Initially, spins point in random directions

In an applied external magnetic field, spins align with the +Z axis as spin up or spin down (Zeeman interaction)

Spin up state is lower energy than the spin down state --> always greater population of spins in the up state

Detector is in the XY plane, cannot detect signals in the Z plane

Apply RF pulse at 90^o --> rotates magnetisation from Z axis into the XY plane

FIDs of closely spaced peaks take a long time to phase out, if the signal decays before that time only one peak is observable

If the time domain signal dies too early, intensity decreases and peaks become broader --> may not be able to resolve peaks that are close in chemical shift

Time and frequency domain data

Effect of chemical exchange on NMR spectra

CPMG relaxation dispersion

Increment delay: Change t₁ delay, repeat many times

For each t₁ point, the entire experiment has to be repeated --> takes time (10-20 min, compared to only 1 min for 1D)

First FT t₂ (directly-detected dimension) --> peak at same point on y axis (corresponding to the resonant frequency of the nucleus being observed) but with modulated intensity due to the influence of the t₁ dimension

Then FT across t₁ (indirectly-detected dimension) --> single peak in the resulting 2D spectrum where each point's intensity and position in the 2D plane provides information about the interaction between the two frequency dimensions

t₁ delay gets incremented to give modulated intensity (interferogram) necessary for the 2D spectrum

Backbone NH groups give characteristic peaks dependent on their local chemical environment --> can be used as a 'fingerprint' for the protein

Side chain Asn and Gln also give peaks (two peaks, because not exactly the same chemical environment, doesn't rotate freely around the bond)

Magnetisation is passed from ¹H to ¹⁵N and then selectively to the carbonyl ¹³C via the ¹⁵N^H–¹³CO J-coupling

Magnetisation is then passed back via ¹⁵N to ¹H for detection

The chemical shift is evolved on all three nuclei resulting in a 3D spectrum

Magnetisation is transferred from ¹H to ¹⁵N and then via the N-Cα J-coupling to the ¹³Cα

Then transferred to the ¹³CO via the ¹³Cα-¹³CO J-coupling

For detection, the magnetisation is transferred back the same way: from ¹³CO to ¹³Cα, ¹⁵N and finally ¹H

The chemical shift is only evolved on ¹H, ¹⁵N and ¹³CO and not on the ¹³Cα, resulting in a 3D spectrum

Because the amide nitrogen is J-coupled both to the Cα of its own residue and that of the preceding residue, both these transfers occur and transfer to both ¹³CO nuclei occurs

Thus for each backbone amide, two carbonyl groups are observed in the spectrum

But the J-coupling between N_i and Cα_i is stronger than that between N_i and Cα_i-1 --> the H_i-N_i-CO_i peak generally ends up being more intense than the H_i-N_i-CO_i-1 peak

Magnetisation is transferred from ¹Hα and ¹Hβ to ¹³Cα and ¹³Cβ, respectively, and then from ¹³Cβ to ¹³Cα

Then transferred first to ¹⁵N^H and then to ¹H^N for detection

Transfer from Cα_i-1 can occur both to ¹⁵N_i-1 and ¹⁵N_i, or viewed the other way, magnetisation is transferred to ¹⁵N_i from both ¹³Cα_i and ¹³Cα_i-1 --> for each NH group there are two Cα and Cβ peaks visible

The chemical shift is evolved simultaneously on ¹³Cα and ¹³Cβ, so these appear in one dimension

The chemical shifts evolved in the other two dimensions are ¹⁵N^H and ¹H^N

Along with the CBCA(CO)NH and HSQC this forms the standard set of experiments needed for backbone assignment

For large proteins the signal-to-noise may not be great and assignment using the HNCA, HN(CO)CA, HNCO and HN(CA)CO may form a better strategy

When using deuterated protein, the spectrum has to be recorded as an ‘out-and-back’ method and the signal-to-noise suffers even further

Magnetisation is transferred from ¹Hα and ¹Hβ to ¹³Cα and ¹³Cβ, respectively, and then from ¹³Cβ to ¹³Cα

From here it is transferred first to¹³CO, then to ¹⁵N^H and then to ¹H^N for detection

The chemical shift is evolved simultaneously on ¹³Cα and ¹³Cβ, so these appear in one dimension

