Biophysical Methods Flashcards
What does EM radiation and its interactions give rise to?
The interaction gives rise to:
A) Absorption - results from transitions from a lower to a higher energy level; e.g. IR, UV/vis
B) Emission - results from transitions from a higher to a lower energy level, e.g. Fluorescence
C) Scattering/ diffraction - results from oscillations indicted in the scatterer by EM radiation
What are the properties of waves?
- Waves have amplitude A; velocity c; wavelength λ frequency n; phase φ; (n=c/λ)
- EM radiation corresponds to 2 waves, at right angles to one another - the E (electric) wave and the M(H) (magnetic) wave - travelling with velocity c
- Polarisation - can be related to the direction of the E waves (M is always 90 degrees to E). Can be unpolarised (E waves have equal intensity in all directions), partially polarised or plane polarised.
- Interference - waves can add (constructive; same phase) or subtract (destructive; out of phase so waves cancel out)
Conversion between scales equations
E=hv (h is Planck constant, 6.63x10-34Js, v is velocity) - converts wavelength to energy
C=λv (velocity of EM radiation of wavelength λ)
V=c/λ (Hz or s-1)
E(energy/atom)=hv/atom (J)
E (energy/mol) = E X avogadros no (6x10 23) (kJ/mol)
V’ (wave number) = 1/λ (used in IR spectroscopy)
Molecules in cells have…
- Concentration
- Structure {f(X,y,z)} e.g atomic orbitals, conformation, assembly
- Dynamics E.g. Thermal motion, diffusion etc.
- Energy (related to structure and dynamics)
Structure - methods to obtain
For molecular structure need atomic resolution (
Dynamics
- Molecular movement - diffusion/membrane transport, ‘waggling’ motion, EPR, fluorescence etc
- Speed of reactions, e.g. Photo cycles in bR
Energetic a
Ligand binding - can measure Kd by monitoring [P] [PL] [L] by fluorescence, NMR, ITC etc. Can also infer from k1 and k-1
DNA melting - UV absorbance vs temperature; Keq = [SS]/[DD]; ΔG=-RTlnKeq; Keq=1 at Tm.
Energy
- Energy is quantised: ground and excited states
- Molecules in a system are distributed among energy levels according to the Boltzmann law: n{u1}/n{g}=exp(-ΔΕ/RT)
- Application of a angelic field Bo splits the energy levels of a system with spin (I) into 2I +1 levels.
Energy of different molecular processes
- Molecular processes have different energy:
i) Electronic transitions approx. 10^5 J/mol
ii) molecular vibrations approx. 10^4 J/mol
iii) Nuclear spin flips approx. 10^3 J/mol - The energy of different molecular processes corresponds to different parts of the EM spectrum.
- Wavelength corresponds to energy.
- The population distribution among energy levesl is very different for different techniques e.g for nuclear spin/NMR the population is u and g are nearly equal while in UV/Vis the population is essentially all in the ground state.
- Note: the greater the population difference the greater the sensitivity.
What is scattering and what does it depend on?
- Scattering results from oscillations induced by applied EM radiation, followed by re-emission at the same wavelength.
- The extent of oscilaltion depends on sample properties, e.g. electron polarisability and scattering cross section.
- Scatterers behave like dirven oscillators
- In a solution the scattering depends on the number of scatterers (concentration) and their size (RG*)
- Scattering can give infomration about the shape of particles in soluation and their motion.
Angular dependence of scattering
- When wavelength>radius of gyration, Raleigh scattering is isotropic (same in all angles).
- When WL is approx RG or WL
What are the 3 main classes of scattering experiment?
1) Measure turbidity - ‘absorbance’
2) Measure I (intensity of scattered light) as a function of MW and theta. e.g. MALS, SAXS/SANS, diffraction.
3) Measure I as a function of wavelength (or v), e.g. DLS and Raman
Multi Angle Light Scattering(MALS)
- The intensity of light scattering informs about molecular weight.
