### Enzymology Lecture 5 - ASAB-NUST

```Enzymology
Lecture 5
Dr. Nasir Jalal
ASAB/NUST
Question: What do cells surf on?
Linear plot of Michaelis-Menten
The plot of v versus [S] is not linear; although initially linear at low [S], it bends over to saturate
at high [S]. Before the modern era of nonlinear curve-fitting on computers, this nonlinearity
could make it difficult to estimate KM and Vmax accurately. Therefore, several researchers
developed linearisations of the Michaelis–Menten equation, such as the Lineweaver–Burk plot,
the Eadie–Hofstee diagram and the Hanes–Woolf plot. All of these linear representations can be
useful for visualising data, but none should be used to determine kinetic parameters, as
computer software is readily available that allows for more accurate determination by nonlinear
regression methods
Why double reciprocal
• Plotting 1/v (reciprocal of rate) vs. 1/[s] (reciprocal of
substrate concentration) yields a straight line. One
can then use the equation of the linear regression to
calculate Vmax and Km.
Lineweaver–Burk plot
• The Lineweaver–Burk plot or double reciprocal plot is a common
way of illustrating kinetic data. This is produced by taking the
reciprocal of both sides of the Michaelis–Menten equation. This is a
linear form of the Michaelis–Menten equation and produces a
straight line with the equation:
• y = mx + c with a y-intercept equivalent to 1/Vmax and an x-intercept
of the graph representing -1/KM
Double reciprocal used to calculate Km
http://courses.washington.edu/conj/enzyme/dblrecip2.html
Quick Quiz
• When you plot 1/v vs. 1/[s]
you get a straight line. What is
the y-intercept?
• What is the slope for this line?
• Calculate Vmax for the
standard data shown above.
(You may give answer or just
set problem up.)
• Calculate Km for the standard
data shown above. (You may
problem up.)
1/Vmax
Km/Vmax
Vmax=1/191=0.0052
Km=14*Vmax=0.073
When used for determining the type of enzyme inhibition, the Lineweaver–Burk plot can
distinguish competitive, non-competitive and uncompetitive inhibitors. Competitive inhibitors
have the same y-intercept as uninhibited enzyme (since Vmax is unaffected by competitive
inhibitors the inverse of Vmax also doesn't change) but there are different slopes and x-intercepts
between the two data sets. Non-competitive inhibition produces plots with the same x-intercept
as uninhibited enzyme (Km is unaffected) but different slopes and y-intercepts. Uncompetitive
inhibition causes different intercepts on both the y- and x-axes but the same slope.
The Lineweaver–Burk plot was classically used but it is prone to error, as the y-axis takes the
reciprocal of the rate of reaction thus increasing any small errors in measurement. Also, most
points on the plot are found far to the right of the y-axis (due to limiting solubility not
allowing for large values of [S] and hence no small values for 1/[S]), calling for a large
extrapolation back to obtain x- and y-intercepts.
Transition State Model
For a reaction involving two molecules,
a transition state is formed when the old
bonds between two molecules are
weakened and new bonds begin to form
or the old bonds break first to form the
transition state and then the new bonds
form after. The theory suggests that as
reactant molecules approach each other
closely they are momentarily in a less
stable state than either the reactants or
the products. In the example below, the
first scenario occurs to form the
transition state:
Old bonds between
molecules
(hydroxide and
bromomethane)
weaken
New bonds
begin to form.
Less stable
state.
New molecule
with new
bonds forms,
Bromide
released
The equation for an enzymatic reaction is:
K‡ is the concentration equilibrium constant, defined as:
This equation can be used to find out the rate constant K
Where,
kB is Boltzmann’s constant,
h is Planck’s constant and
T is the temperature
Boltzmann constant = 1.3806503 × 10-23 m2 kg s-2 K-1
Planck's constant = 6.626068 × 10-34 m2 kg / s
http://www.rpi.edu/dept/chem-eng/Biotech-Environ/Projects00/enzkin/transition.htm
Gibb’s Free Energy
K‡ concentration equilibrium constant resembles the equilibrium constant used to
describe Gibbs free energy, defined as:
where co is the standard state concentration. DGt can be defined as the Gibbs
energy of activation.
The Gibbs energy difference between the ground and transition state can be
used to predict the rate of reaction.
The binding energy associated with the specific substrate-enzyme interaction is
a significant factor in lowering the Gibbs free energy change required for
reaction.
