Introduction to techniques in biophysics.

Transcription

1 Introduction to techniques in biophysics. Goal : resolve the structure and functions of biological objects applying physical approaches 1 At molecular level 1.1 Long-range goal: complete structure determination: location in space of each atom Problem: Mwt (protein, AA) = N = atoms 3N 6 parameters define the structure parameters (structure + chemical identity) huge! simplification: ignore H-atoms parameters still huge! primary structure: bond length and angle, internal rot. angle (not for H) Problem: N = atoms parameters many bond lengths and angles are known still huge! further simplifications: work with residues: 2 angles for relative location + 2 parameters for side chains orientation Problem: Mwt (protein) = (~ 300 residues) parameters Mwt (AA) = (~ 200 residues) 800 parameters symmetry (identical subunits, helices ) still huge! 1.2 Near-field goal: rough size and shape of molecule Example: model the molecule as an ellipsoid of revolution, a rod, a coil of uniform or no stiffness techniques: hydrodynamic and scattering techniques characterize only a part of the macromolecule, of special interest Example: use probe molecules (a part of the macromolecule or externally added) techniques: fluorescence, EPR, some aspects of NMR, chemical modification examine certain general aspects of the structure, ignoring others Example: give a general picture, show constraints on possible 3D structure techniques: CD/ORD, UV, IR, Raman spectroscopy, tritium exchange 2 At supra molecular level: structure and physical properties 2.1 direct visualization of shape and structure: optical techniques 2.2 measure mechanical properties; force/energy: physical approach 2.3 functional characterization: chemical approach Techniques: electron microscopy, hydrodynamics (RD)

2 Structure Determination of Biomolecules by Physical Methods. Macromolecules (proteins, nucleic acids) size - up to few 10 2 nm; weight - up to 10 8 : well defined (synthetic molecules - molecular weight distributions; mean values) Human eyes: 0.2mm Method yields M-range Requirements, comments - Complete chemical analysis M no limit - Quantitative chem. identification of groups (of number M, e.g. CO) M no limit Knowledge of general chemical structure - X-ray diffraction - Neutron diffraction size, shape internal structure no limit Single crystal, heavy atom staining; - Electron microscopy Size, shape > 5000? Radiation damage - Osmotic pressure M n Vapor pressure osmometry - Viscosimetry M v (size, shape) < 10 7 Structural effects - Diffusion measurements M w, size < 10 6 Influence of structure, solvation, concentration - Sedimentation velocity M w, size < 5x10 7 Structure dependent - Sediment. velocity + diffusion M w, size < 5x10 7 Structure effects eliminated - Sedimentation equilibrium M w, M z < 5x10 6 Fast; structure independent - Electrophoresis M (poor value) Separation method for ions - Rotational diffusion, fluorescence depolarization Size, shape, M w no limit Structure dependent - Flow birefringence Size, shape, M w Empirical calibration - Kerr effect Size (shape) no limit - Dielectric dispersion Size (shape) no limit Isolating solvent; electric dipole moment of solute known - Light scattering R G, size M w 10 4 Fast, sensitive to association of molecules - X-ray small angle diffraction - Neutron small angle diffraction Size < 10 5 Dilute solutions Techniques: electron microscopy, hydrodynamics (RD)

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5 Electron Microscopy 1 Features, requirements e - wavelength (de Broglie relationship): λ = h mev e - kinetic energy (if accelerated by voltage Φ): 2 m e 2v = eφ Example: for Φ = V λ = 0.04 Å! (theoretically) EM yields extremely precise structures of small molecules in gas phase work in vacuum (e - are easily stopped/absorbed by thin layers) usually on gold support possible damage of sample by e - -collision low irradiation intensity to be employed contrast sample-to-support decreases problem rule of thumb: e - -scattering (atomic number) 2 Example: U (A = 92) scatters 10 4 times more than H (A=1) 2 Principle (comparison with light microscopy) Light microscope light EM e - source anode Electrons emitted from a hot cathode are attracted to an anode; pass through a hole in the anode and create the e - beam aperture diaphragm condenser specimen objective lens scattered rays Lenses are electromagnets or magnetic coils: zoom lenses a change in the magnetic field changes their focal length objective image projection ocular intermediate lens projection lens Low numerical aperture limits the resolution: Limit of resolution = 0.61λ/numerical aperture = approx. 0.1 nm (1Å) projection image Techniques: electron microscopy (RD)