- Measures scattering at several fixed angles.
- With SEC and refractive index detection (SEC-MALS) it can provide accurate molecular weights.
- The amount of scattering depends on size and concentration of protein.
SAXS and SANS
- The angular dependence of scattering gives more detailed information about shape when WLRg requirement of many biological systems, so they are the main sources used.
- Experiments are known as Small Angle X-ray Scattering (SAXS) and Small Angle Neutron Scattering (SANS).
SAXS plot
- Usually plot is lnI vs Q(/nm)
- At large angles the plot gives information about particle shape.
- At small angles, a Guinier plot (lnI vs Qsquared) is linear and givers information about MW (I intercept) and Rg (slope).
- lnI vs Q plots can be converted to P(r) [probability of distance] vs r plot with a Fourier transform. This MAY define a unique molecular shape.
X-rays and neutrons
- X-rays are scattered by electrons while neutrons are scattered by nuclei. The response depends on the scattering cross section, B.
- For X-rays, B increases directly with number of electrons in atom.
- For neutrons, B can be very different for different isotopes; e.g. H is negative while D is positive.
- What this means is that scattered waves from H and D are 180˚ out of phase.
- Can give more info about particle shape than MALS because of their shorter wavelength.
SANS - contrast matching
- Because H and D scatter with opposite ‘sign’, a large range of solvent scattering cross sections can be achieved by changing the H2O/D2O ratios. We can therefore match the solvent background to various macromolecular components in a solution.
- The plot of Scattering length density vs %D2O shows the variation in scattering for different H2O/D2O ratios, for solvent, lipids, proteins, and DNA (different lines). The contrast is matched where the lines cross.
Dynamic Light Scattering
- Static scatterers emit at frequency Vin but if the scatterer moves then the scattered llight is ‘spread by the Doppler effect.
- The faster the movement, the broader the spectrum.
- Can calculte the diffusion rate (D) from the width of the Raleigh line.
- Diffusion coefficicents (D) measured by DLS give information on sample size, aggregation etc.
- DLS instruments are relatively cheap and easy to use.
What is the Doppler effect?
Frequency depends on whether scattere approaches or recedes from observer.
What is refraction?
Refraction is the bending of light when it enters a medium.
Can be described by n=Co/C
When do evanescent waves form?
- Evanescent waves are formed when EM waves undergo total internal reflection at an interface.
- Evanescent means tending to vanish; the intensity of an evanescent wave decays exponentially with distance from the interface.
How does Surface Plasmon Resonance (SPR) work?
- A sensor technique that utilizes a surface plasmon - an oscillation of electrons in a thin metal film such as gold.
- The SP can interact (resonate) with an evanscent wave in a way that is very sensntive to the properties of the medium near the metal surface.
- Light is shone on a prism such that TIRF occurs.
- Light incident at a particular angle (θspr) generates plasmon resonance on a metal film, causing a minimum in the reflected intensity.
- Changes in refractiv eindex near the metal index cause θspr to change.
SPR to show binding
- The binding of prey moelcules to bait molecules increases the refractive index of the surface layer.
- This alters the resonance angle for plasmon induction, which can be measured by a detector.
When does total internal reflection (TIRF) occur?
TIRF occurs when a light ray passes from a higher to a lower refractive index and the angle of incidence is greater than a ‘critical’ angle.
What is the radius of gyration (Rg)?
- Used to secribe particle size in scattering and hydrodynamic experiments (e.g centrifugation)
- One definition is Rg=[(1/n)∑Ri^2]’^1/2 where n is the number of monomers in the chain and Ri is the distance of each from the centre of mass.
- For our purposes only need to know that Rg can be related to particle dimensions.
Scattering and Diffraction (in different mediums)
- Scattering intensity from isolated particle varies with angle due to interference from different regions of the particle. Shape of the particle is encoded in different xy intensities on the detector.