The large binding energies of substrates are due in part to the complementary
shape of the active site of the enzyme. The Gibbs energy can be considered to
be composed of two terms, DGt, the binding energy and DGs, the activation
energy involved in the making and breaking of bonds leading to the transition
state from enzyme-substrate intermediate (ES). They are related as follows:
DGt = DGt + DGs
Gibb’s Free Energy
DGt can be defined as
the binding energy.
DGs, the activation energy
involved in the making and
breaking of bonds
http://www.rpi.edu/dept/chem-eng/Biotech-Environ/Projects00/enzkin/transition.htm
Using Gibbs free energy
•
In a problem X was trying to figure out if this reaction will proceed as written:
(is the end result a positive/unfavorable or negative/favorable reaction).
(DHAP) --> (GAP)
Standard free energy change ΔG° = +1.8 kcal/mol. Concentration of DHAP = 8
Concentration of GAP = .5
The gas constant (R) is 1.987 kcal/mol
temp in cell = 298 K
And my equation that I should be using is:
ΔG = ΔG° + RTln([products]/[reactants])
So I end up with:
ΔG = 1.8 + (1.987 * 298)ln(0.5/8) = -1641.72
Is this done? It seems like a very improbable answer .
Or is there a NEED to factor in the temperature because the gas constant is calculated for the cell temp
already? And then WE would end up with:
1.8 + (1.987)ln(0.5/8) = -3.709
•
Your gas constant is wrong isn't it?
Shouldn't it be 1.987 cal/°K/mol, rather than 1.987 kcal/mol?
Delta G = 1.8 + ((0.001987 x 298) x ln (0.5/8))
= 1.8 + (0.592 x -2.7725)
= 1.8 + (-1.64132)
= 0.158
Question: Why did the policeman hide under a tree?
Because he worked for the special branch.
Quantum tunneling model
of Enzyme activity
Heisenberg’s Uncertainty Principle
involving energy and time
The more precisely the position is determined, the less precisely
the momentum is known in this instant, and vice versa.
--Heisenberg, uncertainty paper, 1927
• If our measurement lasts a certain time Dt, then we cannot know the
energy better than an uncertainty DE
Quantum Tunneling Model
through an example
To understand the phenomenon, particles attempting to travel between
potential barriers can be compared to a ball trying to roll over a hill;
quantum mechanics and classical mechanics differ in their treatment of this
scenario. Classical mechanics predicts that particles that do not have
enough energy to classically surmount a barrier will not be able to reach
the other side. Thus, a ball without sufficient energy to surmount the hill
would roll back down.
Thus, a ball without sufficient energy to surmount the hill would roll back
down. Or, lacking the energy to penetrate a wall, it would bounce back
(reflection) or in the extreme case, bury itself inside the wall (absorption).
In quantum mechanics, these particles can, with a very small probability,
tunnel to the other side, thus crossing the barrier.
The ball could, in a sense, borrow energy from its surroundings to tunnel
through the wall or roll over the hill, paying it back by making the reflected
electrons more energetic than they otherwise would have been
Quantum Tunneling Model
through an example
 Normally, the car can only get as far as C, before it falls
back again
 But a fluctuation in energy could get it over the barrier
to E!
Early concepts
Warshel and Levitt's study of lysozyme was pioneering in this area.
Warshel, A and Levitt, M. 1976. J. Mol. Biol., 103: 227 [CrossRef], [PubMed], [Web
of Science ®]
The early ab initio QM/MM implementation by Singh and Kollman is notable. The
semiempirical QM/MM method developed by Field et al.
Rules of Quantum Tunneling
• A particle ‘borrows’ an energy DE to get over a
barrier
• Does not violate the uncertainty principle,
provided this energy is repaid within a certain
time Dt
• The taller the barrier, the less likely tunneling
would occur
Quantum tunneling phenomenon
Quantum tunneling through a barrier. The
energy of the tunneled particle is the
same but the amplitude is decreased.
Quantum tunneling through a barrier. At
the origin (x=0), there is a very high, but
narrow potential barrier. A significant
tunneling effect can be seen.
Electron wavepacket simulation
An electron wavepacket directed at a potential barrier. Note the dim spot
on the right that represents tunnelling electrons.
A can toppling over due to quantum
fluctuations of its position
33
years!!
QM/MM modeling
• Some enzymes operate with kinetics which
are faster than what would be predicted by
the classical ΔG‡. In "through the barrier"
models, a proton or an electron can tunnel
through activation barriers. Quantum
tunneling for protons has been observed in
tryptamine oxidation by aromatic amine
dehydrogenase.
