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

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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

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?

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

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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