Enzymes :

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Enzymes Mechanism and Catalysis
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• Enzymes DO NOT change the equilibrium constant of
  a reaction
• Enzymes DO NOT alter the amount of energy
  consumed or liberated in the reaction (standard
  free energy change, ?G)
• Enzymes DO increase the rate of reactions that
  are otherwise possible
• Enzymes DO decrease the activation energy of a
  reaction (?G)

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• Enzymes DO increase the rate of reactions that
  are otherwise possible
• Enzymes DO decrease the activation energy of a
  reaction (?G)

The classic way that an enzyme increases the rate
of a bimolecular reaction is to use binding
energy to simply bring the two reactants in close
proximity. In order for a reaction to take place
between two molecules, the molecules must first
find each other. This is why the rate of a
reaction is dependent upon the concentrations of
the reactants, since there is a higher
probability that two molecules will collide at
high concentrations. The enzyme organizes the
reaction at the active site, thereby reducing
the cost in terms of ENTROPY.
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• How do enzymes catalyze biochemical reactions?
• involves basic principles of organic chemistry
• What functional groups can be involved in
  catalysis?
• almost all alpha amino and carboxyl groups are
  tied up in peptide bonds
• R groups are involved in catalysis
• asp, glu
• his, lys
• ser, cys, tyr
• catalysis occurs when substrate is immobilized
  near these residues at the active site

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General Acid-Base Catalysis

• General acid-base catalysis is involved in a
  majority of enzymatic reactions. General
  acidbase catalysis needs to be distinguished
  from specific acidbase catalysis.
• In General acidbase catalysis, the buffer aids
  in stabilizing the transition state via donation
  or removal of a proton. Therefore, the rate of
  the reaction is dependent on the buffer
  concentration, as well as the appropriate
  protonation state.

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General Base Catalysis IEster Hydrolysis
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General Base Catalysis IIEster Hydrolysis
The hydrolysis of esters proceeds readily under
in the presence of hydroxide. It is base
catalyzed. However, the rate of hydrolysis is
also dependent on imidazole buffer concentration.
Imidazole can accept a proton from water in the
transiton state in order to generate the better
nucleophile, hydroxide. It can also re-donate
the proton to the paranitrophenylacetate in order
to generate a good leaving group.
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General Acid Catalysis Ester Hydrolysis
Electrostatic interactions are much stronger in
organic solvents than in water due to the
dielectric constant of the medium. The interior
of enzymes have dielectric constants that are
similar to hexane or chloroform
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Catalysis by Metal Ions Catalysis IEster
Hydrolysis
Metal ions that are bound to the protein
(prosthetic groups or cofactors) can also aid in
catalysis. In this case, Zinc is acting as a
Lewis acid. It coordinates to the non-bonding
electrons of the carbonyl, inducing charge
separation, and making the carbon more
electrophilic, or more susceptible to
nucleophilic attack.
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Catalysis by Metal Ions Catalysis IIEster
Hydrolysis
Metal ions can also function to make potential
nucleophiles (such as water) more nucleophilic.
For example, the pka of water drops from 15.7 to
6-7 when it is coordinated to Zinc or Cobalt.
The hydroxide ion is 4 orders of magnitude more
nucleophilic than is water.
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Covalent Catalysis Acetoacetate Decarboxylase
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• Enzymes physically interact with their substrates
  to effect catalysis
• E S ? ES ? ES ? EP ? E P
• where
• E enzyme
• S substrate
• ES enzyme/substrate complex
• ES enzyme/transition state complex
• P product
• EP enzyme/product complex

• Enzyme and substrate combine to form a complex
• Complex goes through a transition state
  (ES)
• bound substance is neither substrate nor product
• A complex of the enzyme and the product
  is formed
• The enzyme and product separate
• All of these steps are governed by
  equilibria

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• Substrates bind to the enzymes active site
• pocket in the enzyme
• Substrates bind in active site by
• hydrogen bonding
• hydrophobic interactions
• ionic interactions

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Enzyme/Substrate Interactions

• Lock and key model
• substrate (key) fits into a perfectly shaped
  space in the enzyme (lock)

• Induced fit model
• substrate fits into a space in the enzyme,
  causing the enzyme to change conformation
• change in protein conformation leads to an exact
  fit of substrate with enzyme

• Following catalysis, the product(s) no longer
  fits the active site and is released

Enzymes and Enzyme Kinetics
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• Strain and Distortion model
• The binding of the substrate results in the
  distortion of the substrate in a way that makes
  the chemical reaction easier.

