4.2.1 Exchange regimes

The window in which exchange parameters can be accurately quantified from relaxation dispersion data is defined by exchange rate constants (k _ex) of around 100–2000 s⁻¹. However, by combining ¹⁵N and ¹H^N CPMG profiles with major state-induced ¹⁵N chemical shift changes (Vallurupalli et al. Reference Vallurupalli, Bouvignies and Kay2011), it is possible to increase the upper limit of this window to 4000–6000 s⁻¹ (Sanchez-Medina et al. Reference Sanchez-Medina, Sekhar, Vallurupalli, Cerminara, Munoz and Kay2014). It is essential to establish the exchange regime for the process under investigation, which can be done quantitatively by analyzing the static field dependency of the exchange contribution (R _ex) to the observed transverse relaxation rate, the so-called α-value (Millet et al. Reference Millet, Loria, Kroenke, Pons and Palmer2000). The α-value is defined according to; α = dln(R_ex)/dln(Δω). An estimation of α (α′) can be calculated using:

(5) $$\alpha ^{\prime} = \displaystyle{{({B_{02}} + {B_{01}})} \over {({B_{02}} - {B_{01}})}}\displaystyle{{({R_{{\rm ex2}}} - {R_{{\rm ex1}}})} \over {({R_{{\rm ex2}}} + {R_{{\rm ex1}}})}}$$

where B ₀ is the static magnetic field and R _ex is the exchange contribution under different static fields with no applied CPMG field (i.e. ν _CP equals zero). The subscript ‘n’ denotes the different static magnetic fields (n = 1, 2). It has been shown that for slow exchange 0 ⩽ α ⩽ 1, for intermediate exchange α = 1, and for fast exchange 1 ⩽ α ⩽ 2. Since the extraction of relevant parameters is most effective under an intermediate exchange regime, it can be useful to manipulate the time scale of exchange such that the exchange process occurs within this window. The most convenient way to accomplish this is by varying the temperature (modulation of k _ex) or the static magnetic field (modulation of Δω). In order to retrieve parameters with high-precision when fitting relaxation data to the Carver–Richards equation, it is useful to repeat a relaxation dispersion experiment at two different static magnetic field strengths. This approach significantly reduces any co-variation of fitted parameters that could otherwise preclude accurate quantification of protein dynamics (Kovrigin et al. Reference Kovrigin, Kempf, Grey and Loria2006).

4.2.2 Determining the signs of chemical shifts from relaxation dispersion experiments

An inherent problem with chemical shift differences between major and minor states determined by fitting from relaxation dispersion experiments is that they are obtained as absolute values. This precludes their use as constraints when calculating the structures of minor states or as quantitative measures of protein activation. This problem was resolved when it was discovered that comparisons of chemical shifts in the indirect dimensions in either a pair of heteronuclear single quantum coherence spectroscopy (HSQC) spectra acquired at different magnetic fields or HSQC and heteronuclear multiple quantum coherence spectroscopy (HMQC) spectra acquired at a single field provide the sign of the chemical shift difference (Skrynnikov et al. Reference Skrynnikov, Dahlquist and Kay2002). This finding significantly expands the usefulness of chemical shifts determined by fitting from relaxation dispersion experiments.

4.2.3 Exchange models

As noted above, relaxation dispersion experiments enable the extraction of kinetic (rate constants), thermodynamic (populations), and structural (chemical shifts) parameters for a system undergoing exchange on the μs-to-ms time scale. These parameters are quantified by fitting analytical or numerical solutions of the Bloch-McConnell equations to the observed data. The most commonly used exchange model is the two-state model, which has been demonstrated (typically by means of statistical tests such as F-tests) to account for the observed CPMG field-dependent modulation of R _2,eff. It is however obvious that in most cases a two-state model will represent a significant simplification of a system undergoing exchange. On the other hand the two-state assumption is very important and its use has enabled many major discoveries. Expansions to three-state models require data of outstanding quality (Sugase et al. Reference Sugase, Dyson and Wright2007) and complexity, such as results from experiments conducted at multiple static magnetic field strengths or temperatures. In very favorable cases a three state model can be used without additional constraints such as addition of ligands or change of temperature (Meinhold & Wright, Reference Meinhold and Wright2011). There exist a few cases in which three-state models have successfully been applied to proteins undergoing exchange, such as the study by Grey et al. (Reference Grey, Wang and Palmer2003) on the multiple states induced by disulfide bond isomerization in the basic pancreatic trypsin inhibitor, and the calculation of structural ensembles of folding intermediates for two Fyn SH3 domain variants reported by Korzhnev et al. (Reference Korzhnev, Salvatella, Vendruscolo, Di Nardo, Davidson, Dobson and Kay2004). It should be noted that the three-state model in Korzhnev et al. (Reference Korzhnev, Salvatella, Vendruscolo, Di Nardo, Davidson, Dobson and Kay2004), was applied under the assumption that (i) the chemical shift differences between exchanging states are temperature-independent, and (ii) the temperature dependence of the rate constants obeys standard transition-state theory (Fersht, Reference Fersht2000). Analyses based on a three-state model have also shown that a C-terminal extension in the PBX homeodomain with an unfolded main ground state also populates two states in which it is either folded or misfolded (Farber et al. Reference Farber, Slager and Mittermaier2012). The three-state model was applied by incorporating additional information (in this case, ligand-induced chemical shift changes) in the fitting procedure, and the paper includes a description of a grid-based search procedure that can be used to extract dynamic parameters based on a three-state model.

