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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**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 NNLS MEM**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

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