Analytical Ultracentrifugation

Transcription

1 Analytical Ultracentrifugation Stephen McLaughlin Biophysics MRC Laboratory of Molecular Biology Macromolecular Dynamics D Folding N Binding K N-D K D k D agg Aggregation Crystallisation 1

2 Macromolecular Dynamics Changes in Shape Mass Solvent interaction Higher Order Structures How? Up to 60,000 rpm Force up to 280,000g Detection Timing Concentration vs radial distance vs time Analysis based on Hydrodynamic theory 2

3 History 1920s Thé, I see a dawn * Thé Svedberg ( ) Uppsala University *Svedberg s student Fåhraeus on centrifuging Haemoglobin The Nobel Prize in Chemistry 1926 "for his work on disperse systems" AUC Timeline Svedberg equation Lamm continuity equation Mwt of proteins Svedberg proteins subunits Hydrodynamic theory TMV size and shape 1920s 1930s 1940s Yphantis seminal Paper 1964 Multi-components analysis High-speed meniscus depletion Shapes of proteins Mechanism of replication of DNA Discovery of ribosomes (30S+50S =70S) 1970s Insulin Hexamers Computer interactions with AUC Rebirth of hydrodynamics Tubulin 1960s 1950s XLI Proteome 1980s 1990s 2000s Crisis: limitations of machine Model E obsolete! Renaissance of Ultracentrifugation Future? Fluorescence detection system Computer software for data analysis 3

4 13/03/18 The future of centrifugation New Beckman AUC 2017 Optima Faster scans More wavelengths Higher radial resolution Higher res CCD camera XL-I Use of Analytical Ultracentrifugation What? Protein Peptides Nucleic acids Polymers Polysaccharides Dyes Compounds Complexes Why? What s in the sample? Mass Shape and size Solvent interactions Associations Binding affinity Cooperativity Multi-protein complexes Kinetics of binding Advantages: in solution no labels or tags (usually) batch measurement (fixed concentration) can be low volume recover sample afterwards 4

5 13/03/18 Rotor and cells Quartz and sapphire windows 4 hole and 8 hole rotors Up to 60krpm Temperatures: 4-30 C 2 and 6 channel centrepieces Absorbance detection system Toroidal Diffraction Grating Sample Reference Top View Reference Sample Reflector Sample/Reference Cell Assembly Rotor Imaging System for Radial Scanning radius (cm) Aperture Slit (2 nm) Xenon Flash Lamp Absorbance (a.u.) Incident Light Detector A=-log(I/Io) A=εl[c](Beer-Lambert law) Photomultiplier Tube nm range 5 nm bandpass (up to 3 wavelengths). Radially scans across channel 30 s per scan per cell 5

6 Interference detection system 670 nm Laser diode source In phase Out of phase Sample Reference Δn Sample Reference CCD detector images the entire cell Only ~10 s delay between scans Interference detection system In phase In phase Sample Reference Sample Reference ΔY = Δn*l/λ ΔY = vertical fringe displacement Δn = refractive index difference (s/r) l = optical pathlength (3mm, 12mm) ΔY=C (dn/dc) l/λ =3.33*C[mg/ml] RI gradient 6

7 Fluorescence detection system Photomultipler Tube Pin hole 50 µm > 505 nm cut-off filter Dichroic Mirror Rotor Focus Focus Solid-state Laser 488nm Mirror Very sensitive down to pm Needs label or GFP-fusion Possible to look at sedimentation in complex samples such as serum Absorbance Interference Fluorescence Sensitive 0.1 OD Can choose wavelength Scan time s Samples with high Abs or low extinction Scan 1 s Very sensitive 1 nm Selective Scan time 90 s Limited range (0.1<A<1.3) Can exploit lamp peak at 230 nm: 80 µg/ml at 280nm 10 µg/ml at 230nm 0.05 mg/ml = 0.1 fringes to high concentrations (< 70 fringes/mm) Excellent precision Care with buffers and baselines Large dynamic range (5-6 log) Excitation at 488 nm Need fluorescent cell Small quantities Typically monitor Absorbance and Interference together 7