4.2.4 Data clustering to increase precision of fitted parameters

Slow protein fluctuations such as conformational changes involve concerted movements of large groups of atoms. Hence when such processes are studied with relaxation dispersion methodology it can be expected that individual probes (nuclei) should share k _ex values and populations of major and minor states. Global or cluster fits (assuming shared k _ex values and populations) of groups of nuclei are therefore justified on physical grounds. Global fits have the advantage of increasing the precision with which exchange parameters are estimated (Demers & Mittermaier, Reference Demers and Mittermaier2009) but care must be taken with respect to how grouping is performed. Grouping can be performed by simply grouping nuclei, which yields exchange parameters similar to those obtained when nuclei are treated individually. Alternatively a structure-based approach can be used in which grouping is performed on the basis of secondary or tertiary structure elements and their arrangement. Regardless of the chosen approach, it is important to apply statistical tests such as those outlined by Ishima & Torchia (Reference Ishima and Torchia2005) to avoid over-fitting and/or incorrect grouping.

4.2.5 Properties/structures of minor states

As noted above, relaxation dispersion experiments can be performed to identify the exchange of major protein ground states and high-energy minor states. Accurate evaluation of the properties and functional relevance of these minor states is essential for understanding the influence of dynamics on protein function. When characterizing minor states it is generally informative to compare fitted chemical shifts to observations obtained by independent measurements. The following sections describe both direct and indirect methods for defining the properties of minor states.

4.2.6 Correlation between fitted and measured chemical shift differences

In an extensive study on the thermodynamics and kinetics of ligand binding to the Fyn SH3 domain, fitted and calculated chemical shifts were used to confirm that the binding event can be accurately described with a two-state model. Hansen et al. (Reference Hansen, Vallurupalli, Lundström, Neudecker and Kay2008) showed convincingly that the chemical shifts obtained from relaxation dispersion experiments were robust by comparing chemical shifts determined directly from NMR spectra to shifts determined from fits to dispersion data. In ¹⁵N relaxation dispersion experiments using a sample with a ligand:protein ratio of around 1·5, the fitted chemical shifts obtained by regression of the CPMG data show an one-to-one agreement with chemical shifts obtained by direct measurement in NMR spectra (Demers & Mittermaier, Reference Demers and Mittermaier2009). This correlation of the chemical shifts unambiguously demonstrated that the minor state corresponded to a ligand-bound protein structure. This example, which features tight experimental control over the major and minor states, demonstrates the validity of using fitted chemical shifts to identify the properties of minor states observed in CPMG experiments. Correlations between fitted chemical shift differences and experimentally determined chemical shifts for adjacent complexes in the catalytic cycle were also exploited in a study where the free energy landscape of dihydrofolate reductase was defined on the basis of CPMG experiments (Boehr et al. Reference Boehr, Mcelheny, Dyson and Wright2006b).

4.2.7 Structure determination of minor states from fitted chemical shifts

A more involved way of obtaining detailed structural information on minor states is to use chemical shifts obtained from CPMG experiments for structure calculations. This approach has been used to compute the structures of folding intermediates that are populated in two Fyn SH3 domain variants (Korzhnev et al. Reference Korzhnev, Religa, Banachewicz, Fersht and Kay2010, Reference Korzhnev, Salvatella, Vendruscolo, Di Nardo, Davidson, Dobson and Kay2004) and to determine a minor state structure of a Lysozyme variant (Bouvignies et al. Reference Bouvignies, Vallurupalli, Hansen, Correia, Lange, Bah, Vernon, Dahlquist, Baker and Kay2011). In the latter case, the structure calculation was performed by using chemical shifts for several nuclei from CPMG experiments to guide Rosetta loop building and refinement (Wang et al. Reference Wang, Bradley and Baker2007).