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7 3 Transmission electron microscopy: more relevant for biological samples Anode Tungsten thermionic cathode overall magnification: 100x to x or 2µm to 0.4nm Resolution limit depends on: electron wavelength performance of the magnetic lenses stability of magnetic fields (1-50kV) Sample mounted on a transparent grid Electromagnetic lens ( x) Lens system ( x) Difficulties: melting in the intense electron beam damage: e - interact with the e - shell inducing energy transfer and not elastic scattering Example: bonds in aliphatic chains would break; aromatic rings would endure electrostatic charging evaporation and decomposition solvated structures are destroyed during the dry-sample preparation partially avoided when using replicas Fluorescent screen (additional 5-10 x) Possible 3D presentation: by shadow casting (firing electrons under an angle) Vacuum is required in the e - beam path usually only dead, dehydrated specimens may be viewed by EM. Exception: cryo-em; works with frozen specimen (vaporization of water is negligible) Specimen Preparation for TEM Dehydration: required except for cryo-em Embedding in epoxy resins or polyester (Vestopal) Sections: cut with an ultramicrotome, floated on water, picked up on a support grid; sections for TEM must be very thin ( nm) Exception: very high voltage (10 6 V) TEMicroscopes permit viewing thicker sections Grid (copper) may be coated with a support film of low atomic weight material; tissue sections are viewed through holes in the grid tissue slices on EM grid Techniques: electron microscopy (RD)

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9 4 Staining techniques: heavy atom stains improve contrast, but reduce resolution Positive staining: incorporation of heavy atoms (e - -dense stain) e.g. specific complexation Example: binding uranyl ions (from uranyl acetate) to DNA; osmium (osmium tetroxide) fixation to lipid bilayers Negative staining: the sample is flooded in solution of an e - -dense stain (e.g. phosphotungstic acid, uranyl acetate); placed on a grid; dried When viewed by TEM, areas occupied by sample (not penetrated by stain) are seen to be less e - dense. sample dried solution of e - -dense stain EM grid support film Negative Staining Shadowing evaporation of heavy metal at an angle EM grid with support film Shadowing: heavy metal (e.g. tungsten) is evaporated/sprayed at an angle, under vacuum; shadows form where the metal builds up; the sample is dissolved by acid, and the metal replica viewed by TEM Autoradiography: radioactive sample placed in a fine photographic emulsion resolution - limited by the silver grains size, the traveling distance of decay particles; problem decay time (i.e. exposure time) Techniques: electron microscopy (RD)

10 5 Freeze fracture / freeze etching: for viewing surfaces of organelles Fracturing: freeze rapidly and cut specimen Bell jar (under vacuum to prevent frosting of the knife) support liquid freon Cold knife Specimen table liquid N 2 Fracturing occurs mainly along the interface of the 2 hydrocarbon layers of the membrane Etching: sublimation of ice in vacuum (at 100 C) Inner surface Fractured face ridge surface Outer surface Normal etching Deep etching Visualizing: the exposed surface is shadowed with platinum and carbon; the deposited film is removed: replica for EM Techniques: electron microscopy (RD)

11 6 Scanning electron microscopy: resolution about 10nm BSE - back scattered electrons SE - secondary electrons SC - specimen current EBIC - electron-beam-induced current X - X-rays CRT - cathode-ray tube the electron beam diameter (5-10 nm) limits the resolution beam electron current: A SE - emitted at low voltage easily deflected to follow curved paths of the collector 3D image depth field: times bigger than for light microscope (better contrast) Magnification can be increased by decreasing the scan-coiled current Specimen Preparation for SEM Samples are fixed and dried Non-conducting surfaces (e.g. biological objects) are coated by evaporation under vacuum with a heavy metal (to avoid disturbing electrostatic effects) Techniques: electron microscopy (RD)