8 Equilibrium and Velocity sedimentation Velocity Equilibrium Fast Slow Velocity Sedimentation Meniscus Time Time Radius 8

9 Velocity Sedimentation Top Buoyancy Friction Centrifugal force Bottom Centrifugal force: Buoyancy: F sed = m p ω 2 r m p is the mass of the particle ω is the angular velocity r is the radius from centre of rotation F b = m s ω 2 r m s is the mass of the solvent displaced r Friction: F f = fu u is the velocity of the particle Velocity Sedimentation Top Buoyancy Friction Centrifugal force Bottom Forces balance as particle is moving at a constant velocity, r F sed = F b + F f m p ω 2 r = m s ω 2 r + fu m p ω 2 r m s ω 2 r = fu m s = m p vρ m p (1 vρ)ω 2 r = fu m p is the mass of the particle ω is the angular velocity r is the radius from centre of rotation m s is the mass of the solvent displaced u is the velocity of the particle f is the frictional coefficient v is the partial specific volume of protein ρ is the solvent density V ml/g for proteins ml/g for DNA 9

10 Velocity Sedimentation Buoyancy Top Friction Centrifugal force Bottom Forces balance as particle is moving at a constant velocity, r Rearrange Where m p (1 vρ)ω 2 r = fu m p (1 vρ) f s = u ω 2 r m p (1 vρ) f = u ω 2 r = s A sedimentation coefficient (S) describes the velocity (u) at which a particle moves through a centrifugal field and is reported in units of Svedbergs (S) 1 S = 1 x s can be +ve or ve (flotation) Velocity Sedimentation Buoyancy Top Friction Centrifugal force Bottom f = k BT D = 6πηR s where k B is the Boltzmann s constant D is diffusional rate η is solvent viscosity R s is the Stokes radius r BSA s-vale of 4.3 S sediments at 0.8 µm/s at 50,000 rpm and experience a frictional force of 0.05 fn The relative frictional coefficient is express relative to R o (same mass and density) f/fo = Rs/Ro for globular proteins. Measure of asymmetry, shape? 10

11 Velocity Sedimentation Top Buoyancy Friction Centrifugal force Bottom f = k B T D m p (1 vρ) = s f r Where Substitute in To give k B = R N A m p (1 vρ) = s f DM(1 vρ) RT = s R is the gas constant N A is Avogradro s number Svedberg equation Velocity Sedimentation Top Buoyancy Friction Centrifugal force Bottom DM(1 vρ) RT = s Svedberg equation s is a constant for a macromolecule under ideal solution conditions It relates s and D to M r 11

12 Velocity Sedimentation: Solutions Top diffusion sedimentation Bottom j sed = cu = csω 2 r s = u ω 2 r j sed = csω 2 r j diff = D dc dr j(r) = j sed j diff j(r) = csω 2 r D δc δr Sedimentations causes a change of concentration along the radius. This is due to a flux of components due to sedimentation (j sed ) or diffusion (j diff ) Overall flux at point r Velocity Sedimentation: Solutions Top diffusion sedimentation Bottom where j(r) = csω 2 r D δc δr δc δr = 1 δrj r δr δc δr = 1 δc rd r δr cω 2 r 2 s so substituting in j(r) Lamm equation Relates experimental data to diffusion and sedimentation No exact analytical solutions are known Solutions are possible via numerical and analytic methods 12

13 Velocity Sedimentation δc δr = 1 " δc rd r δr cω % 2 r 2 s # $ & ' Lamm Equation Solve through number crunching S D S Size and shape information Equilibrium sedimentation Top diffusion sedimentation Bottom Relatively slow rotor speeds Slow sedimentation opposed by diffusional spreading of boundary from bottom to top After time diffusional flux and sedimentation flux reach equilibrium No further movement of boundary 13

