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

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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

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


Time resolved fluorescence as a probe of protein conformation and dynamics

BIOPOLYMERS: Folded Proteins

Structurally well-defined

STRUCTURAL TOOLS:

X-ray crystallography

NMR spectroscopy


Time resolved fluorescence as a probe of protein conformation and dynamics

Protein Conformations and Dynamics

Genetics &

Environment

Misfolding

Ribosome

n

Nascent

polypeptide chain

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

Aggregation

Disease


Time resolved fluorescence as a probe of protein conformation and dynamics

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


Time resolved fluorescence as a probe of protein conformation and dynamics

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)


Time resolved fluorescence as a probe of protein conformation and dynamics

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


Time resolved fluorescence as a probe of protein conformation and dynamics

FLUORESCENCE ENERGY TRANSFER:

femtosecond laser

r

  • 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


Time resolved fluorescence as a probe of protein conformation and dynamics

STEADY-STATE FLUORESCENCE ENERGY TRANSFER:

Limitations for heterogeneous samples

A

D

em(single mode) ~ em(bimodal)


Time resolved fluorescence as a probe of protein conformation and dynamics

  • STEADY-STATE FLUORESCENCE ENERGY TRANSFER:

    • Limitations in

    • Probing Folding

    • Mechanisms

F

A

A

D

D

Two-state

U

F

Continuous

U

?


Time resolved fluorescence as a probe of protein conformation and dynamics

STEADY-STATE FLUORESCENCE ENERGY TRANSFER:

Protein Folding Probes

Two-state

Continuous


Time resolved fluorescence as a probe of protein conformation and dynamics

TIME-RESOLVED FLUORESCENCE ENERGY TRANSFER:

Protein Folding Probes


Time resolved fluorescence as a probe of protein conformation and dynamics

DISTRIBUTED FLUORESCENCE DECAY:

Förster:k = ko{1 + (ro/r)6}

P(r)  P(k)

Model: I(t) = ko{P(k)/k} ekt 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


Time resolved fluorescence as a probe of protein conformation and dynamics

DISTRIBUTED FLUORESCENCE DECAY:

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

Minimize 2: 2/{P(kj)} = 0

I(t1) = P(k1)exp(t1k1) + P(k2)exp(t1k2) +    + P(km)exp(t1km)

I(t2) = P(k1)exp(t2k1) + P(k2)exp(t2k2) +    + P(km)exp(t2km)

  

  

  

I(tn) = P(k1)exp(tnk1) + P(k2)exp(tnk2) +    + P(km)exp(tnkm)

n  m

Equivalent Matrix Equation: I = A  P

The Problem is Linear, but ill-posed.


Time resolved fluorescence as a probe of protein conformation and dynamics

EXAMPLE: Disordered Polymer

A

D

unquenched decay


Time resolved fluorescence as a probe of protein conformation and dynamics

EXAMPLE: Disordered Polymer

S/N = 100

A

D

unquenched decay


Time resolved fluorescence as a probe of protein conformation and dynamics

EXAMPLE: Disordered Polymer

S/N = 10

A

D

unquenched decay


Time resolved fluorescence as a probe of protein conformation and dynamics

DIRECT INVERSION: P(r) = A1  I(t)

kj+1/kj = 1.5

A

D


Time resolved fluorescence as a probe of protein conformation and dynamics

DIRECT INVERSION: P(r) = A1  I(t)

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

A

D


Time resolved fluorescence as a probe of protein conformation and dynamics

DISTRIBUTED FLUORESCENCE DECAY:

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

Minimize 2: 2/{P(kj)} = 0

I(t1) =P(k1)exp(t1k1) + P(k2)exp(t1k2) +    + P(km)exp(t1km)

I(t2) =P(k1)exp(t2k1) + P(k2)exp(t2k2) +    + P(km)exp(t2km)

  

  

  

I(tn) =P(k1)exp(tnk1) + P(k2)exp(tnk2) +    + P(km)exp(tnkm)

Equivalent Matrix Equation: I = A  P

Reduce oscillations by increasing 


Time resolved fluorescence as a probe of protein conformation and dynamics

DIRECT INVERSION: P(r) = A1  I(t)

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

A

D


Time resolved fluorescence as a probe of protein conformation and dynamics

DIRECT INVERSION: P(r) = A1  I(t)

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

A

D


Time resolved fluorescence as a probe of protein conformation and dynamics

DISTRIBUTED FLUORESCENCE DECAY:

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

Minimize 2: 2/{P(kj)} = 0

I(t1) =P(k1)exp(t1k1) + P(k2)exp(t1k2) +    + P(km)exp(t1km)

I(t2) =P(k1)exp(t2k1) + P(k2)exp(t2k2) +    + P(km)exp(t2km)

  

  

  

I(tn) =P(k1)exp(tnk1) + P(k2)exp(tnk2) +    + P(km)exp(tnkm)

Equivalent Matrix Equation: I = A  P

Constrained Linear Least Squares: P(kj)  0


Time resolved fluorescence as a probe of protein conformation and dynamics

NONNEGATIVE LINEAR LEAST SQUARES:

kj+1/kj = 1.5

A

D


Time resolved fluorescence as a probe of protein conformation and dynamics

NONNEGATIVE LINEAR LEAST SQUARES:

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

A

D


Time resolved fluorescence as a probe of protein conformation and dynamics

NONNEGATIVE LINEAR LEAST SQUARES:

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

A

D


Time resolved fluorescence as a probe of protein conformation and dynamics

NONNEGATIVE LINEAR LEAST SQUARES:

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

A

D


Time resolved fluorescence as a probe of protein conformation and dynamics

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


Time resolved fluorescence as a probe of protein conformation and dynamics

MAXIMUM ENTROPY METHOD:

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

A

D


Time resolved fluorescence as a probe of protein conformation and dynamics

NNLS vs MEM:

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

A

D

NNLSMEM


Time resolved fluorescence as a probe of protein conformation and dynamics

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


Time resolved fluorescence as a probe of protein conformation and dynamics

Research Generously Supported by:

National Science Foundation

National Institutes of Health

Arnold and Mabel Beckman Foundation


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