Lecture 10. Biochemistry 3521 - Fordham University - 1999

---

Some of this material is taken and modified from:

Biochemistry 3033 at Florida International University (kind permission of Dr. Kelsey Downum)

Biochemistry 242 at Illinois State University (kind permission of Dr. Reef Morse)

Biochemistry 100B at UCSC (Dr. Robert Fink)

---

Version: 2/9/99

---

TOPICS TO BE COVERED

A. Introduction to enzymes and catalysis

        Enzyme Data Bank

B. Introduction to Thermodynamics and Bioenergetics

C. Introductions to enzyme reactions and kinetics

---

Lecture 11

A. Enzyme Inhibition

B. Enzyme regulation and allosterics

---

---

A.Introduction to enzymes and catalysis

---

Summary of enzyme characteristics

• Proteins
• Biological catalysts
• Very efficient catalysts
• Very specific catalysts
• Reduce energy of activation for reaction (by binding the transition state)
• Carry out catalysis in a special region of the molecule, the Active-site
• Exhibit special kinetics
• Subject to regulatory control of various sorts

• Enzymes
• Globular proteins that function as biological catalysts to mediate specific biochemical chemical reactions
• Enzymes are not changed by the reactions they mediate
• Functional units of metabolism - responsible for all biochemical reactions
• May require cofactors/coenzymes for reaction to occur
• metal ions - e.g., Mn, Zn, Fe
• coenzymes (NAD+, TPP, THF, etc.)
• Apoenzyme - enzyme lacking essential cofactor
• Holoenzyme - intact & functional enzyme containing all cofactors/coenzymes
• Substrate (S) - biomolecules that enzymes react with
• Product (P) - the biomolecules formed by enzyme-mediated reactions
• Extraordinarily efficient and selective biological catalysts
• Accelerate the biochemical reaction rates by reducing the energy of activation needed to reach the transition state between reactant and product
• Most reactions catalyzed by enzymes would not proceed in their absence in a reasonable time without extremes of temperature, pressure, or pH
• Enzyme-catalyzed reactions, or enzymatic reactions, are 10³ to 10¹³ times faster than the corresponding uncatalyzed reactions.
• Enzymes are true catalysts
• enhance the rate of a specific rxns, but do not participate in the rxn
• do not shift the equilibrium of reactions
• are regenerated following the reaction (therefore, not consumed in reaction)
• effective in minute concentrations compared to the [S]
• Catalytic efficiency
• A typical enzyme will convert around a thousand molecules of substrate to product in 1 second! Some will convert as many as a million!! There are of course slower enzymes as well
• Substrate Specificity -- Highly specific for the reactants, or substrates with degree of substrate specificity dependent on enzyme
• Most enzymes are highly specific for their particular S (one E -- one S)
• Some enzymes will only catalyze one type of reaction for one type of compound
• In some cases for only one substrate and thus very high and selective specificity
• Some enzymes recognize structurally similar substrates
• Thus they have broad specificity
• Specificity is due to an enzymes' active site (positioning & catalytic sites) - chymotrypsin example
• Compare trypsin vs. chymotrypsin vs. elastase (see Stryer p. 227 and Fig. 9-40)
• They are also very stereospecific
• Assymetric active sites -- yeast ADH can distinguish between two prochiral H's of alcohol (Weistheimer and Vennesland)
• Consider thrombin, an enzyme in the blood-clotting cascade, and glucose oxidase:

	Thrombin	Glucose Oxidase
Type of reaction catalyzed	hydrolysis	oxidation
Type of bond	peptide	sugar hemiacetal
Structure about bond	between Arg and Gly	glucose
Stereospecificity	both must be L amino acids	D configuration

[Aside: cascades are "nature's way" of amplifying signals: Obviously blood clotting must be very carefully controlled (to prevent undesirable hemorrhaging or clotting). A cascade is a series of enzymes, each of which can exist in an active and inactive form. The amplification works by starting with them all in the inactive form. On triggering the system each one in turn activates the next; thus very rapidly one gets tremendous amplification of the initial signal. Thrombin is the last enzyme in the clotting cascade, it is activated from prothrombin, and in turn converts fibrinogen which is soluble into insoluble fibrin (clots).]
 

