytic activation, in contrast with allosteric control and reversible covalent modification, can occur just once in the life of the enzyme molecule.

13.6.4 The digestive enzymes that hydrolyze proteins are synthesized as zymogens in the stomach and pancreas.

13.6.5 Blood clotting is mediated by a cascade of proteolytic activation.

13.6.6 Some protein hormones are synthesized as inactive precursors (e.g., insulin is derived from proinsulin by proteolytic removal of a peptide).

13.7 Amount of some enzymes are increased when certain inducers (often enzyme substrates) are present in the cells.

13.7.1 This is often seen in bacterium cells.13.7.2 The presence of lactose in a culture

medium induces a large increase in the amount of -galactosidase (and two other enzymes, galatoside permease and thiogalactoside transacetylase)

13.8 Both the synthesis and degradation of the certain important enzymes are tightly controlled. For example, in cell cycle control and in cancer. Either overexpression or overproduction of a protein or a failure to turn off and destruct a protein can lead to cancer.