BIOS S-10
Principles of Biochemistry
Enzymes affect reaction rates, not equilibria
Spontaneous reaction (ΔG<0) without a catalyst
An energy barrier has to be overcome
during the conversion of S into P .
The energy barrier is the energy required for:
- Alignment of reacting groups
- Transient unstable charges
-  Bond rearrangements
At the transition state the reaction has an
equal probability to proceed toward the
formation of P or S
The rate of the reaction is affected by the activation energy (ΔG‡): a higher activation
energy correspond to a slower reaction.
An enzyme lowers the activation energy
Formation of an enzyme-substrate complex
Several observations have suggested the formation of an ES complex:
- The high degree of specificity exhibited by enzymes suggests that substrate and enzyme have
complementary surfaces that interact with each other. Key-lock mechanism proposed by Fisher in 1894.
- Substrates frequently protect enzymes from inactivation
- Experiments with substrate analogs.
Enzymes are extraordinary catalysts
The rate of enhancement of a reaction by an enzyme is in the range of 5 to 17 orders of magnitude.
This rate is much higher than most of the enhancement rates observed with chemical catalysts.
Enzymes are extremely specific.
Enzymes are extraordinary catalysts
Two main factors explain why enzymes are good catalysts:
1. They form transient covalent bonds with the substrate.
These bonds activate the substrate
In many cases, the bonds involve chemical groups from the side chain of residues located in an usually
small region of the protein called the active site.
The formation of the covalent bonds lower the activation energy.
2. Non-covalent interactions (weak bonds) are formed between the enzyme and the substrate.
The formation of weak bonds is associated with the release of energy (binding energy) which is the major
source of free energy used by enzymes to lower the activation energy.
Weak bonds are optimized in the transition state and not during the initial enzyme-substrate binding step.
Therefore, the key-lock mechanism described by Fisher does not perfectly reflect enzyme catalysis.
A decrease of ΔG‡ by 5.7 kJ/mol results in a 10-fold increase of the rate of a reaction, while the
binding energy released by the formation of a single weak bond is 4 to 30 kJ/mol.
The rate increase observed for many enzymes requires a decrease of activation energy by 60-100 kJ/mol.
Therefore, the formation of few weak bonds between enzyme and substrate is enough to achieve the
expected decrease of activation energy.
Enzymes are extraordinary catalysts
Weak interactions are optimized at the transition state
Contribution of the enzyme tertiary structure to catalysis
The active site of an enzyme is small compared to
the size of the whole enzyme. Few residues (2 or 3)
participate in substrate binding/catalysis.
Why are enzymes large proteins as opposed to small
peptides containing only the essential R-groups?
The positions of the essential R-groups have to be
precisely fixed in space to interact with the substrate
and to drive catalysis.
The tertiary fold of a large protein makes this required
spatial relationship possible.
Fixed bond length and bond angles prevent in the short
peptide the proper positioning of the essential R-groups.
Three-point attachment
The stereospecificity of the enzyme active site play a critical role in catalysis.
Ex: Alcohol dehydrogenase always transfers the same hydrogen to NAD+
Rate enhancement by entropy reduction
The 2 reactants are free
The 2 reacting groups are linked
by covalent bonds. Free rotation
is possible
The 2 reacting groups are linked
by covalent bonds. Free rotation
is precluded
By constraining the motion of 2 reactants (decreased entropy) you can increase the rate of a reaction
Factors affecting the rate of a reaction
The formation of weak bonds between the enzyme and its substrate contributes to the reduction of the
activation energy.
The binding of the substrate(s) reduces the entropy of the system and allows the correct positioning of
reacting groups on the substrate(s) and on the enzyme.
The desolvation of the substrate contributes to reaction rate enhancement. Weak enzyme-substrate
interactions replace most of the hydrogen bonds existing between the free substrate and the
surrounding water.
The enzyme undergoes a change in conformation upon substrate binding (Induced fit hypothesis).
The lock-and-key hypothesis cannot explain a certain number of observations.
1. Compounds that resemble the normal substrate chemically but possessed less bulky groups often fail to
react, yet they certainly should have fit the lock .
2. Compounds with more bulky groups often fail to react (as expected), yet they were found to bind tightly
to the enzyme.
