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)
Measurement of UV/Vis spectra
- Standard spectrophotometer: can measure one wavelength
- Diode array spectro-photometer: can measure simultaneously at many wavelengths, and so is much faster.
Measurement of concentration using UV/Vis
A=log(Io/It)
Beer law: A=εcl
UV/Vis spectra of proteins and nucleic acids
-The peptide bond absorption occurs at ≈200nm.
-Trp, Phe, and Cys (S-S) absorption dominate above 230nm.
-Protein concentration can be calculated at 280nm using:
ε(prot)=n(trp) x ε(trp) + n(tyr) x ε(tye) + n(cys) x ε(cys)
where n is the number of
-The absorption of nucleic acids is in the 230-290nm range and occurs mainly from the bases.
-For dsDNA, A260 is 0.020µg/mL/cm and 0.027µg/mL.cm for ssDNA and RNA.
-The absorption can be calculated using online servers.
What are Isobestic points?
- If A and B are in equilibrium, then the observed spectrum at wavelength, ƛ, will be the sum S(ƛ)=ε(Aƛ)[A] + ε(Bƛ)[B]
- If ε(Aƛ)[A] = ε(Bƛ)[B] then the absorbance will be the same for all ratios of [A]/[B].
- Such isobestic points are useful for measuring absolute concentrations.
- a wavelength at which the absorption of light by a mixed solution remains constant as the equilibrium between the components in the solution changes.
Hypochromism in DNA
- Interactions (interacting π orbitals) between chromophores in native dsDNA reduces the absorption intensity.
- DNA melting - Tm is dependent on GC content.
- Can tell if DNA is native or denatured because denatured DNA does not have stacking or interacting π orbitals and so has a different spectrum (higher absorbance)
X-ray Absorption Spectroscopy (XAS/EXAFS)
- UV/Visible detects transitions between outer level electrons.
- High energy X-rays can be absorbed by inner core electrons.
- e.g. An electron is ejected from the K shell (1s) by an X-ray beam. K can be refilled (from L, M shells etc) causing X-ray fluorescence. (XRF is characteristic of the atom type)
- XAS spectra have two main regions:
i) Transitions from K,L states etc. give a spectral edge.
ii) Extended X-ray absorption fine structure (EXAFS) arises from interference between outgoing ejected electrons and back-scattered waves. - The method is useful for studying features of metallo-protein active sites.
What is optical activity?
- A Chromophore is said to be optically active if it rotates the plane of polarization of a beam of light passing through it.
- The activity arises from intrinsic ‘handiness’/chirality of a molecule or activity that is induced by local structure, e.g. a helix.
What is the physical basis of optical activity?
- Remember that induction of a g→e trasnition by EM radiation requires a charge displacement.
- The associated transition dipole moment can have a linear (µe) component that interacts with E in EM radiation, and a circular (µm) component interacting with M.
- Optical activity occurs when a transition has both µe and µm components, i.e. involves a helical charge displacement - can effect the plane of polarization of the light.
How do you measure optical activity?
- Optical rotatory dispersion (ORD) arises from differential rotation of left (L) and right (R) circularly polarized light (how much does the plane of rotation change with L or R polarised light)
- Circular dichroism (CD) arises from differential absorption of L and R.
- CD and ORD are equivalent but CD is the more commonly used for biological applications.
How do we generate polarised light?
E and M waves at 90º
To get plane polarised light, only allow light of one angle to pass through polariser.
How do you generate circularly polarised light/
- Add 2 perpendicular E waves with 90º phase shift.
- Note: if we add 2⏊E waves with Δɸ=+90º we get E(R) but if Δɸ=-90º we get E(L).
CD Parameters
ΔA = A(L) - A(R) = Δεcl
Note: Δε is smalll compared to ε
ΔA is expressed as moalr ellipicity at a particular ƛ, written as θ
CD and protein secondary structure
- Comparison of far-UV experimental CD curves with ines generated from standard curves can give a good measure of protein secondary structure content.
