SAXS and collapse in protein folding

Prof. Tobin Sosnick

Univ. of Chicago

with Jaby Jacob, Bryan Krantz, & Shane Dothager

And P. Thiyagarajan (ANL)

NIH and Packard Foundation for their generous support.

Protein folding

1D Sequence

Unique 3D Structure

Vast conformational search over in milliseconds!

local structure

long-range structure

How to reduce the Conformational Search?How to reduce the Conformational Search?

Solve problem locally(e.g. Diffusion-collision model)

2º collapse Early Collapse(e.g. most simulations)

collapse 2º

Knowledge of when collapse occurs delineates folding models.

Measure dimensions at early folding stages using SAXSBioCat beam-line, Advanced Photon Source, Argonne National Lab

rapid mixing apparatus(1-2 msec)

~20 µM focus1 mm capillary

θ APS2D detector

0.03 0.05 0.10 0.15

1E-7

1E-6

1E-5

I(Q)

Q3

0

22

)(gRQ

eIQI−

=

1/width ∝ Rg

Does the polypeptide collapse upon denaturant dilution?

or

26 Å

High denaturant

Rg ~ 26 Å

DiluteDenaturant

~2 msec

Fold to completion

(takes 10+ msec)

<20 Å?

Experimental strategy:

Measure I(Q) for 0.4 s during continuous-flow period where protein has folded for ~2 msec.

Ubiquitin in 1.5 M guanidine hydrochloride

Sample concentration - 2 mg/ml

Exposure time - 360 msec

Number of exposures - 5 repeats for sample and buffer

Guinier plots of refolding and refolded Ubiquitin

Right after denaturant dilution

(∼2 msec)

After folding has completed(10+ msec)

-7.5

-7.0

-6.5

-6.0

-5.5

-5.0

-4.5

-4.0

Ln(

I(Q

))

(cm

-1)

3.5x10-33.02.52.01.51.00.5

Q2 (Å-2)

Rg=25.3 ± 0.2 ÅGdm = 6.0

Rg=27.6 ± 0.1 ÅGdm = 4.69

Rg=26.6 ± 0.1 ÅGdm = 3.37

Rg=25.93 ± 0.03 ÅGdm = 0.75 Rg=26.5 ± 0.04 Å

Gdm = 1.5

-7.5

-7.0

-6.5

-6.0

-5.5

-5.0

-4.5

-4.0

Ln(

I(Q

))

(cm

-1)

10x10-38642

Q2 (Å-2)

Rg=25.9 ± 0.1 ÅGdm = 6.0

Rg=25.40 ± 0.07 ÅGdm = 4.5

Rg=16.67 ± 0.03 ÅGdm = 3.37

Rg=14.18 ± 0.01 ÅGdm = 1.5

Rg=14.42 ± 0.01 ÅGdm = 0.75

Ubiquitin:

Size after equilibration

Fold

Jacob et al,JMB, 2004)

Ubiquitin (& ctAcp): Negligible collapse upon dilution of denaturant!

Size after denaturant dilution

Dilute denaturant

Chemically denatured Proteins: Rg scales with length the same as a self-avoiding random walk

From K. Plaxco

Rg = 2.1 N0.585

Rg

(Å)

N

Unfolded Ub & ctAcp fall on this line even under aqueous conditions(Ub: 26 versus 26.5 and ctAcp: 31 versus 30.7A)

Polypeptides can behave like random coils under aqueous conditions

No denaturant or Temperature dependence for Rg

Equilibrium mode using non-folding polypeptide (RNase A with disulfide bonds broken)

0 1 2 3 4 5 60

10

20

30

40

50

Rg (Å

)

[Gdm]

Increased strength of protein-protein interactions at lower denaturant concentrations does not result in compaction (protein-water interactions are stronger).

0 20 40 60 80 1000

10

20

30

40

50

Temperature (C)

Unfolded peptides are in the high temperature limit, where T∆Sconfig>> ∆H

(shrinking or expanding reduces number of conformations, i.e. entropy)

Why is water such a good solvent for polypeptides?

Hydrophobic interactions are strong (and will eventually drive folding to the native state for foldable sequences).

