Discussion Session prior to the Second Examination: Sunday evening April 13 6 to 8 pm. 161 Noyes Laboratory

Transcription

1 Discussion Session prior to the Second Examination: Sunday evening April 13 6 to 8 pm 161 Noyes Laboratory

2 Determination of the Stokes Radius by measuring the Rotational Diffusion Coefficient: D rot D rot = kt f rot = kt 8πηR 3 s Isotropic rotation D x = D y = D z D x = D y D z D x D y D z Measure D rot If you know R s η microviscosity D rot = kt 8πηR 3 s If you know η R s molecular size, shape

3 Rotational Diffusion Rate can be determined by Fluorescence Spectroscopy Fluorescence polarization (anisotropy) can measure how rapidly a molecule is tumbling in solution excitation light sample r µ 01 r µ 01 I t 1 t I fluorescent light

4 Fluorescence anisotropy For polarized excitation light, the probability of absorption of a photon depends on cos θ hυ E r θ µ r 01 X preferential excitation r of molecules whose µ 01 is parallel to the electric field vector of the excitation light Y E r Before (random) After excitation non-random distribution

5 Fluorescence anisotropy After formation of the excited state, the molecule can rotate during the time prior to photon emission hυ E r orientation r upon absorption µ 01 θ rot orientation at the time of emission X Y

6 Fluorescence polarization I Y I X θ ω µ r 01 X The probability of detecting the emitted photon depends on the orientation of the transition r dipole moment of the excited state molecule µ 01 AT THE TIME OF EMISSION and the orientation of the polarizer in the detection device r µ z-component = µ cosθ r µ sinθ cosω x-component = y-component = r 01 r µ sinθ sinω 01 probability of detecting the photon with polarization along the z-axis = µ cos θ x-axis = (sinθ cosω) y-axis = (sinθ sinω) I z proportional to < cos θ > Average over population I x proportional to < sin θ > < cos ω > I Y proportional to < sin θ > < sin ω >

7 Fluorescence polarization µ r 01 I II = I Y I X = I θ ω X Define I = I If we start with excitation light polarized along the z-axis, then I x = I y = I The total light intensity at the detector is I tot = I II + I Define: polarization, P = I II - I I II + I anisotropy, A = I II - I I II + I A = P 3-1

8 Polarization Relate Anisotropy to < cos θ > A = I II - I I II + I = < cos θ > - < cos ω > < sin θ > < cos θ > + < cos ω > < sin θ > ^ θ ω X Since we excite with light polarized along, we must have symmetry about this axis - so ω will always be random => < cos ω > = 1/ Y A = 3 < cos θ > - 1 By measuring I X and I we can compute < cos θ > for the emitting molecules

9 What goes into < cos θ >? I Photoselection θ µ Probability of absorption cos θ E ex The excited state population is not randomly oriented immediately after excitation E µ of excited state molecules Excitation beam Before (random) After excitation non-random (I II > I )

10 What goes into < cos θ >? II µ 0 Change in µ for absorption + emission IC 1 µ 0 abs µ 01 em Fixed angle λ hυ 1 hυ µ 01 0 photoselection Change µ

11 What goes into < cos θ >? III Rotational diffusion: Rotate Rotational diffusion coefficient D rot photoselection Change µ rotation

12 View each of these as a series of isotropic displacements of the average direction of the transition dipole moment µ θ λ Step 1 Step Step 3 θ rot photoselection Change µ rotation Goal: Find average displacement (θ) in terms of known parameters

13 Use Soleillet s equation - from geometry, describing a series of isotropic displacements of a vector 3 < cos θ > - 1 = 3 < cos α 1 > < cos α > < cos α Ν > - 1 α 1 α etc. Perrin s equation: A = 3 < cos θ > - 1 Measure this = 3 < cos θ 0 > < cos λ > < cos θ rot > - 1 Find this θ rot D rot Stokes radius

14 Photoselection Photoselection: A = 3 < cos θ > - 1 = 3 < cos θ 0 > < cos λ > < cos θ rot > - 1 Measure this 1 3 Find this Probability of absorption cos θ 0 < cos θ 0 > = 3/5 This is derived in the 346 Class Notes 1 So A = 0.4 P = 0.5 Maximum values of Anisotropy and Polarization Step 1 θ µ

15 Emit from a different transition after internal conversion Change in µ : µ 0 Large λ X X Y 0.4 from photoselection Y µ 01 A 0 = < cos λ > - 1 A 0 is the anisotropy obtained in the absence of molecular rotation - e.g., using frozen solutions or solutions with high viscosity Depends on excitation + emission wavelengths Maximum value for λ = 90 so limits on A 0 and P 0 are -0. A P 0 0.5

16 Rotational Diffusion: will always tend to bring A 0 or P 0 A = A 0 3 < cos θ rot > - 1 θ rot Anisotropy of frozen sample < cos θ rot > = 1 if there is no rotation: A = A o < cos θ rot > =1/3 for random orientation: A = 0