The chemical shifts evolved in the other two dimensions are ¹⁵N^H and ¹H^N

The chemical shift is not evolved on ¹³CO

Results in a spectrum that is similar to CBCANH, but is selective for the ¹³Cα and ¹³Cβ of the preceding (i-1) residue

Along with the CBCANH and HSQC this forms the standard set of experiments needed for backbone assignment

For large proteins, the signal-to-noise may not be great and assignment using the HNCA, HN(CO)CA, HNCO and HN(CA)CO may form a better strategy

When using deuterated protein, the spectrum has to be recorded as an ‘out-and-back’ method and the signal-to-noise suffers even further

Magnetisation is passed from ¹H to ¹⁵N and then via the N-Cα J-coupling to the ¹³Cα and then back again to ¹⁵N and ¹H for detection

The chemical shift is evolved for ¹H^N as well as the ¹⁵N^H and ¹³Cα, resulting in a 3D spectrum

Since the amide nitrogen is coupled both to the Cα of its own residue and that of the preceding residue, both these transfers occur and peaks for both Cαs are visible in the spectrum

However, the coupling to the directly bonded Cα is stronger and thus these peaks will appear with greater intensity in the spectra

Magnetisation is passed from ¹H to ¹⁵N and then to ¹³CO

From here it is transferred to ¹³Cα and the chemical shift is evolved

Magnetisation is then transferred back via ¹³CO to ¹⁵N and ¹H for detection

The chemical shift is only evolved on he ¹H^N, the ¹⁵N and the ¹³Cα, but not for the ¹³CO

This results in a spectrum which is like the HNCA, but which is selective for the Cα of the preceding residue

Typically used to assign resonances (peaks) in the 2D spectra to protein atoms

Combinations of different experiments tells you which peak is i and which is i-1

Molecular dynamics method

The starting structure is heated in simulation i.e. the atoms of the starting structure get a high thermal motility

During cooling steps the starting structure can evolve towards the energetically favourable final structure under the influence of the force field

Structure is an ensemble, proteins can adopt higher energy states in solution that are important for function

Biological functions of proteins depend on different conformations in the native-state free energy well

Low energy states are highly populated and can be studied by techniques such as PX and standard NMR

• PX structure is usually the lowest energy state, but this is not the only conformation a protein can adopt in solution

Higher energy states have a minor population and can be understood only by a specific set of NMR techniques

The native state free energy landscape is composed of a number of minima divided by energy barriers

The higher the energy barrier, the longer the timescale for the associated conformational fluctuation

• Dynamics within each energy well, very small and fast conformational changes (ns-ps dynamics)

• Jumping between energy wells is slower (μs-ms dynamics)

The biological 'employment' of specific protein dynamics depend on their timescales

Z axis: Longitudinal magnetisation

XY plane: Transverse magnetisation

We apply a 90^o RF pulse to rotate the net magnetic moment

When the magnetic moment is in the XY plane, this is called transverse magnetisation

Small protein --> small R2 --> large T2 --> stays in XY plane for long enough, slow decay of time-domain signal -FT-> sharp peak, good resolution

Large protein --> large R2 --> small T2 --> time-domain signal decays too quickly -FT-> broad peak, poor resolution

In relaxation experiments, we add to the 2D heteronuclear NMR a new block of pulses with new time 'τ' (delay time)

Multiple HSQC experiments will be made at different values of τ

The pulse sequences set up so that the decay of signal intensities as a function of τ are proportional to either R1 or R2 (decay of the signal intensities over time depends on the relaxation properties of the nuclei)

Measure how the peak intensities change at different values of τ --> obtain information about the motion and environment of the nuclei in the sample (some peaks may disappear entirely, indicating complete relaxation or other dynamic processes affecting those nuclei)

Record a series of HSQC spectra with varying τ

Fit intensities as a function of delay time (τ) to the single exponential function I(t)=I₀e^(-Riτ) --> obtain R1 or R2 (depending on the pulse sequence employed) for every peak (hence every residue) present in the HSQC

The backbone ¹H-¹⁵N heteronuclear NOE provides information about the motion of individual NH bond vectors