- Learn curves!
Fluorescence
- Arises from emission from an upper electronic state, an e→g transition.
- Parameters: emission and excitation spectra, lifetime (≈ns), polarisation.
- Uses: very sensitive (≈nm/single molecule), probes of local environment, molecular dynamics (ns range), different fluorophore colours.
Physical basis of fluorescence
- Remember Franck-Condon principle (straight up/straight down).
- This means that absorbance usually populates a higher vibrational state (because r(e)>r(g)).
- The excitation then decays to the lowest vibrational level in the excited state, follwed by emission.
- This emission is, on average, at longer ƛ (lower energy) than absorbance.
- Like UV/Vis absorbance, the positions of the energy levels, and hence the fluorescence spectra, depend on the environment.
- Rates and quantum yield: the depopulation rate, ko, of the excited state can be charactersied by two processes:
a) A fluorescence decay rate, k(f)
b) A ‘radiationless’ decay rate k(r) (this mainly arises from interactions with other molecules in the solution). - It follows that k(o)=k(r)+k(f) (ko is in the range 10^6-10^9/s)
- The quantum yield ɸ(f) is the fraction of molecules decaying via fluorescence: ɸ(f) = k(f)/{k(r)+k(f)}
- Notes: ɸ(f)=1 when k(r)=o; rates are related to 1/lifetime (𝓣), thus ɸ(f) = k(f)/k(o) = 𝓣(o)/𝓣(f)
Measurement of fluorescence
source → Monochromator1 (excitation) → sample cuvette → Monochromator 2 at 90º to incoming light (emission) → detector → spectrum
Types of fluorophores
- Intrinsic: trypotphan, NADH, chlorophyll, Y base (C or T) in the Phe tRNA (not many)
- Extrinsic: dyes added to the system, e.g. ethidium bromide (labels DNA) and ANS (binds to hydrophobic areas of proteins and change its quantum yield leading to higher fluorescence) or via labeled protein, GFP etc.
Protein unfolding probed by extrinsic fluorscence
- Some fluorophores, such as ANS and Sypro orange, only fluoresce when bound to exposed hydrophobic groups (denatured protein).
- Thermal denaturation can be measured rapidly in a RT-thermal cycler.
- Increased Tm implies a more stable protein/complex.
Quenching and fluorescence
- Certain substances, e.g. O2, salts etc (quenchers) can increase k(r) if they are in the vicinity of the fluorophore.
- Accessibility of quencher to the fluorophore can be tested with a plot of relative quantum yield vs quencher concentration [Q].
- For example tryptophan fluorescence in proteins is quenched by O2.
Polarization and fluorescence
- Consider a cuvette containing fluorophores.
- Absorbance and hence fluorescent intensity (emission), depends on the direction of the transition dipole moment ⬆. Polarized light thus only excites a subset of fluorophores (photo-selection) at a particular orientation.
- The output light is then also polarized.
- If the molecules move during their lifetime there will be depolarization of the output compared to the static situation.
- The polarization anisotropy, A, is defined as the degree of polarization divided by the total fluorescence output: A= (I(//) - I(⏊)) / (I(//) + 2I(⏊))
- A can be measured using static or pulsed methods.
- Example of static depolarization used in binding studies.
Förster resonance energy transfer (FRET)
- Energy can be transferred when the excitation spectrum of an acceptor overlaps the emission spectrum of a donor.
- fl(d) and Fl(a) depend on spectral overlap and separation, r, between donor and acceptor. We can define efficiency of transfer as E(t)=1-F(d)/Fl(o) where Fl(d) is fluorescence intensity of donor in presence of acceptor and Fl(o) is intensity in absence of acceptor.
- It can be shown that E(t) = R(o)^6 / (r^6+R(o)^6) where R(o) (Förster distance) is distance when E(t) = 0.5.
FRET in a GFP/BFP system
GFP and BFP expressed together with a trypsin-sensitive linker. As the trypsin cleaves the linker, the proteins diffuse apart and FRET peak at ≈520nm (Fl(a)) is abolished.