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Enzyme Kinetics

• The rate of the reaction catalyzed by enzyme E
• A B ? P
• is defined as
• -DA or -DB or DP
• Dt Dt Dt
• Enzyme activity can be assayed in many ways
• disappearance of substrate
• appearance of product
• continuous assay
• end point assay
• For example, you could measure
• appearance of colored product made from an
  uncolored substrate
• appearance of a UV absorbent product made from a
  non-UV-absorbent substrate
• appearance of radioactive product made from
  radioactive substrate

Enzymes and Enzyme Kinetics
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Higher temperature generally causes more
collisions among the molecules and therefore
increases the rate of a reaction. More collisions
increase the likelihood that substrate will
collide with the active site of the enzyme, thus
increasing the rate of an enzyme-catalyzed
reaction.
Each enzyme has an optimal pH. A change in pH can
alter the ionization of the R groups of the amino
acids. When the charges on the amino acids
change, hydrogen bonding within the protein
molecule change and the molecule changes shape.
The new shape may not be effective. The diagram
shows that pepsin functions best in an acid
environment. This makes sense because pepsin is
an enzyme that is normally found in the stomach
where the pH is low due to the presence of
hydrochloric acid. Trypsin is found in the
duodenum, and therefore, its optimum pH is in the
neutral range to match the pH of the duodenum.
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At lower concentrations, the active sites on most
of the enzyme molecules are not filled because
there is not much substrate.  Higher
concentrations cause more collisions between the
molecules.  With more molecules and collisions,
enzymes are more likely to encounter molecules of
reactant. The maximum velocity of a reaction is
reached when the active sites are almost
continuously filled. Increased substrate
concentration after this point will not increase
the rate.  Reaction rate therefore increases as
substrate concentration is increased but it
levels off.
If there is insufficient enzyme present, the
reaction will not proceed as fast as it otherwise
would because there is not enough enzyme for all
of the reactant molecules. As the amount of
enzyme is increased, the rate of reaction
increases. If there are more enzyme molecules
than are needed, adding additional enzyme will
not increase the rate. Reaction rate therefore
increases as enzyme concentration increases but
then it levels off.
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• The velocity (V) of an enzyme-catalyzed reaction
  is dependent upon the substrate concentration S
• A plot of V vs S is often hyperbolic
  (Michaelis-Menten plot)

Enzymes and Enzyme Kinetics
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• The Michaelis-Menten equation describes the
  kinetic behavior of many enzymes
• This equation is based upon the following
  reaction
• S ? P
• k1 k2
• E S ? ES ? E P
• k-1
• V Vmax S
• KM S
• the reverse reaction (P ? S) is not considered
  because the equation describes initial rates when
  P is near zero

Enzymes and Enzyme Kinetics
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• V Vmax S
• KM S
• V is the reaction rate (velocity) at a substrate
  concentration S
• Vmax is the maximum rate that can be observed in
  the reaction
• substrate is present in excess
• enzyme can be saturated (zero order reaction)
• KM is the Michaelis constant
• a constant that is related to the affinity of the
  enzyme for the substrate
• units are in terms of concentration
• KM k-1 k2
• k1