5.1.1 Nitrogen regulatory protein C (NtrC)

Two component signaling systems are crucial for signal transduction in bacteria. As the name suggests, they have two evolutionarily conserved components: a histidine kinase and a response regulator, the latter of which has receiver and output domains (Parkinson & Kofoid, Reference Parkinson and Kofoid1992). These systems handle various signaling tasks relating to processes such as chemotaxis and metabolic adaption to changes in carbon and nitrogen availability; for a more extensive overview, please see the work of Parkinson & Kofoid (Reference Parkinson and Kofoid1992). Phosphorylation of an aspartate residue in the receiver domain of NtrC (NtrC^r) stimulates oligomerization of the dimeric output domain and thus down-stream activation. To understand the structural consequences of NtrC^r phosphorylation, the Wemmer laboratory developed a protocol to study this inherently unstable species (Kern et al. Reference Kern, Volkman, Luginbuhl, Nohaile, Kustu and Wemmer1999). NMR samples of phosphorylated NtrC^r were prepared by adding a large excess of carbomylphosphate together with Mg²⁺. Under these conditions the samples remained stably phosphorylated for 36 h. To enable acquisition of 3D datasets of sufficient quality, the authors co-added multiple data-sets (more effective stabilization was subsequently achieved by mimicking phosphorylation with BeF₃ ⁻ (Gardino et al. Reference Gardino, Villali, Kivenson, Lei, Liu, Steindel, Eisenmesser, Labeikovsky, Wolf-Watz, Clarkson and Kern2009; Hastings et al. Reference Hastings, Lee, Cho, Yan, Kustu and Wemmer2003)). The NMR structure of phosphorylated NtrC^r (Kern et al. Reference Kern, Volkman, Luginbuhl, Nohaile, Kustu and Wemmer1999) exhibits significant structural changes relative to the un-phosphorylated state (Volkman et al. Reference Volkman, Nohaile, Amy, Kustu and Wemmer1995). These changes are confined to one face (denoted the ‘3445-face’) of the molecule and extend over the region between α–helix 3 and β–strand-5 (Fig. 4). An NMR structure of BeF₃ ⁻-NtrCr confirmed the overall features of the conformational change, although some differences with respect to the orientations of some segments were identified (Hastings et al. Reference Hastings, Lee, Cho, Yan, Kustu and Wemmer2003). In a subsequent study, the authors designed experiments that ultimately showed that the structural change depends on the redistribution of already existing structural states (Volkman et al. Reference Volkman, Lipson, Wemmer and Kern2001). That is, the un-phosphorylated species samples the active conformation, and in this state the key aspartate residue is primed for phosphorylation. This conclusion was primarily drawn on the basis of ‘Model-free’ driven deconvolution (Clore et al. Reference Clore, Szabo, Bax, Kay, Driscoll and Gronenborn1990; Lipari & Szabo, Reference Lipari and Szabo1982a) of R _ex contributions to observed R ₂ relaxation rates. The R _ex contributions of the phosphorylated species are quenched in comparison with both the wild type and a constitutively active mutant. These relaxation data were interpreted to mean that the phosphorylated species is ‘locked’ into the active conformation, leading to a quenching of R _ex, but the R _ex contribution of the mutant and un-phosphorylated forms remains strong due to the sampling of both active and inactive conformations. This interpretation was buttressed by the observation of linear chemical shift perturbations for NtrC^r variants with varying activity. Overall, this study elegantly describes MWC-like two-state allosteric behavior in a single domain protein. The findings related to NtrC were based on the assumption of a two-state model with exchange between inactive and active species. This assumption both explained the experimental data and enabled the development of a new concept for the activation of a single-domain protein. Two more recent studies on this protein have identified the molecular transition pathways between active and inactive NtrC states (Pontiggia et al. Reference Pontiggia, Pachov, Clarkson, Villali, Hagan, Pande and Kern2015; Vanatta et al. Reference Vanatta, Shukla, Lawrenz and Pande2015).

Fig. 4. Two state allosteric behavior of NtrC. Shown is a structural superimposition of phosphorylated NtrC (orange) and non-phosphorylated NtrC (blue) indicating the structural difference between active and inactive states, respectively. This figure was adapted from reference Kern et al. (Reference Kern, Volkman, Luginbuhl, Nohaile, Kustu and Wemmer1999).

5.1.2 DHFR

DHFR is an enzyme found in all organisms that catalyzes the reduction of 7, 8-dihydrofolate (DHF) to 5, 6, 7, 8-tetrahydrofolate (THF) with hydride transfer from the cofactor NADPH (Schnell et al. Reference Schnell, Dyson and Wright2004). THF is essential for purine and thymidylate synthesis and thus for cell growth and proliferation. The reaction catalyzed by DHFR is dependent on five kinetic intermediates (Fierke et al. Reference Fierke, Johnson and Benkovic1987) for which structural models derived from x-ray crystallography are available (Sawaya & Kraut, Reference Sawaya and Kraut1997). These intermediates are known as E:NADPH, E:NADPH:DHF, E:NADP⁺:THF, E:THF and E:NADPH:THF where ‘E’ stands for the enzyme DHFR. In NMR experiments, the Michaelis complex corresponding to the E:NADPH:DHF intermediate has been mimicked using the ternary complex E:NADP⁺:folate. In a spin relaxation study of the five kinetic and structural intermediates during DHFR catalysis, Wright and co-workers established a firm coupling between DHFR function and conformational dynamics (Boehr et al. Reference Boehr, Dyson and Wright2006a; Schnell et al. Reference Schnell, Dyson and Wright2004). Under substrate-saturating conditions, these five intermediates collectively represent a full catalytic cycle in which either the cofactor and/or products or substrates are bound to the enzyme. Notably, under the conditions imposed during the NMR experiments, all of the observed relaxation effects could be attributed to conformational changes in the enzyme. This was also shown explicitly by conducting relaxation dispersion experiments at different NADP⁺ concentrations. Relaxation dispersion was acquired for ¹⁵N (Loria et al. Reference Loria, Rance and Palmer1999; Tollinger et al. Reference Tollinger, Skrynnikov, Mulder, Forman-Kay and Kay2001) and ¹H^N (Ishima & Torchia, Reference Ishima and Torchia2003) nuclei at two static magnetic field strengths. The five different intermediates exhibited specific kinetic behavior signatures that were obtained from their relaxation dispersion patterns. The authors propose a model where each of the different ground states (i.e. the five intermediates described above) is in exchange with the ground state that precedes it and the one that follows it in the catalytic cycle. Consequently, the enzyme is primed for the subsequent step in the cycle by sampling the corresponding structural state. In addition it was found that several of the microscopic steps connecting the five intermediates are rate limited by conformational transitions. These conclusions were drawn by comparing fitted chemical shifts from relaxation dispersion experiments to direct measurements in NMR spectra, which showed (among other things) that there is a striking linear dependency of chemical shifts between the E:THF and E:NADP+:THF states for residues that are sensitive to cofactor binding (Boehr et al. Reference Boehr, Mcelheny, Dyson and Wright2006b).