- Scattering intensity from a solution of randonly orientated partviels varies with angle, but intensities across different axes are averages out due to particle rotation - information is lost! (SAXS/SANS experiment)
- Scattering itensity from an ordered array or particles (i.e. a crystal) gives intensities similar to the independnt particle but seen through a ‘grate’ (diffraction). infomration on intensiites across different axes is retained.
Diffraction patterns and reciprocal space
- Diffraction arieses from scattering and interference between scattered waves.
- More slits=sharper pattern of spots
- The closer the slits the further apart the diffraction spots
- i.e there is reciprocal relationship.
- The crystal behaves like thousands of slits in 3D.
- Cooridnates in real space (x,y,z) are related to spots in the diffraction pattern (reciprocal space (h,k,l))
Sources of radiation in diffraction experiments
- X-rays: good sources are widely available.
- Two main ways of generating X-rays:
i) electron bombardment of metal
ii) electron acceleration in a synchrotron - Neutrons - nuclear reactor
- Electrons - electron microscope
Sample and detection in diffraction experiments
- The sample should be fibre (have periodicity in z-direction) or crystal (need to be well-ordered).
- Detection: there are good x-ray detecctors available; mostly direct ‘pixel’ detectors older tech is charge coupled devices (CCD).
- Pixel detectors take >30images/sec. Data collection lasts 1-5 minutes.
Information from diffraction patterns
-Spot positions give direct information on the dimensions and symmetry of the array (crystal).
(Indirectly we can infer the number of molecules in a crystal unit)
-Spot positions may report on strong repeptitive spacing in the molecule (fibre diffraction)
-Spot intesities provide partial information on atomic coordinates (phasing problem).
-Spacing intensities provide partial information on atomic coordinates.
Indirect interpretation of diffraction and the phase problem
- There is no lens for short ƛ X-rays.
- Therefore, a model must be reconstucted from the diffraction data.
- We can recover the scattering intensities by integrating diffraction spots (convulation theorem).
- Detectors record only amplitude of intersecting EM wave. The wave phase is lost.
- If phases were known, we could go from |F(hkl)| to ⍴(xyz) with a Fourier transform.
- However the iɸ terms are unknown, so the model cannot be calculated directly.
- This is the phase problem.
How do you determine phase?
-Most common method is molecular replacement (MR).
-MR relies on having a previously-solved, closely-related structure to your own protein.
Procedure:
1. integrate your data I(hkl) → |F(hkl)|
2. identify similar model (homology, strucuture prediction methods)
3. calcjulate PAtterson map from your data
4. calculate Patterson map of model in all possible orientations and xyz positions
5.Compare!
Transformations (Patterson function)
- Since |F(hkl)| are known, we can perform ƒT by setting all ɸ to 0, to get ⍴(uvw)
- ⍴(uvw) is called Patterson function; this is a complex 3D map related to ⍴(xyz) and cannot be directly interpretated for large bio-molecules.
- The Patterson maps of strucuturally related models will be closely similar if the correct orientation and position of the model in the crystal can be identified. This is done by software (Phase, Molrep); automated servers also exist (Balbes, MrBUMP etc.)
- Probability of finding a goof MR solution generally depends on data quality, how siilar the model is to our molecules, and how much of our molecule we can model.
- MR will give us a starting model for our molecule, from which theoretical scattering phases can be calclated. Together with |F(hkl)| we can derive and ekectron map of the object.
- Once we have an electron density map we build molecule into map; this depends on map quality.
Other methods to solve the phase (table)
Method Requirements Comment
Molecular A known similar structure, Eliminates need for replacement whose coordinates are used heavy atom derivatives to calculate phases (Very common)
Single / Multiple An anomalously scattering Powerful method for
wavelength group in crystal (e.g. seleno- recombinant and
anomalous methionine). A tunable metallo-proteins
dispersion synchrotron X-ray source (Common)
(SAD/MAD)
Multiple At least two heavy atom The most general method
isomorphous derivatives. Crystals must (uncommon today) replacement (MIR) NOT be be affected by HA
Single One very good heavy Requires additional
isomorphous atom derivative information replacement (SIR)
Resolution
-The further our the diffraction pattern goes the higher the resolution.