Enzymes and Enzyme Kinetics
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Enzyme (E) Substrate (S) K_M (in M) k_cat (in
s-1) k_cat/K_M (in M-1s-1) Acetylycholi
ne esterase Acetylcholine 9.5 x 10-5 1.4 x
104 1.5 x 106 Carbonic Anhydrase CO_2 0.012 1.0
x 106 8.3 x 107 Carbonic Anhydrase HCO_3- 0.026
4.0 x 105 1.5 x 107 Catalase H_2O_2 0.025 1.0 x
107 4.0 x 108 Fumerase Fumerate 5.0 x
10-6 800 1.6 x 108 Fumerase Malate 2.5 x
10-5 900 3.6 x 107 Urease Urea 0.025 1.0 x
104 4.0 x 105
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Lineweaver-Burk Plot
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• KM is also the substrate concentration at which
  the enzyme operates at one half of its maximum
  velocity
• if S KM
• V Vmax S
• 2S
• V Vmax
• 2

Enzymes and Enzyme Kinetics
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• To determine KM and Vmax, decide on a number of
  different S values, and measure V at each
  concentration (hold E constant)

Enzymes and Enzyme Kinetics
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• Michaelis-Menten plot is not useful for
  estimating KM and Vmax
• it is better to transform the Michaelis-Menten
  equation to a linear form
• actual values for KM and Vmax determined from
  graph
• double reciprocal plot or a Lineweaver-Burk plot

Enzymes and Enzyme Kinetics
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• By taking the inverse of the Michaelis-Menten
  equation
• same form as y mx b
• plot is y vs x
• y is 1/V
• x is 1/S
• KM/Vmax is slope
• y intercept is 1/Vmax
• x intercept is -1/ KM

V Vmax S KM S 1 KM
S V Vmax S Vmax S 1 KM . 1
1 V Vmax S Vmax
Enzymes and Enzyme Kinetics
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Enzyme Inhibition

• Certain compounds inhibit enzymes
• decrease the rates of their catalysis
• inhibition can be reversible or irreversible
• 3 types of reversible inhibitors
• competitive inhibitors
• non-competitive inhibitors
• un-competitive inhibitors
• Irreversible inhibition
• suicide inhibitors
• the various types of inhibitors can be
  distinguished by the kinetics of their inhibition

Enzymes and Enzyme Kinetics
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• Competitive inhibition
• inhibitor mimics substrate
• fits into active site
• malonate is a competitive inhibitor of succinate
  dehydrogenase

Enzymes and Enzyme Kinetics
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• Competitive inhibitors can be identified by the
  kinetics of their inhibition
• In the presence of a competitive inhibitor
• KM increases
• Vmax stays the same
• The effects of competitive inhibition can be
  overcome by increasing S

Enzymes and Enzyme Kinetics
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• Non-competitive inhibition
• inhibitor binds to a site other than the active
  site
• Non-competitive inhibitors can be identified by
  the kinetics of their inhibition
• In the presence of a non-competitive inhibitor
• KM stays the same
• Vmax decreases
• The effects of non-competitive inhibition cannot
  be overcome by increasing S

Enzymes and Enzyme Kinetics
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• Un-competitive inhibition
• inhibitor binds to a site other than the active
  site, but only when substrate is bound
• Un-competitive inhibitors can be identified by
  the kinetics of their inhibition
• In the presence of an un-competitive inhibitor
• KM decreases
• Vmax decreases
• The effects of un-competitive inhibition cannot
  be overcome by increasing S

Enzymes and Enzyme Kinetics
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• Irreversible inhibition
• enzyme is covalently modified after interaction
  with inhibitor
• derivatized enzyme is no longer a catalyst
• Organofluorophosphates used as insecticides and
  nerve gases
• irreversible inhibitors of acetylcholinesterase
• form covalent product with active site serine
  residue
• enzyme no longer functional

Enzymes and Enzyme Kinetics
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• When chymotrypsin is treated with DIPF
• only ser 195 reacts is derivatized
• other ser residues are not labeled
• ser 195 is in the enzymes active site
• Why is only ser 195 labeled?
• adjacent amino acid residues in active site make
  ser 195 more reactive