5.1.3 Ubiquitin

Posttranslational modification of proteins by ubiquitin is central in many cellular pathways, although the best understood function of ubiquitination is in proteasome-mediated proteolysis (Harper & Schulman, Reference Harper and Schulman2006). Ubiquitin binding domains bind non-covalently to ubiquitin and thereby control different cellular events (Hicke et al. Reference Hicke, Schubert and Hill2005). Interestingly, the ubiquitin components of complexes of ubiquitin with different target proteins exhibit a remarkable level of structural heterogeneity (Lange et al. Reference Lange, Lakomek, Fares, Schroder, Walter, Becker, Meiler, Grubmuller, Griesinger and De Groot2008). This suggests that ubiquitin's ability to bind to a very wide range of proteins is partly due to an appreciable degree of structural plasticity in its apo state. RDCs (Tjandra & Bax, Reference Tjandra and Bax1997; Tolman et al. Reference Tolman, Flanagan, Kennedy and Prestegard1995) are sensitive to motions that occur over ps to ms (Meiler et al. Reference Meiler, Prompers, Peti, Griesinger and Bruschweiler2001, Reference Tolman, Al-Hashimi, Kay and Prestegard2001, Reference Tolman, Flanagan, Kennedy and Prestegard1997; Peti et al. Reference Peti, Meiler, Bruschweiler and Griesinger2002) and thus fill a gap between the time windows that can be studied using Lipari-Szabo order parameters (Lipari & Szabo, Reference Lipari and Szabo1982a, Reference Lipari and Szabob) (sub-τ _c motion) and relaxation dispersion experiments (Loria et al. Reference Loria, Rance and Palmer1999; Tollinger et al. Reference Tollinger, Skrynnikov, Mulder, Forman-Kay and Kay2001) (between 50 µs and 100 ms). In an extensive RDC-based study, the laboratories of Griesinger and de Groot developed a method (denoted EROS) that enabled a precise determination of a structural ensemble of apo ubiquitin that is sensitive to motions in the ps- to ms- regime (Lakomek et al. Reference Lakomek, Fares, Becker, Carlomagno, Meiler and Griesinger2005, Reference Lakomek, Lange, Walter, Fares, Egger, Lunkenheimer, Meiler, Grubmuller, Becker, De Groot and Griesinger2008b); this regime is henceforth referred to as the supra-τ _c regime. The ensemble refinement was performed by using 42 RDC datasets (Briggman & Tolman, Reference Briggman and Tolman2003; Ottiger & Bax, Reference Ottiger and Bax1998; Ruan & Tolman, Reference Ruan and Tolman2005). Notably, the EROS ensemble covers the complete range of ubiquitin conformations as observed in 46 different ubiquitin complexes (Lange et al. Reference Lange, Lakomek, Fares, Schroder, Walter, Becker, Meiler, Grubmuller, Griesinger and De Groot2008). In a recent combined computational and NMR study, the dynamics of ubiquitin were explored in more detail, showing that the binding selectivity for ubiquitin targets can be tuned by perturbing ubiquitin's pre-existing conformational equilibrium (Michielssens et al. Reference Michielssens, Peters, Ban, Pratihar, Seeliger, Sharma, Giller, Sabo, Becker, Lee, Griesinger and De Groot2014). For most residues, the order parameters derived from the EROS ensemble are lower compared with those predicted by Lipari-Szabo analysis (Chang & Tjandra, Reference Chang and Tjandra2005). Analysis of the supra-τ _c regime thus reveals additional mobility, in good agreement with the structural heterogeneity observed in the EROS ensemble. In summary it is evident that ubiquitin has innate dynamic properties that enable engagement with target proteins through conformational selection mechanisms, i.e. a multitude of different structural states are sampled in absence of target proteins and the presence of a specific target can select a specific ubiquitin structure. Finally, it is important to note that while this section focused on EROS, several other approaches for interpreting dynamics on the basis of RDCs exist (Bouvignies et al. Reference Bouvignies, Markwick, Bruscheweiler and Blackledge2006, Reference Bouvignies, Markwick and Blackledge2007; Tolman, Reference Tolman2002; Tolman et al. Reference Tolman, Al-Hashimi, Kay and Prestegard2001; Ulmer et al. Reference Ulmer, Ramirez, Delaglio and Bax2003).

