Principles of Bioenergetics and Catalysis ? Kinetics

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Principles of Bioenergetics and Catalysis ?
Kinetics
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Lec 1 Substrate diffusion and catalyis

• What are bacteria? The advantage of being small.
• What do bacteria do? Catalyse exergonic redox
  reactions.
• Substrate diffusion to the cell Can we predict
  the random diffusion of a molecule? Not of one,
  but of many molecules.
• What is the kinetics of substrate diffusion (1st
  order kinetics, Ficks law).
• What is diffusion driven by? Order, Concentration
  gradient,
• How come that many molecules seem to have a
  behaviour but an individual molecule does not?
• What is the principle of catalysing redox
  reaction? The enzyme does not bind to the
  substrate.

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What do bacteria do?

• Catalyse exergonic redox reactions
• Exergonic, (downhill) reactions loose Gibbs Free
  Energy. (DGnegative)
• Bacteria utilise a portion of the free energy
  released for growth processes and multiplication

S
G
?G
P
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What does ?G (Gibbs Free Energy Change) mean?

• Spontaneous reactions are downhill reactions
• Energy of substrates is higher than of products
• Products are more stable than Substrate (stable
  low energy)
• The driving force hill height difference
  in G Delta (?) G ?G G (prod.) G (substr.)
• The reaction is driven by the loss in G ? Change
  in G is a negative value (e.g. ? G -256 kJ/mol)

S
G
?G
P
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Does the ? G allow to predict the reaction rate ?

• No
• But for ? G zero, reaction rate will be zero
• For ? G positive, reaction would go backwards
  (P?S)
• The rate is determined by the activation energy
  (AE)
• In biological reactions the AE is largely
  determined by the presence of enzymes (lower AE)
• Now how do they do that?

AE
S
G
?G
P
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The ?Go of redox reaction is related to the ?Eo
of e- donor and acceptor

• ?Eo is the difference in redox potential of the
  half reactions
• Couple with lower Eo will become e- donor
• If not reaction would reverse
• ?Go n F ? Eo
• Microbes that use electron donors of a very low
  Eo (e.g. H2 and an electron acceptor of a very
  high level e.g. O2) have a lot of free energy
  available for growth

e- don.
-Eo
?E
e- acc.
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What is an enzyme reaction ?
A reaction catalysed by a protein. What are the
consequences of enzyme catalysis? The rate of a
spontaneous reaction is increased. If the
reaction is already spontaneous, why do we need
an enzyme? Spontaneous downhill
exergonic Enzymes can not catalyse uphill
endergonic reactions If catalysed uphill
reactions proceed in the reverse direction
(Products ? Substrates)
G
G
Reaction path
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How do enzymes catalyze ?
A. By lowering the activation energy barrier! B.
By binding to the substrate like a lock to a
key??? This is the simplified textbook
explanation, but how can we visualise it? How can
an enzyme convert a substrate to product by
binding to it? Binding means stabilising (lower
Energy level) and hence slowing Example Antibody
binding to antigen. Antibody is a protein
designed by the immune system to bind and
neutralise a foreign substances (the antigen).
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Why dont antigens catalyze?
Will an antibody against the substrate be able to
catalyse the reaction? No What is the difference
between an antigen and an enzyme. Both bind, one
catalyses the other does not. Does the enzyme
have perhaps a special mechanism (lever) that can
break into the substrates? No
P
S
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How do enzymes catalyse ?
Example Substrate stick, Product broken
stick For the stick to be broken it must go
through a transition state (T) How does the
enzyme (stickase, of course) catalyse by binding
to the stick? Binding to the stick stabilises
rather than activates the substrate ? not making
reaction easier The simplified concept of the
enzyme binding to the substrate does not make
sense Lets have a closer look at the energy
diagram for clues.
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How do enzymes catalyse ?
High Energy Unlikely, reactive, activated Low
Energy Likely to exist, stable
needed to lower the activation energy level a
way to make the transition (T) state more likely
S
G
P
Reaction path
Note T not an intermediate just a deformed
molecule that makes forward and backward
reaction equally likely
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How do enzymes catalyse ?
Example Substrate stick, Product broken
stick For the stick to be broken it must go
through a transition state (T) The enzyme
(stickase, of course) binds to T ?stabilises
T ?makes T more likely ?higher quantities of T
available ?higher likelyhood for P to form (P
cannot form when T is in ultra low
concentration) Enzymes catalyse by binding to
the transition state and making it more likely.
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How do enzymes catalyse ?
Significant product formation depends on
availability of T. Non catalysed reactions are
slow because T is low By binding to T enzymes
increase the chances of T to exist, hence speed
up the reaction. Binding does not mean, holding
on to T but releasing T rapidly, either as S or
as P.
S
G
P
Reaction path
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How do enzymes catalyse ?
The enzyme substrate complex (ES) is not a
transitional state but a true, existing, defined
intermediate Intermediates are in a
valley Transition states are on a peak
S
ES
G
P
Reaction path
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How far will the catalysed reacton go?
With decreasing substrate concentration the
energy content of the substrates
sinks. Increasing product concentrations lift the
energy content of the products. The reaction
continues until the difference in G (Delta G) is
zero. Then the energy level of substrate equals
that of the product Reaction is at
equilibrium Rate of backwards reaction equals
that of forward reaction. The ratio P/S now
represents the equilibrium constant keq.