Distance calculation from FRET
-Efficiency of energy transfer, as a function of distance between dansyl and napthyl groups, separated by a polyproline “rod” of varying length (n=1-12). The solid line is calculated r^-6 dependence.
Applications of fluorescence
- Microscopy and single molecule analysis
- FISH (fluorescnet in situ hybridisation)
- DNA sequencing
- Real time quantitative PCR
- FACS (fluroescence activated cell sorting)
FISH procedure
1) Fluorescently-labelled probe DNA
2) Hybridize to denatured native DNA
3) Light up chromosome and observe in microscope
DNA sequencing procedure
1) Single stranded DNA
2) 4 sequencing reactions, with different fluorescently labelled primers for each dideoxynucleotide
3) Gel electrophoresis of pooled products
4) Laser excites the labelled DNA fragments passing through a gel. Fluorescence is detected and analysed in 4 colours.
Real time quantitative PCR (qRT-PCR)
- Detects and quantifies DNA (or mRNA, reverse transcribed to DNA)
- Uses oligonucleotide probes with a fluorescent reporter dye attached to the 5’ end and quencher at the 3’ end.
- The probes are designed to hybridize to a PCR product.
- In the intact molecule the proximity of the fluorophore and quencher gives no fluorescence.
- During PCR, the 5’-nuclease activity of the polymerase cleaves the probe.
- This decouples the fluorescent and quenching dyes and fluorescence increases in each cycle.
Fluorescence activated cell sorting (FACS)
Labelled cells (e.g. with a fluorescent antibody) are detected and a charge is applied allowing labelled cells to be separated from others.
Applications of NMR
- Medicine, Psychology: Tissues/cells imaging
- Pharma: Drug screening
- Structural biology: Macromolecules, ‘solid-state’, ‘solution state’
Principles of NMR
- Nuclei have the property of spin (0, 0.5, 1, 2 etc). This depends on isotope (1H, 13C and 15N and 0.5) (as depends on number of protons and neutrons)
- Nuclei with non-zero spin (I) have multiple spin states (2I+1, i.e. 2 states for spin 0.5)
- In a strong magnetic field (Bo) the spin states have different energies.
- The energy differences fall in the radio frequency (rf) range (30-1000Hz)
- Bo is generated by a ‘superconducting’ magnet cooled in liquid helium (≈4ºK)
- A rf coil surrounds the sample and is used to excite the sample and record what comes out.
- Is insensitive - as only small difference in n(g) and n(e) so only small signal.
Nuclear moments and precession
- A nucleus with spin has a magnetic moment (µ)
- µ has the property of angular momentum (tendency to continue spinning)
- A magnetic moment (µ) interacts with a magnetic field Bo (like a compass needle) (magnetic moment tends o align with magnetic field)
- The interaction with Bo and angular momentum leads to precession.
- The precession frequency ω=𝛾Bo where 𝛾 is a constant dependent on nucleus type.
NMR and magentization
- For I=0.5, spins have two allowed directions in Bo (two states - energy levels)
- The Bo direction is defined as the z axis
- In a typical NMR experiment there are many spins
- There is a slight excess (1001 vs 1000( in the lower energy state, at equilibrium, with net magnetization (M) along z, with a magnitude proportional to n(g)-n(e)
- NMR detects changes in the orientation of M
The applied radio frequency (B1)
- Rf is applied as pulses of different length (t, 2t etc) at right angles to Bo and ‘in resonance’ with rotating spins.
- It induces re-orientation of M.
- NMR experiments are sequences of rf pulses and delays.
- The NMR signal results from M being perturbed by rf pulses.
FID and Fourier Transform in NMR
- A 90º pulse moves M to the xy plane.
- M rotates on the xy plane thereby producing a transient rf signal (free induction decay, FID) that we can detect.
- The FID can be converted from the time domain to the frequency domain by a Fourier transform.
- Using FT multiple frequencies in the FID can be obtained at the same time.