14 Equilibrium sedimentation Top diffusion sedimentation Bottom At equilibrium j sed = csω 2 r j diff = D dc dr j sed = j diff j(r) = csω 2 r D dc dr = 0 Flux of molecules due to sedimentation Flux of molecules due to diffusion Overall flux at point r Equilibrium sedimentation Top diffusion sedimentation Bottom Re-arrange Integrate j(r) = csω 2 r D dc dr = 0 sω 2 D = 1 dc where c rdr sω 2 D = d lnc dr 2 2 c(r) = c(r 0 )e ( ) sω 2 2D r2 2 r 0 d(ln c) dc = 1 c 14

15 Equilibrium sedimentation Top diffusion sedimentation Bottom c(r) = c(r 0 )e ( ) sω 2 2D r2 2 r 0 Substiute c(r) = c(r 0 )e M (1 vρ ) ω 2 2 RT r2 2 ( r 0 ) DM(1 vρ) = s RT srt D = M(1 vρ) rearrange Equilibrium sedimentation Top diffusion sedimentation Bottom c(r) = c(r 0 )e M (1 vρ ) ω 2 2 RT r2 2 ( r 0 ) Exponential steepness is dependent on mass and rotor speed and not shape 15

16 Equilibrium sedimentation Top Bottom c(r) = c(r 0 )e M (1 vρ ) ω 2 2 RT r2 2 ( r 0 ) M b = M(1 vρ) M b = M M vρ Remember, measuring the buoyant mass: the mass of the macromolecule less the mass of solvent it displaces. M b = M " #(1 vρ)+ B 1 (1 v 1 ρ)+ B 3 (1 v 3 ρ) $ % The macromolecule isn t dry and may have bound water (B 1 ) and co-solutes (B 2 ). At low solvent densities these are not important i.e. close to water they are invisible Software: Data Analysis Sedfit and Sedphat UltraScan UltraSpin Peter Schuck Borries Demeler Dmitry Veprintsev DCDT+ -(John Philo) Sedview-(Hayes & Stafford)- check as spin running g(s) analysis Sedanal -(Walter Stafford) GUSSI Chad Brautigam (UT Southwestern) 16

17 Software: Hydrodynamic parameters SEDNTERP (John Philo) for νbar, η and ρ HYDROPRO & SOMO- (Jose García de la Torre) Bead modeling for hydrodynamic parameters e.g. frictional coefficient ratio Direct measure using viscometer and densitometer AUC workflow Primary information: Purity: SDS-PAGE, UV spectrum, gel filtration, stability Amino acid sequence: ν, ε, Mwt Mass-spec: any modifications? Buffer: density, viscosity, composition, ph ionic strength Initial Characterisation: Multiple concentration SV 50 krpm C(s) analysis Not pure pure Interacting components Yes Change in distributions Label one component, repeat SV, SE analysis multiple concentrations for Kd No Further analysis: M, f reasonable? SE analysis for Mwt 17

18 Velocity sedimentation Load concentrations S load multiple concentrations (OD= ): Dilution series for non-interacting Titration for interacting (A: 5x K d :B: x K d ) Volumes >400 µl 12mm, 80 µl for 3mm FDS Detection A230nm, 280nm, 488nm and IF or FDS Speed Fit Data 50 krpm or slower for large complexes (>1 MDa) collect 400 scans (overnight) C(s) for S distributions: Mass and shape, K d s Equilibrium sedimentation Load concentrations load multiple concentrations span a large range: above + below K d to populate all species Volumes >160 µl 2 channel >110 µl 6 channel Detection Speed A230nm, 280nm, 488nm and IF Slow 3 speeds: low for high mass; high for meniscus depletion and low mass/baseline. 12 scans with 8 hrs between scans (1 week) Fit Data Self-association, Masses, equilibria, Kd 18