• Enzymes are temperature and pH dependent
• Enzymes usually work in a narrow pH-range near neutrality
• There are exceptions, e.g. pepsin, in the stomach, which is a protease and that breaks down proteins into peptides: operates in the pH 2-5 region
• Some RNA molecules and Ab also exhibit catalytic activity (to be discussed later in course)
• Active Site
• That region of the enzyme molecule where the substrate binds and the catalytic reaction occurs (see p. 190-191)
• (see Figs. 8-11 to 8-14)
• Usually a cleft or pocket on the surface of the enzyme, often at the interface of two domains
• Where direct contact is made between protein residues and the substrate
• Typically somewhat hydrophobic
• Usually only involves a small fraction of the enzyme surface.
• Is complementary to the substrate shape and polarity
• Contains binding site for the substrate (attracts and positions substrate)
• The shape and polarity of the binding site accounts for much of the specificity of enzymes.
• There is complementarity between the shape and polarity of substrate and the active site.
• In some cases binding of the substrate induces a conformational change.
• This is particularly common where there are two substrates.
• Binding of the first sets up a conformational change which results in formation of the binding site for the second substrate.
• Hexokinase is a good example of this (see Kinemage illustration conformation change; #7).
• Contains catalytic groups, these are the reactive side chains of aa's or cofactors, which carry out the bond breaking/forming reactions involved
• Usually the amino acid side chains and/or cofactors which can act as catalysts: e.g.
• Acids: -COOH, -imidazolium
• Bases: -NH2, imidazole, -S- (from Cys)
• Nucleophiles: imidazole, -S-, -OH
• Electrophiles: often metal ions e.g. Zn+2
• Binding involves non-covalent interactions (H-bonding, electrostatic interactions, hydrophobic interactions, Van der Waals interactions).
• Rest of the protein structure provides a superstructure to position the substrate and catalytic groups, flexibility for conformational changes, a means for regulatory control and sites for recognition by other biomolecules.
• Models of how enzymes bind substrates include (see Figs. 8-11 to 8-14)
• Lock and key = substrate and enzyme have complementary shapes that fit together perfectly
• Induced fit = assumes enzyme's active site changes its shape to fit and accomodate the substrates molecular configuration as the substrate binds (hexokinase)
• Kinetics -- Enzyme-catalyzed systems often exhibit special form of kinetics known as "saturation" kinetics
• Saturation kinetics reflect fact that reaction only occurs after the substrate has bound to the enzyme
• Once all the enzyme molecules have substrate bound -- no further rate increase is possible.
• Regulatory Control -- Enzymes control the flux of metabolites through metabolic pathways (i.e. the amount and rate of material passing through the pathway).
• Enzymes are subject to regulatory control and there are many levels at which such control is exerted; For example
• Alteration of the number of enzyme molecules
• Alteration of enzyme activity
• Compartmentalization
• Typically globular proteins and therefore possess the main functional characteristic of globular proteins
• Regulatory enzymes, generally have a more complex structure than unregulated enzymes
• Regulatory enzymes are typically oligomeric molecules that have separate binding sites for substrates and modulators (allosterics)