Usually, hetNOE is measured in steady state mode

The steady state hetNOE compares the signal of the z-magnetisation (signal intensity) of the ¹⁵N in thermal equilibrium (I_eq) to the z-magnetisation of the ¹⁵N at equilibrium when ¹H is saturated (I_¹Hsat)

hetNOE values are interpreted as indicators of molecular dynamics: A rigid NH bond vector results in a hetNOE value close to 0.9, highly dynamic NH bond vector gives a hetNOE value much less than 1

¹⁵N relaxation is the most popular, it infers on N-H

¹³C relaxation is also measurable e.g. C’-Ca

Proteins can exist in multiple states: Multiple energy wells/local minima (e.g. states A and B), picosecond dynamics within

Slower (μs-ms) dynamics are normally associated with larger scale structural rearrangements: Chemical exchange between A and B, jumping from one energy well to another

Many important biological systems rely on chemical exchange

Stabilisation of specific states by drugs is an important avenue for drug design

In the above spectra, the both have pB = 50%, only the k_ex is different

State A and B have different chemical shifts (different resonance in the XY plane)

50:50 populations --> height of the peaks is the same

Slow exchange rate --> two peaks observed

Very fast exchange rate --> observe one peak at the population weighted average

Exchange rate similar to frequency difference --> no peak observed (intermediate exchange)

Shutter speed: Chemical shift difference Δω

Walking speed: Exchange rate k_ex

Chemical exchange between different states affects NMR spectra

The effect depends on the kinetics of interconversion

In reality, it is unlikely to be a 50:50 population, more likely to be a skewed population e.g. 90:10

The exchange regime is determined by the ratio of the exchange rate (k_ex) to chemical shift difference (Δω)

Height of the peak is proportional to the population

Very quickly lose the small, low population peak

Tall, high population peak will shift a bit towards the small peak at fast exchange

Provides structural information at the residue level

Not all the peaks of the spectrum will be suitable for CPMG, because not all the parts of the protein are normally in conformational exchange

Delay before = delay after (τ) --> vector ends up where it started on the X axis if no exchange occurs

In a CPMG experiment, τ (total delay time) does not change but the number of pulses does

Vector becomes smaller because of T2 relaxation and exchange

If exchange is present (two states with different frequencies), the number of pulses matters, we measure R₂^A and R_ex

Chemical exchange occurs between pulses --> frequency changes --> does not end up on the X axis anymore --> weak peak, high apparent R₂ (R₂^A + R_ex)

Increasing the number of pulses gives less time to change from A to B --> increase the likelihood that magnetization remains on the X-axis --> increases the observed signal, decreases apparent R₂ (just observe R₂^A)

14 kDa enzyme

Catalyses transphosphorylation of single-stranded RNA

No cofactors or metal ions

Rate-limiting step in the catalysis is product release (k_cat ≈ k_off)

CPMG is sensitive to dynamics ranging in the μs to ms timescale

CPMG is most effectively used when two conformations are in intermediate exchange

CPMG provides three major data: Populations, k_ex and Δω

Proteins exist in continuum of functional dynamics: from mainly ordered proteins, proteins with folded domains and disordered regions (IDRs) or completely disordered proteins (IDPs)

At least 30% of the proteome is disordered and often the disordered regions are those that are functionally important

Current AI based tools (like AlphaFold) completely fail to characterize IDRs/IDPs 

Chemical shifts are sensitive to the local backbone structure

Since chemical shifts are averaged the secondary structure element does not have to be present 100% of the time

Using this principle we can take advantage of the chemical shifts to estimate propensities/populations of helices, strands, poly-proline helices, β-turns even if they are not fully formed

Many programs/servers exist that can do this e.g. Talos, δ2D

Attach labels with lone electrons (paramagnetic species) to Cys (can engineer) --> increases R₂ of nearby groups --> broader peaks

We can attach spin labels at various places on a protein and see which regions are affected --> allows us to determine the topology of secondary structure elements

Imperfect repeats of KTKEGV motif throughout the 1-70 region --> positively-charged, disordered N terminus

Negatively-charged C terminus

Add SUVs -> CD spectrum dips to around 220 nm, characteristic of α helix

Affinity is 3x higher for POPG than DOPC/DOPS/DOPE lipids

N-terminal 25 residues --> rigid helix

Residues 26-97 --> intermediate behaviour (dynamics/structure)

C terminal residues 98-140 --> unstructured and highly dynamical

Attach spin labels to membrane --> changes (increased R2) observed in peaks corresponding to residues involved in binding the membrane