5.1.4 Adk

Adk catalyzes the magnesium-dependent reversible interconversion of AMP and ATP into two ADP molecules. Adk is vital for cellular energy-homeostasis and present in all organisms. The enzyme harbors two distinct nucleotide binding sub-domains that are denoted ATPlid and AMPbd, respectively. Adk undergoes a large conformational change in response to ligand binding that shuttles the protein into a closed and active conformation where phosphoryl transfer occurs (Rhoads & Lowenstein, Reference Rhoads and Lowenstein1968). Because of its favorable properties – specifically, its tendency to yield excellent NMR spectra (Ådén & Wolf-Watz, Reference Ådén and Wolf-Watz2007; Schrank et al. Reference Schrank, Bolen and Hilser2009), catalysis of a reversible reaction, and large conformational changes (Müller et al. Reference Müller, Schlauderer, Reinstein and Schulz1996; Müller & Schulz, Reference Müller and Schulz1992) – Adk has emerged as one of the principal model systems for analyzing the linkage between dynamics and enzymatic turnover (Arora & Brooks, Reference Arora and Brooks2007; Hanson et al. Reference Hanson, Duderstadt, Watkins, Bhattacharyya, Brokaw, Chu and Yang2007; Nagarajan et al. Reference Nagarajan, Amir, Grupi, Goldenberg, Minton and Haas2011; Schrank et al. Reference Schrank, Bolen and Hilser2009; Shapiro et al. Reference Shapiro, Kahana and Meirovitch2009, Reference Shapiro, Sinev, Sineva, Tugarinov and Meirovitch2000; Shapiro & Meirovitch, Reference Shapiro and Meirovitch2006). In an extensive multi-approach effort, the Kern laboratory has shown that substrate-free Adk from the hyperthermophilic bacterium Aquifex aeolicus samples ‘closed like’ structures (Henzler-Wildman et al. Reference Henzler-Wildman, Thai, Lei, Ott, Wolf-Watz, Fenn, Pozharski, Wilson, Petsko, Karplus, Hübner and Kern2007). This conclusion was drawn from (i) an x-ray structure containing three molecules in the asymmetric unit in which ATPlid and AMPbd adopted orientations that lay on a trajectory from open to closed structures, (ii) ¹⁵N relaxation dispersion measurements that detected motion on a time scale of 950 ± 150 s⁻¹ at 10 °C in hinge regions and also in parts of both nucleotide binding sub-domains, (iii) paramagnetic relaxation enhancement experiments that showed enhanced relaxation in regions that are expected to be far apart in the open state but in close proximity in the closed state and (iv) single molecule FRET measurements that sampled opening/closing events with reaction kinetics of around 7000 s⁻¹ at 20 °C. Taken together, these results suggest that apo Adk samples structural states that lie on a trajectory leading to the catalytically competent closed state. Hence the dynamics that are relevant for substrate binding are already present in the substrate-free enzyme and the enzyme exists in a conformational equilibrium before substrate addition (Henzler-Wildman et al. Reference Henzler-Wildman, Thai, Lei, Ott, Wolf-Watz, Fenn, Pozharski, Wilson, Petsko, Karplus, Hübner and Kern2007). This pre-equilibrium has also been observed in ensemble analyses of RDCs measured for apo Adk (Esteban-Martin et al. Reference Esteban-Martin, Fenwick, Aden, Cossins, Bertoncini, Guallar, Wolf-Watz and Salvatella2014). The pre-existing equilibrium can be perturbed in the directions of closure or opening by addition of the osmolyte TMAO or by removal of one inter-domain hydrogen bond, respectively. Notably, these changes in the equilibrium constant are mirrored by compensatory effects on k _cat and K _M such that the specificity constant (k _cat/K _M) remains invariant (Ådén et al. Reference Ådén, Verma, Schug and Wolf-Watz2012; Kovermann et al. Reference Kovermann, Aden, Grundstrom, Elisabeth Sauer-Eriksson, Sauer and Wolf-Watz2015). This effect, denoted ‘k _cat versus K _M’ compensation, stems from the fact that Adk is rate limited by conformational dynamics (see the section below), and is apparently evolutionarily robust against mutations that simultaneously affect k _cat and K _M values. A more intuitive variation in k _cat/K _M values, i.e. a direct scaling of k _cat/K _M versus the population of a high-energy state, has been observed for the phosphorylation of phospholamban (Masterson et al. Reference Masterson, Yu, Shi, Wang, Gustavsson, Mueller and Veglia2011b) and the Dbl homology domain of Vav1 (Li et al. Reference Li, Martins, Amarasinghe and Rosen2008). The compensatory effects on k _cat and K _M that have been observed in Adk are phenomenologically related to enthalpy-entropy compensation (Dunitz, Reference Dunitz1995; Leffler, Reference Leffler1955), which is well-known to be important for protein folding (Fersht, Reference Fersht2000) but has also been observed in bio-molecular interactions (Cooper et al. Reference Cooper, Johnson, Lakey and Nollmann2001). The catalytic model for Adk catalysis (Wolf-Watz et al. Reference Wolf-Watz, Thai, Henzler-Wildman, Hadjipavlou, Eisenmesser and Kern2004) contains an additional high-energy state corresponding to a substrate-bound open conformation. This state has now been directly observed by NMR spectroscopy (Kovermann et al. Reference Kovermann, Aden, Grundstrom, Elisabeth Sauer-Eriksson, Sauer and Wolf-Watz2015) and it was shown that the interconversion of this high-energy state with a ground state structure that has been characterized by x-ray crystallography is rate limiting for catalysis (as discussed further below).

