View
214
Download
0
Category
Tags:
Preview:
Citation preview
Proteins:The Unfolding
Story
Protein Folding Problem
1931 - Hsien Wu1936 - Mirsky & Pauling1950s - Anfinsen
Protein Folding - spontaneous acquisition of native conformation under physiological conditions
Who needs models?Human
CognitionSeeing is believing
Seeing is deceiving
Preview
€
←→U N
The Levinthal Paradox
StericsThe Folding
Reaction
Re-equilibration
Protein folding is a thermodynamic
problemThe problem
has been with us for ~70
years
What’s missing?
The Folding Reaction - what we
know
Ginsburg and Carroll (1965)
The Folding Reaction - what we
don’t know
€
←→U N
?
Random Coil Model
•No strongly preferred backbone conformations
•Energy differences among backbone conformations ~kT
•Statistical coil - chain configuration only becomes Gaussian for infinite chains. All real polymers are statistical coils.
The Freely Jointed Chain
€
2r =l n
€
G2R =
1n+ 1
⎡
⎣ ⎢
⎤
⎦ ⎥ Gi
2Ri=0
n∑
∑=
=N
iilr
1
rrrr
Mean-square end-to-end distance grows as root
Radius of gyration, Rg, measures coil dimensions
The Central Thermodynamic
Question in Protein FoldingHow can a polypeptide chain
overcome conformational entropy and fold to its native
state?
Native state
The Levinthal Paradox
Cα
C' Cα
C'
Cβ
C
Ο
Ν
Ο
Ν
φψ
If each ψ pair can adopt either of two values, then a chain of 100 residues has 2100 = 1030 accessible conformers. A dilute protein solution contains ~1015 molecules.
Why haven’t hard-sphere sterics played a more
significant role in protein folding studies?
Ramachandran, Ramakrishnan, Sasisekharan
(1963)
Influence of sterics does not extend beyond the
dipeptide
The Unfolded StateHow large is conformational
space?If each ψ pair can adopt one of two values, then a chain of 100 residues has 2100 = 1030 accessible conformers.
Flory isolated-pair hypothesis, the simplifying assumption that each ψ pair is sterically independent.
Rohit V. Pappu
“A simple model for poly-proline II structure in unfolded states of
alanine-based peptides”
Pappu & Rose
Protein Sci. (2002) 11:2437-2455.
“The Flory isolated-pair hypothesis is not valid for polypeptide chains - implications for protein folding”
Pappu, Srinivasan & Rose
PNAS (2000) 97:12565-12570.
How to count: tiling ψ-space into mesostates
B
C
D
H N
P
Q
S
T
U
V
W
X
S
m
r
q
p
n
m
g
l
k
j
i
h
g
A
B
C
D
E
F
A
-150
-150
-90
-90
-30
-30
30
30
90
90
150
150
ψ
φ
A
F
E
A
G M
L R
K
J
I O
o
G M
Revisiting Ramachandran, Ramakrishnan & Sasisekharan
How to count: tiling ψ-space into mesostates
Generate 50,000 random dipeptide conformers within each mesostate, and capture the Acceptance Ratio. The acceptance ratio is the fraction of conformers that is clash free. Each mesostate has an acceptance ratio that ranges from 0 to 1.
But it’s not!B
C
D
H N
P
Q
S
T
U
V
W
X
S
m
r
q
p
n
m
g
l
k
j
i
h
g
A
B
C
D
E
F
A
-150
-150
-90
-90
-30
-30
30
30
90
90
150
150
ψ
φ
A
F
E
A
G M
L R
K
J
I O
o
G M
If the Flory Isolated Pair hypothesis is valid, then the overall acceptance ratio for longer strings will be the product of the individual dipeptide acceptance ratios.
B
C
D
H N
S
T
U
V
W
X
S
m
r
q
p
n
m
g
l
k
j
i
h
g
A
B
C
D
E
F
A
-150
-150
-90
-90
-30
-30
30
30
90
90
150
150
ψ
φA G M
The isolated-pair hypothesis does not hold for polypeptides
No. expected conformations X 10-50
4
8
12
4 8 12
Exhaustive counting (in allowed regions of allowed
mesostates)No. expected = No. generated x acceptance
ratios
+ 100 random extended mesostate strings
* 100 random contracted mesostate
strings
The Unfolded StateHow shall I conform thee,
let us count the ways.
Polyalanine = pure backbone
Sterics + hydrogen bond
Two atoms can’t be in the same place at the same time.
How large is conformational space? Let us count the
ways.Exhaustive counting of 14N strings
(N=7): 7.5x106 strings, 5x108 conformers/string
For energy = :
Weight ith string = giallowede[-βui()]/Z[14N]
For = 0 (sterics only):
Weight ith string = giallowed/Z[14N]
With gi’s obtained from acceptance ratios or sampling, depending on the string.