3. Many bireactant enzymes would not bind substrate B before substrate A, yet according to the
lock-and-key mechanism the binding site for B should be accessible to B even in the absence of A.
In 1958, Daniel Kohsland proposed the induced fit hypothesis to take into account these observations
Induced Fit
Induced Fit of a different kind
β-galactosidase assay
Effect of substrate concentration on V0
The initial velocity is measured at increasing initial concentration of substrate [S] and at a constant
enzyme concentration [E]
At low [S], most of the enzyme is free.
The reaction rate is proportional to [S]
At Vmax, the enzyme is saturated with
its substrate. Most of E is in a complex
with S.
The pre-steady state is a brief period
(few microseconds) when the enzyme is
first added to an excess of S.
ES builds up during the pre-steady state.
V0 reflects the steady-state of a reaction.
[ES] remains almost constant during in
steady state
Michaelis-Menten kinetics
This equation is typical of an hyperbolic equation (y = ax/b + x)
When [S] is low, KM >> [S] and
V0 = (Vmax [S])/KM
V0 exhibits a linear dependence on [S]
When [S] is very high, [S] >> KM and
V0 = (Vmax [S])/[S] = Vmax
When [S] = KM, the M&M equation can be
written as follow:
V0 = (Vmax)/ (KM/[S]) +1
= (Vmax)/ ([S]/[S]) +1
= (Vmax)/ 1 +1 = (Vmax)/ 2
KM is the concentration of substrate at which V0 is half of Vmax, in other words it is the
concentration of S at which half of the enzyme sites are in a complex with S (ES).
KM= [E][S]/[ES]: If KM is high, [ES] is low and the enzyme has a low affinity for S
If KM is low, [ES] is high and the enzyme has a high affinity for S
KM is an indicator of enzyme affinity only when k2 is the rate limiting step in the reaction
Relationship between [S] and Km in cells
The Km of a given enzyme establishes an approximate value for the intracellular level of substrate for
this enzyme.
Vo = Vmax ([S] /(Km + [S]))
If [S] intracellular << Km
Vo~ [S] (Vmax/Km)
Vo is very sensitive to changes in [S], however most of the catalytic potential of the enzyme would be
wasted since Vo<<Vmax
There is no physiological sense in maintaining [S]>>Km since Vo cannot exceed Vmax.
For example the difference in velocity between [S] = Km and [S] = 1000Km is only 2-fold.
Vo([S] = Km) = Km Vmax/(Km + Km) = 1/2 Vmax.
Vo([S] = 1000Km) = 1000Km Vmax / (Km + 1000 Km) = 0.999 Vmax ~ Vmax
Turnover number (kcat)
The Kcat/KM ratio is used to compare different enzymes or the turnover of different substrates by
the same enzyme
kcat = k2
kcat = k3
kcat = turnover number = the number of substrate molecules transformed into product in a given unit of time and by a
single substrate-saturated enzyme molecule.
Two enzymes with identical kcat may catalyze two reactions with very different rates in the absence of enzymes. In
this case one of the enzyme has an enhancement rate much higher than the other enzymes.
The Km of an enzyme tends to have a value close to the intracellular concentration of reaction s substrate and two
enzymes with similar enhancement rate may have very different Km due to different intracellular concentration of the
two substrates.
Therefore, the kcat/Km ratio is a better descriptor of enzymes, and allows for direct comparison between enzymes. The
kcat/Km ratio has a upper limit imposed by the diffusion rate of enzymes and substrates in solution.
Double reciprocal plot: Lineweaver-Burk plot
Reversible inhibition: competitive inhibition
Models of competitive inhibition
Reversible inhibition: uncompetitive inhibition
Predictions from the equilibrium:
1. At any [I], even when [S] is high, not all the
enzyme is in a complex with S (ES), some
non-productive ESI is formed. Therefore, Vmax must
decrease.
2. The formation of ESI drives the equilibrium between
E + S and ES toward the formation ES. Therefore, Km
must decrease.
Reversible inhibition: Mixed inhibition
When α = α , the inhibitor is called a non-competitive inhibitor. S has the same affinity for EI and E. In this
case, Ki = K i and the dissociation constants of ESI ([EI][S]/[ESI]) and of ES ([E] [S]/[ES]) are equal.
As predicted for the uncompetitive inhibition Vmax decreases.