Enzymes and Enzyme Kinetics
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The Acyl Enzyme Intermediate
Diisopropylflurophosphate is an inhibitor of
chymotrypsin. It diffuses into the active,
wherein a nucleophilic amino acid attacks the
phosphate, releasing fluoride anion. This
results in a covalent bond between the
nucleophile and the inhibitor. It inhibits the
reaction because it blocks entry of normal
substrates. The enzyme-inhibitor adduct is very
stable. Upon hydrolysis of the protein (6 N HCl,
110C) and amino acid analysis on the
hydrolysate, a novel amino acid was isolated. It
was the diisopropylphosphoryl derivative of
serine.
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Coenzymes and Prosthetic Groups

• some enzymes employ coenzymes and prosthetic
  groups at their active sites
• used for reactions that amino acid R groups cant
  perform
• coenzymes
• metals or small organic molecules
• not covalently bound to protein
• often function as co-substrates
• precursors are often vitamins
• prosthetic groups
• small organic molecules
• covalently linked to protein

Enzymes and Enzyme Kinetics
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Enzyme Regulation 1. Control of Enzyme
Activity Level A. Noncovalent modifiers cause
conformational change between less active and
more active states of the enzyme. B. Covalent
Modification causes interconversion between
inactive and active forms of the enzyme. 2.
Control the Amount of the Enzyme A. Isozymes -
forms of the enzyme which differ in properties
but catalyze the same reaction. For example,
enzyme forms which differ in Vmax and/or Km. The
isozymes can be forms found in different tissues
and organs of an animal or for any eukaryotic
organism, isozymes can be located in different
parts of the cell. For example, different
isozymes of lactate dehydrogenase are found in
muscle and liver. Malate dehydrogenase occurs in
different forms in the cytoplasm and the soluble
matrix phase of the mitochondria. B.
Biosynthesis of the enzyme protein can be
controlled at the level of the gene via
regulation of transcription (ie synthesis of the
enzyme's mRNA). This is more of a molecular
biologic type of regulation and involves
molecules which bind to DNA and influence gene
expression. This type of control where the amount
of the enzyme is governed can also be done after
the mRNA is made, but this is quite rare. In this
mechanism, the mRNA is prevented from being
translated and since mRNA is rather unstable, it
is degraded before it is effectively used by the
ribosomes to make the protein.
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Allosteric Regulation Control of Enzyme Activity
by Non-Covalent Modifiers is usually called
allosteric regulation since the modifier binds to
the enzyme at a site other than the active site
but alters the shape of the active site.
Allosteric is a word derived from two Greek
words 'allo' meaning other and 'steric' meaning
place or site so allosteric means other site and
an 'allosteric enzyme' is one with two binding
sites - one for the substrate and one for the
allosteric modifier molecule, which is not
changed by the enzyme so it is not a substrate.
The molecule binding at the allosteric site is
not called an inhibitor because it does not
necessarily have to cause inhibition - so they
are called modifiers. A negative allosteric
modifier will cause the enzyme to have less
activity, while a positive allosteric modifier
will cause the enzyme to be more active. In order
for allosteric regulation to work, the enzyme
must be multimeric (ie. a dimer, trimer, tetramer
etc.). The concept is easily illustrated using a
dimer as the model system, but it applies equally
well to higher order multimers such as trimers
and tetramers, etc.
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Cooperativity
Enzyme can bind two substrates molecules at
different binding sites.
k1
k2
S E
C1
P E
k-1
k3
k4
S C1
C2
P E
k-3
or
S
S
E
C1
C2
S
S
P
P
E
E
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• The velocity (V) of an enzyme-catalyzed reaction
  is dependent upon the substrate concentration S
• For allosteric enzymes, a plot of V vs S shows
  a sigmoidal relationship

Enzymes and Enzyme Kinetics
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Positive/negative cooperativity

• Usually, the binding of the first S changes the
  rate at which the second S binds.
• If the binding rate of the second S is
  increased, its called positive cooperativity
• If the binding rate of the second S is
  decreased, its called negative cooperativity.