But…

1. Collapse is inhibited by the loss of conformational entropy:

ΩU ~ 1070 versus Ωcollapsed ~ 1020

∆G ~ 70 kcal mol-1

2. Removal of water from backbone is very demanding – Must satisfy H-bonding requirements.

Each unsatisfied, buried amide and carbonylcosts several kcal mol-1

Net stability of a protein < 10 kcal mol-1

Therefore, non-specific hydrophobic collapse is unfavorable

Conclusions (for small proteins which fold cooperatively)

1. Early collapse is not an obligatory step in folding

2. Water is a good solvent for unfolded chains (prior to the major folding event).

3. Polypeptides can behave like random coils in water

Exceptions occur for larger proteins, and those with disulfide bonds or prosthetic groups.

New area: RNA folding

Ribozyme P RNA

P15.1

G U U C U U AA C GU U C G GGUAAUC

G

A

A A A C C CA A A U

UUU

GGUAGGG

GAAC CU U C U U

AA C G GA

AUU

CAACGG

AGAGAAGG

ACAGAA UG

CUUUCUGUAGAUAGAUGAUUGCC GC

CUG

A GU

ACG

A GG

UGA U

GAG

CC G

UU

UGCAG

UA

CG

AUG

G A A C AA

AACAUGGCUUACAGAACGUUAGA

CCACUU

GU

CC

UGCUCGC

ACGGUGC

UG

AGAUGCCCGUAG

UG U UCGUGC

CU

AG

CGA

AGUCAUA

A GCUAGG

GCAGUCUUUA

G A GGCU GAC G

GCAGGA

AAAAAGCC

UAC

GUCUUC GGAU AU GGC

UG A GUAUC CU

U GAAAGU

GCCACA

GU G A C GAAG

UCUCACUAGA

AAUGGUGAGA

GUG

GA

ACGCGGUA

AACC

CC U CGA GC GA G

CUGCAGAUCUUGA A U C U GU AG

AGGAAA

1

20

40

60

100

120

140

160

200

220

260

280

300

320340

360

380

240

400

80

P1P2

P4

P15

P18

P19

P3

P5

P7

P5.1

P8

P9P10

P11

P10.1P12

Catalytic C-domain (~255 nt)

Specificity S-domain (~150 nt)

Model by Westhof & Co.JMB 1998

RNA Folding Rules are different Many highly collapsed intermediates

Rg

(Å)

0.01 0.1 1 10

40

60

80

100

N

I

U

Mg2+ (mM)0 20 40 60 80

100

80

60

40

20

0

N

Ik1

Ieq

Perc

ent c

ompa

ctio

n

Time (s)

Uurea

C-domain (255 nucleotide 80kD, 0.3 mg/ml)

w/ Prof. Tao PanUniv. of Chicago

From Fang et al, Biochemistry, 2000

PNAS 2002

<10-3 s

Ieq N I1k I2

k

5 s30 s <1 s

Relativecompaction 0 94% 99% 100%

Technical Issues:

1. Lower backgroundsi) reliably access lower Q ii) less sample iii) less potential aggreg’niv) less sensitive to

background subtraction

2. Detectors that can do time-resolved studies at high fluxesOften CCD’s take seconds to read-out.Hence, no “on-the-fly” studies on the subsecond time-scale(current experiments were conducted in continuous-flow mode)

3. Reproducibility – invariably need to take multiple acquisitions:Detector issues, beam movement?(lower backgrounds would help)

“Many small, monomeric proteins fold with simple two-state kinetics and show wide variation in folding rates, from microseconds to seconds.” From S. Jackson Folding & Design 1998How do small single-domain proteins fold?

(see also Sosnick et al, NSB 1994, Sosnick et al, Proteins 1996, Krantz & Sosnick, Biochemistry 1999, Krantz et al. JMB 2002)

Two-state folding ≡ only the U and N states populate

U

N

All the energy and surface burial occur in the sole barrier crossing.

Precludes formation of early collapsed intermediate.

IU

N

Lack of an early collapse phase places constraints on computer simulations.

short-lived, post-transition state intermediates

Observable (e.g.

Rg )

timeN

U tfold

short-lived, collapsed species

The black illustrative trace is consistent with ensemble behavior, as the observable probe has either the value of the unfolded state or native state for the majority of the trajectory.

The blue and red trajectories are inconsistent with ensemble two-state folding behavior and the present SAXS data, as collapsed intermediates populate.

