protein folding and structure...
Post on 27-Mar-2021
5 Views
Preview:
TRANSCRIPT
Protein Folding and Structure Prediction
A Statistician’s View
Ingo Ruczinski
Department of Biostatistics, Johns Hopkins University
Proteins
Amino acids without peptide bonds. Amino acids with peptide bonds.
� � Amino acids are the building blocks of proteins.
Proteins
Both figures show the same protein (the bacterial protein L). The right figure alsohighlights the secondary structure elements.
Space
1 10 100 1000 10000 100000
1nm 1µm
Distance [ A° ]
C−C bond
Glucose
Hemoglobin
Ribosome
Resolution limit of a light microscope
Bacterium
Red blood cell
Distance [ A° ]
Energy
0.1 1 10 100 1000
Energy [ kcal/mol ]
Thermal
Noncovalent bond
ATP
Green light
C−C bond
Glucose
Non-Bonding Interactions
Amino acids of a protein are joined by covalent bonding interactions. The polypep-tide is folded in three dimension by non-bonding interactions. These interactions,which can easily be disrupted by extreme pH, temperature, pressure, and denatu-rants, are:
� Electrostatic Interactions (5 kcal/mol)� Hydrogen-bond Interactions (3-7 kcal/mol)� Van Der Waals Interactions (1 kcal/mol)� Hydrophobic Interactions ( � 10 kcal/mol)
The total inter-atomic force acting between two atoms is the sum of all the forcesthey exert on each other.
Energy Profile
DenaturedState
TransitionState
NativeState
Radius of Gyration of Denatured Proteins
Do chemically denatured proteins behave as random coils?
� The radius of gyration Rg of a protein is defined as the root mean square dis-tance from each atom of the protein to their centroid.
� For an ideal (infinitely thin) random-coil chain in a solvent, the average radiusof gyration of a random coil is a simple function of its length n: Rg � n0.5 �
� For an excluded volume polymer (a polymer with non-zero thickness and non-trivial interactions between monomers) in a solvent, the average radius of gyra-tion, we have Rg � n0.588 (Flory 1953).
� � The radius of gyration can be measured using small angle x-ray scattering.
Radius of Gyration of Denatured Proteins
Length [residues]
Rg
[A°]
10 50 100100 500
10
20
30
40
50
60
708090
Angiotensin II
Creatine Kinase
Confidence interval for the slope: [ 0.579 ; 0.635 ]
Deviations from Random Coil Behaviour
Are there site-specific deviations from random coil dimensions?
Forster Resonance Energy Transfer enables us to measure the distance betweentwo dye molecules within a certain range. This can be used to study site-specificdeviations from random coil dimensions in highly denatured peptides.
Deviations from Random Coil Behaviour
0 200 400 600 800 1000
0
20
40
60
80
time
num
ber
of p
hoto
ns
0 10 20 30 40 50
0
5
10
15
20
25
30
time
num
ber
of p
hoto
ns
Deviations from Random Coil Behaviour
0 20 40 60 80
0
50
100
150
200
number of red photons
num
ber
of g
reen
gre
en
We have two underlying distributions forthe green and red photons:
� One stemming from a peptide onlyhaving a donor dye.
� One stemming from a peptide beingproperly tagged with a donor and anacceptor dye.
Assume a photon has probability ��� of be-ing red in the former situation, and � � inthe latter.
Deviations from Random Coil Behaviour
Assume we observe ��� photons at time point�. Then the number of red photons
is simply Bernoulli( ����� � � ), where � � is either ��� or � � . Assume that the probabilityof observing photons from a peptide without an acceptor dye at any time is � ,independent of the total number of photons observed. Let � be the number of redphotons. Then� � � � ��� � ��� � � � ��� ��� � � � � � ��� ��� � � � � ��� � � � � � ��� ��
� ���� � � ������ ��� �� ��
� � �!��" �$#%� � � �&� � � ��'��� ��� �� ��� � ���(" �)#*� � � ��
� ��� �and hence
+,� � � � � � ��� � -. �0/ �21
� ������3� ��� �� ��� � �!��" �$#%� � � �2� � �4��'��� ��� �� ��
� � ���(" �5#%� � � ��� ���76 �
Deviations from Random Coil Behaviour
50 60 70 80 90 100
0
20
40
60
80
total number of photons
num
ber
of r
ed p
hoto
ns
Deviations from Random Coil Behaviour
0.0 0.2 0.4 0.6 0.8 1.0nred
nred + ngreen
p1 = 0.431
Energy Profile
Dmutant
Dwildtype
Tmutant
Twildtype
Nmutant
Nwildtype
∆∆GN−D
∆∆GT−D
� � The � -value is defined as the ratio ��� GT-D���� GN-D.
Energy Profile
Dmutant
Dwildtype
Tmutant
Twildtype
Nmutant
Nwildtype
∆∆GN−D
∆∆GT−D = ∆∆GT−D
Dmutant
Dwildtype
Tmutant
Twildtype
Nmutant
Nwildtype
∆∆GN−D
∆∆GT−D = 0
� If the part of the protein that contains the mutant amino acid is fully structuredin the transition state, we have ��� GT-D = ��� GN-D � and hence � = 1.
� If the part of the protein that contains the mutant amino acid is equal in dena-tured and the transition state, we have ��� GT-D = 0, and hence � = 0.