Chorismate mutase and QM/MM
An enzyme (chorismate mutase) partitioned into a QM region (shown as red spheres) and an
MM region consisting of protein (yellow cartoons) and solvent (cyan sticks). Here the system is
truncated to an approximate sphere (in this case with radius 25 Å), typical of the approach used
in many QM/MM simulations of enzyme-catalysed reaction mechanisms (e.g. applying
‘stochastic boundary’)
Theoretical basis of QM/MM
• The theoretical basis of QM/MM methods are
outlined here. The system is divided into a
(small) QM region and an (usually much
larger) MM region. The total energy of a
QM/MM system can be expressed as:
E QM and E MM are the energies of the QM and MM regions,
respectively, calculated in a standard way at those levels. For
example, the MM energy is defined by the potential of the
force field used.
Theoretical basis of QM/MM
• Current standard MM force fields for proteins treat atoms
as point charges with van der Waals radii, which together
determine the non-bonded interactions.
• Force fields also include terms to describe interactions
between bonded atoms, e.g. bond, angle and dihedral
terms.
• E QM/MM describes the interaction between the QM and
MM regions, and can be treated in various ways.
• E Boundary is a term to account for the fact that the system
may have to be truncated for practical reasons (e.g.
QM/MM calculations are computationally demanding, and
it may not be possible or desirable to include the whole of
an enzyme molecule).
Considerations for QM/MM
• Broadly speaking, there are two particularly
important considerations in the interaction
between the QM and MM regions:
• (i) the treatment of non-covalent interactions
between the QM and MM regions and
• (ii) where covalent bonds exist between atoms
in the QM and MM regions, the treatment of
bonds at the frontier between the two
regions.
• The QM treatment of the electronic structure of a
small active site region allows chemical reactions to be
modeled, including the effects of the environment
through an empirical MM treatment.
• Enzyme mechanisms can be tested, transition states
(TSs) and reactive species identified and characterised
and the effects of mutations investigated.
• The dynamics of proteins can also be simulated,
identifying conformational changes that may be
associated with reaction.
oxidative deamination of tryptamine
The rate-limiting proton transfer step in the oxidative deamination of tryptamine by aromatic
amine dehydrogenase (AADH). A primary H/D KIE of 55 ± 6 has been reported for this step from
experimental studies, one of the highest KIEs reported for an enzyme-catalysed proton transfer .
Calculations indicate that quantum tunnelling is important in this reaction, but find no role for
large-scale protein dynamics in driving the reaction.
John D. McGeagh, Kara E. Ranaghan, Adrian J. Mulholland, Biochimica et Biophysica Acta (BBA) Proteins and Proteomics. Volume 1814, Issue 8, August 2011, Pages 1077–1092
Question: Which animal likes baseball the most?
A bat of course……………!
Combined QM/MM methods
Goal: to do quantum chemical calculations of reactions and
electronically excited states of large molecular systems.
QM
24-40 Å
MM
Heff = Hqm + Hqm/mm + Hmm
Combined QM/MM Simulation
 Generalized Hybrid Orbital (GHO) for the treatment
of QM and MM boundary
 Balancing Accuracy and Applicability
QM models can be systematically improved.
Semiempirical QM models can be parameterized for
specific reactions and properties.
MM force fields can be applied to large systems.
 Bond-Making and Breaking Processes
 Electronic polarization by the dynamics of the
environment is naturally included.
Model Reaction Strategy
H
O2C
O
Phenoxide ion
CH3
Alanine
NH3
H
H
O
O2C
O
CH3
AlaR
N
H
CH3
N
H
O
H 3C
O2C
O
N
H
Ala-PLP(H+)
Ala-PLP
H 3C
N
ENZYMES
The activity of a cell is largely controlled by the activity of the network of enzymes
within it.
Monod (1972) describes networks of enzymes as 'microscopic cybernetics'. They are a
clear-cut example of adaptive computation occuring on a subcellular level.
Enzymes are, in most cases, incredibly specific. They are also orders of magnitude more
powerful than non-organic catalysts.
Networks of enzyme-mediated reactions are not simply a matter of enzymes catalysing
the production of other enzymes. There are additional multiple feedback and
feedforward effects.
For example, enzymes can be activated by the degradation of their metabolites. This will
tend to stabilise the level of the metabolites in the system.
Enzymes may also be activated by the metabolites of enzymes in another sequence.
Allosteric enzymes inhibit and/ or enhance the efficacy of other enzymes, as well as
acting as catalysts themselves.
ENZYMES & QUANTUM TUNNELING
At least some enzymes catalyse using quantum tunneling. In actuality, quantum
tunneling may be the norm in enzyme catalysis:
Hydrogen-transfer processes are expected to show appreciable quantum mechanical
behaviour. Intensive investigations of enzymes under their physiological conditions
show this to be true of practically every example investigated. (Klinman 2003).
