Introduction to techniques in biophysics. CD/ORD, UV, IR, Raman spectroscopy, tritium exchange 2 At supra molecular level: structure and physical properties 2.1 direct visualization

Techniques: electron microscopy, hydrodynamics (RD)

Introduction to techniques in biophysics.

Goal : resolve the structure and functionsof biological objects applying physical approaches

1 At molecular level1.1 Long-range goal:

1.1.1 complete structure determination: location in space of each atomProblem: Mwt(protein, AA) = 30 000 N = 4 000 atoms

3N – 6 parameters define the structure16 000 parameters (structure + chemical identity) huge!

simplification: ignore H-atoms 8 000 parameters still huge!

1.1.2 primary structure: bond length and angle, internal rot. angle (not for H)Problem: N = 4 000 atoms 10 000 parameters

many bond lengths and angles are known 2 000 still huge!

further simplifications: work with residues: 2 angles for relative location

+ 2 parameters for side chains orientationProblem: Mwt(protein) = 30 000 (~ 300 residues) 1 200 parameters

Mwt(AA) = 30 000 (~ 200 residues) 800 parameterssymmetry (identical subunits, helices…)

still huge!

1.2 Near-field goal: 1.2.1 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

1.2.2 characterize only a part of the macromolecule, of special interestExample: use probe molecules (a part of the macromolecule or externally added)

techniques: fluorescence, EPR, some aspects of NMR, chemical modification

1.2.3 examine certain general aspects of the structure, ignoring othersExample: 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 properties2.1 direct visualization of shape and structure: optical techniques2.2 measure mechanical properties; force/energy: physical approach2.3 functional characterization: chemical approach

Structure Determination of Biomolecules by Physical Methods.

Method yields M-range Requirements, comments

- Complete chemical analysis M no limit

- Quantitative chem. identification ofgroups (of number ∝ M, e.g. CO)

M ∼ no limit Knowledge of generalchemical structure

- X-ray diffraction- Neutron diffraction

size, shapeinternal structure

∼ no limit Single crystal, heavy atomstaining;

- Electron microscopy Size, shape > 5000 ? Radiation damage

- Osmotic pressure Mn 104 ÷ 106 + Vapor pressure osmometry

- Viscosimetry Mv (size, shape) < 107 Structural effects

- Diffusion measurements Mw , size < 106 Influence of structure,solvation, concentration

- Sedimentation velocity Mw , size < 5x107 Structure dependent

- Sediment. velocity + diffusion Mw , size < 5x107 Structure effects eliminated

- Sedimentation equilibrium Mw, Mz < 5x106 Fast; structure independent

- Electrophoresis M (poor value) Separation method for ions

- Rotational diffusion, fluorescencedepolarization

Size, shape, Mw ∼ no limit Structure dependent

- Flow birefringence Size, shape, Mw Empirical calibration

- Kerr effect Size (shape) ∼ no limit

- Dielectric dispersion Size (shape) ∼ no limit

Isolating solvent; electricdipole moment of soluteknown

- Light scattering RG, size Mw ≥ 104 Fast, sensitive to associationof molecules

- X-ray small angle diffraction- Neutron small angle diffraction

Size < 105 Dilute solutions

Macromolecules (proteins, nucleic acids) size - up to few 102nm;weight - up to 108 : well defined

(synthetic molecules - molecular weight distributions; mean values)Human eyes: 0.2mm

Techniques: electron microscopy, hydrodynamics (RD)

Electron Microscopy

2 Principle (comparison with light microscopy)Electrons emitted from a hot cathode are attracted to an anode; pass through a hole in the anode and create the e- beam

Lenses are electromagnets or magnetic coils: “zoom”lenses – a change in the magnetic field changes their focal length

Low numerical aperture limits the resolution:

Limit of resolution = 0.61λ/numerical aperture

= approx. 0.1 nm (1Å)

anode

scattered rays

light

aperture diaphragm

objective lens

objective image

projection ocular

projection image

e- source

condenser

specimen

projection lens

intermediatelens

Light microscopeEM

Techniques: electron microscopy (RD)

1 Features, requirementse- wavelength (de Broglie relationship):

e- kinetic energy (if accelerated by voltage Φ):

Example: for Φ = 100 000 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 supportpossible damage of sample by e--collision low irradiation

intensity to be employed contrast sample-to-support decreases… problemrule of thumb: e--scattering ∝ (atomic number)2

Example: U (A = 92) scatters 104 times more than H (A=1)