17 Rotational Diffusion 3 Rotational Diffusion: will always tend to bring A 0 or P 0 A o value from photoselection plus change in µ A = A 0 3 < cos θ rot > - 1 Break down rotation into a series of N isotropic steps of size δθ 3 < cos θ > - 1 = 3 < cos δθ > < cos δθ > < cos δθ > - 1 δθ δθ etc. cos δθ = 1 - sin δθ 1 δθ For a small step Rotational Diffusion: < δθ > = 4 D rot δt = 1-4 D rot δt 3 < cos θ rot > - 1 N = (1-6 D rot δt) t/δt

18 Rotational Diffusion 3 < cos θ rot > - 1 N = (1-6 D rot δt) t/δt But (1-x) e -x for x << 1 3 < cos θ rot > - 1 = e - 6 D t rot A = A 0 e - 6 D rot t Time-resolved Anisotropy yields D rot Monitor anisotropy following a pulse of excitation light: A Calculate D rot time

19 Steady State Measurement of Fluorescence Anisotropy Fraction of photons emitted in (t, t+dt) = f(t)dt t t+δt f ( t) = e t /τ τ dt f(t)dt t Average anisotropy A = 0 A( t) f ( t) dt A(t) t A = 0 6D t A e rot / τ 0 e ( 1/ τ ) dt A = A 0 (1 + 6 D rot τ) -1 Perrin s equation

20 Various forms of Perrin s equation (1) () substitute : V molecular volume (3) Perrin plot (4) 1 P Define: rotational diffusion time = T η (5)

21 Result for steady state fluorescence from a rotating molecule Measure this kt 8πηR s 3 Fluorescence lifetime Define: rotational diffusion time =

22 Protein Rotational Diffusion I. Extrinsic Probes + H N Dansyl chloride II. Results τ = 14 nsec Protein M ρ ρ/ρ 0 Avidin 71, BSA 67, Enolase 8, rigg 160, LDH 138, ρ 0 = (3ηV) / (kt) = (3hV M) / (NkT) [(mol.wt) / 1.15] x 10-3 nsec (Α 0 / A) = 1 + (3τ / ρ) Measure A 0, A, τ find ρ

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24 Example: Fluorescence Anisotropy Measurement of Protein-Protein Interactions TATA-box Binding Protein (TBP) binds with high affinity to TBP-associated Factor subunit TAF130p 1. Label TBP with tetramethyl rhodamine at a reactive cysteine residue.to a solution of 100 nm TBP (labeled) titrate increasing amounts of TAF130p (0-55 nm) 3. Exitation at 540 nm; emission monitored at 575 nm Conclude: High affinity binding (K d = 0.5 nm) Biological consequence: binding of TAF130p to TBP competes with DNA binding to TBP J. Biol. Chem., Vol. 76, Issue 5, , December 8, 001

25 Fluorescence Anisotropy used to monitor Protein-DNA Interactions nm Rhodamine labeled DNA. Titrate TBP 3. Excitation at 580 nm/emission at 630 nm SHOWS 1:1 COMPLEX 1. 1:1 DNA:TBP complex, with labeled DNA (50, 100, 50 nm TBP). Titrate TAF130p SHOWS ELIMINATION OF TBP-DNA COMPLEX BY COMPETING TAF130p nm labeled DNA. Titrate with TAF130p SHOWS NO COMPLEX BETWEEN DNA AND TAF130p J. Biol. Chem., Vol. 76, Issue 5, , December 8, 001

26 Fluorescence anisotropy used to measure microviscosity The rotational diffusion coefficient can be related to Molecular volume: V V molecular volume Measure this If you know V You can determine η

27 Fluorescent Probes dissolved are used to measure Membrane microviscosity Diphenyl hexatriene (DPH) Perylene Hydrophobic probes: partition into membrane bilayer do not bind to protein rotation reports local viscosity Probe dissolved in membrane bilayer Measure for specific probe Molecular constant: determine for probe in known viscosity (η) Then: A => η

28 Typically: for biological membranes η 1 Poise 100-times the viscosity of water Note: (1 / η) = fluidity of membrane

29 Example: The effect of deletion of the gene encoding ω-6-oleate desaturase in Arabidopsis thaliana Changes the fatty acid composition of the mitochondrial membrane: mostly oleic acid is present in the mutant (fad) J. Biol. Chem., Vol. 76, Issue 8, , February 3, 001

30 Membrane Fluidity monitored by the fluorescence Anisotropy of anthroyloxy fatty acid derivatives: the fluorophore is located at different depths in the membrane bilayer mutant mitochondrial membranes Extracted lipids wild-type CONCLUDE: Decrease in unsaturation of the fatty acid components in the membrane results in increased anisoptropy, or increase in membrane viscosity Biological Consequence: decreased respiration and altered bioenergetics of the mitochondria depth in the membrane bilayer/position in fatty acid chain) 18