Enzymology Lecture 4-5 - lectureug4

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Enzymology

Lecture 5

Dr.
Nasir

Jalal

ASAB/NUST

Question: What do cells surf on?


Answer: Microwaves.


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

K
M

and

V
max

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

=

m
x

+

c

with

a

y
-
intercept

equivalent

to

1
/
V
max

and

an

x
-
intercept

of

the

graph

representing

-
1
/
K
M


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

give

answer

or

just

set

problem

up
.
)


1/
Vmax



Km/
Vmax



Vmax
=1/191=0.0052




Km=14*
Vmax
=0.073

Advantage and disadvantage of LWP

Disadvantage
:



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
.

Advantage
:

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

V
max

is

unaffected

by

competitive

inhibitors

the

inverse

of

V
max

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

(
K
m

is

unaffected)

but

different

slopes

and

y
-
intercepts
.

Uncompetitive

inhibition

causes

different

intercepts

on

both

the

y
-

and

x
-
axes

but

the

same

slope
.

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
:



Transition State Model

Old bonds between
molecules
(hydroxide and
bromomethane
)
weaken

New bonds
begin to form.


Less stable
state.

New molecule
with new
bonds forms,
Bromide
released

K


is the concentration equilibrium constant, defined as:

The equation for an enzymatic reaction is:

Where,

k
B

is Boltzmann’s constant,

h is Planck’s constant and

T is the temperature

Boltzmann constant = 1.3806503
×

10
-
23

m
2

kg s
-
2

K
-
1

Planck's constant = 6.626068
×

10
-
34

m
2

kg / s

This equation can be used to find out the rate constant
K

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

c
o

is

the

standard

state

concentration
.

D
G
t

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,

D
G
t
,

the

binding

energy

and

D
G
s,

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
:



D
G
t

=
D
G
t

+
D
G
s


Gibb’s Free Energy

http://www.rpi.edu/dept/chem
-
eng/Biotech
-
Environ/Projects00/enzkin/transition.htm

D
G
s,

the activation energy
involved in the making and
breaking of bonds

D
G
t

can be defined as
the binding energy.

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


If
our measurement lasts a certain time
D
t
, then we cannot know the
energy better than an uncertainty
D
E

The more precisely the position is determined, the less precisely
the momentum is known in this instant, and vice versa.


--
Heisenberg, uncertainty paper, 1927



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








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!

Quantum Tunneling Model

through an example

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
D
E

to get over a
barrier



Does not violate the uncertainty principle,
provided this energy is repaid within a certain
time
D
t



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

Have to wait about 10
10
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
.

Advantages of QM


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……………!

QM

MM




H
eff

= H
qm

+ H
qm/mm
+ H
mm


Combined QM/MM methods

Goal
:
to do quantum chemical calculations of reactions and


electronically excited states of large molecular systems.

24
-
40 Å

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

N
H
3
O
2
C
C
H
3
H
O
N
O
H
3
C
N
H
O
2
C
C
H
3
H
O
N
O
H
3
C
N
H
O
2
C
C
H
3
H
O
H
AlaR

Phenoxide ion

Alanine

Ala
-
PLP(H
+
)

Ala
-
PLP

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

iron
-
sulfur

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
.


Coenzymes

include

NADH,

NADPH

and

adenosine

triphosphate

.

These

molecules

act

to

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

pathway

and

S
-

adenosylmethionine

by

methionine

adenosyltransferase

.

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 Mg
2+
, Zn
2+
, Fe
2+
, Ca
2+



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 B
12

acts as coenzyme B
12

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 Zn
2+
is required for the enzyme carbonic
anhydrase

to function.


41

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


D. In the quantum tunneling model, the enzyme tends to overcome:


(1) Substrate

.


(2) Energy deficit.


(3) A gradient.


(4) Climb a hill.



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.



Learning Check
E3

43

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.