NMR Chemical Shift Perturbation: Mapping a Binding Interface

An amide nitrogen and its attached proton resonate at frequencies fixed by their local electronic environment. Bring a binding partner alongside and those frequencies move. That is the entire basis of the method: label one molecule, add the other unlabelled, and read out residue by residue which parts of the labelled molecule noticed. Chemical shift perturbation follows changes in the chemical shifts of a protein when a ligand is added, and uses these to determine the location of the binding site, the affinity of the ligand, and possibly the structure of the complex ^[1]. It is cheap in sample and fast in acquisition compared with structure determination, and the map it produces is easy to over-read, because a residue whose peak moved has not necessarily touched anything.

The titration

The standard arrangement holds the isotopically labelled partner at fixed concentration and adds the unlabelled partner in steps, recording a two-dimensional correlation spectrum — most often a ¹H,¹⁵N HSQC — at each point. One backbone amide gives one cross peak, so a single spectrum is a residue-resolved snapshot of the whole chain. This is conventional practice, stated here without citation. It demands assigned peaks: an unassigned spectrum yields a count of moving peaks and nothing else.

For a peptide ligand the labelled partner is the receptor and the peptide is the titrant. Tracking ¹H and ¹⁵N chemical shift changes over the course of a peptide titration into isotopically labelled protein identifies the amide NH pairs whose chemical environment changes on peptide binding; mapped onto a structure of the protein, this approach can identify the peptide-binding interface or regions undergoing conformational changes within the protein on ligand binding, and the same series can be used to determine the binding affinity of a weak protein–peptide interaction — set out in detail for peptide binding to the C-terminal SH2 domain of PLCγ1 ^[2]. That disjunction is the authors' own, and it is the caveat this article turns on.

Size sets the outer boundary. One survey of the solution NMR methods available for protein–protein interfaces — intermolecular NOEs, cross-saturation, chemical shift perturbation, exchange perturbation, paramagnetic methods, dipolar orientation — noted that most are routinely applied to complexes of total molecular mass 60 kDa and can likely be applied to systems up to about 1000 kDa ^[3].

Combining the shifts, and what the combination discards

A ppm of ¹⁵N and a ppm of ¹H are not the same quantity of information, so the two axes cannot simply be added. The nuclei also respond to different physics: ¹H shifts are influenced to a large extent by through-space interactions, ¹³C^α and ¹³C^β shifts more by through-bond effects, while ¹⁵N and ¹³C' shifts are influenced both by through-bond and by through-space hydrogen-bonding interactions. For locating a bound ligand from shift change the usually most appropriate route is therefore to measure ¹⁵N HSQC spectra, calculate the geometrical distance moved by the peak, weight ¹⁵N shifts by a factor of about 0.14 compared with ¹H shifts, and select those residues for which the weighted shift change is larger than the standard deviation of the shift for all residues; ¹³CH₃ signals are the main alternative probe ^[1]. Later titrations on three contrasting proteins found that the optimal weighting of ¹⁵N to ¹H chemical shifts is protein dependent, but is around that consensus value of 0.14 ^[4].

A systematic comparison of published and unpublished procedures for computing the combined perturbation, spanning a variety of functional forms and per-nucleus weighting factors, reached an uncomfortable conclusion. The predictive power of all shift mapping methods depends on the magnitude of the overlap of the chemical shift distributions of interacting and non-interacting residues and on the cut-off criterion used; in general the quality of the prediction on the basis of chemical shift changes alone is rather unsatisfactory, although combining shift changes on the basis of the Hamming or the Euclidian distance can improve the result, and the corrected standard deviation to zero of the combined shift changes can provide a reasonable cut-off criterion ^[5]. Read that as a warning about the threshold: on protein–protein data the interface you report is partly a thresholding decision, not purely an observation.

The combined shift is a magnitude, and it throws away the direction each peak travelled. Analysis of the sign of the ¹⁵N/¹H shift changes of the PDZ1 domain of Scribble on interaction with two pairs of phosphorylated and unphosphorylated peptides recovered detailed differences in the molecular basis of that PDZ–ligand interaction to which the classical combined chemical shift perturbation analysis is insensitive; the same work reported a correlation between affinity and millisecond motions ^[6]. Two residues with identical combined shifts may have moved in opposite directions in the plane and mean opposite things.

The exchange regime decides what is measurable

What the spectrum does during the titration is governed by the exchange rate between free and bound relative to the frequency difference between the two states. When the off-rate k_off is greater than the chemical shift difference between free and bound — which typically equates to an affinity K_d weaker than about 3 µM — exchange is fast on the chemical shift timescale, the observed shift is the population-weighted average of free and bound, and K_d can be determined from measurement of peak positions provided the measurements are made appropriately; slow to intermediate exchange rates lead to line broadening and make K_d values very difficult to obtain ^[1]. In genuinely slow exchange, separate free and bound cross peaks coexist and the bound peak grows at the expense of the free one, so populations come from intensities rather than positions — standard lineshape behaviour, stated here without citation.