S
G
P
Reaction path
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The dynamic equilibrium

• The ratio P/S now represents the equilibrium
  constant keq.
• An original very exergonic reaction needs lots of
  P to accumulate until equilibrium is reached?
• at equilibrium P/S is very high (e.g. 10,000)
• endergonic reactions have low keq (e.g. 0.00001)
• The enzyme does not affect the spontaneity or
  reversibility of reaction but the energetics
  does.
• Not surprisingly the reaction driving force is
  related to keq ?G RT ln keq

P
S
G
Reaction path
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Binding Energy
Where does the energy come from to overcome
activation energy? An enzyme/substrate to be more
precise enzyme/T complex forms hydrogen bonds and
hydrophobic interaction bonds. The binding energy
released is the energy source of lowering the
activation energy (analogy of magnets in
stickase) H bonds of T with H2O are replaced by
bonds with E (dry bonding)
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What is the effect of activation energy on
reaction rate?
The overal rate constant (k) of the reaction
depends directly on the activation energy k
(B/PT)e -DG(activ.)/RT B/PBolzman/Planck
constant E.g. lowering the activation energy by
5.7kJ will increase rate 10 fold
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Part 2 Biological Reaction Kinetics

• The kinetic background of enzyme catalyzed
  reactions.
• Comparision of 2 biological reaction types with
  classical chemical reaction kinetics.
• Four reaction kinetics types
• Zero order, First order, Michaelis Menten,
  exponential (multiplication of biocatalyst)