• Most enzymes are named by adding the suffix -ase to the name of the substrate they act on or to a descriptive term for the reactions they catalyze. (exceptions occur = trypsin and chymotrypsin)
• Examples
• Named for its substrate: substrate-ase
• lactase catalyzes: lactose --> glucose + galactose
• If you are lactose intolerant, you can buy lactase in a powdered form to help you digest the food. (An enzyme with this function, produced by the bacterium E. coli is called b-galactosidase.)
• Named for its action
• Deoxyribonuclease, or DNase catalyzes: DNA ---> dNMP nucleotides
• the enzyme might be an endonuclease or an exonuclease
• A committee of the International Union of Biochemistry and Molecular Biology (IUBMB) maintains a classification scheme that categorizes enzymes according to the general class of organic chemical reaction catalyzed. The six categories include
• Oxidoreductases (1....)(Note the links are to the enzyme database if you are interested in enzymes type)
• Oxidoreductases catalyze oxidation-reduction reactions. Most of these enzymes are referred to as dehydrogenases, but some are called oxidases, peroxidases, oxygenases, or reductases
• Example: Alcohol dehydrogenase catlyzes the oxidation of an alcohol to an aldehyde
• Transferases (2....)
• Transferases catalyze group-transfer reactions, and many require the presence of coenzymes. In group-transfer reactions, a portion of the substrate molecule usually binds covalently to the enzyme or its coenzyme. This group includes the kinases.
• Example: Phosphotransferase catalyzes the transfer of a phosphoryl group from one molecule to another
• Hydrolases (3....)
• Hydrolases catalyze hydrolysis or the breaking of a covalent bond using water. They are a special class of transferases, with water serving as the acceptor of the group transferred.
• Example: Peptidase hydrolyzes a peptide bond
• Lyases (4....)
• Lyases catalyze nonhydrolytic and nonoxidative elimination reactions, or lysis of a substrate, generating a double bond. In the reverse direction, lyases catalyze addition of one substrate to a double bond of a second substrate. A lyase that catalyzes an addition reaction in cells is often termed a synthase.
• Example: Decarboxylase removes a carboxyl group to form carbon dioxide
• Isomerases (5....)
• Isomerases catalyze structural change within one molecule, that is, isomerization reactions. Because these reactions have only one substrate and one product, they are among the simplest enzymatic reactions.
• Example: Racemase catalyzes the rearrangement of an alpha carbon atom
• Ligases (6....)
• Ligases catalyze ligation, or joining, of two substrates forming a covalent bond. These reactions require the input of the chemical potential energy of a nucleoside triphosphate such as ATP. Ligases are usually referred to as synthetases
• Example: Pyruvate carboxylase catalyzes the formation of a carbon-carbon bond from pyruvate and carbon dioxide to form oxaloacetate

The 'ENZYME' data bank contains the following data for each type of characterized enzyme for which an EC number has been provided:

- EC number

- Recommended name

- Alternative names (if any)

- Catalytic activity

- Cofactors (if any)

- Pointers to the SWISS-PROT entrie(s) that correspond to the enzyme (if any)

- Pointers to disease(s) associated with a deficiency of the enzyme (if any)

You can conduct searchs of The Enzyme Data Bank based on the following:

Search by EC number

Search by enzyme class

Search by description or alternative name

Search by chemical compound

Search by cofactor

Check the database out using the following help:

Look for the enzyme "alcohol dehydrogenase" or "trypsin" using the "Search by description or alternative name"

Now see what comes back from your search of the Enzyme Commission number for alcohol dehydrogenase or trypsin. Search for alcohol dehydrogenase via 1.1.1.1 or trypsin via 3.4.21.4 using the "Search by EC number"

Next see what type of enzymes are returned when you look for the word "alcohol" using the "Search by chemical compound"

To see a breakdown of the individual enzyme classes or to search within a class try the Search by enzyme class and check out the category that includes 3.4.21.x known as the serine endopeptidases

Thermodynamics is the transformation and use of energy by cells = study of energy transformation in cells

Understanding thermodynamics provides a framework for predicting the likelihood that

a particular reaction will proceed

the direction of a particular reaction ( A + B <---> C + D)

Organisms have a balance between

• Catabolism --> complex molecules converted into simple molecules
• Results in release of energy from biomolecules (called free energy)
• Exergonic process; spontaneous
• free energy converted into chemical energy (ATP)
• oxidation
• Anabolism --> simple converted into complex molecules
• Use of energy for formation of biomolecules
• Endergonic process; non-spontaneous
• ATP used to do work - ATP bond energy converted into other bonds, etc. (assemble complex molecules)
• some energy may be lost as heat - total remains constant
• reduction

The change in free energy for an enzyme reaction in the cell is denoted as G.

delta G = Gibbs Free Energy = delta H - T x delta S

delta H = energy change at constant pressure

delta S = entropy, a measure of the randomness of a system

T = absolute temperature

This term can be calculated (eqn 1) for an enzyme reaction in the cell by knowing the concentrations of the product(s) and reactant(s), and the standard free energy constant, G^o' (the prime indicates that pH = 7.0).

• When considering a metabolic pathway, the G term is the most important, since G^o' is simply a point of reference.
• It is noteworthy that a decrease in product concentration lowers G so that the reaction becomes more favorable (LeChatelier Principle, mass action effect).