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Independent binding sites
S
S
2k
k
E
C1
C2
2k-
k-
S
S
P
P
E
E
Just twice the single binding rate, as expected
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Pseudo-steady assumption
Note the quadratic behaviour
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Hill equation
In the limit as the binding of the second S
becomes infinitely fast, we get a nice reduction.
VERY special assumptions, note.
Hill equation, with Hill coefficient of 2.
This equation is used all the time to describe a
cooperative reaction. Mostly use of this equation
is just a heuristic kludge.
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http//www.cs.stedwards.edu/chem/Chemistry/CHEM43/
CHEM43/chymotrypsin.mov
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Lysozyme

• Lysozyme is a small globular protein composed of
  129 amino acids.
• It is also an enzyme which hydrolyzes
  polysaccharide chains, particularly those found
  in the peptidoglycan cell wall of bacteria. In
  particular, it hydrolyzes the glycosidic bond
  between C-1 of N-acetyl muramic acid and C-4 of
  N-acetyl glucosamine.
• It is found in many body fluids, such as tears,
  and is one of the bodys defenses against
  bacteria.
• The best studied lysozymes are from hen egg
  whites and bacteriophage T4.
• Although crystal structures of other proteins had
  been determined previously, lysozyme was the
  first enzyme to have its structure determined.

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Lysozyme Active Site
The X-ray crystal structure of lysozyme has been
determined in the presence of a non-hydrolyzable
substrate analog. This analog binds tightly in
the enzyme active site to form the ES complex,
but ES cannot be efficiently converted to EP. It
would not be possible to determine the X-ray
structure in the presence of the true substrate,
because it would be cleaved during crystal growth
and structure determination. The active site
consists of a crevice or depression that runs
across the surface of the enzyme. Look at the
many hydrogen bonding contacts between the
substrate and enzyme active site that enables the
ES complex to form. There are 6 subsites within
the crevice, each of which is where hydrogen
bonding contacts with the sugars are made. In
site D, the conformation of the sugar is
distorted in order to make the necessary hydrogen
bonding contacts. This distortion raises the
energy of the ground state, bringing the
substrate closer to the transition state for
hydrolysis.
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General Acid-Base Catalysis in Cleavage by
Lysozyme
At what position does water attack the sugar?
When the lysozyme reaction is run in the presence
of H218O, 18O ends up at the C-1 hydroxyl group
at site D. This suggests that water adds at that
carbon in the mechanism. From the X-ray
structure, it is known that the C-1 carbon is
located between two carboxylate residues of the
protein (Glu-35 and Asp-52). Asp-52 exists in
its ionized form, while Glu-35 is protonated.
Glu can act as a general acid to protonate the
leaving group in the transition state. Asp can
function to stabilize the positively charged
intermediate. Glu then acts as a general base to
deprotonate water in the transition state.
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Importance of Strain in Catalysis
Stable Chair conformation
Distorted boat conformation
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The Serine Proteases

• The serine proteases are a class of enzymes that
  degrade proteins in which a serine in the active
  site plays an important role in catalysis.
• The family includes among many others,
  Chymotrypsin and trypsin, which weve talked
  about, and Elastase.
• All three enzymes are similar in structure, and
  they all have three important conserved
  residuesa histidine, an aspartate, and a serine.
• Chymotrypsin cleaves after mainly aromatic amino
  acids, while trypsin cleaves after basic amino
  acids. Elastase is fairly nonspecific, and
  cleaves after small neutral amino acids. Notice
  how their active sites are suited for these
  tasks.

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Chymotrypsin Mechanism (Step 1)
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Chymotrypsin Mechanism (Step 2)
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Chymotrypsin Mechanism (Step 3)
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Chymotrypsin Mechanism (Step 4)
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Chmyotrypsin Mechanism (Step 5)
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Chymotrypsin Mechanism (Step 6)
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Chymotrypsin Mechanism (Step 7)