Φ= evme

2

2

vmh e=λ

3 Transmission electron microscopy: more relevant for biological samples

overall magnification: 100x to 500 000xor 2µm to 0.4nm

Difficulties:melting in the intense electron beamdamage: e- interact with the e- shell inducing

energy transfer and not elastic scatteringExample: bonds in aliphatic chains would break; aromatic rings would endure

electrostatic chargingevaporation and decompositionsolvated structures are destroyed during

the dry-sample preparation

→ partially avoided when using replicas

Resolution limit depends on: electron wavelengthperformance of the magnetic lensesstability of magnetic fields (1 - 50kV)

Tungsten thermioniccathode

Anode

Sample mounted ona transparent grid

Electromagnetic lens (10 - 200 x)

Lens system (50 - 400 x)

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 TEMDehydration: required except for cryo-EMEmbedding 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 (50-100 nm)Exception: very high voltage (106 V) TEMicroscopespermit viewing thicker sections

Grid (copper) may be coated with a support filmof low atomic weight material; tissue sections are viewed through holes in the grid

tissue sliceson EM grid


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 lesse- dense.

Autoradiography: radioactive sample placed in a fine photographic emulsion

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

EM grid support film Negative Staining

sample dried solution ofe--dense stain

evaporation of heavy metal at an angle

Shadowing

EM grid with support film

resolution - limited by the silver grains size, the traveling distance of decay particles; problem – decay time (i.e. “exposure” time)


5 Freeze fracture / freeze etching: for viewing surfaces of organelles

Fracturing: freeze rapidly and cut

specimen

support

liquidfreon

liquid N2

Bell jar (under vacuumto prevent frosting of the knife)

Cold knife

Specimen table

Fractured face

Normal etching Deep etching

ridge

Outer surface

Inner surface

Etching: sublimation of ice in vacuum (at –100°C)

surface

Visualizing: the exposed surface is shadowed with platinum and carbon;the deposited film is removed: replica for EM

Fracturing occurs mainly along the interface of the 2 hydrocarbon layers of the membrane


6 Scanning electron microscopy: resolution – about 10nm

BSE - back scattered electronsSE - secondary electronsSC - specimen currentEBIC - electron-beam-induced currentX - X-raysCRT - cathode-ray tube

the electron beam diameter (5 - 10 nm)limits the resolutionbeam electron current: 10-10 - 10-12ASE - emitted at low voltage ⇒easily deflected to follow curved paths of the collector → 3D imagedepth field: 300 - 500 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)


Some classical examples:

Experiments:Fick , 1855 - on diffusionSvedberg, 1920s - on sedimentationPoiseuille, 1846 - on viscosity

Theories for simple shapes (e.g. spheres and ellipsoids): Stokes (1847)Einstein (1906) / Brownian movementPerrin (1936) / translation and diffusion of an ellipsoid

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 recent developments:

Experiments:dynamic laser light scatteringnanosecond fluorescence depolarization measurementsfluorescence recovery after photobleachingfluorescence correlation spectroscopypulsed field gradient NMR improved analytical ultracentrifuge design

Theory: new theoretical and computational tools

Techniques: hydrodynamics (RD)

translational frictional coefficient, ft

v -velocityFf - frictional force:

applied force (e.g. centrifugation or electrophoresis)concentration gradient (as in diffusion)

“-” the frictional force opposes the particle motion

rotational frictional coefficient, fr

ω - angular velocityTr - frictional torque:

applied electric or hydrodynamic flow fielddiffusion of molecular axes

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

2 Frictional coefficients

RFf v

Trω

cgs units: dyne.s/cm2 = poise*

*Poiseuille: viscous flow in tubes (1946)

At 20°C η = 0.01002 poise or 1.002 centipoise (cp)

for 0 ≤ t ≤ 20°C

for 20 ≤ t ≤ 100°C

2.2 Spheres

ft - much less sensitive to molecular dimensions

Stokes’ law, R - Stokes radius

varies with volume


2.3 Ellipsoids of revolution

oblates

prolates (models for cylindrical rods)

ab

a

b

a/b = p - axial ratio

V = (4/3)πab2p < 1

p > 1

Re - equivalent radius (of the sphere of equal volume)

2.4 Random coilshave on average a spherical domain ⇒ behave hydrodynamicallylike 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

b

n – number of

(33) - rotation around the axis of highest symmetry (11) - for either axis perpendicular to it

Friction ratios:

r


3 Experimental determination of hydrodynamic properties

3.1 Sedimentation coefficient (centrifugation, ultracentrifugation)

Types of sedimentation experiments: 1) measure the velocity of molecular motion2) 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 M2 ;

partial specific volume )3 – other small molecules (salts, buffer)

ω - angular velocityr - distance from axis

buoyancy angularacceleration

balanced by(steady state)