Protocol treatments of protein–protein chemical shift titrations discuss the appearance of the spectra in the fast, intermediate and slow regimes and how those regimes affect the analysis of the interface-mapping and affinity data ^[7]. Establish the regime first: a fast-exchange model fitted to intermediate-exchange data returns a number that does not mean what its units say.

Vanished peaks are a measurement, not a failure

A common report from a difficult titration is that peaks at the interface broadened beyond detection partway through, then reappeared near the end. Nothing failed. Broadening maximal at intermediate points is the signature of an exchange rate comparable to the frequency difference between free and bound states, and it is localised to exactly the residues with the largest shift differences — which is to say, the ones you care about. That is standard exchange behaviour rather than a published finding. Treating those residues as missing data discards the strongest evidence in the dataset.

Lineshapes can be analysed rather than merely lamented. NMR titration experiments are a rich source of structural, mechanistic, thermodynamic and kinetic information that can be extracted through quantitative analysis of resonance lineshapes, but such analyses are frequently limited by the peak overlap inherent to complex biomolecular systems, and systematic errors may arise from analysing two-dimensional data using theoretical frameworks developed for one-dimensional experiments; direct quantum mechanical simulation and fitting of entire two-dimensional experiments, implemented in the TITAN software, addresses both problems and was expected to be particularly useful in providing information on multi-step or multi-component interactions ^[8].

Accuracy has been quantified for the classical version of the analysis. Applied to a single set of ¹H–¹⁵N 2D HSQC spectra from a precise titration of a system in the fast exchange regime, with k_off around 3,000 s⁻¹, classical line shape analysis returned k_off with accuracy better than 5% judged against quantum mechanical NMR simulations, and Monte Carlo simulation put the experimental precision at 13%; further simulations indicated the potential to give reasonably accurate and precise k_off values over a range from 100 to 15,000 s^{−1 [9]}. Keep the referent straight: that 5% figure belongs to the fast-exchange test case, not to a broadened intermediate-exchange system.

Where exchange really is intermediate or slow, relaxation-based experiments take over from the titration curve. R₂ relaxation dispersion and ZZ-exchange yield kinetic information in the intermediate- and slow-exchange regimes, with methods that determine the association rate k_on, the dissociation rate k_off and K_D; these are suited to interactions with a micromolar or sub-micromolar dissociation constant but not to very weak interactions, which are typically in very fast exchange, and it is critical to choose an appropriate kinetic model, such as a two- or three-state exchange model, to derive the correct kinetic information ^[10]. The two failure modes are symmetric: the fast-exchange titration cannot resolve tight binding, and the relaxation experiments cannot see the weakest.

Affinity from the curve, and the range in which it is valid

NMR is well suited to analysis of protein–protein and protein–ligand interactions with dissociation constants ranging from about 2 µM to about 1 mM and kinetics in the fast exchange regime ^[11]. For a 1:1 interaction the protein and ligand concentrations must necessarily be similar in magnitude to K_D, and nonlinear least squares analysis of chemical shift changes as a function of ligand concentration returns estimates of K_D and the maximum chemical shift change. In a typical titration where the initial protein concentration is held nearly constant, the most accurate parameters require an initial protein concentration of about 0.5 × K_D and a maximum titrant concentration of about 10 × that protein concentration; because those conditions are often difficult to achieve, Monte Carlo simulations showed that co-varying the ligand and protein concentrations during a titration increases the precision of the fitted K_D and maximum shift change when the protein concentration exceeds K_D ^[11]. That first condition binds in practice: a titration run far above the K_D is a stoichiometry experiment wearing the clothes of an affinity experiment.

How the curve is fitted matters as much as how it is collected. Analysis of chemical shift perturbation titrations on three contrasting proteins concluded that simultaneous fitting of all the raw shift data to a single dissociation constant is both the most accurate and the most precise method ^[4]. Fitting residues one at a time and averaging the answers is not the same operation and does not inherit that property.

Sample logistics can be engineered around. A simulation-guided swapping protocol begins from two samples, one with zero and the other with maximum ligand concentration but both containing identical protein concentrations, and generates the intermediate ligand concentrations by exchanging volumes between them; no concentrated ligand stock is needed, protein concentration stays constant, K_d can be estimated from early titration points, and the remaining points can be optimised on the fly ^[12]. For a peptide titrant with limited solubility or stability at elevated concentration, that removes a real obstacle. Ligand binding at more than one site can often be characterised by simultaneous fitting of many measured shift changes, or more simply by adding substoichiometric amounts of ligand ^[1].