- The FID signal is long lived and so the peaks are sharp (high spectral resolution)
Chemical Shift
-Nuclei are shielded from the applied Bo by electron clouds that are sensitive to their bonding and environment.
-Depends on nucleus type and the effective magnetic field felt by that nucleus.
-ω=𝛾B(eff)=𝛾(Bo-Bs)
-The shielding is directly proportional to electron density.
-The degree of shielding is usually characterized by the chemical shift δ, usually measured in ppm.
δ = frequency of signal – frequency of reference/ x 106
spectrometer frequency
-For Bio-NMR, the reference frequency (0ppm) is often given by the CH3 resonances of DSS (Si with 3Me)
-The chemical shift is sensitive to changes in chemistry and environment (both affect electron cloud, hence shielding)
-The chemical shift is the basis for NMR resolution (our ability to discriminate peaks = chemical environments = nuclei)
-Bs depends on how electronegative/positive a nuclei is
-Spectrometers are very sensitive so can tell apart minute differences - can tell where peaks come from in protein
-Resolution is the ability to discriminate two peaks in the spectrum
-A smaller electron cloud = less shielding = higher freq.
-Shift is sensitive to protein structure:
-When a protein is folded each amino acid is in a different chemical environment and has a unique chemical shift.
-In the ‘unfolded’ state the shifts tend to be the same
Spin Coupling (J)
- If two atoms are covalently bonded (share e- cloud), their nuclear energy levels are affected by the spin state (direction) of their neighbour.
- Hence, the peaks split (high-energy, low-energy component etc)
- Peaks split in a neighbor-dependent way (multiplicity); e.g. for I=0.5
- One neighbour can be ⬇ or ⬆so peaks split into doublet
- Two neighbours can be ⬇⬇, ⬆⬇, or ⬆⬆ with probability 1:2:1 (triplet)
- Three neighbours give a 1:3:3:1 (quartet) etc
- Peak splitting can help us ‘assign’ the NMR spectrum of small molecules
- Coupling strength gives bond-angle information for biomolecules
Relaxation phenomena
-Remember the net magnetization can be at Mz (equilibrium) or Mxy (after a rf pulse)
-Over time Mxy returns to equilibrium:
decay rate of Mxy ∝1/T2
recovery rate of Mz ∝ 1/T1
-T1 relaxation occurs along the Bo field direction (longitudinal).
-T2 relaxation occurs in the xy plane (transverse)
-Relaxation rates give information about molecular dynamics and distances.
How do you measure T2?
- Can be measured from the decay rate of the FID and linewidths
- The FID contains information about the decay rate in the xy plane (1/T2).
- The peak linewidth at half height in the frequency domain (Δv(o.5)) inversely depends on T2 {Δv(1/2)=1/(πT2)}
- Longer T2 = narrower peaks = higher spectral resolution
How do you measure T1?
- Can be measured using an inversion-recovery experiment
- M is inverted from z to -z at t=0, but then recovers along Bo (z direction).
- The recovery is exponential with a rate constant 1/T1Ѡ
What causes relaxation in NMR?
- In biological systems the main relaxation mechanism arises from magnetic dipole interactions between nuclei
- Consider dipoles X and Y, close in space (
Dependence of relaxation in NMR
- Relaxation times T1 and T2 depend on 𝒯c (plot)
- The T1 vs 𝒯c plot goes through a minimum; T1 gets longer again at slow 𝒯c because frequecny spectrum does not contain the right components. (T2 is also affected by low frequencies so does not go through a minimum).
- Relaxation also depends on the amplitude of Bloc; which depends on the separation (r) and the number of dipole neighbours (n). This is the basis of NMR as a strucutural tool.
- Relaxation ≈ n𝑓(𝒯c)r^-6
- 𝑓(𝒯c) is different for T1 and T2. Note the r^-6 dependence (close by nuclei affect more than remote)
Effect of a paramagentic centre on relaxation in NMR
- In some systems there are free electrons (radicals, metal ions Mn++, Gd+++, etc).