12 Biomolecular Hydrodynamics 1 Hydrodynamic properties sedimentation coefficient diffusion coefficient rotational relaxation time intrinsic viscosity viscoelastic relaxation time give information about: molecular weight, size, hydration, shape, flexibility, conformation, degree of association of biological macromolecules Some classical examples: Experiments: Fick, on diffusion Svedberg, 1920s - on sedimentation Poiseuille, on viscosity Theories for simple shapes (e.g. spheres and ellipsoids): Stokes (1847) Einstein (1906) / Brownian movement Perrin (1936) / translation and diffusion of an ellipsoid Some recent developments: Experiments: dynamic laser light scattering nanosecond fluorescence depolarization measurements fluorescence recovery after photobleaching fluorescence correlation spectroscopy pulsed field gradient NMR improved analytical ultracentrifuge design Theory: new theoretical and computational tools Techniques: hydrodynamics (RD)

13 2 Frictional coefficients translational frictional coefficient, f t v -velocity F f - frictional force: applied force (e.g. centrifugation or electrophoresis) concentration gradient (as in diffusion) F f R v - the frictional force opposes the particle motion rotational frictional coefficient, f r ω - angular velocity T r - frictional torque: applied electric or hydrodynamic flow field diffusion of molecular axes ω T r 2.1 Viscosity of water η Def: force per unit area needed to maintain unit velocity gradient between two parallel surfaces moving relative to one another in the fluid cgs units: dyne.s/cm 2 = poise* *Poiseuille: viscous flow in tubes (1946) At 20 C η = poise or centipoise (cp) for 0 t 20 C for 20 t 100 C 2.2 Spheres Stokes law, R - Stokes radius f t - much less sensitive to molecular dimensions varies with volume Techniques: hydrodynamics (RD)

14 2.3 Ellipsoids of revolution a b oblates p < 1 a/b = p - axial ratio V = (4/3)πab 2 a b prolates (models for cylindrical rods) p > 1 Friction ratios: R e - equivalent radius (of the sphere of equal volume) r b 2.4 Random coils have on average a spherical domain behave hydrodynamically like spheres with effective hydrodynamic radius radius of gyration for a coil with N bonds of length b not swollen by excluded volume the effective hydrodynamic radius 2/3 radius of gyration 2.5 Oligomeric arrays of spheres model for proteins n number of (33) - rotation around the axis of highest symmetry (11) - for either axis perpendicular to it Techniques: hydrodynamics (RD)

15 3 Experimental determination of hydrodynamic properties 3.1 Sedimentation coefficient (centrifugation, ultracentrifugation) Types of sedimentation experiments: 1) measure the velocity of molecular motion 2) the centrifuge runs until equilibrium is reached and one measures the unchanging concentration distribution Usual components in the system: 1 water (density ρ) 2 polymer solute (molecular weight M 2 ; partial specific volume ) 3 other small molecules (salts, buffer) ω - angular velocity r - distance from axis balanced by (steady state) buoyancy angular acceleration Ultracentrifugation: ω 2 r 10 6 m/s m/s Sedimentation coefficient: range of S: s S-units: [s]; s = 1 Svedberg ω-units: [rad/s] or [rpm]; 1rpm = 60/2π rad/s determine S calculate M 2 /f t S measurable via optical techniques: r r m For nucleic acids: measure A260 as a function of r For proteins: measure around 280 nm or in the absorption band of some chromophore With an admixture of heavy salts (e.g. CsCl): molecules accumulate within a sharp layer - used for separating isotopically labeled molecules ( density gradient method ) More details: diffusional broadening, concentration dependence, interaction of charged molecules Techniques: hydrodynamics (RD)

16 3.2 Translational diffusion coefficient thermal bombardment random in magnitude and direction When a concentration gradient is set up: on macroscopic level concentration gradient or chemical potential at the molecular level the random motion of molecules translational diffusion coefficient D t 1/f t Fick s laws of diffusion First law of Fick: Second law of Fick: assumption: D t is independent on c (i.e. x) Solution: Protein with D t = 6x10-7 cm 2 /s 10s at t = 0 delta function 100s 1000s Monitoring c t : light absorption refractive index change quasi elastic light scattering Disadvantages: long observation times (1-2 days), T-drifts, mechanical vibrations Techniques: hydrodynamics (RD)