Burst Rg and secondary structure formation (CD)

0 1 2 3 4 5 610

15

20

30

Requilg

Rburstg

R

g (Å

)

[GdmCl] (M)

-5,000

-4,000

-3,000

-2,000

-1,000

0

CDequil

CDburst

0 1 2 3 4 5 6 710

15

20

25

30

35

[Urea] (M)

Requilg

Rburstg

CDequil

CDburst

Ub ctAcp

[θ22

2] (d

eg c

m2 d

mol

-1)

-6,000

-5,000

-4,000

-3,000

-2,000

-1,000

0

25

Burst phase CD signals:

The removal of denaturant subtly alters the distribution of backbone dihedral φ,ψ angles, most likely resulting in a shift from the polyproline II region to the helical region of the Ramachandran map.

Kratky and P(r) plotsQualitatively demonstrates absence of any significant collapse from the random coil conformation in the “burst phase” upon

dilution to low denaturant

0 20 40 60 80 100 1200.000

0.001

0.002

0.003

0.004

Equilibrium Burst phase 0.75M 0.75M

0.92M 1.50M 1.50M 3.75M 4.03M 5.25M 4.69M 6.00M 6.00M

P(r

) (Å

-1)

r (Å)

Same result with CtACP: Negligible collapse upon dilution of denaturant

Dilute denaturant

Size after denaturant dilution

Size after equilibration

Folding times are msec to seconds – maybe we’re not looking fast enough?

No

Assume there is an early stable intermediate

IU

N

mumf

mo

Surface burial: mo=mu+mf ∆Gf‡

∆G

∆Gu‡

Underestimate Energy : ∆Gu‡-∆Gf

‡<∆G

mumf

mo

And surface burial: mo>mu+mf

fast

observe

U

N

∆Gf‡

∆G

∆Gu‡

Energy conservation: ∆Gu‡-∆Gf

‡=∆G

observe

No missing energy, no missing surface burial -Therefore, the no early formation of a stable species which buries surface!

Two-state Ubiquitin folding

A) Chevron and amplitude data at 25 C, showing no rollover or missing amplitude.

B) Folding rates down to low urea (0.4 M Na2SO4, pH 5.0, 10 C) show no rollover because the 1 msec dead time and other precautions avoided factoring in the slower phases. These and other results at a variety of conditions obey the 2-state chevron criteria.

ctAcp satisfies the Chevron criteria for two-state folding.

0 1 2 3 4 5 6 7

-2

-1

0RT

ln k

obs (k

cal m

ol-1

) Deuterated Protonated

[Urea] (M)

All the ∆G and surface burial in the U↔N reaction are fully accounted for in the observed kinetic phase.

Inconsistent with the accumulation of an early intermediate.

Time-resolved small-angle X-ray scattering studies are uniquely capable of measuring the collapse of the entire protein during the refolding process. We have measured the dimensions of two proteins within milliseconds of denaturant dilution using synchrotron-based, stopped-flow SAXS. Even upon a jump to strongly native conditions, neither ubiquitin nor common-type acylphosphatase contract prior to the major folding event. Thus, for these two denatured states, collapse is not energetically downhill processes even under aqueous, low-denaturant conditions. In addition, water appears to be as good a solvent as that with high concentrations of denaturant, when considering the over-all dimensions of the denatured state. Experimental considerations of conducting such experiments will be discussed.

Demonstrating 2-state behavior: Chevron Analysis

K =[U][N]

kukf

=

transitionstate∆Gf

‡=-RT ln kf

∆G

∆Gu‡=

-RT ln kuU

N

U Nku

kf

denaturant

denaturant

All the ∆G and surface burial is fully accounted for in the observed kinetic phase.

∴no early stable intermediates – 2-state folding!

Kineticskobs=kf +ku

‡

mf , mu∝surface area exposed going from starting state to transition state

mu

mf

Κeq= kf/ku=1

Equilibrium

mo∝surface area exposed on unfolding

∆G(Den)= ∆G(0)-mo*[Den]mo

denaturant

Agreement between equil. and kinetics implies 2-state model is adequate:

Energy: K= kf/ku(i.e. ∆Gkin =∆Gu

‡-∆Gf‡=∆Geq)

Surface burial: mokin=mu+mf=mo

kin