- The dipole moment of an electron is 658x that of a proton.
- This means that large relaxation effects can be seen when a free electron (paramagentic centre) is introduced in a sample.
Distance between atoms (NOEs)
-If A and B are H separated by
NMR exchange processes
- T2 is relatively long in NMR (msec or more).
- In many situations we therefore see chemical exchange during data collection, thereby averaging the spectra.
- Consider a simple case with two resonances from states A and B: A↔B, k in forward direction.
- The appearance of the spectrum depends on k and the separation (Δv) between them.
- 2 lines = “slow” exchange
- 1 line = “fast” exchange
Examples of exchange phenomena
- Hydrogen exchange: Expect a triplet for ethanol OH but get a singlet because of fast exchange
- Bond rotation: Two methyl groups, seen separately at 26ºC, but merge to a singlet at 120ºC because of rapi d rotation around the central bond.
MRI (magnetic resonance imaging)
- An image is obtained by collecting spectra while magnetic field gradients are applied to the sample.
- Positions in space have thus different frequencies, ω=𝛾B(eff)=𝛾(Bo+B(G)) and and image can be reconstructed.
In vivo NMR studies
often called MRS - magnetic resonance spectroscopy
- NMR used to produce spectra from abundant molecules in living cells and tissues
- The Pi chemical shift is sensitive to pH (an average of acid and base shifts is seen because exchange rate k is fast).
- This means that chemical shift can be used as an in vivo pH meter
NMR of macromolecules
- NMR can be used to determine structure, dynamics and interactions of biological macromolecules.
- Can be done closer to the physiological state of the molecule than say crystallography.
Problems and solutions of NMR of macromolecules
- Problems:
i) Sensitivity (need >200µM solution/ >0.3ml)
ii) Resolution (of spectra - distinguish between peaks) - not comparable to crystallography/EM
iii) Assignment (need to assign each resonance to a specific atom)
iv) Size limit (large molecules give broad peaks ∴ tumble slowly + fast relaxation) - Technical Solutions:
i) High magnetic fields
ii) Multi-dimensional NMR (spread out resonances)
iii) Isotopic labeling (use 15N or 13C)
Magnet technology in NMR
The development of superconducting magnets at higher fields (up to 1GHz) has led to improvements in hte quality of NMR spectra. Both sensitivity and resolution have improved dramatically.
Multi-dimensional NMR
- Higher dimensionality provides resolution (peaks close together in the 1D can be discriminated) and visulisation of “connectivities” between nuclei.
- 2D spectra are drawn as contour plots
- Off-diagonal peaks arise from connections between nuclei. These can be through-bond (COSY experiment, J-coupling) or through space (NOESY experiment, NOE)
COSY: through-bond (≤3 bonds)
-2D experiment allowing you to see which nuclei are close to other nuclei through (covalent) bonds
NOESY: through-space (≤0.5nm)
-Measure intensities of correlation which will tell us about distance between nuclei
NMR of solids
- In solution, the molecules tumble rapidly and many of the NMR phenomena are averaged out.
- In solids molecules move relatively slowly so there is little averaging.
- In a solid, any NMR parameter that depends on field direction gives a different spectrum for each angle made with Bo.
- When all angles wrt to Bo are present we get a powder spectrum.
- note: ⏊ angles are more likely than // angles so an asymmetric spectrum is obtained.
Problems and Solutions of solid-state NMR compared to solution
- Problems:
i) Broad peaks (spectral overlap)
ii) Low sensitivity
iii) Difficulty in assigning spectra - Solutions:
i) ‘Magic angle” spinning (fast, kHz, sample rotation inclined at 54.7º to Bo)
ii) High field magnets (e.g. 1GHz)
iii) Complex 13C labeling patterns - This technique is particularly powerful if the sample doesn’t want to solubilise, e.g. a membrane protein.