Quantum tunneling reduces the amount of energy required to catalyze a reaction.
There would therefore be strong evolutionary pressures this more energy-efficient
catalysis to develop.
There is a huge literature on this subject, most of it very technical.
Redox chains are chains of electron transfer (by quantum tunneling) which occur as
part of actual catalytic process. Redox chains can intersect at nodes called redox
clusters. (See Moser, Page, Chen and Dutton 2000 for a discussion of redox chains).
Maps of redox chains within the catalytic process display a similar structure (nodes;
multiple linkages) to maps of chains of catalytic reactions.
Enzymes as proteins
Cofactors
Cofactors (non-protein component of an enzyme):
Some enzymes do not need any additional components to show full activity. However,
others require non-protein molecules called cofactors to be bound for activity.
Cofactors can be either inorganic ( e.g. , metal ions e.g., Mn+2, Zn+2, Fe+2, Ca+2 and ironsulfur clusters) or organic compounds, (e.g., flavin and heme).
Organic compounds (Posthetic group/Co-enzymes):
Prosthetic groups, which are tightly bound to an enzyme, or coenzymes, which are
released from the enzyme's active site during the reaction.
transfer chemical groups between enzymes. carbonic anhydrase, with a zinc cofactor
bound as part of its active site. These loosely-bound molecules are usually found in the
active site and are involved in catalysis but not released from the active site.
For example, flavin and heme cofactors are often involved in redox reactions. Enzymes
that require a cofactor but do not have one bound are called apoenzymes . An
apoenzyme together with its cofactor(s) is called a holoenzyme (this is the active form).
Most cofactors are not covalently attached to an enzyme, but are very tightly bound.
However, organic prosthetic groups can be covalently bound.
Co-enzymes
Coenzymes :
Coenzymes Coenzymes are small organic molecules that transport chemical
groups from one enzyme to another. Some of these chemicals such as
riboflavin, thiamine and folic acid are vitamins, (acquired). The chemical groups
carried include the hydride ion (H - ) carried by NAD or NADP + , the acetyl
group carried by coenzyme A , … etc.
Since coenzymes are chemically changed as a consequence of enzyme action, it
is useful to consider coenzymes to be a special class of substrates, or second
substrates, which are common to many different enzymes. For example, about
700 enzymes are known to use the coenzyme NADH. Coenzymes are usually
regenerated and their concentrations maintained at a steady level inside the
cell: for example, NADPH is regenerated through the pentose phosphate
Recap
prosthetic group – the non-amino acid part of a conjugated protein.
cofactor - a nonprotein molecule or ion required by an enzyme for catalytic activity
- can be an organic molecule or metal ion,
such as Mg2+, Zn2+, Fe2+, Ca2+
coenzyme - an organic cofactor
apoenzyme - a catalytically inactive protein
(formed by removal of the cofactor from the active enzyme).
- activated by a cofactor
apoenzyme + cofactor(coenzyme or inorganic ion) --> active enzyme
An important group of coenzymes are vitamins.
For example, vitamin B12 acts as coenzyme B12 in the shift of H atoms between adjacent carbon atoms and in the
transfer of methyl groups.
Another example, niacin acts as nicotinamide adenine dinucleotide (NAD+) in hydrogen transfer.
Another important group of cofactors are minerals in our diet.
For example, the coenzyme Zn2+ is required for the enzyme carbonic anhydrase to function.
Learning Check E2
A. The active site is
(1) the enzyme
(2) a section of the enzyme
(3) the substrate
B. In the induced fit model, the shape of the
enzyme when substrate binds
(1) Stays the same
(2) adapts to the shape of the substrate
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Learning Check E3
C. In the transition state model, the enzyme’s reactive stage can be defined as:
(1) Staying the same.
(2) Changing before binding with substrate.
(3) Changing after binding with substrate.
(4) Changing during binding with substrate.
D. In the quantum tunneling model, the enzyme tends to overcome:
(1) Substrate.
(2) Energy deficit.
(4) Climb a hill.
Solution E2, E3
A.
The active site is
(2) a section of the enzyme
B. In the induced fit model, the shape of the enzyme when substrate
binds
(2) adapts to the shape of the substrate
C. In the transition state model, the enzyme’s reactive stage can be
defined as:
(4) Changing during binding with substrate.
D. In the quantum tunneling model, the enzyme tends to overcome:
(2) Energy deficit.
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