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

  2. BIOPOLYMERS: Folded Proteins Structurally well-defined STRUCTURAL TOOLS: X-ray crystallography NMR spectroscopy

  3. Protein Conformations and Dynamics Genetics & Environment Misfolding Ribosome n Nascent polypeptide chain Characterize disordered proteins by distribution functions: e.g., P(r) Aggregation Disease

  4. 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

  5. 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)

  6. 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

  7. 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

  8. STEADY-STATE FLUORESCENCE ENERGY TRANSFER: Limitations for heterogeneous samples A D em(single mode) ~ em(bimodal)

  9. STEADY-STATE FLUORESCENCE ENERGY TRANSFER: • Limitations in • Probing Folding • Mechanisms F A A D D Two-state U F Continuous U ?

  10. STEADY-STATE FLUORESCENCE ENERGY TRANSFER: Protein Folding Probes Two-state Continuous

  11. TIME-RESOLVED FLUORESCENCE ENERGY TRANSFER: Protein Folding Probes

  12. 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 

  13. 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.

  14. EXAMPLE: Disordered Polymer A D unquenched decay

  15. EXAMPLE: Disordered Polymer S/N = 100 A D unquenched decay

  16. EXAMPLE: Disordered Polymer S/N = 10 A D unquenched decay

  17. DIRECT INVERSION: P(r) = A1  I(t) kj+1/kj = 1.5 A D

  18. DIRECT INVERSION: P(r) = A1  I(t) kj+1/kj = 1.5; S/N = 100 A D

  19. 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 

  20. DIRECT INVERSION: P(r) = A1  I(t) kj+1/kj = 2.25; S/N = 100 A D

  21. DIRECT INVERSION: P(r) = A1  I(t) kj+1/kj = 2.25; S/N = 10 A D

  22. 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

  23. NONNEGATIVE LINEAR LEAST SQUARES: kj+1/kj = 1.5 A D

  24. NONNEGATIVE LINEAR LEAST SQUARES: kj+1/kj = 1.5; S/N = 100 A D

  25. NONNEGATIVE LINEAR LEAST SQUARES: kj+1/kj = 1.5; S/N = 10 A D

  26. NONNEGATIVE LINEAR LEAST SQUARES: kj+1/kj = 1.25; S/N = 100 A D

  27. 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

  28. MAXIMUM ENTROPY METHOD: kj+1/kj = 1.25; S/N = 100 A D

  29. NNLS vs MEM: kj+1/kj = 1.25; S/N = 100 A D NNLS MEM

  30. 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

  31. Research Generously Supported by: National Science Foundation National Institutes of Health Arnold and Mabel Beckman Foundation

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