17 3.2.1 Frictional resistance and Brownian motion Einstein (1906): 1D 2D 3D Diffusion is an efficient way of traversing short distances (e.g. membrane thickness, interior of a cell) but very inefficient for long distances Diffusion across a porous barrier classical method of determining D t of small molecules e.g. drugs A c 1 c 2 and A - difficult to measure calibration with a compound of known D t monitored by radioactivity of labeled molecules or by some optical property Broadening of sedimentation boundaries - in sedimentation velocity experiment The width of the boundary (approximately the standard deviation of a Gaussian profile) = Techniques: hydrodynamics (RD)

18 3.2.5 Dynamic laser light scattering (quasielastic light scattering or photon correlation spectroscopy) The electric field and scattered intensity fluctuate with time. Three types of fluctuations: Occupation number fluctuations Phase fluctuations from translation of the molecule over a distance λ -rapid ( s); observable from molecules over a wide range in sizes - for 1% fluctuations - N 10 4 in a scattering volume of 1 mm 3 i.e. very low concentration; - slow, not important for macromolecules Amplitude fluctuations - from rotation and internal motions of molecules - motions must have a characteristic length comparable to λ; e.g DNA, large proteins 1 T autocorrelation function G (2) (t) = <I(0)I(t)> = lim It (') It (' + tdt ) ' T 2T T resolution limit G (2) Solvent Latex log 10 (t/s) β an instrumental constant q the scattering vector θ - scattering angle Fluorescence photobleaching recovery (FRP or FRAP) 2D diffusion in cell membranes or in concentrated solutions Fluorophores: green fluorescent protein (GFP) fluorescent label bound to a protein, nucleic acid, lipid spot bleached by a laser Recovered fluorescence fraction: time ω Gaussian beam waist Techniques: hydrodynamics (RD)

19 3.2.7 Pulsed field gradient NMR Apply a magnetic field gradient G in the same direction as the dominant magnetic field H: the magnetization M changes as the molecules diffuse δ duration of pulse gradient time spacing γ magnetogyric ratio 3.3 Rotation scales as R 3 sensitive to small changes in molecular size detection based on differences in optical properties of biomolecules along their principal molecular axes F -state variable jump Method: fluorescent depolarization S 1, τ F x(t) t 0 X 0 t 0 =0 τ R fixed polarizer time x(t) = x x 0 /e exp( t/ 0 τr hν e hν f UV or vis. ) D r - rotational diffusion coefficient (s -1 ) τ F 1ns - mean life time (~ fluorescence decay time) S 0 ν e sample ν f light E (z-polarization) E and E x turnable polarizer y Perrin: I P = I 1 P p p I + I 1 = 3 s s 1 P ( 1+ 6D r τ ) F Photodetector - component: I p - component: I s P 0 degree of polarization without molecular rotation (frozen solution) Techniques: hydrodynamics (RD)

20 3.4 Intrinsic viscosity h A Shear force (Newton): η depends on concentration (intermolecular interactions) size structure For spheres occupying volume fraction φ in dilute solution (Einstein) v h c 2 - volume occupied by 1g of hydrated polymer - weight concentration of polymer measure η at several concentrations and extrapolate to c 2 = 0. larger for nonspherical particles 3.5 Electrophoresis E - electric field Q - particle charge elactrophoretic mobility: F el u = = QE v E = Q f EQ v = f QDAB = kt Gives poor results due to complicated friction mechanism for ions: counterion and solvation shell (ζ-potential), shell deformation at higher velocities Techniques: hydrodynamics (RD)

21 Pressure 3.6 Electroacustics High frequency sound wave (up to 1MHz) Particle motion; faster response of the electric double layer Colloidal vibrational potential Distance Opposite approach - also possible: AC field Particle motion; faster response of the electric double layer Sound wave generation: electrokinetic sonic amplitude (ESA) Advantage: application to concentrated solutions 4 Summary on sizing methods Techniques: hydrodynamics (RD)