Principles of Bioenergetics
and Catalysis  Kinetics
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, Fick’s 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.
What do bacteria do?
• Catalyse exergonic
redox reactions
• Exergonic, (downhill)
reactions loose Gibbs
Free Energy.
G
(DG=negative)
• Bacteria utilise a portion
of the free energy
released for growth
processes and
multiplication
S
ΔG
P
What does ΔG (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)
G
• The driving force = hill height
= difference in G = Delta (Δ) G
ΔG = G (prod.) – G (substr.)
• The reaction is driven by the loss
in G  Change in G is a negative
value (e.g. Δ G = -256 kJ/mol)
S
ΔG
P
Does the Δ G allow to predict the
reaction rate ?
• No
• But for Δ G = zero, reaction
rate will be zero
• For Δ G = positive, reaction
would go backwards (PS)
• The rate is determined by
G
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?
S
AE
ΔG
P
The ΔGo of redox reaction is related
to the ΔEo of e- donor and acceptor
• ΔEo is the difference in
redox potential of the
half reactions
• Couple with lower Eo
will become e- donor -Eo
• If not reaction would
reverse
• ΔGo = n F Δ 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
edon.
ΔE
eacc.
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.
G
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
Reaction path
7
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).
8
Why don’t antigens catalyze?
P
S
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
9
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?
T
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
Let’s have a closer look at the energy diagram for
clues.
10
How do enzymes catalyse ?
High Energy=
T
Unlikely, reactive, activated
P
needed to lower the activation
energy level:
a way to make the transition (T)
state more likely
P
Low Energy=
S
G
Likely to exist, stable
Reaction path
Note T not an intermediate just a “deformed molecule” that makes
forward and backward reaction equally likely
11
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
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.
12
How do enzymes catalyse ?
Significant product formation
depends on availability of T.
T
Non catalysed reactions are slow
because [T] is low
S
G
P
P
Reaction path
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.
13
How do enzymes catalyse ?
The enzyme substrate complex
(ES) is not a transitional state but a
true, existing, defined intermediate
T
S
Intermediates are in a “valley”
ES
G
Transition states are on a “peak”
P
P
Reaction path
14
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.
S
The reaction continues until the difference
in G (Delta G) is zero.
`
G
Then the energy level of substrate equals
that of the product
P
Reaction is at equilibrium
Reaction path
Rate of backwards reaction equals that of
forward reaction.
The ratio [P]/[S] now represents the
equilibrium constant keq.
15
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
S
`
G
P
at equilibrium [P]/[S] is very high (e.g.
10,000)
endergonic reactions have low keq (e.g.
0.00001)
Reaction path
The enzyme does not affect the
spontaneity or reversibility of reaction but
the energetics does.
Not surprisingly the reaction driving force16is
related to keq ΔG =RT ln keq
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.
T
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)
17
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/P*T)*e -DG(activ.)/RT
B/P=Bolzman/Planck constant
T
E.g. lowering the activation energy by 5.7kJ
will increase rate 10 fold
18
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)
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
T
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.
20
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
E +S
k1
k-1
ES
k2
E+P
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.)
21
Foundation of Michaelis Menten
kinetics
k1
E +S
k-1
ES
k2
E+P
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)
22
Foundation of Michaelis Menten
kinetics
k1
E +S
k-1
ES
k2
E+P
At substrate saturation no free enzyme is available ([E]=0)
overall rate is determined by k2 ( kcat = k2)
(btw: kcat= vmax/(total enzyme concentration (Et, E+ES))
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
23
Derivation of MM kinetics from first principles
k1
E +S
k-1
ES
k2
E+P
k-1+ K2 = km
k1
At steady state: rate of ES disintegration =rate of ES formation
k-1*ES + K2*ES
= k1*ES
k-1ES + K2ES
= k1(Et-ES)S
k-1ES + K2ES
= k1EtS - k1ESS
(Et=E+ES)
k-1ES + K2ES + k1ESS = k1EtS
multiply out right
k1ESS
bracket out ES
ES (k-1+ K2 + k1S )
= k1EtS
ES
= k1EtS / (k-1+ K2 + k1S )
k1EtS
solve for ES
ES = k + K + k S
-1
2
1
24
k1
E +S
ES
ES
=
k-1
ES
k2
k1EtS
cancel k1
k-1+ K2 + k1S
=
Et S
km+S
vo
=
k2
vo =
vo =
k-1+ K2 = km
k1
E+P
=
EtS
k-1+ K2 +S
k1
(as vo = k2 *ES  ES = vo/k2 ) 
Et S
km+S
(as vmax =k2*Et) 
k2Et S
km+S
vmax S
km+S
(k2 is also called kcat)
25
The Michaelis Menten Model has
been derived:
(students don’t need to be able to derive it but
to know the final equation)
vo = vmax
S
km + S
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
26
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.
S
vo =seen
vmaxwhere the most widely used
After we have
km + S
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
First Order Kinetics
• 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)
P
S
V
Time
V
S
Exponential Kinetics
• 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)
S
P
V
Time
V
P
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 2
Phase 1
V
S
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
S
Decide Order or
Kinetics
1. Decide which order the reaction S
kinetics is:
• v constant, S decrease linear
 Zero order
• v increasing  exponential
• v continuously slowing (1st, 2nd,
3rd order)
1
• v constant , then slowing 
MM kinetics
Time
Enz
Exp
V
0
Time
Summary
• Microbes catalyze downhill reactions by lowering the
activation energy needed.
• Spontaneity can be expressed as G
• Catalysis is achieved by stabilizing the transitional state
of the substrate not by binding to the substrate
• Zero, first, second, MM and exponential are different
reaction orders occuring in microbial reactions
• Reaction order is essential for process modelling.