5.1.5 RNase A

Quantification of enzyme dynamics that are relevant for substrate turnover is most readily performed for enzymes that catalyze reversible reactions (Eisenmesser et al. Reference Eisenmesser, Bosco, Akke and Kern2002; Wolf-Watz et al. Reference Wolf-Watz, Thai, Henzler-Wildman, Hadjipavlou, Eisenmesser and Kern2004). However, many enzymes such as proteases catalyze irreversible reactions. For these enzymes, alternative approaches must be used to mimic and characterize Michaelis complexes (Michaelis & Menten, Reference Michaelis and Menten1913). One option that was explored in a study on RNase A (Beach et al. Reference Beach, Cole, Gill and Loria2005) reported by the Loria laboratory was to use a small unreactive molecule that mimics the contacts that are expected in the Michaelis complex. RNase A primarily catalyzes the cleavage of single stranded RNA between purines and pyrimidines (Katoh et al. Reference Katoh, Yoshinaga, Yanagita, Ohgi, Irie, Beintema and Meinsma1986). Determination of a x-ray structure (at 2·0 Å) of a complex between RNase A and the dinucleotide 5′-phosphotymidine (3′−5′) pyrophosphate adenosine 3′-phosphate (pTppAp) (Russo & Shapiro, Reference Russo and Shapiro1999) established that this small molecule is a relevant mimic of the Michaelis complex for RNase A catalysis. An additional important aspect of pTppAp is that its K _D for RNase A binding is sufficiently low – only 16 nM (Kovrigin et al. Reference Kovrigin, Cole and Loria2003) – that any contributions from ligand association and dissociation can be safely neglected in the analysis of relaxation dispersion experiments. Analysis of relaxation dispersion experiments (Loria et al. Reference Loria, Rance and Palmer1999; Mulder et al. Reference Mulder, Skrynnikov, Hon, Dahlquist and Kay2001b) showed that both apo and pTppAp bound RNase A contain a large set of residues with motions on the order of 1000 s⁻¹ at T = 283 K. Notably, these residues cluster in the same regions in the two forms of the enzyme and given the K _D value for pTppAP binding it was concluded that the dynamics observed in the presence of pTppAp are intra-molecular and independent of association and dissociation kinetics. Hence, the dynamics observed in the model Michaelis complex are already present in the apo enzyme. Based on a comparison of the exchanging states’ chemical shift signs as determined using a HSQC/HMQC approach (Skrynnikov et al. Reference Skrynnikov, Dahlquist and Kay2002), and a direct measurement of the difference between the apo and pTppAp states, the authors concluded that the minor state observed in the apo state resembles the substrate-bound enzyme while the minor state of the pTppAp-bound complex resembles the conformation of the apo state. Subsequent studies on RNase A have shown that its dynamic processes are orchestrated through networks that are operational over long distances within the enzyme (Doucet et al. Reference Doucet, Khirich, Kovrigin and Loria2011; Kovrigin & Loria, Reference Kovrigin and Loria2006; Watt et al. Reference Watt, Shimada, Kovrigin and Loria2007). For instance the global dynamic process observed in pTppAp-bound RNaseA can be disturbed by introducing the substitution D121A: even though position 121 is distant from the active site and does not influence the active site properties, the D121A substitution causes a 90% reduction in k _cat. Consequently, the slow dynamics observed for the wild type enzyme in the Michaelis complex, which involve a concerted process occurring at 1900 s⁻¹, are replaced by a sequence of two processes occurring at 2400 and 730 s⁻¹, respectively (Kovrigin & Loria, Reference Kovrigin and Loria2006). Hence concerted dynamic processes in enzymes are dependent on a fine balance of interactions and can be highly sensitive to subtle changes.