At any [I] the forms of E (E and EI) which can combine with S have an equal affinity for S, therefore the
presence of I does not change Km.
The effect of a non-competitive inhibitor on a reaction is comparable to a decrease in [ET].
Peptide bond cleavage by chymotrypsin
1
2
Chymotrypsin cleaves the peptide
bond on the C-side of Trp, Phe,
and Tyr.
3
Peptide bond cleavage by chymotrypsin
3
4
Peptide bond cleavage by chymotrypsin
6
5
1
7
y-series identification by isotope labeling
The biological activity of proteins is regulated in 5
principal ways
1. Regulation via energy charge :
Competitive inhibition by the reaction product (P), while [S] + [P] remains constant
2. Allosteric control:
- The allosteric proteins contain distinct regulatory and substrate binding sites
Allosteric proteins show the property of cooperativity. Consequently, a slight change in
substrate concentration can produce substantial changes in activity.
- 
Allosteric proteins are information transducers: their activity can be modified in response
to signal molecules or to information shared among active sites.
3. Multiple forms of enzymes (Isozymes or isoenzymes):
- Isozymes are homologous enzymes that catalyze the same reaction but differ slightly
in structure and more obviously in Km, Vmax as well as regulatory properties.
- Very often, isoenzymes are expressed in a distinct tissue or organelle or at distinct stages of
development.
4. Reversible covalent modifications:
The activity of many proteins is altered by the covalent attachment of a modifying group (in
most of the cases a phosphoryl group). These proteins cycle between an active and an
inactive form.
5. Proteolytic activation:
Some proteins are irreversibly converted into an active state by proteolysis.
Regulation via energy charge
If [S] + [P] remains constant, the rate of the reaction S--> P depends on the relative concentration of S and
P, and P can be considered as a competitive inhibitor.
This type of competition is common in enzymes using ATP as a substrate. ATP-utilizing reactions are
often inhibited by their products: ADP or AMP.
In a cell, the pool of adenine nucleotide (adenylate: AMP, ADP and ATP) is constant and a cell is
characterized by its Energy charge = ([ATP] + 1/2[ADP])/[ATP] + [ADP] + [AMP].
This term is an attempt to simulate the total adenylate pool in a cell, 1/2 [ADP] is an ATP equivalent that
derives from the equilibrium, in cells, catalyzed by adenylate kinase: ATP + AMP <--> 2 ADP
The adenylate pool is equivalent to an electrochemical storage battery;
- The system is fully charged ( Energy charge = 1) when all adenylate is present as ATP
- The system is fully discharged ( Energy charge = 0) when all adenylate is present as AMP
- A system in which all ATP has been converted into ADP as an energy charge of 0.5
Regulation via energy charge
Distribution of adenylate as a function of the energy charge of a system
Regulation via energy charge
P-utilizing enzyme
(ATP-generating enzyme)
S-utilizing enzyme
(ATP-utilizing enzyme)
Velocity response to changing [S]/[P] ratio.
S
P reaction: off-on switch. The velocity of an ATP-utilizing reaction will increase substantially in a
fully charged system.
P S reaction: on-off switch. The velocity of an ATP-producing reaction will increase substantially in a
discharged system
ATCase reaction
ATCase
End-product of the biosynthetic pathway
CTP inhibits ATCase
CTP illustrates a common regulatory mechanism of metabolic pathways called feed-back or
end-product inhibition.
CTP has no structural similarity with the ATCase substrates
Ultracentrifugation studies of ATCase
No treatment
Treatment with
P-hydroxymercuribenzoate
The chemical treatment dissociates ATCase into its regulatory (r) and its catalytic (c) subunits
Purified catalytic subunits have a CTP-independent catalytic activity
Purified regulatory subunits have no catalytic activity but they bind to CTP
Structure of ATCase
Quaternary structure of ATCase as viewed from the top: a single catalytic trimer is visible, the
second trimer is hidden behind the one visible. The 6 regulatory subunits are visible.
PALA is a bisubstrate analog
Aspartate
Carbamoyl
phosphate
The binding of PALA induces a conformational change in ATCase
The T-state predominates in the absence of substrates or substrate analogs
The R-state predominates in the presence of substrates or substrate analogs
The enzyme exists in equilibrium between the T- and R-states.