A moved peak is not a contact

Here is the caveat that governs every interpretation above, and it is blunter in the primary literature than in most methods sections: there is no good way to distinguish changes in chemical shift due to direct binding of the ligand from changes in chemical shift due to allosteric change ^[1]. Not difficult — no good way.

The scale of the problem is not marginal. A substantial fraction of the protein complexes surveyed in one review showed distinct effects of induced fit affecting structural and dynamical properties beyond the contact interface ^[3]. Interfaces of large protein–protein complexes identified using chemical shift perturbation and hydrogen–deuterium exchange of main-chain amides are not always identical to those revealed using X-ray crystallography, and it was precisely to identify contact residues more accurately that cross-saturation in combination with TROSY detection in an optimally deuterium-labelled system was developed ^[13]. A recent preprint — not peer reviewed, and its numbers should be read as indicative — compiled apo and holo chemical shift data and reported that across a set of 139 protein–protein complexes, 74% of all significant perturbations are non-local to the binding site, that more than 35% of significant perturbations outside the binding site occur in residues whose shortest receptor–ligand interatomic distance exceeds 10 Å, and that every protein analysed exhibited more than 8% of perturbations distant from the binding site ^[14].

One quantitative handle exists, with a condition attached. Chemical shift changes of individual residues can be fitted to give residue-specific affinities, and residues with affinities significantly stronger than average were found in close contact with the ligand and were suggested to form a rigid contact surface — but only when the binding involves little conformational change ^[4]. Where binding does reorganise the receptor, that ranking loses its claim on contact, which is the same boundary restated in a different observable.

The non-interface perturbations are not simply noise to be thresholded away. Correlated perturbations across two separate binding events define networks of functional groups responding to each ligand and identify groups that respond to both, which are candidates for transmitting information between the binding sites; applied to the ion channel KcsA with proton and potassium binding, the role of one such residue was validated by site-specific mutagenesis, electrophysiology and NMR-detected thermodynamic analysis of allosteric coupling ^[15]. That system is not a peptide complex, but the logic transfers: a second perturbation dataset, from a second ligand or a second condition, converts an ambiguous map into a testable network.

Controls

Four checks separate an interface claim from a list of restless residues, and the first three are ordinary practice rather than published findings.

• Reverse titration. Move the isotope label to the other partner and repeat, mapping the interface from the opposite side. Two independent maps whose footprints abut is a far stronger claim than one map alone. Inverting the addition order — adding labelled protein into a solution of the unlabelled partner — separately tests whether the result depends on the sequence of additions.
• Buffer-only titration. Run the same volume series with titrant buffer alone. Amide shifts respond to pH, ionic strength and temperature, so a peptide stock reconstituted at a different pH will move peaks with no binding whatsoever, and dilution alone shifts a self-associating titrant.
• Titrant self-behaviour. A peptide taken to ten-fold excess may aggregate; a spectrum of the titrant alone across the same concentration range establishes whether the species you added at the last point is the species you added at the first.
• An orthogonal contact measurement. Cross-saturation was built for this purpose ^[13]. Intermolecular NOEs and mutagenesis of the implicated residues answer the same question by different physics.

What the map licenses you to say

The output is a list of residues and a magnitude for each. It is not coordinates, not distances, and not the kind of restraint set that supports a structure calculation — the NOE-derived bounds covered in this library's guide to solution NMR peptide structure are a separate measurement with separate failure modes. What perturbation data can do is drive a docking calculation. Chemical shift changes can be used as restraints for docking a ligand onto a protein ^[1]; HADDOCK introduces such data as ambiguous interaction restraints, each defined as an ambiguous distance between all residues shown to be involved in the interaction, and for three molecular complexes — two with NMR titration data available, one with mutagenesis data — the lowest intermolecular energy structures generated were closest to the published structure of the respective complex, within 2.0 Å backbone RMSD ^[16]. The restraint is ambiguous by construction, and it encodes the proposition — these residues are involved — that a perturbation map cannot itself establish. Quantitative calculation of ligand-induced chemical shift changes is making it possible to determine not just the position but also the orientation of ligands ^[1]; that hedge is the review's own.

A methods section worth reading states which partner was labelled and at what concentration, the titrant stock concentration, whether protein concentration was held constant or co-varied, field and pulse sequence, temperature, pH and buffer, the evidence for the exchange regime assigned, the weighting factor and the exact combined-shift expression, the cut-off rule and how it was derived, the fitting model and whether the fit was global, and the residues that broadened beyond detection. That last item is the one most often omitted, and frequently the most informative part of the dataset. State the conclusion at the strength the data supports: a set of residues perturbed above threshold is a hypothesis about the interface, to be closed by a method that measures contact.