5.1.6 Maltose binding protein (MBP)

MBP is responsible for maltose uptake (Boos & Shuman, Reference Boos and Shuman1998) and consists of two domains that are connected by three linker segments. Structures of apo (Sharff et al. Reference Sharff, Rodseth, Spurlino and Quiocho1992) and holo (Spurlino et al. Reference Spurlino, Lu and Quiocho1991) states determined by x-ray crystallography have revealed a hinge-bending motion within the linker region resulting in a 35° rigid body reorientation of the relative domain orientations (Sharff et al. Reference Sharff, Rodseth, Spurlino and Quiocho1992). MBP has been extensively characterized by NMR spectroscopy in both the apo and holo states, and RDC analysis showed that these two states predominantly populate the crystallographic structures in solution (Evenäs et al. Reference Evenäs, Tugarinov, Skrynnikov, Goto, Muhandiram and Kay2001). PRE can be utilized to detect minor states (Iwahara & Clore, Reference Iwahara and Clore2006; Tang et al. Reference Tang, Iwahara and Clore2006) that cannot be observed using methods based on RDCs, which are linear weighted averages of all species present in solution. (Tang et al. Reference Tang, Schwieters and Clore2007). Using PRE experiments, it was shown that the holo state in solution is well-described by the crystallographic holo structure. In contrast, the apo state was found to display PRE values that are inconsistent with either apo or holo structures. This discrepancy was attributed to a minor state in equilibrium with the major apo structure. The structure of the minor state was determined with a conjoined rigid-body/torsion-angle simulated annealing refinement (Clore & Bewley, Reference Clore and Bewley2002) and was found to correspond to a partially closed MBP structure. Hence, apo MBP samples high-energy structures that are probably on the trajectory towards the ‘bound’ conformation, but MBP appears to require interaction with substrate molecules before it can adopt the fully closed structure (Tang et al. Reference Tang, Schwieters and Clore2007).

5.1.7 Additional examples

There are several other cases in which NMR experiments have suggested transient populations of functionally important states. Notable examples include HIV protease (Ishima et al. Reference Ishima, Freedberg, Wang, Louis and Torchia1999), estrogen receptor DNA-binding domain (Wikström et al. Reference Wikström, Berglund, Hambraeus, Van Den Berg and Härd1999), the C-terminal domain of Sendai virus nucleoprotein (Jensen et al. Reference Jensen, Houben, Lescop, Blanchard, Ruigrok and Blackledge2008; Schneider et al. Reference Schneider, Maurin, Communie, Kragelj, Hansen, Ruigrok, Jensen and Blackledge2015), Abl and Src kinases (Agafonov et al. Reference Agafonov, Wilson, Otten, Buosi and Kern2014; Wilson et al. Reference Wilson, Agafonov, Hoemberger, Kutter, Zorba, Halpin, Buosi, Otten, Waterman, Theobald and Kern2015), calmodulin (Gsponer et al. Reference Gsponer, Christodoulou, Cavalli, Bui, Richter, Dobson and Vendruscolo2008). In addition, it has been suggested that the GPCR β2AR uses a conformational selection mechanism (Deupi & Kobilka, Reference Deupi and Kobilka2010), clearly demonstrating that concepts arising from the application of NMR spectroscopy to established model systems are likely to be generally relevant to protein function.

5.2.1 Adk

Adk catalyzes the magnesium-dependent interconversion of AMP and ATP into two ADP molecules. The reaction is fully reversible and the equilibrium constant in the direction of ADP formation is 2·8 in the absence of magnesium (Rundqvist et al. Reference Rundqvist, Ådén, Sparrman, Wallgren, Olsson and Wolf-Watz2009). Since the reaction catalyzed by Adk is reversible, it is possible to study the dynamics of the enzyme during turnover conditions using endogenous substrates. In a study from the Kern laboratory, the dynamics of mesophilic (Escherichia coli) and hyperthermophilic (Aquifex aeolicus) Adk were studied by means of ¹⁵N relaxation dispersion measurements (Wolf-Watz et al. Reference Wolf-Watz, Thai, Henzler-Wildman, Hadjipavlou, Eisenmesser and Kern2004). The substrate concentrations used (20 mM) were well above the K _M values of the enzymes, thus ensuring that the quantified slow motions were of intramolecular nature. Due to the catalytic action of the enzymes, the substrate mixtures for which the dynamics were quantified corresponded to equilibrium mixtures (i.e. AMP, ATP and ADP were all present simultaneously). The process that produced the observed dispersion profiles was identified by showing that the dynamics of the hyperthermophilic variant in the presence of the equilibrium mixture were very similar to those observed in a mixture containing AMP and the non-hydrolysable analogue AMPPNP. It was thus concluded that the detected motion corresponded to opening and closing dynamics in the presence of the bound substrate. It was further found that the microscopic rate constants for domain opening closely matched the catalytic turnover numbers obtained from a coupled ATPase assay (Rhoads & Lowenstein, Reference Rhoads and Lowenstein1968). In conclusion, on the basis of converging rate constants between catalytic turnover and conformational dynamics it was inferred that these two Adk variants are rate limited by conformational dynamics (Wolf-Watz et al. Reference Wolf-Watz, Thai, Henzler-Wildman, Hadjipavlou, Eisenmesser and Kern2004). The finding also resolved the question of why thermophilic enzymes often display lower activities than their mesophilic counterparts at ambient temperatures (Zavodszky et al. Reference Zavodszky, Kardos, Svingor and Petsko1998). In the case of Adk, the entire activity difference between the hyperthermophilic and mesophilic variants at ambient temperatures is explained by the rate constants of conformational dynamics, which are significantly slower in the hyperthermophile (Wolf-Watz et al. Reference Wolf-Watz, Thai, Henzler-Wildman, Hadjipavlou, Eisenmesser and Kern2004). In a recent paper from the same laboratory it was shown that the rate constant of the chemical transformation is indeed significantly faster than that of conformational dynamics in Adk (Kerns et al. Reference Kerns, Agafonov, Cho, Pontiggia, Otten, Pachov, Kutter, Phung, Murphy, Thai, Alber, Hagan and Kern2015). As a final note, the use of enzymes from different organisms with different catalytic properties in comparative studies is a powerful way of addressing functional questions while avoiding epistasis (as discussed in more detail below). While it is also possible to investigate functional questions by using point mutations, this carries the risk of changing both the targeted property and additional important properties of the protein.

