Time-Resolved Fluorescence as a Probe of Protein Conformation and Dynamics

Time-Resolved Fluorescence as a Probe of Time-Resolved Fluorescence as a Probe of Protein Conformation and DynamicsProtein Conformation and Dynamics

BIOPOLYMERS: Folded Proteins

Structurally well-defined

STRUCTURAL TOOLS:

X-ray crystallography

NMR spectroscopy

Protein Conformations and Dynamics

Ribosome

Nascentpolypeptide chain

Aggregation

Disease

Misfolding

Genetics &Environment

n

Characterize disordered proteins by distribution functions: e.g., P(r)

10-7 10-5 10-3 10-1 10110 –12 10 –10 10 –8 10 –6 10 –4 10 –2 10 0 10 2

side-chain rotations

helixformation

intrachaindiffusion

ligand substitution

prolineisomerization

DYNAMICS

TRIGGERS

unfoldedprotein

hydrophobiccollapse

moltenglobule

folded protein

fluorescence anisotropy

laser T-jump

ultrafast mixing

stopped-flow

photochemistry

T-jump

seconds

Protein Folding Dynamics

molecular dimensions (small-angle X-ray scattering)

solvent/ion exclusion(fluorescence quenching)

distance(fluorescence energy transfer)

ligand substitution(absorption) secondary structure

(far-UV CD)

hydrogen bonding(H/D exchange)

CO

NH

SO3H

NHHNS

O

Protein Folding Probes

PROTEIN FOLDING PROBES: Fluorescence

Advantages•High sensitivity (M – nM; single molecules)

•Environment sensitive

•Structural information (Förster energy transfer)

Disadvantages•Few intrinsic protein fluorophores

•Dye labeling – structure, dynamics perturbations

•Data analysis

femtosecond laserr

Dipole-dipole interaction energy ~ r 3

Dipole-dipole energy transfer rate ~ r 6

Förster equation: k = ko{1 + (ro/r)6}

Förster distance ro (20 – 50 Å):

function of spectral overlap, dipole-dipole orientation, donor quantum yield

FLUORESCENCE ENERGY TRANSFER:

STEADY-STATE FLUORESCENCE ENERGY TRANSFER:

Limitations for heterogeneous samples

10 15 20 25 30 35 40 45 50 55 600

0.01

0.02

0.03

0.04

0.05

0.06

0.07

r, Angstroms

dP(r)

/dr

em(single mode) ~ em(bimodal)

DA

Two-state

Continuous

U

F

F

U


Limitations inProbing FoldingMechanisms

DA

D

A

?

Two-state

Continuous



o)()(

kkktekPtI

6o

oobsd 1rrkk

TIME-RESOLVED FLUORESCENCE ENERGY TRANSFER:


DISTRIBUTED FLUORESCENCE DECAY:

Förster: k = ko{1 + (ro/r)6}

P(r) P(k)

Model: I(t) = ko {P(k)/k} ekt dk

Data Fitting:

2 = in {I(ti)obsd I(ti)model}2

Create a discrete distribution of rate constants:

k k1, k1, . . . , km

P(k)/k P(kj)/kj


Data Fitting Parameters: P(kj), kj+1/kj =

Minimize 2: 2/{P(kj)} = 0

I(t1) = P(k1)exp(t1k1) + P(k2)exp(t1k2) + + P(km)exp(t1km)


I(tn) = P(k1)exp(tnk1) + P(k2)exp(tnk2) + + P(km)exp(tnkm)

n mEquivalent Matrix Equation: I = A PThe Problem is Linear, but ill-posed.

EXAMPLE: Disordered Polymer DA

10 15 20 25 30 35 40 45 50 55 600

0.02

0.04

0.06

r, Angstroms

dP(r)/dr

7.5 8 8.5 9 9.5 100

1

2

x 10-9

log(k)

dP(k)/dk

10-11 10-10 10-9 10-80

5000

10000

time, s

I(t) unquenched decay

EXAMPLE: Disordered Polymer

S/N = 100D

A

10 15 20 25 30 35 40 45 50 55 600

0.02

0.04

0.06

r, Angstroms

dP(r)/dr

7.5 8 8.5 9 9.5 100

1

2

x 10-9

log(k)

dP(k)/dk

10-11 10-10 10-9 10-80

5000

10000

time, s


EXAMPLE: Disordered Polymer

S/N = 10D

A

10 15 20 25 30 35 40 45 50 55 600

0.02

0.04

0.06

r, Angstroms

dP(r)/dr

7.5 8 8.5 9 9.5 100

1

2

x 10-9

log(k)

dP(k)/dk

10-11 10-10 10-9 10-80

50

100

time, s


DA

DIRECT INVERSION: P(r) = A1 I(t)

kj+1/kj = 1.5

10 15 20 25 30 35 40 45 50 55 600

0.02

0.04

0.06

r, Angstroms

dP(r)/dr

7.5 8 8.5 9 9.5 10 10.5 11

0.51

1.52

x 10-9

log(k)

dP(k)/dk

10-11 10-10 10-9 10-80

5000

10000

time, s

I(t)