When an enzyme reaction in the cell yields energy it is an exergonic reaction and the free energy is negative. Such a reaction proceeds spontaneously.

An enzyme reaction requiring energy input is an endergonic reaction. The free energy is positive and it cannot proceed spontaneously. However, it can be driven by coupling to an exergonic reaction.


Reaction equilibrium occurs when the forward and backward reaction rates are the same -- delta G = 0.

Relevant points

• Gibbs free energy and changes in free energy reflect maximum energy available to do biochemical work
• delta G is an indication of the spontaneity of a reaction
• Sign (+/-) indicates direction of a reaction
• (+) endergonic reaction - requires an input of free energy
• (-) exergonic reaction - releases free energy (spontaneous)
• If delta G is negative, the reaction favors the products
• Magnitude of delta G is an indication of amount of work that can be done by chemical reaction before it reaches equilibrium
• represents the amount of work that can be done by chemical reaction
• delta G depends on the nature of the reactants (delta G^0' )
• delta G depends on the concentration of the reactants (log[products]/[reactants]
• A + B <---> C + D
• Free energy is thus a function of the ratio of the products to reactants
• This means that if the ratio of products to reactants is far away from equilibrium, the system has more energy. In a sense, delta G tells us how much the reaction "wants" to go toward equilibrium
• delta G values are additive or substractive and can be coupled to drive reactions

Enzyme kinetics is the study of the rates of enzyme-catalyzed reactions.

Kinetic studies provide indirect information concerning the specificities and catalytic mechanisms of enzymes.

Kinetics provides quantitative measurements of the affinity of the enzyme for its substrate and its specificity (or that of inhibitors) and the maximal rates of catalysis (and turnover).

Enzymes do not alter the equilibrium of reactions, but increase the rate

• There are two ways to increase reaction rates in general
• Increase temperature - increases molecular motion
• Lower activation energy or the delta G of activation (i.e., add a catalyst) - reduces activation energy (how enzymes work)
• Raise free energy ground state of substrate
• Lower G of the transition state
• Enzymes also lower activation energy by binding and bringing substrates together which increases the chance of a reaction and by facilitating conversion to transition state or tight binding of the transition state. The transition state denoted as B* below is an intermediated state in the conversion of substrate to product during catalysis
• A -->B*-->C
• More of the substrate (A) will reach the transition state (B*), i.e. the transition state is stabilized. This in turn leads to the formation of more product (C).
• See Figure 8-7 From Stryer (1995)
• Note that, with or without the enzyme the initial and final energy levels are the same and delta G is the same, i.e. the thermodynamics of the reaction are unchanged.

• Rates of single enzyme-single substrate reactions can be calculated by measuring disappearance of substrate or formation of product over time
• Methods to monitor enzyme-catalyzed reactions include
• Change in spectral property (typically UV or vis absorbance, fluorescence) with a spectrometer
• Release or uptake of H+ or OH- with a pH-stat ( a device which automatically adds acid or base to keep the pH constant)
• Chemical analysis by HPLC (chromatography), or NMR, or TLC (ATPase)
• Isotope analysis (e.g. radioactive 32P)
• Coupled reactions - used in cases where there is no easy way of following the reaction of interest. Instead another enzyme is added to react with the product in a reaction which typically generates a spectral signal, e.g.

• Example of Assay of trypsin: A protease which hydrolyzes proteins into peptides
• Synthetic substrate = acetyl-lysine p-nitrophenyl ester
• The reaction is
                    trypsin

AcLyspNP -------------> AcLys + pNP-OH
• Follow the formation of product using a spectrophotometer at 415 nm since
• p-nitrophenyl ester is colorless
• Product, p-nitrophenol, is bright yellow.
• Starting with a low (around micromolar) concentration of substrate, if we plot the absorbance at 415 nm as a function of time we find that the reaction is a first order reaction
• This implies v = k[S] (see Figure)