Electron Paramagnetic Resonance (EPR) Principles
- Very similat to NMR, but for electrons and more sensitive
- EPR signals arise if there are unpaired electrons, e.g. free radicals and transition metal ions
- For most applied magnetic fields (Bo), resonances occur in the microwave range (v=3-100GHz, ƛ=10-0.2cm)
- The main parameters of EPR are :
i) g-factor (g-hv/βBo, β≈10^-3J/Tesla); similar to chemical shift in NMR
ii) A, the hyperfine splitting (similar to J-coupling)
iii) lineshape (remember NMR relaxation) - Main uses of EPR are for mobility probes, transition metals in proteins and distance measurements.
The EPR spectrometer
-Diagram
-In NMR we hold Bo constant and excite multiple frequencies, whereas in EPR we use a single excitation frequency and vary the Bo field.
-Field modulation gives derivative mode signals
-Te EPR signal is transformed into a sine wave with an amplitude proportional to the slope of the signal.
As a result the first derivative of the signal is measured.
-EPR spectra are usually displayed as the first derivative of the absorption spectrum.
Hyperfine structures and EPR
- EPR spectra show “hyperfine” structure because of interactions between electrons and nuclei with spin I (observe 2I+1 lines)
- When I=1/2 (e.g 13C, H) get a 2 line spectrum
- When I=5/2 (e.g. Mn++) get a 6 line spectrum
- The hyperfine structure depends on direction of free radical compared to Bo (it is anisotropic)
- Position of the peak depends on the effective field felt by electron, which depends on the Bo.
Spin labels - probes of mobility
-The anisotropy of the hyperfine splitting results in spectra that are very sensitive to motion.
-Spectra of a spin label at different temperatures are shown
At 43ºC the molecule tumbles rapidly and it gives a spectrum with 3 narrow lines. At -100ºC the molecule is nearly immobilized, with a broad spectrum.
EPR for monitoring protein dynamics
- Nitroxide spin label - can introduce onto protein, modifies cys residues to give spin label
- Stable radial with a free electron in the vicinity of N. A reactive group X allows the label to be attached to a protein’ e.g. via an SH group
- Strategy: Engineer a cysteine in a specific position, attach a spin label and analyse its spectrum in terms of mobility.
Resolution limits in microscopy
- Images are limited by light diffraction and lens aberrations
- The resolution depends on ƛ/a. Large a (wide aperture) and short ƛ give the best resolution.
- Abbe calculated the resolution limit to be 0.61ƛ/nsinθ
- nsinθ is called the numerical aperture (NA)
- For light microscopes sinθ≈0.9, using oil with n≈1.5 so NA>1. The practical resolution limit for ƛ≈500nm is thus ≈225nm.
- Compare to EM where ƛ≈0.004nm for an accelerating voltage of 100keV, but NA is ≈0.01 for experimental reasons, thus resolution limit is ≈0.2nm.
- Resolution limit = ƛ/2
Lens abberations
- Light: chromatic aberration (different wavelengths give different focal points) and spherical aberrations (off-axis rays have different focal points).
- These aberrations are reduced if NA (slit width, beam divergence) is small.
- Light lenses can correct most aberrations so slits can be large
- Electrons have good lenses (focusing is done by applying magnetic and/or electric fie;ds) so slits have to be small.
Contrast in biological samples
- Contrast: the ability of an individulal specimen detail to be distinguished from background and adjacent features
- Contrast in effect is the difference in light intensity between specimen and background
- Contrast is low in biological samples
- Solutions:
i) Staining (gram - colours peptidoglycan layer in bacteria, Eosin - nuclei, Haematoxylin - blood cells). Most staining requires specimen fixations (kills cells) and permeabilisation.
ii) Phase contrast or Differential Interference contrast (DIC) microscopy.
Phase contrast in the light microscope; a method to improve contrast
- Remove bright background and diffused light from specimen
- Scattered and transmitted light cancel because of 90º phase shift introduced by phase plate.
- Very sensitive to changes in refractive index in specimen.
