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

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

BIOPOLYMERS: Folded Proteins

Structurally well-defined

STRUCTURAL TOOLS:

X-ray crystallography

NMR spectroscopy

Protein Conformations and Dynamics

Genetics &

Environment

Misfolding

Ribosome

n

Nascent

polypeptide chain

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

Aggregation

Disease

Protein Folding Dynamics

DYNAMICS

hydrophobic

collapse

unfolded

protein

folded

protein

molten

globule

side-chain

rotations

helix

formation

intrachain

diffusion

ligand

substitution

proline

isomerization

seconds

fluorescence anisotropy

ultrafast mixing

stopped-flow

laser T-jump

10 0

10 –6

10 –4

10 –12

10 –10

10 –2

10 –8

10 2

T-jump

photochemistry

TRIGGERS

Protein Folding Probes

distance

(fluorescence energy transfer)

solvent/ion exclusion

(fluorescence quenching)

C

O

hydrogen bonding

(H/D exchange)

H

N

ligand substitution

(absorption)

secondary structure

(far-UV CD)

molecular dimensions (small-angle X-ray scattering)

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

FLUORESCENCE ENERGY TRANSFER:

femtosecond laser

r

- Dipole-dipole interaction energy ~ r3
- Dipole-dipole energy transfer rate ~ r6
- Förster equation:k = ko{1 + (ro/r)6}
- Förster distance ro (20 – 50 Å):
- function of spectral overlap, dipole-dipole orientation, donor quantum yield

STEADY-STATE FLUORESCENCE ENERGY TRANSFER:

Limitations for heterogeneous samples

A

D

em(single mode) ~ em(bimodal)

- STEADY-STATE FLUORESCENCE ENERGY TRANSFER:
- Limitations in
- Probing Folding
- Mechanisms

F

A

A

D

D

Two-state

U

F

Continuous

U

?

STEADY-STATE FLUORESCENCE ENERGY TRANSFER:

Protein Folding Probes

Two-state

Continuous

TIME-RESOLVED FLUORESCENCE ENERGY TRANSFER:

Protein Folding Probes

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

DISTRIBUTED FLUORESCENCE DECAY:

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(t2) = P(k1)exp(t2k1) + P(k2)exp(t2k2) + + P(km)exp(t2km)

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

n m

Equivalent Matrix Equation: I = A P

The Problem is Linear, but ill-posed.

EXAMPLE: Disordered Polymer

A

D

unquenched decay

EXAMPLE: Disordered Polymer

S/N = 100

A

D

unquenched decay

EXAMPLE: Disordered Polymer

S/N = 10

A

D

unquenched decay

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

kj+1/kj = 1.5

A

D

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

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

A

D

DISTRIBUTED FLUORESCENCE DECAY:

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(t2) =P(k1)exp(t2k1) + P(k2)exp(t2k2) + + P(km)exp(t2km)

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

Equivalent Matrix Equation: I = A P

Reduce oscillations by increasing

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

kj+1/kj = 2.25; S/N = 100

A

D

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

kj+1/kj = 2.25; S/N = 10

A

D

DISTRIBUTED FLUORESCENCE DECAY:

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(t2) =P(k1)exp(t2k1) + P(k2)exp(t2k2) + + P(km)exp(t2km)

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

Equivalent Matrix Equation: I = A P

Constrained Linear Least Squares: P(kj) 0

NONNEGATIVE LINEAR LEAST SQUARES:

kj+1/kj = 1.5

A

D

NONNEGATIVE LINEAR LEAST SQUARES:

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

A

D

NONNEGATIVE LINEAR LEAST SQUARES:

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

A

D

NONNEGATIVE LINEAR LEAST SQUARES:

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

A

D

DISTRIBUTED FLUORESCENCE DECAY:

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 = 100

A

D

NNLS vs MEM:

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

A

D

NNLSMEM

INTRACHAIN DIFFUSION IN DISORDERED PROTEINS

A

A

A

A

D

D

D+

D+

Measure both

fluorescence energy transfer

and

triplet electron transfer to obtain

P(r) and D

kdiff

ket

Physically based regularization

kdiff

Research Generously Supported by:

National Science Foundation

National Institutes of Health

Arnold and Mabel Beckman Foundation