19 Extra considerations Match reference buffer especially for interference Absorbance: keep buffer < 0.2OD at wavelength Nucleotides: use interference Ionic strength: greater than 10 mm ( mm best) Density: near water if possible, otherwise may create density gradients Buffer composition and its total absorbance (< 1mM DTT). May change overtime. Fluorescence: GFP, fluorescein of FlSAsH tag, VS only, can use cell lysate, serum etc. Need to measure degree of labeling, and removal of free dye. Check for protein dye binding. Application of SV Absorbance Detection Meniscus buffer-to sample Bottom Abs 280 nm Data range Meniscus buffer-to air V-bar Solvent properties Noise to account for aberrations in optics Regularization Is recombinant α-synuclein folded tetramer or unfolded monomer? 19

20 Application of SV Absorbance Detection Meniscus Abs 280 nm c(s) s = m p Is recombinant α-synuclein folded tetramer or unfolded monomer? ( 1 vρ) O Sedimentation coefficient (s) f Bottom Scan data - Fits Error bitmap Residuals One sedimenting species at 1.2S consistent with a monomer with high frictional coefficient Application of SV Interference detection Is RelBE toxin-antitoxin a tetramer or dodecamer? Meniscus Bottom Include jitter, integral fringe shift, and time-invariant baseline in the model 20

21 Application of SV Interference detection Is RelBE toxin-antitoxin a tetramer or dodecamer? Majority tetramer, no indication of higher species Bøggild et al. (2012) Structure Effect of Kinetics on Sedimentation Distributions What happens it my components interconvert over the timescale of the run? Depends on the relative microscopic rate constants of dissociation compared to runtime k off < 10-4 s -1 separate species Can measure the relative concentrations from integrated peaks and hence Kd if at eqm before run! s s k off > 10-2 s -1 time-average populations c.f. nmr. Can still fit timeaveraged populations to determine s-coefficients and Kds 21

22 13/03/18 Example of slow kinetics SPATA-2 The sedimentation value for the complex doesn t change with concentration of components. Therefore can infer mass and shape from s-value Elliot et al. (2016) Mol Cell,63(6): Typical Applications of SV Does my protein self-associate? Do these two components associate? What range of species are in my sample? What is the mass/stoichiometry of the complex? My binding is weakly/strong. What is the Kd? I have a multi-component system: what binds to what? 22

23 Is my complex fully formed? Molar mass (g/mol) SEC-MALS 2.3 mg/ml 0.5 mg/ml mg/ml 0.5 Refractive index (a.u.) Time (min) µm At highest concentration, the major species has a mass of approx. 101 kda = heptamer/octomer. 76 µm At the lowest concentration, the mass ranges from approx kda. 28 µm 9 µm The system is polydisperse with multiple species interconverting and so difficult to assess c(s) (AU/S) Velocity AUC: Hybrid/Continuous Sedimentation coefficient (S) Analysis Cell 1 Percentage species µm Cell 2 Percentage species µm Cell 3 60 The velocity AUC was fitted using SEDPHAT with hybrid/continuous analysis wherein the model assumes the sedimenting species, consist of oligomers of a protein with a mass of 14, Da. Percentage species Percentage species Percentage species µm Number of subunits 6.7 µm The major species has a sedimentation coefficient (S w20 ) of around 5.9 S with a mass corresponding to an octomer (right) This analysis depends on the shape of the species and may not reflect the true identity of species especially if they have different shapes and hence frictional ratios. (see later) µm Number of subunits 23

24 Application of SV Fluorescence detection Homo and Hetero-oligomerisation R4* D M Fit Gaussian distributions Integrate areas Areas correlated to species concentrations Calculate Kd Rossmann et al. (2011) EMBO J. Mechanistic Studies Phage-display selected bicycle-peptide Constrained by incubation with TBMB organic core Raised against trimeric TNF-α Where does it bind? Luzi et al. (2015) PEDS 24