-The ability to build a good model depends on map resolution:
5Å = Helices stand out as rods
4Å = β-sheets are traceable
3Å = Get chain fold right, and see where side chains are
2.5Å = Typical resolution obtained for a protein
1Å = Some information about H atoms is even obtained
-Electron density can be weak in some regions, e.g in loops, because of motion or heterogeneity in the crystal.
Chain tracing and model building
- Modelling programs are used to visualize density maps.
- A molecular model is built into a density map, using standard structures of amino acids and a known sequence.
- Initial maps are often poor but can be improved by a process called refinement.
Refinement
- The model is refined by adjusting the atomic coordinates to minimize |Fo| - |Fc| (subject to restraints, e.g. bond lengths etc)
- We calculate new scattering |Fo(hkl)| we compute and new electron map.
- An R factor, R≈∑(|Fo|-|Fc|)/∑|Fo| is used to define how good teh data are; usually R≈0.2.
- This is biased because we are striving to minimize |Fo|-|Fc| in our model to reduce the R factor.
- An R(free) factor is defined similar to R but uses a fraction of |Fo| values not included in the |Fo|-|Fc| minimization, and so it not biased.
Validation
- It is important to check the protein structure obtained.
- One way is to use a Ramachandran plot; most observed angles Ψ,φ angles should be in allowed regions.
Summary of X-ray structure determination
- Prepare suitable crystals
- Collect data {I(hkl)}
- Estimate starting phases {starting structure factors, F(hkl)}
- Compute initial electron density map; ⍴(xyz)↔F(hkl)
- Build model in electron density
- Refine model by minimizing Δ|Fo|-|Fc|
- Repeat steps 5 & 6
- Validate model
- Deposit in RCSB
Other features of crystallography
- Temperature (B) factors
- Time resolved studies
- Neutron diffraction
- High (X-ray) and low (EM) resolution data combined
Temperature (B) factors
- Atomic size (motion) from angular dependence
- A temperature (B) factor, related to apparent size, can be assigned to every atom in the crystal.
- High B factors are often seen in functionally-relevant parts of molecules, e.g. active sites
- If atom is moving faster will have a larger apparent atom size, therefore scattering intensity will fall faster.
Time resolved X-ray studies
- Aim to visualize short-lived species, e.g. in an enzyme reaction.
- Observation of intermediates is possible by:
i) Diffusion trapping: slowing down the reaction (e.g. use sub-optimal pH, mutant proteins, freezing etc)
ii) Pump-probe: reaction is triggered by laser light prior to X-ray collection.
Neutron diffraction
- Neutron beam intensity (flux) and detectors are generally inferior to those for X-rays, so need larger crystals and longer times.
- Major advantage of neutrons over X-rays is that hydrogens can be detected (give negative density)
What does absorption spectra include?
- Include XAS, UV/Vis, IR, EPR, (NMR).
- These correspond to different parts of the EM spectrum and measure different molecular properties (vibrations, electron transitions, spin reorientation, etc)
General points about absorption
- Absorption involves transitions between quantized energy levels
- The Boltzman distribution is recovered by relaxation
- Applied EM radiation stimulates absorption and emission equally (that is why we need a population difference to see an effect)
- Sensitivity (signal/noise, S/N) depends on the population difference (ng-ne)
- We get a spectrum of energy absorbed vs E (ƛ, v, v’ etc) with “lines” (resonance)
- In many kinds of spectroscopy we get broad peaks arising from a superposition of unresolved lines.
- Peak linewidth (Δv) depends on lifetime (𝓣) of excited state; if decay is fast, position is uncertain and line is broad; if decay is slow (e.g. NMR) lines are sharp.