DIRECT INVERSION: P(r) = A1 I(t)kj+1/kj = 1.5; S/N = 100

DA

10 15 20 25 30 35 40 45 50 55 60-200

-100

0

100

r, Angstroms

dP(r)/dr

7.5 8 8.5 9 9.5 10 10.5 11-1

0

1x 10-5

log(k)

dP(k)/dk

10-11 10-10 10-9 10-80

5000

10000

time, s

I(t)







Equivalent Matrix Equation: I = A PReduce oscillations by increasing


DA

10 15 20 25 30 35 40 45 50 55 60-0.05

0

0.05

r, Angstroms

dP(r)/dr

7.5 8 8.5 9 9.5 10 10.5 110

1

2

x 10-9

log(k)

dP(k)/dk

10-11 10-10 10-9 10-80

5000

10000

time, s

I(t)


DA

10 15 20 25 30 35 40 45 50 55 60

-0.2

0

0.2

r, Angstroms

dP(r)/dr

7.5 8 8.5 9 9.5 10 10.5 11

-5

0

5

x 10-9

log(k)

dP(k)/dk

10-11 10-10 10-9 10-80

50

100

time, s

I(t)







Equivalent Matrix Equation: I = A PConstrained Linear Least Squares: P(kj) 0

NONNEGATIVE LINEAR LEAST SQUARES:

kj+1/kj = 1.5D

A

10 15 20 25 30 35 40 45 50 55 600

0.020.040.060.08

r, Angstroms

dP(r)/dr

7.5 8 8.5 9 9.5 10 10.5 110

1

2

x 10-9

log(k)

dP(k)/dk

10-11 10-10 10-9 10-80

5000

10000

time, s

I(t)


kj+1/kj = 1.5; S/N = 100D

A

10 15 20 25 30 35 40 45 50 55 600

0.05

0.1

r, Angstroms

dP(r)/dr

7.5 8 8.5 9 9.5 10 10.5 110

1

2

x 10-9

log(k)

dP(k)/dk

10-11 10-10 10-9 10-80

5000

10000

time, s

I(t)


kj+1/kj = 1.5; S/N = 10D

A

10 15 20 25 30 35 40 45 50 55 600

0.05

0.1

r, Angstroms

dP(r)/dr

7.5 8 8.5 9 9.5 10 10.5 110

1

2

3x 10-9

log(k)

dP(k)/dk

10-11 10-10 10-9 10-80

50

100

time, s

I(t)


kj+1/kj = 1.25; S/N = 100D

A

10 15 20 25 30 35 40 45 50 55 600

0.1

0.2

r, Angstroms

dP(r)/dr

7.5 8 8.5 9 9.5 10 10.5 110

2

4

x 10-9

log(k)

dP(k)/dk

10-11 10-10 10-9 10-80

5000

10000

time, s

I(t)


Regularization methods

Minimize = 2: + g{P(kj)}

/{P(kj)} = 2/{P(kj)} + g{P(kj)}/{P(kj)} = 0

Data Fitting Parameters: P(kj), kj+1/kj = ,

Regularization Functions:

g{P(kj)} = kg{P(kj)}

g{P(kj)} = 2kg{P(kj)}

g{P(kj)} = S = j{P(kj)}ln{P(kj)}

Maximize while retaining good fit to data

MAXIMUM ENTROPY METHOD:

kj+1/kj = 1.25; S/N = 100D

A

10 15 20 25 30 35 40 45 50 55 600

0.02

0.04

0.06

r, Angstroms

dP(r)/dr

7.5 8 8.5 9 9.5 10 10.5 110

1

2

x 10-9

log(k)

dP(k)/dk

10-11 10-10 10-9 10-80

5000

10000

time, s

I(t)

NNLS vs MEM:

kj+1/kj = 1.25; S/N = 100D

A

NNLS MEM

10 15 20 25 30 35 40 45 50 55 600

0.1

0.2

r, Angstroms

dP(r)/dr

7.5 8 8.5 9 9.5 10 10.5 110

2

4

x 10-9

log(k)

dP(k)/dk

10-11 10-10 10-9 10-80

5000

10000

time, s

I(t)

10 15 20 25 30 35 40 45 50 55 600

0.02

0.04

0.06

r, Angstroms

dP(r)/dr

7.5 8 8.5 9 9.5 10 10.5 110

1

2

x 10-9

log(k)

dP(k)/dk

10-11 10-10 10-9 10-80

5000

10000

time, s

I(t)

INTRACHAIN DIFFUSION IN DISORDERED PROTEINS

DA

AD

D+

A

A

D+

kdiff

kdiff

ket

Measure bothfluorescence energy transfer

and triplet electron transfer to obtain

P(r) and D

Physically based regularization

Research Generously Supported by:

National Science Foundation

National Institutes of Health

Arnold and Mabel Beckman Foundation

Documents

Time-Resolved Fluorescence as a Probe of Protein Conformation and Dynamics