Then Sort
A 7-residue polyAla chain is 2-state
Hydrogen bond strength in kcal/molHydrogen bond strength in kcal/molHydrogen bond strength in kcal/molHydrogen bond strength in kcal/mol
Tug of war between H-bond enthalpy and conformational
entropy
Why is the folding of a short polyalanine chain largely
two-state? Specifically, why are αβ hybrid conformers
depleted in this population?
1) Energetic preference for particular structure?
2) Steric clash in hybrids?
Yes - e.g, polyproline II
Yes
When are two conformers
distinguishable: structurally?
thermodynamically?Investigator Space Protein
SpaceSpontaneous fluctuations are
free
Thermodynamics vs. Structure
If structurally distinct confomers can inter-convert via spontaneous fluctuation, they do not differ thermodynamically.
CV = <E>2 - <E2>/RT2
Do fluctuations occur about preferred
basins?
Identify the basins:
•Without explicit solvent
•With explicit solvent
Without explicit solvent
Minimize density of chain around itself: mimic good solvent and maximize wiggle room, i.e. chain entropy
Hard sphere Soft sphere repulsive potential
Inverse Power PotentialU = ij<i(ij/rij)n
S = hard sphere contact distancer = interatomic separation
Pappu & Rose (2002) Protein Sci. 11:2437-2455
Without explicit solvent
Polyalanine 7-mer. Global minimum is left-handed
polyproline II helix
With explicit solvent
Grand canonical ensemble Monte Carlo simulations in
TIP3P water
Prof. Mihaly Mezei Dept. Physiology & Biophysics Mt. Sinai School of Medicinehttp://inka.mssm.edu/~mezei
Mezei et al (2004) Proteins 55: 502-507
Solvation free energy of a 12-residue polyAla peptide posed in 4
conformers
Helix -2.0±0.3PII -4.7±0.3||β -3.9±0.3anti||β -4.0±0.3
A (kcal/mol/res)
With explicit solvent
β-strand
Polyproline II
β-strand with water bridges
Mezei et al (2004) Proteins 55: 502-507
Connecting thermodynamics and
structureA few basins account for most of the thermodynamic population. The basins are highly degenerate. Most of the chain is within a room-temperature fluctuation of left-handed polyproline II helix.
Polyproline II structure in a sequence of seven alanine residues. Shi et al (2002) PNAS 99: 9190-9195.
At 2° C, the chain is ~90% PII. At 55°, the chain is ~80% PII, ~10% strand. Large enthalpy PIIstrand.
Experimental confirmation
Why is the folding of a short polyalanine chain largely
two-state? Specifically, why are αβ hybrid conformers
depleted in this population?
1) Energetic preference for particular structure?
2) Steric clash in hybrids?
Yes - e.g, polyproline II
Yes
Systematic local steric clashes winnow the number
of accessible chain conformations
•Depletion of mixed conformers serves to stiffen the chain.
•Reduction in the number of conformers also promotes structure in the unfolded state.
But what kinds of clashes?
Are there steric restrictions beyond the alanyl dipeptide?
Steric restrictions beyond the alanyl
dipeptide
An α-helix cannot be followed by a contiguous β-strand
Fitzkee & Rose Protein Science (2004) 13: 633-639.
Definition of α, β, PII
-180.0 -90.0 0.0 90.0 180.0180.0
0.0
90.0
-90.0
-180.0
2. Hard sphere simulations
Two Tests
1. Examine the database
PDB select has 37,563 occurrences of ααα~α but only 7 of these are
αααβ
Two Tests
2. Hard sphere simulationsα4-*-α4
-180.0 -90.0 0.0 90.0 180.0180.0
0.0
90.0
-90.0
-180.0
-180.0 -90.0 0.0 90.0 180.0180.0
0.0
90.0
-90.0
-180.0
-180.0 -90.0 0.0 90.0 180.0180.0
0.0
90.0
-90.0
-180.0
Consequences of eliminating αβ hybrids
•Winnows the size of conformational space.
•Limits the number of protein domains.
•Simplifies molecular recognition.
•Suggests the possiblity of additional steric restrictions.
Conclusions
€
←→U N
The Levinthal paradox
The folding reaction
The size of accessible conformational space is much smaller than previously believed
Unfolded population is more folded than we thought -- repopulation under changed solvent/temperature conditions
Recent lab members
-6 -4 -2 00
20
40
60
80
100
Rohit PappuWashington Univ.-St. Louis
Raj SrinivasanTCS - Hyderabad, India
Teresa PrzytyckaNIH
Current lab members
Nick Fitzkee
Pat Fleming
ln k (calculated)
Haipeng Gong
Venk Murthy
Nick Panasik
Recommended