Overview of Lecture Topics by RC

1) Substrate diffusion and catalysis

2) Biological reaction kinetics

3) Biological reactions that change the environment

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, 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.

Catalysis15 min Lecture block

What do bacteria do?

• Catalyse exergonic redox reactions

• Exergonic, (downhill) reactions loose Gibbs Free Energy. (DG=negative)

• Bacteria utilise a portion of the free energy released for growth processes and multiplication

G

S

P

ΔG

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)

• 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)

G

S

P

ΔG

Does the Δ G allow to predict the reaction rate ?

• No• But for ΔG = zero, reaction

rate will be zero• For ΔG = positive, reaction

would go backwards (PS)• 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?

G

S

P

ΔG

AE

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

• 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

-Eo

e- don.

ΔE

e- acc.

8

What is enzyme catalysis? The rate of a spontaneous reaction is

increased.

If the reaction is already spontaneous, why

do we need an enzyme?

The activation energy needs to be

overcome.

Spontaneous = downhill = exergonic

Enzymes can not catalyse uphill =

endergonic reactions

If catalysed uphill reactions proceed in the

reverse direction (Products Substrates)

G

Reaction path

G

9

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 down reaction rates.

Example: Antibody binding to antigen.

Antibody is a protein designed by the immune system to bind and “neutralise” a foreign substances

(the antigen).

10

Why don’t 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 the

substrate into product(s) ?

No

P

S

11

How do enzymes catalyse ?

P

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

Let’s have a closer look at the energy diagram for clues.

S

T

12

High Energy=

Unlikely, reactive, activated

Low Energy=

Likely to exist, stable

G

Reaction path

P

S

P

S

T

needed to lower the activation energy level:a way to make the transition (T) state more likely

Note T not an intermediate just a “deformed molecule” that makes

forward and backward reaction equally likely

How do enzymes catalyse ?

13

P

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 Tmakes T more likelyhigher quantities of T availablehigher 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.

S

T

How do enzymes catalyse ?

14

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.

G

Reaction path

P

S

P

S

T

How do enzymes catalyse ?

15

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”G

Reaction path

P

S

P

S

T

ES

How do enzymes catalyse ?

16

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.

`

G

Reaction path

P

S

17

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 ΔG =RT ln keq

`

G

Reaction path

PS

The dynamic equilibrium

18

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)

T

Binding Energy

19

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

E.g. lowering the activation energy by

5.7kJ will increase rate 10 fold

T

Microbial ChemistryLec 2 2006

21

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.

T

22

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.)

Foundation of Michaelis-Menten Kinetics

k1E + S ES E + P

k-1

k2

23

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)

k1

k-1

k2E + S ES E + P

24

Foundation of Michaelis Menten kinetics

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

k1

k-1

k2E + S ES E + P

25

Derivation of MM kinetics from first principles

At steady state: rate of ES disintegration =rate of ES formation

k-1*ES + K2*ES = k1*ES (Et=E+ES)

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 =

k1

k-1

k2E + S ES E + P = km

k-1+ K2k1

k1EtS

k-1+ K2 + k1S

26

ES =

ES =

k1

k-1

k2E + S ES E + P

k1EtS

k-1+ K2 + k1S

cancel k1

= EtS

k-1+ K2k1

+S

= km k-1+ K2

k1

Et S

km+S (as vo = k2 *ES ES = vo/k2 )

Et S

km+S

vo k2

=

k2Et S

km+Svo =

vmax S

km+S

(as vmax =k2*Et)

(k2 is also called kcat)vo =

27

S

km + Svo = vmax

(students don’t 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

The Michaelis Menten Model has been derived:

28

S

km + Svo = vmax

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).

Microbial Reaction Kinetics:

Kinetics15 min Lecture block

30

S

km + Svo = vmax

The substrate (reactant) of bioprocesses can disappear

according to different time courses, such as linear

disappearance, first order, exponential, mixed kinetics

(such as Michaelis Menten) or incompletely such as for

product inhibition or approaching of the thermodynamic

equilibrium.

Students should be able to sketch the different types

and explain which kinetic types occur in which

processes.

Microbial Reaction Kinetics:

Zero Order kinetics

• 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

PS

Time

S

V

V

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

Time

S

V

V

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)

P

S

Time

P

V

V

Michaelis Menten Kinetics

• 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)

PS

Time

S

V

V

Phase 1Phase 2

Phase 1 Phase 2

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

Time

S

V

Time

0

1Enz Exp

Decide Order or Kinetics

Time

S

V

Time

0

1Enz Exp

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

Possible Lec 3 Biological Reactions that Change the Environment

The two big reactions: Photsynthesis and Respiration match each other

What do bacteria do without oxygen ? Examples of anaerobic respiration.

Stoichiometry of anaerobic respirations

Impact of anaerobic respirations