Inductions of transitions by EM radiation
a) Resonance: remember driven oscillator. We get a maximum effect when the applied energy (hv) matches the energy level separation (ΔE).
b) The EM radiation only interacts effectively if there is a charge displacement on changing energy states. This leads to selection rules:
For example in UV/Vis spectroscopy 1s→2s transition is “forbidden” but s→p and π→π* are “allowed.
c) The bigger the charge displacement on going from g to e, the more probable the transition (stronger absorbance)
d) A ‘transition dipole moment’ (µ) is a useful way of quantifying the charge displacement.
The E component of the EM radiation is usually dominant in inducing the transition; this corresponds to a linear charge displacement (also get circular charge displacement arising from interactions with the M component)
e) Transition dipole moments (µ) have a direction that depends on chemical structure.
f) The directional properties of a transition dipole, µ, mean that excitation is angle dependent. When the polarization of the excitation is 90º to µ there is no induced transition.
Infra-red spectroscopy - properties, uses and limitations
-IR detects molecular vibrations
-Observable range v’=700-4000/cm (ƛ=14-2.5µm)
-Uses: sensitive to H bonding, secondary structure, H/D exchange, ionization states
-Limitations:
Large number of lines (3n-6 vibrations for an n atom molecule). This gives problems of resolution, and assignment of lines to specific vibrations in proteins etc. (signal is short so broad peak so cannot distinguish)
Strong absorption from solvents (water) and cells.
Infra red spectra - measurement
1) Source - e.g. heated metal carbide (multiple ƛ)
2) Monochromator - grating or prism (single ƛ)
3) Sample - cells must be non-absorbing, e.g. CaF2, LiF, NaCl
4) Detector - heat detector → spectra
- This kind of spectrometer is now replaced by Fourier transform, IR and attenuated total reflectance FTIR, which is much faster and more sensitive.
What is the physical basis of IR?
-Assume bonded atoms vibrate like springs and undergo Simple Harmonic Motion (SHM) with vibration frequency:
v(vib)=1/(2π√k/M) where k is spring force constant and M is mass
The influence of isotopes on IR
- A change in mass causes a change in vibrational frequency.
- e.g. frequency changes by ≈1.37x when NH→ND
- Isotopic substitution is very useful in assigning observed vibrational bonds to specific groups.
Applications of IR
- Frequencies of some protein-related IR absorption bands are sensitive to H-bonding. Formation of H-bonds changes the vibrational frequency. Note solvent bands obscure some peaks.
- Protein secondary structure: ‘Amide I’ and ‘amide II’ are characteristic IR bands observed in proteins. They arise from vibrations in the peptide group. Their positions are sensitive to protein secondary structure (helix peaks shifted to right of sheet)
Raman Scattering
- Changes in ƛ(v) of scattered light gives information about the vibrational states of the scatterer.
- Complementary to FTIR:
- Raman scattering depends on Rg (stronger for larger particles)
- Solvent absorption effects are reduced
- Different selection rules apply. Raman requires a change in electronic distribution (polarizability) while IR requires a change in displacement (transition dipole moment)
- in general, Raman spectra are weak but ‘resonance Raman’ and other methods, e.g. surface-enhances Raman spectroscopy (SERS) can be very sensitive.
The physical basis of Raman scattering
- Change in vibrational state of scatterer can lead to change in scattering ƛ(v).
- Several types of scattering can be identified: Raleigh (same frequency), Stokes (lower), anti-Stokes (higher).
UV/Vis spectra
- Observation range ƛ=200-750nm
- Detect electronic transitions
- Molecules that absorb in this range are called chromphores
- Examples of chromophores include: aromatic amino-acids, nucleotide bases, NADH, flavins, chlorophyll, haem and some transition metals
- Uses/advantages: sample concentration (Beer law), very sensitive (µM), inexpensive, simple, can measure very fast processes.
Physical basisi of electronic trsnitions
a) Ground and excited states can be described by energy curves with vibrational levels and characteristic r (mean electron position). Usually r(g)