Chevron Plots
��� GT-D = RT ��� log(kwildtypef ) – log(kmutant
f ) ���� GN-D = RT ��� log(kwildtype
f ) – log(kwildtypeu ) – log(kmutant
f ) + log(kmutantu ) �
−2
0
2
4
6
Denaturant concentration ( GuHCl [M] )
log(
k obs
)
Wildtype
Mutation I28A
0 1 2 3 4 5 6 7 8
log(kobs) = log � exp � log(kf)+ mf � CGuHCl
RT � + exp � log(ku)+ mu � CGuHCl
RT ���
More Chevron Plots
−2
0
2
4
6
log(
k obs
)
0 1 2 3 4 5 6 7 8
Mutation I28A
−2
0
2
4
6
0 1 2 3 4 5 6 7 8
Mutation I28L
−2
0
2
4
6
0 1 2 3 4 5 6 7 8
Mutation I28V
−2
0
2
4
6
log(
k obs
)
0 1 2 3 4 5 6 7 8
Mutation V55A
−2
0
2
4
6
Denaturant concentration ( GuHCl [M] )
0 1 2 3 4 5 6 7 8
Mutation V55M
−2
0
2
4
6
Denaturant concentration ( GuHCl [M] )
0 1 2 3 4 5 6 7 8
Mutation V55T
−2
0
2
4
6
Denaturant concentration ( GuHCl [M] )
log(
k obs
)
0 1 2 3 4 5 6 7 8
Wildtype
UC Santa Barbara
Rice University
UC Berkeley
Variability
−2
−1
0
1
2
φ
φ − values
UC Santa Barbara
Rice University
UC Berkeley
−10
−5
0
5
10
∆∆G
N−D
∆∆GN−D − values
Wild
type
−I2
8A
Wild
type
−I2
8L
Wild
type
−I2
8V
I28A
−I2
8L
I28A
−I2
8V
I28L
−I2
8V
Wild
type
−V
55A
Wild
type
−V
55M
Wild
type
−V
55T
V55
A−
V55
M
V55
A−
V55
T
V55
M−
V55
T
Variability
average ∆∆GN−D values
σ lab
Between lab φ − value standard deviation
1
2
3
4
5
6
7
8
910
11
12
1
2
3
4
5
6
7
8
9
10
11
12
Wild type−I28A
Wild type−I28L
Wild type−I28V
I28A−I28L
I28A−I28V
I28L−I28V
Wild type−V55A
Wild type−V55M
Wild type−V55T
V55A−V55M
V55A−V55T
V55M−V55T
0 1 2 3 4 5 6 7 8 9 10 11 12
0.00
0.25
0.50
0.75
1.00
1.25
1.50
Variability
−10 −5 0 5 10
−10
−5
0
5
10
∆∆GN−D
∆∆G
T−D
UC Santa Barbara
Rice University
UC Berkeley
Some Simulation
2 4 6 8 10 12
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
average ∆∆GN−D values
σ lab
Some Simulation
2 4 6 8 10 12
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
average ∆∆GN−D values
σ lab
Some Simulation
2 4 6 8 10 12
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
average ∆∆GN−D values
σ lab
Some More Simulations
∆∆GN−D values
φ
0 1 2 3 4 5 6 7 8 9 10 11 12 13
0.37
0
1
D ( φ | φ , ∆∆G )
Some More Simulations
φ
1 2 3 4 5 6 7 8 9 10 11 12
0.10
1
1 2 3 4 5 6 7 8 9 10 11 12
0.20
1
1 2 3 4 5 6 7 8 9 10 11 12
0.3
0
1
φ
1 2 3 4 5 6 7 8 9 10 11 12
0.4
0
1
1 2 3 4 5 6 7 8 9 10 11 12
0.5
0
1
1 2 3 4 5 6 7 8 9 10 11 12
0.6
0
1
average ∆∆GN−D values
φ
1 2 3 4 5 6 7 8 9 10 11 12
0.7
0
1
average ∆∆GN−D values
1 2 3 4 5 6 7 8 9 10 11 12
0.8
0
1
average ∆∆GN−D values
1 2 3 4 5 6 7 8 9 10 11 12
0.9
0
1
Phi-Value Estimation
∆∆GTD
6 8 10 12 14
∆∆GND
6 8 10 12 14 7.0 7.5 8.0 8.5 9.0
10.5
11.0
11.5
12.0
12.5
13.0
13.5
∆∆GTD
∆∆G
TD
�������� TD������ ND ��� �
1 � ��� TD
����� ND
6 � 1��� � �� �� � � 6 �with
� � � � F � � � F �� � � F � � � F � � � U � � � U � �����W � F � � U � �����
M � F � � U �� � � � F � � � F � ���W � F � � U � ���
M � F � � U �
Phi-Value Estimation
�� � �
� ��� TD������ ND
� � � � �with � � � ������ ND ��� � � ������ ND � ��� � � �� ��� TD
�� ��� ND � �
������ TD � � �
Φ
0.55 0.60 0.65 0.70 0.75
Phi-Value Estimation
� � ���� � ��� ����"����%"�� # � � �� ��� �
� � ��� ����"����*"�� # � � ��� �! ?
0.0
0.2
0.4
0.6
0.8
1.0
Φ
Evolution and Folding Kinetics
Are amino acids in proteins conserved because of folding kinetics?
To what extent does natural selection act to optimize the details of protein foldingkinetics? Is there a relationship between an amino acid’s evolutionary conservationand its role in protein folding kinetics?
Some comments:� Our studies of sequence conservation among residues known to participate
in the folding nuclei of all of the appropriately characterized proteins reportedto date have not provided any evidence that highly conserved residues aremore likely to participate in the protein folding nucleus than poorly conservedresidues.
� This is in contrasts to some of the beliefs stemming from theoretical considera-tions (good science, good people).
� This is also in contrast to the conclusions certain people drew from experimentaldata (really aweful statistics).
� These people do not like us.
top related