Discussion topic for week 5 : Enzyme reactions • The lock in key hypothesis (Emil Fischer) asserts that both the enzyme and the substrate possess specific complementary geometric shapes that fit exactly into one another. What are the problems associated with this hypothesis?
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Discussion topic for week 5 : Enzyme reactions The lock in key hypothesis (Emil Fischer) asserts that both the enzyme and the substrate possess specific.
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Discussion topic for week 5 : Enzyme reactions
• The lock in key hypothesis (Emil Fischer) asserts that both the
enzyme and the substrate possess specific complementary
geometric shapes that fit exactly into one another.
What are the problems associated with this hypothesis?
Enzymes and Molecular Machines (Nelson, chap. 10)
Enzymes are biological catalysts that enhance the rate of chem. reactions.
Machines use free energy from an external source (e.g. ATP,
concentration or potential difference) to do useful work. Examples:
• Motors: transduce free energy into linear or rotary motion
– myosin on actin in muscles, kinesin on microtubules in cells.
• Pumps: create concentration differences across membranes
– sodium-potassium pump transports 3 Na+ ions out of the cell and
2 K+ ions into the cell in one cycle.
• Synthases: drive chemical reactions to synthesize biomolecules
– ATP synthase synthesizes the ATP molecules that are used by
most of the molecular machines in the cells.
Enzymes
An extreme example: catalese
Consider the decomposition of hydrogen peroxide: H2O2 H2O + ½ O2
G0 = 41 kT so the reaction is highly favoured but due to a high
activation barrier it proceeds very slowly:
for 1 M solution the rate is 108 M/s (reaction velocity)
Adding 1 mM catalese into the solution increases the rate by 1012 !
103 NA catalese molecules perform 104NA hydrolisis reactions per sec.
So 1 catalese molecule catalyses 107 reactions per sec. (rate: 107 s)
H2O2 is produced in cells while eliminating free radicals. Because it is
toxic, its rapid breakdown is important.
More typical rates for enzymes are around 103 s
Simple model of enzyme reactions:
Chemical reactions involving biomolecules are extremely complex.
Free energy surface typically involves thousands of coordinates.
Nevertheless a reaction usually proceeds along the path of least
resistance (called reaction coordinate) which allows a simple description.
A simple reaction: H + H2 H2 + H
transition state
An enzyme facilitates a chemical reaction by binding to the transition
state and thereby reducing the activation energy, G‡ (but not G)
Free energy surface along the reaction coordinate
kTEkTEkSkTSTEkTG eeeee )(rate
Substrate Enzyme + substrate
G‡
G‡
G G
Direction of the reaction is controlled by G. By changing G, we can
reverse the direction. The reverse reaction does not necessarily follow
the same reaction coordinate.
reaction reversefumarate malate-Lfumarase
A schematic picture of an enzyme E binding to a substrate S:
E + S ES EP E + P
E+S: The enzyme has a binding site that is a good match for the subst. S
ES: In order to bind, S must deform which stretches a bond to breaking pt.
EP: Thermal fluctuations break the bond producing an EP complex
E+P: The P state is not a good match to the binding site, hence it unbinds,
leaving the enzyme free for binding of the next substrate.
Corresponding
free energy
surface
Enzyme Kinetics:
Consider an enzyme reaction with rate constants k1, kand k3
Assume:
For a single enzyme, the reaction simplifies to
Let probability of E unoccupied be PE and occupied PES = (1 PE)
The rate of change of PE is
},{,,},,{ 2133322 kkkkkkkccc PES
ESESE PkkPck
dt
dP211
PEEPESSEk
k
k
k
k
k
3
3
2
2
1
1
PEESSE k
k
ck S
2
1
1
Assuming quasi-steady state, the time derivative vanishes, yielding
Rate of production of P per enzyme:
Reaction velocity for a concentration cE of enzymes
1
212max
max
121
122
,k
kkKkcv
cK
cvv
ckkk
ckkcPkcv
ME
SM
S
S
SEESE
S
SES
ESEsS
ckkk
ckP
PkkPck
121
1
211 0)1(
ESPk2
Michaelis-Menten (MM) rule
Experimental data for pancreatic carboxypeptidase
S
M
SM
S
c
K
vvcK
cvv 1
11
maxmax
vmax=0.085 mM/s
KM=6.4 mM
MM rule displays saturation kinetics, which has very general validity
The key idea is the processing time for S P
At low substrate concentrations, there are more enzymes than S so that
there is no waiting and hence v is proportional to cS
As cS is increased beyond KM, there is competition among S for access
to an enzyme, and they have to queue for processing.
Maximum velocity of the reaction is determined by the number of
enzymes available and the processing rate (the rate limiting step)
Modulation of enzyme activity:
• Regulate the rate of enzyme production
• Competitive inhibition: direct binding of another molecule
• Noncompetitive inhibition: binding of a molecule to a second site
kTGek2
Recent developments (Adenylate kinase)
We know very little about the
actual dynamical processes
occurring in enzymes.
There are only a few simple
cases where the physical
mechanism is understood, e.g.
oxygen binding in myoglobin.
Adenylate kinase catalyzes:
ADP + ADP ATP + AMP
Recent work indicates that the
rate limiting step is the
enzyme conformation, and not
the chemistry.
Molecular motors in muscles: myosin and actin
For structure of the myosin and actin filaments in a myofibril, see