- Diagram
The fluorescence microscope
- Very powerful and sensitive because sample emits light
- Allows very high contrast (approach resolution limit)
- Fluorescence not typically found in cell so you only view what you have fluorescently labelled.
How to fluroescently label a sample
- Immunofluroescence
- fluorescence labeled antibodies
- usually two sets of antibodies are used; a primary antibody binds the antigen of interest and a secondary dye-coupled antibody binds the primary antibody.
- Cells and tissues are frequently permeabilised with detergent prior to labelling.
- Also remember that GFP can be genetically fused to any protein of interest to track its location
Photobleaching, FRAP and FLIP
- Photo-bleaching is the destruction of fluorophore by applied light; it can be a problem in microscopy but can also be exploited.
- FRAP: Diffusion of fluorescently labelled protein back into field of view is monitored after a patch of fluorophores is photo-bleached. Used for looking at a particular molecule and to study kinetics/mobility of molecules in the cell.
- FLIP: Look at fluorescence of one part of the cell but bleach continuously a different part of the cell. Use for global kinetics throughout cell. Eventually all fluorescence lost (if mobile).
FRAP vs FLIP
- Region of interest (inside or outside the spot)
- Single bleaching event (FRAP) vs multiple (FLIP)
- Rates of motion: fast (FRAP) vs slow (FLIP)
- Local events (FRAP) vs global trafficking (FLIP)
Confocal microscopy
- In normal light microscopy the whole specimen is illuminated, and light is emitted from outside the focal plane reducing contrast.
- In confocal microscopy the illuminating light is focused on a single 3D spot in the specimen.
- The spot is scanned.
- The result is that unwanted light is eliminated and a much clearer image is obtained.
- 3D reconstructions are also possible.
- Is improved light microscopy but does take longer
Detecting a sub-set of fluorophores in microscopy
- Total internal reflection fluorescence (TIRF) microscopes only detect fluorophores excited by an evanescent field.
- TIRF produces ≈5 times thinner slice than confocal
Beyond the Abbé resolution limit (super-resolution)
-Example: the scanned spot in confocal microscopy
The size of a spot (Point Spread Function PSF) produced by a lens is diffraction limited to ≈200nm in the xy direction and ≈500-700nm in the z direction.
-If the spot size could be reduced we would get better resolution in a scanned confocal image.
-In 4Pi microscopy back-to-back lenses reduce z-axis spread of the spot to 100-150nm (5-7x improvement)
-4Pi microscopy (reduction of z focal spot) can be combined with stimulated emission depletion (STED).
-The point spread in the xy direction can be reduced t ≈50nm.
-As well as the normal excitation, a ring of light is applied at wavelength that stimulates depopulation of the excited state.
-The net effect is to produce an excitation spot with a reduced diameter.
-images with ≈50nm resolution are possible
-Note: higher resolution images take longer to collect; need to compromise between speed and resolution.
Properties of light vs electron microscopes
TABLE lecture 9
Electron Microscopy
-Two main modes - transmission (TEM) and scanning (SEM)
-Limitations for biomolecules: limited contrast and fragile samples (vacuum and radiation damage) affect resolution
Solutions: sample staining, chemical fixation, cryo-EM, data processing (and improved instrumentation)
-Huge impact on our understanding of cell structure, but, increasingly, also of molecules and complexes.
Traditional TEM methods
- Biological sample: Low contrast (few electrons scattered) + Sensitive to electrons = low signal/noise
- Positive/Negative Staining: Stain (e.g. uranyl acetate) covers the sample (positive) or the background (negative). Sample distortions by fixations, dehydration, stain. Resolution limited by metal deposit; imaging of exposed surface only.
- Rotary shadowing: a metal is sprayed onto molecules adsorbed on a surface. Rotation gives even more exposure. Good signal but low exposure (“grainy”)
- Freeze fracture: Freeze → Knife edge → carbon evaporation → platinum shadowing → tissue digested away leaving replica. Particularly good for molecules in the lipid bilayer.