• If enzyme concentration [E] is held constant, a plot of  product concentration [P] vs. time for various concentrations of substrate shows that v_o or the initial velocity of the reaction increases with increasing [S] up to a maximum velocity referred to as V_max.
• See Figure of plots illustrating Velocity vs. S or see Figs at MIT Enzyme kinetics 3.1
• A initial rate or velocity (v_o) for an enzyme-mediated reaction is how fast the reaction proceeds or the change in concentration of product produced as a function of  time (M/min -- moles per minute)

• The initial velocity can be determined by calculating the slope of the linear portion of a graph of [S] vs. time or [P] vs. time.
• v_o = delta S/ delta t = S_f - S_i/t_f - t_i
• plot will give a negative slope as [S] decreases
• v_o = delta P/delta t
• plot gives a positive slope as [P] increases

• If we start with a high substrate concentration (>mM) we observe an initial linear increase in reaction rate as a functino of substrate concentration which then levels off = This is a hyperbolic curve
• Such a curve is neither 0, 1st, or 2nd order in kinetics! Suppose we were to carry out this reaction at a series of different starting substrate concentrations, and in each case measure the initial velocity ( i.e. the slope of a tangent at time = 0)
• For examples of the resulting plot of v vs. [S]
• See Figure of plots illustrating Velocity vs. S or Figs at MIT Enzyme kinetics 3.1
• If we look carefully we note that the initial part of the curve corresponds to a first-order reaction, and the final part corresponds to a zero-order reaction.

• This sort of a plot (V vs. [S]), i.e. hyperbolic, is known as a saturation plot because it implies that when the enzyme becomes "saturated" with substrate, i.e. each enzyme molecule has a substrate molecule associated with it, the rate becomes independent of substrate concentration. This implies that there is an equilibrium process preceding the rate-limiting step, i.e.
• dP/dt = k[ES]
• where ES represents the enzyme-substrate complex.
• Thus as the substrate concentration is increased a point will be reached when all enzyme molecules are in the form of the ES complex, i.e. the enzyme is saturated with substrate.
• Since the rate = k[ES], the rate of product formatino will not increase further since there can be no higher concentration of ES.
• Thus at low [S] the reaction is first-order (v = k[S]) and at high [S] the reaction is 0 order.
• The formation of the ES complex which is implied by such observations is crucial for enzyme catalysis.
• See Figure of plots illustrating Velocity vs. S or see Figs at MIT Enzyme kinetics 3.1
• Compare first order vs. zero order reaction (as velocity asymtotically approaches max)
• First order = initial reaction rate for single substrate depends only on [substrate]
• v = k[A]
• Zero order = rate of reaction remains same regardless of >>[substrate] since all enzyme is saturated
• v = k
• Second order = initial reaction rate for two substrate depends on both [substrate]
v = k [A][B]

• First order reaction where V = change in [S]_/change in time = k[S]

• k₁ = binding of E and S
• k₃ = formation and release of P from E
• k₂ = reverse reaction of k₁

• In analyzing this simple model for a single substrate, the following assumptions are made
• [ES] at steady state = Rate of ES complex formation is constant and is balanced by rate of conversion of the complex to product (thus the  concentration of the complex is constant at equilibrium)
• Rates are analyzed only at the start of the reaction where for kinetic analysis of enzymes
• negligible product has been formed so that the reverse reaction E + P ---> ES is negligible
• [S] >>>[E]
• The initial rate or v_o of formation of product is = k₃ [ES]
• When the enzyme is saturated, the maximum rate (V_max) = k₃ [Et] and the overall equilibrium also known as Michaelis constant is K_m = k₂ + k_{3 /}k₁
• k₁ considered rate limiting and therefore V_max = turnover of ES to E + P or k_cat
• In general, one cannot measure ES, therefore one must assume that the maximum rate of the reaction (V_max) will occur when the enzyme is saturated with substrate

See Figure of plots illustrating Velocity vs. S (from R. Morse at ILSTU, Biochem 242)

• The lower plot is often called a Michaelis-Menten Plot (see Stryer Fig. 8-15)

Hyperbolic curve is typical of many biological reactions and thus the Michaelis-Menten equation shown below is often valid for many reactions including:

• transport of substrates
• binding of ligands (such as hormones) to receptors
• other drug-related effects

• M-M plot is not extremely useful because v_o approaches V_max asymptotically - so v_o never quite reaches V_max, therefore an accurate determination of V_max is not possible!
• Because of this problem, two alternate characteristics can be used to describe the kinetics of the reaction
• 1/2 V_max
• K_m (the Michaelis constant)
• Since V_max cannot be accurately determined (because it occurs at an infinitely large [S]), an estimate of V_max is used to determine 1/2 V_max.
• The [S] necessary to achieve 1/2 V_max is called the K_m value or K_m amount of S.