25 Mechanistic Studies What is the oligomeric status of TNF-α? Mechanistic Studies How does the oligomeric status of trimeric TNF-α change when incubated with bicycle peptide? c(s) (fringes/s) Interference + TNFα + M21-Cy Sedimention coefficient (S) 25

26 Mechanistic Studies Where does the bicycle-peptide bind? + Mechanistic Studies Where does the bicycle-peptide bind? + 26

27 Mechanistic Studies Where does the bicycle-peptide bind? + Mechanistic Studies Where does the bicycle-peptide bind? Label the protein with fluorophor Fluorescence TNFα* at 5 C c(s) (Fl/S) Sedimention coefficient (S) 27

28 Mechanistic Studies Where does the bicycle-peptide bind? Label the bicycle-peptide with fluorophor Follow timecourse Fluorescence TNFα + M25* at 4 C c(s) (Fl/S) Sedimention coefficient (S) Mechanistic Studies Where does the bicycle-peptide bind? Label the bicycle-peptide with fluorophor Follow timecourse + TNF-α* +peptide* 28

29 Glycoproteins Exploit difference in vbar between protein and oligosaccharide and diffusional properties. Analysis based on opposing trends of observed vs theoretical mass. 1 ψ(1 ν Pρ) q int = 1+ ψ(ν P ν C ) ψ = nm P,monoD GP s GP RT Intercept of theoretical mass against measured mass gives the degree of glycosylation, q int Kwon et al., Cell, 137, 1213 Membrane proteins No buffer matching Properties of protein/detergent/micelle treated explicitly. M = srt D(1 φ 'ρ) 1 φ 'ρ = (1 vpρ)+δ D (1 vdρ) φ ' = vp +δ D vd δ D ρ δ D = a i ε p λ a a dn / dc D dn / dc P dn / dc D Solve value of δ D by measuring signals in both interference and absorbance. Le Maire et al., Nat. Protoc., 3,

30 Membrane proteins Once we know δ D, there are three approaches traditionally available: 1. Plausibility of f/f Calculating M P from s and D. 3. Calculating M P from s and R S Determine oligomeric state Determine how stoichiometry of bound detergent or lipid Applications of SE: mass of my complex? 15 Fringes 10 5 Residuals r (cm) To obtain an accurate mass for the oligomer, a 1:2 dilution series of Arcadin-1 were centrifuged at three different speeds. The data were fitted using Ultraspin and SEDPHAT using a simple single exponential model to obtain the average mass of species: Mass = 116,500 ± 273 Da which is close to that expected for an octomeric species (116,485 Da). Izoré, T. et al(2016) elife, 5. pii: e

31 Is a dimer real or a packing artifact? Dimer in X-ray? Dimer in SE AUC Obtain Kd Mark van Breugel et. al (2011) Science Applications of SE: Monomer or dimer? Single Double 31

32 Applications of SE: Self-association Dimer + Monomer Calculated free monomer [M] Kd = [D] 2 Concentration must be high enough to populate equilibrium so individual species contribute to the measures sedimentation profile Change speed and concentration to change equilibria and not just non-interacting particles. Applications of SE: Self-association WT Dimer Kd =600 µm FE mutant Monomeric van Breugel et al. (2014) elife 32

33 Applications of SE: Hetero-association Many different models to fit data A+2B K d1 AB +B K d2 ABB Exploit differences in absorbance e.g. DNA vs protein Can globally fit multi-signals e.g. absorbance and interference Hetero-association using labels A+B AB Kd = [A][B] [AB] Absorbance Interference Absorbance (488nm) Measured [AB] [A] Fringes Measured [AB] + [B] r r Kd = CA CAB (CB CAB) 33

34 13/03/18 Further reading Biophysics on internal website AUC at the LMB Dedicated AUC Room at 3N190 Further advice/discussion Stephen McLaughlin 34