Sedimentation coefficient: range of S: 10-13 – 10-10 s

S-units: [s]; 10-13 s = 1 Svedbergω-units: [rad/s] or [rpm]; 1rpm = 60/2π rad/s

S – measurable via optical techniques:

rm

r 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…

determine S calculate M2/ft

Ultracentrifugation: ω2r ∝ 106 m/s2

∝ 10-6 m/s


3.2 Translational diffusion coefficientthermal bombardmentrandom in magnitude and direction

When a concentration gradient is set up:on macroscopic level – concentration gradient or chemical potentialat the molecular level – the random motion of molecules

translational diffusion coefficient Dt ∝ 1/ft

3.2.1 Fick’s laws of diffusion

First law of Fick:

Second law of Fick:

assumption: Dt is independent on c (i.e. x)

Solution:

100s

1000s

10s

Protein with Dt = 6x10-7 cm2/s

at t = 0 – delta function

Monitoring : light absorptionrefractive index changequasi elastic light scattering

tc

∂∂

Disadvantages: long observation times (1-2 days), T-drifts, mechanical vibrations


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

3.2.3 Diffusion across a porous barrierclassical method of determining Dt of small molecules e.g. drugs

c2c1

A

⇒ calibration with a compound of known Dt

and A - difficult to measure

monitored by radioactivity of labeled moleculesor by some optical property

3.2.4 Broadening of sedimentation boundaries- in sedimentation velocity experiment

The width of the boundary (approximately the standard deviation of a Gaussian profile) =


Phase fluctuations – from translation of the molecule over a distance ≈ λ- rapid (10-3 – 10-7s); observable from molecules over a wide range in sizes

Three types of fluctuations:

Occupation number fluctuations ∝- for 1% fluctuations - N ≤104 in a scattering volume of 1 mm3 i.e. very low concentration; - slow, not important for macromolecules

3.2.5 Dynamic laser light scattering(quasielastic light scattering or photon correlation spectroscopy)

The electric field and scattered intensity fluctuate with time.

Amplitude fluctuations - from rotation and internal motions of molecules- motions must have a characteristic length comparable to λ; e.g DNA, large proteins

G(2)(t) = <I(0)I(t)> = limT T

T

TI t I t t dt

→∞ −⋅ +∫1

2( ' ) ( ' ) 'autocorrelation function

SolventLatex

log10(t/s)-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4

G(2)

resolutionlimit

β – an instrumental constantq – the scattering vectorθ - scattering angle

3.2.6 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

time

spot bleached by a laser Recovered fluorescence fraction:

ω – Gaussian beam waist


3.2.7 Pulsed field gradient NMRApply 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 spacingγ − magnetogyric ratio

3.3 Rotationscales as R3 sensitive to small changes in molecular size

detection – based on differences in optical properties of biomoleculesalong their principal molecular axes

F -state variable

t0 timex(t)

t0=0

X0

τR

x0/e

)t/exp(xx(t) r0 τ−=

jump

Dr- rotational diffusion coefficient (s-1)

S0

S1, τF

hνe hνf

τF ≈ 1ns - mean life time (~ fluorescence decay time)

x

y

light

fixed polarizer

turnablepolarizer

νe

νf

sample

Photodetector|| - component: Ip⊥ - component: Is

E| |(z-polarization)

E| | and E⊥

Method: fluorescent depolarization

UV or vis.

sp

sp

IIII

P+−

=

( )F0

6131

P1

31

P1 τDr+

−=

−Perrin:


P0 – degree of polarization without molecular rotation (frozen solution)

3.4 Intrinsic viscosity

η depends on concentration (intermolecular interactions) sizestructure

A

h

Shear force (Newton):

For spheres occupying volume fraction φ in dilute solution (Einstein)

vh - volume occupied by 1g of hydrated polymerc2 - weight concentration of polymer

measure η at several concentrations and extrapolate to c2 = 0.

larger for nonspherical particles

kTQD

fQ

Evu

fEQvQEF

AB

el

===

==E - electric fieldQ - particle charge

elactrophoreticmobility:

Gives poor results due to complicated friction mechanism for ions:counterion and solvation shell (ζ-potential), shell deformation at higher velocities

3.5 Electrophoresis


4 Summary on sizing methods

Pres

sure

Distance

High frequency sound wave(up to 1MHz)

Particle motion; faster response of the electric double layer

Colloidal vibrationalpotential

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

3.6 Electroacustics


Documents

Introduction to techniques in biophysics. CD/ORD, UV, IR, Raman spectroscopy, tritium exchange 2 At supra molecular level: structure and physical properties 2.1 direct visualization