Molecular electron microscopy (improved methods)
- With ‘traditional’ metal staining, dehydration in a vacuum, electron damage etc. the resolution limit for biological samples use os ≈2nm or worse.
- Using various technical improvements, much better resolution (≈0.3nm) is now possible
- Some of these improvements arise from: embedding the sample in vitreous ice (rapid freezing), no metal staining, minimising radiation damage by cooling sample (e.g. to 4K), improved electron detectors and data processing software.
Tomography
- Collect series of images at different angles
- Use images to reconstruct object
- Useful or large cellular structures
- Limited electron dosage = low signal/noise ratio (few electrons per image as have to collect lots of images without damage)
- Some angles are inaccessible
- Reconstruction can be improved by signal averaging if multiple copies available.
Single-particle Cryo-EM
- Freeze rapidly (vitreous ice-has water solution properties)
- Molecules are distributed randomly in ice; so that many different projections are obtained in the EM images
- Derive ‘views’ by grouping and averaging particular projections
- Reconstruct and average over all views
- Can derive atomic resolution using this technique.
- Often used instead of X-ray crystallography as do not have to grow crystals
- Does require a molecule of sufficient size however, hundreds of kDa
Electron crystallography
- Gives atomic resolution (≈0.2nm)
- Sample has to be ordered; e.g. a 2D crystals (proteins in a lipid bilayer) or a helical array
- Many molecules contribute to the diffraction pattern, with resulting improvement in signal/noise ratio compared to single particle EM.
- Sample tilting (similar to rotating a crystal) to increase data completeness
- Final data are anisotropic for planar arrays i.e. better resolution for the array plane (xy) than in depth (z)
- Electron diffraction data have the same phase problem as X-ray data. To solve this the data are combined with images produced by tomography.
Scanning Electron Microscopy (SEM)
- A beam of primary electrons is scanned across sample
- Lower resolution than TEM (≈3nm)
- Sample ‘sputtered’ with gold (i.e. we are imaging the surface)
- Images have a 3D appearance (good depth information)
- Can also be used to analyse the atomic composition of the sample.
- Gives images of metal-coated objects.
Atomic force microscopy (AFM)
- AFM involves scanning a fine tip back and forward over a sample.
- Deflections in the probe are detected by an optical lever.
- The sample can be in aqueous solution and lateral resolutions of ≈0.5nm can be achieved.
- Disadvantage: tip may damage sample; tapping mode is less damaging
- Gives 2D image with height information
Single molecule experiments
- Most biophysical studies involve measurements of many molecules at the same time - this improves signal/noise but gives an ensemble averaged result
- Following one molecule does not give the same result as taking an average over all molecules
- Single molecule studies give new information about molecular properties and stochastic events.
- Detection of events at the single molecule level require high signal/noise: Fluorescence and methods that immobilise single molecules are among few approaches that work.
Detection of single fluorophores with a focused beam
- With very dilute solutions and a highly focused spot (e.g. in a microscope), single molecules can be induced to fluoresce as they diffuse through the spot.
- With a pair of attached fluorophores we can measure the donor and acceptor spectra and interpret ‘single pair’ FRET.
- Single pair FRET is used to study conformational changes and binding events (no FRET if no binding)
- Fluorescence correlation spectroscopy (FCS) measures the speed of molecular diffusion and extrapolates the molecule size; have thin beam, see molecules as they enter and exit beam. If the sample is very dilute can track single molecules and measure diffusion rate - can determine the oligomeric state of a protein from the diffusion rate.
Optical tweezers (traps): force by EM radiation
- A change in the direction of light due to scattering results in a change in momentum - this generating a small, but useful, force.
- In a light gradient, particles with suitable refractive index bend light.
- The particle then experiences a net force from the EM radiation (≈10 picoNewtons) that can be used to trap and/or move the particle.
- Magentic traps can also manipulate single molecules e.g. to drive rotation of F1Fo ATP synthase.
- AFM for measuring unfolding of single proteins - pull with tip.