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What is the effect of activation energy on
reaction rate?
After we have concluded that the enzyme (E)
catalyses the substrate (S) conversion by forming
an Enzyme-substrate complex Let us see how we
can derive the kinetic behaviour of the enzyme
reaction from first principles. The widely
accepted enzyme kinetics model is the Michaelis
Menten model.
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Foundation of Michaelis-Menten Kinetics
For the overall enzyme reaction a number of rate
constants need to be considered The rate of
conversion of E and S to ES is k1 k-1 is the
rate constant for ES going back to E and S k2 is
the rate for conversion of ES to E and P In
enzyme assays P is negligible (startup velocity
of reaction) ?k-2 is not included. (Rate
constants mean first order kinetics rate
constants as explained below.)
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Foundation of Michaelis Menten kinetics
Rate constant of first order reaction predicts
that the rate is proportional to the substrate
concentration The rate for ES to go to E P is
given by ES (mM) k2 (h-1) ? (mM/h)
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Foundation of Michaelis Menten kinetics
At substrate saturation no free enzyme is
available (E0)? overall rate is determined by
k2 ( kcat k2) (btw kcat vmax/(total enzyme
concentration (Et, EES)) The ratio of ES
formation over ES disintegration is km
(formula?) km (k2 k-1)/k1 ? enzyme with low
km ES formation faster than disintegration
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Derivation of MM kinetics from first principles
At steady state rate of ES disintegration rate
of ES formation k-1ES K2ES k1ES
(EtEES)? k-1ES K2ES
k1(Et-ES)S multiply out
right? k-1ES K2ES k1EtS - k1ESS
k1ESS? k-1ES K2ES k1ESS k1EtS
bracket out ES? ES (k-1 K2 k1S )
k1EtS solve for ES? ES k1EtS /
(k-1 K2 k1S ) ES
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cancel k1
ES ES
(as vo k2 ES ? ES vo/k2 ) ?
(as vmax k2Et) ?
vo
vo
(k2 is also called kcat)
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The Michaelis Menten Model has been derived
(students dont need to be able to derive it but
to know the final equation)
Vo the initial velocity (no products present) S
substrate km half saturation constant, also
called kS vmax maximum velocity under substrate
saturation when overall reaction only depends on
k2
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Microbial Reaction Kinetics
The Michaelis Menten (MM) model is not only
useful for enzymatic reactions but overall
microbial reactions such as algal blooms or
microbial growth in bioreactors. After we have
seen where the most widely used biological
kinetic mode comes from let us compare 2 types
of microbial kinetics (MM and exponential
kinetics) with traditional chemical kinetics
(zero and first order).
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Zero Order kinetics
S
P

• constant velocity
• velocity independent of S
• v K (M/s)
• Ex limited access to S (O2 diffusion to food)
• water loss
• enzyme reactions at high S

V
Time
V
S
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First Order Kinetics
P

• velocity decreases over time (parallel to S)
• velocity is determined by and hence proportional
  to S
• v S K (s-1)
• K is the rate constant
• Ex Most chemical reactions
• Radioactive decay (half time)

V
S
Time
V
S
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Exponential Kinetics
S
P

• velocity exponentially increasing over time
• independent of S but related to P
• Can give appearance of sudden increase in P
• v P K (s-1)
• a product must enhance reaction velocity (e.g.
  heat, chain reaction)
• Biological examples
• bacterial spoilage (e.g. milk) multiplication of
  catalyst
• Auto-oxidation of fats (radicals propagation)

V
Time
V
P
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Michaelis Menten Kinetics
Phase 1
Phase 2
S
P

• Two reaction phases
• 1 zero order, Enzyme limiting
• 2 first order, S limiting
• Why do we get first and zero order if S or E is
  limiting?
• S changes, E does not change!
• v vmax S / (s kS)
• Examples
• Most biochemical reactions
• Microbial reaction in the environment when S is
  low (pollution, groundwater, soil, ocean)

V
Time
Phase 1
Phase 2
V
S
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Kinetics Summary

• At least 4 different types of reaction can occur
  in biological environments
• Development of reaction rate can increase,
  decrease or stay the same.
• There are clear mechanistic reasons for reaction
  behaviour
• Significance When knowing the reaction kinetics
  the behaviour biological material (e.g. food,
  bioreactors, body) can be predicted
• 2nd order reaction (dependence on two substrates)
  is similar to 1st order and neglected here

S
Time
1
Exp
Enz
V
0
Time
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Decide Order or Kinetics
S

• 1. Decide which order the reaction kinetics is
• v constant, S decrease linear ? Zero order
• v increasing ? exponential
• v continuously slowing (1st, 2nd, 3rd order)
• v constant , then slowing ? MM kinetics

Time
1
Exp
Enz
V
0
Time