Allosteric proteins demonstrate cooperative properties
The binding of Asp is measured in the absence of allosteric modulators (CTP, or ATP)
The binding curve is a sigmoid with native ATCase. ATCase behaves like an allosteric protein
The binding curve is a typical hyperbolic curve with purified catalytic subunits. The catalytic
subunit behaves like a Michaelien enzyme
Saturation of hemoglobin with oxygen
Hemoglobin is an allosteric protein
The binding of oxygen induces conformational changes
O2
Deoxyhemoglobin
Oxyhemoglobin
The quaternary structure changes include:
- Change in the structure of the heme which adopt a more planar structure
- Adjustment of the α/β subunit interfaces
- Narrowing of the pocket between the β subunits.
The Monod, Wyman, & Changeux (MWC) model
T0
T1
T2
R0
R1
R2
The MWC model is based on the following assumptions:
1. Allosteric proteins are polymeric and contain binding units arranged in
a symmetrical fashion.
2. Each unit, or protomer, contains one and only one binding site for any
given ligand (substrate, inhibitor, activator).
3. The oligomer can exist in at least 2 different conformations (T & R)
which are in equilibrium. The transition between conformations is an
all-or-nothing event.
4. There are no hybrid states where some protomers have changed their
conformation while others have not.
T3
R3
T4
R4
5. The affinity of a binding site for a given ligand depends on the
oligomer conformation. The binding of a ligand to one particular
conformation will cause the equilibrium between oligomer configurations
to shift in favor of the conformation with the bound ligand
6. The T-state has a lower affinity for ligands.
MWC equation of a theoretical binding curve for an
allosteric protein with n binding sites
MWC model: theoretical binding curve
The cooperativity depends upon the value of L and c:
1. The cooperativity is more marked when L is large (equilibrium strongly in favor of T0) or
when the intrinsic dissociation constant ratio c is small.
2. When L is very small (equilibrium strongly in favor of R0) or when c =1 (the affinity for
both states for the ligand is the same) the cooperativity disappears and the binding curve
becomes hyperbolic.
A curve established with n = 4, L = 3 x 105, and c = 0.01 fits the
oxygen binding curve of hemoglobin
The MWC model provides a very simple explanation for
the control of allosteric protein activity
The MWC model predicts that allosteric modulators alter the R-T ratio by preferentially stabilizing
one of the forms.
- An inhibitor binds preferentially to the T-state and causes the transition to the R-state to be more difficult.
- An activator functions by binding to the R state and by increasing its concentration.
In extreme cases, an activator will displace the R-T equilibrium to such an extend that the R-state
predominates and that cooperativity is abolished. In this case the binding curves become hyperbolic.
Heterotropic allosteric enzymes
Heterotropic enzyme: the modulator of enzyme activity is different from the enzyme substrate.
In some cases, both the substrate and the modulator have differential affinities toward the
T and R states. Therefore, the presence of the modulator will modify the apparent affinity
of the protein for the substrate.
Vmax is unchanged
Activators decrease K0.5 (substrate concentration for v = Vmax/2
Inhibitors increase K0.5
Heterotropic allosteric enzymes
In some cases, the substrate has the same affinity for both R and T states but one state has a
much higher value of kcat.
The modulator binds preferentially to one of the 2 states and modulates the protein activity
by changing the equilibrium position between the two. Depending on whether the
modulator has maximum affinity for the active or for the inactive state, it will behave as an
activator or as an inhibitor
Vmax is changed:
- Increased by activators
- Decreased by inhibitors
K0.5 is nearly constant
The Kohsland-Nemethy-Filmer (KNF) model
In the MWC model, the symmetry assumption minimizes the number of intermediate
states and is only an approximation.
The KNF model avoids the presumption of symmetry but uses another simplifying
features
The progress from T to the ligand-bound R state is a sequential process.
The conformation of each subunit changes in turn as it binds the ligand.
KNF assumptions:
1. In the absence of ligands, the protein exists in 1 conformation
2. Upon binding, the ligand induces a conformational change in
the subunit to which it is bound. This change may be
transmitted to neighboring vacant subunits via subunit
interfaces
The general model (Eigen model)
KNF
MWC
MWC
KNF
In the general model, the MWC and KNF models are limiting cases of a general
scheme involving all possible combinations.