N terminal anchor: Membrane contacts in the rigid region of the protein

CEST is an NMR method to probe exchange of NMR visible species with excited states

If the excited state has a very large MW, the method is also called dark exchange saturation transfer (DEST)

Based on the application of a weak saturating field (B1) at various places (offsets) on the spectrum

When an NMR resonance is saturated (i.e. when the B1 field is applied at its frequency, offset ~0), its intensity is diminished (dark blue)

If there is exchange with another conformation that has a large MW, saturation of the main observable species is observed at large offsets (light blue)

This happens because saturation of the large excited state is transferred to the small NMR observable main state through chemical exchange

Can control the strength and 'location' of the B1 field, monitor the intensity of a particular peak

B1 field on top of peak --> sharp drop in intensity, recovers when B1 field moves off peak (intensity vs offset plot)

Large MW --> faster relaxation --> broader peak

If exchange occurs, the drop in intensity occurs before you actually hit the main peak and takes longer to recover (broad drop rather than fast drop)

Allows you to indirectly observe the broad intensity by monitoring the change in intensity of the main peak

Some residues are stably bound (low I/I₀)

Other residues are in exchange between bound and unbound (intermediate I/I₀)

We can probe the binding of αS to membranes on a per-residue basis

Determine the regions that are bound and the kinetics of binding

K80E --> more negative --> binds 2^nd membrane better --> promotes vesicle fusion

Primary requisites: Same aminoacidic composition, same overall charge

Intended requisites: Same membrane affinity, more exposed NAC region

Modulated by Ca²⁺

Amyloid fibrils good cryo EM structural studies

Highly toxic oligomers much harder to study structurally (transient, unstable)

Non-toxic and toxic structures, differences in terms of 2^o structure

Toxic oligomer structure has more dynamic N terminus

IDPs can form many different structures even when in oligomers

ssNMR in the cross polarisation regime for rigid regions of membrane bound proteins

ssNMR in the INEPT region for dynamic regions of membrane-bound proteins

CEST probing the interaction from the unbound state perspective

Allows easy discrimination of tumors (and grade), neurodegeneration etc.

Sensitive to acidosis (pH modification)

Applicable at clinical fields (≤ 3 T)

Exchangeable protons that resonate at a different frequency from the bulk water protons

The bulk water signal (4.75 ppm) is saturated when we use a saturation band applied at 8.25 ppm (saturates amides??)

Saturate solute protons--> transfer of saturated protons to water --> water signal goes down

Glutamate (Glu), a neurotransmitter in the brain, shows a pH- and concentration-dependent chemical exchange transfer effect (GluCEST) between its amine group and bulk water

GluCEST map shows the regional distribution of Glu in the brain, higher GluCEST contrast observed in gray matter compared to white matter

Sensitive to [Glu] and pH

Contrast favourable at high fields (≥ 7 T)

Imaging of: Stroke, Alzheimer's, Huntington's e.g. AD mice exhibited notable reduction of GluCEST contrast (~30%) in all areas of the brain

CEST provides key information from indirect measurements

Wide range of applications: from protein-ligand binding to protein-membrane interactions, and medical applications in MRI

αS function and aggregation can be characterised by a number of solution and ssNMR methods

Protein dynamics are directly related to function

They take place at a range of timescales that are relevant to biology

NMR is the prime method to study protein motion

ns-ps dynamics: Motion within an energy well --> T1, T2 relaxation, het NOE

μs-ms dynamics: Exchange between different states --> CPMG and CEST/DEST

IDPs are a classic example of functionally relevant dynamics: Chemical shifts (local structure) and PREs (topology)

ssNMR can be used to study large assemblies

Low R₂/R₁ ratio --> small R2 and large R1 --> rigid, compact protein or region

Large R₂/R₁ ratio --> large R2 and small R1 --> flexible, non-compact protein or region

Saturation: CEST starts by selectively saturating (or exciting with a strong radiofrequency pulse) the protons of interest that are bound to molecules other than water (could be protons in metabolic products or proteins)

Chemical Exchange: Following saturation, these protons exchange with the protons in water molecules

Detection: When the water protons (which are now in excess and not initially targeted by the saturation pulse) exchange with the saturated protons, they carry some of the saturation with them, this exchange alters the signal from the water protons that is detected by the MRI