• The equation that describes M-M plots is:
• v_o = Vmax[S]/(Km + [S])
• see Stryer p. 192-193 for derivation (if it helps you understand this better)
• v_o = initial velocity
• Vmax = maximal velocity
• Km = Michaelis constant
• [S] = substrate concentration

• The relationship between V_max and K_m can be demonstrated by substituting V_max/2 for v_o.
• The equation reduces to Km = [S] only when v_o is equal to V_max/2.

• K_m for an enzyme-mediated reaction is useful because it is characteristic of an enzyme (see Table 8-2)
• Can be intuitively described as a measure of how tightly the substrate is bound to the enzyme
• K_m values are typically in the physiological range of enzyme substrates (micro to millimolar)
• In initial velocities, changes in [S] can have a great affect on enzyme rates

• Summary of kinetic parameters for an enzyme reactions
• Km = [S] where half the enzyme is saturated and reaction at half-maximal velocity
• Measure of how much [substrate] required to get to full speed reaction
• V_max = the maximum rate at which the enzyme can operate
• Measure of how fast the enzyme can go at full speed and is a rate
• These parameters are experimentally determined and are different for each enzyme
• They are determined by running a series of reactions with constant E, vary [S], and measure velocity
• Plot as described below via Lineweaver-Burke
• see Measuring Km and Vmax at MIT for further discussion of this

• M-M plot is not extremely useful because v_o approaches V_max asymptotically - so v_o never quite reaches V_max, therefore an accurate determination of V_max is not possible!

Reciprocal of M-M eq:    1/vo = Km + [S]/Vmax[S]
Rearrange:               1/vo = Km/Vmax 1/[S] + 1/Vmax
                                 (y = mx + b, eq. of a straight line)
y = mx + b, where

slope = Km/Vmax     y-intercept = 1/Vmax     x-intercept = -1/Km

y = 1/V0        x = 1/[S]

1. L-B plot gives a linear relationship between vo and [S].
2. Yields an accurate determination of both Vmax and Km.
y-intercept = 1/Vmax --> Note that if 1/[S]=0, equation reduces to 1/vo = 1/Vmax
      x-intercept = -1/Km --> Note that if 1/V=0, equation reduces to -1/Km =1/[S]

• kcat =Vmax / [E₀] (therefore this is another way of expressing Vmax
• First order rate constant for converting enzyme-substrate complex to product
• Turnover numbers vary from 1 - 10⁶/sec
• k(trypsin, chymotrypsin) = 100/sec
• k(catalase) = 2 x 10⁵/sec
• k(laboratory reaction) = 10^-3/sec

• Unit = amount of enzyme that produces 1 mmol of product per minute (micromole/sec)

• In hyperbolic curve in first order reaction, 2-fold >[S] results in 2-fold >V
• In sigmoidal curve, 2-fold >[S] could result in 5-fold >V
• see plot of V vs. S for an allosteric PFK enzyme from "A Student's Survival Guide for Biochemistry"

---

---

---

COURSE HOMEWORK PROBLEMS and STUDY AID:

Study Questions & Answers on Bioenergetics and Kinetics 

---

OnLine Supplement:

Problems & Answers on Enzyme Biochemistry (Introductory Course in Biology at MIT):

Solving Chemical Equilibrium Problems

Solving Enzyme Mechanism Problems

3.5 Solving Enzyme Kinetics Problems

Solving Feedback Regulation Problems

Practice Problems!

---

For a advanced tutorial on enzyme kinetics:

Enzyme Kinetics Tutorial at Jefferson 

---

Supplementary Video

---

Activity Assays

Electronic Information Center at Walsh Library

---

 Lecture 10 - 3521 

---

---

BACK to the Top of this document

BACK to the Biochemistry 3521 Home Page