5.2.2 RNase A

Since RNase A catalyzes an irreversible reaction it is not possible to quantify its dynamics during catalytic turnover as was done for Adk. Therefore, the Loria group used a different approach to investigate the motions of RNase A that are relevant to its turnover (Beach et al. Reference Beach, Cole, Gill and Loria2005). In short, a molecule denoted pTppAp was carefully analyzed and a crystallographic structure of this molecule in complex with RNase A revealed that the specific base and phosphate interactions satisfy the established criteria for a realistic substrate-mimic. Using the approaches discussed above, it was found that the dynamics of a pTppAp:RNase A complex as revealed by relaxation dispersion experiments corresponded to the interconversion of RNase A structures resembling the substrate-free and substrate-bound states. As discussed in the paper (Beach et al. Reference Beach, Cole, Gill and Loria2005) the rate constant of conformational interconversion of RNase A in the presence of pTppAp is similar to the k _cat value measured for real substrates. Therefore, it was suggested that conformational dynamics are the rate limiting step for RNase A catalysis.

5.2.3 DHFR

As discussed above DHFR catalyzes the reduction of DHF to THF through a number of populated intermediates. Quantitative analysis of conformational exchange rate constants from relaxation dispersion profiles provided new insight into the influence of dynamics on the catalytic efficiency of DHFR (Boehr et al. Reference Boehr, Mcelheny, Dyson and Wright2006b). It was found that the first-order rate constant for the rate determining release of THF from the E:NADPH:THF complex (12·5 s⁻¹) matched that of the conformational transition between the ground state (E:NADPH:THF) and a high-energy state resembling the E:NADPH complex. This observation has the interesting implication that product release probably occurs from the high-energy state, which is important not just in the context of dynamics but for enzymology in general: it clearly shows that studying ground state structures alone is not always sufficient to understand enzymes’ catalytic power. It was also found that the rate constant for hydride transfer was very similar to that for the conformational transition between the ground state of the E:NADP+:THF and an excited state resembling the E:NADP+:folate complex (which was used as a model for the Michaelis complex corresponding to E:NADPH:DHF). Taken together, these results clearly show that the rate constants for conformational dynamics have profound effects on the overall catalytic efficiency of DHFR (Boehr et al. Reference Boehr, Mcelheny, Dyson and Wright2006b).

5.2.4 Tyrosine phosphatases

Protein tyrosine phosphatases (PTPs) catalyze the cleavage of the tyrosine phosphate monoester (pY) of their protein substrates followed by subsequent hydrolysis of the phosphoenzyme intermediate. Thus, the overall turnover of these enzymes is dictated by the two rate constants k _cleavage and k _hydrolysis. In a comparative study (Whittier et al. Reference Whittier, Hengge and Loria2013), the dynamics associated with the cleavage reaction were quantified for YopH, a virulence factor from Yersinia (Brubaker, Reference Brubaker1991), and for PTP1B, a human phosphatase involved in regulating leptin, insulin and epidermal growth factor signaling (Zhang, Reference Zhang2001). Although the two enzymes’ substrate interactions are very similar, their k _cat values differ significantly: 700–100 s⁻¹ for YopH and 15–30 s⁻¹ for PTP1B at T = 293 K (Zhang et al. Reference Zhang, Thieme-Sefler, Maclean, Mcnamara, Dobrusin, Sawyer and Dixon1993). The enzymes harbor a ten residue segment known as the WPD loop that contains an aspartic acid which serves as the general acid that protonates the leaving group. The WPD loop undergoes a substantial displacement on going from the open (inactive) to the closed (active) state, which places the general acid in close proximity to the oxygen of the leaving group of the substrate. By using both relaxation dispersion and ¹H-¹⁵N-TROSY Hahn-echo experiments (Wang et al. Reference Wang, Rance and Palmer2003) it was found that the rate constant of WPD loop closure in each enzyme closely matched their rate constants in the presence and absence of a peptide substrate mimic. Thus it appears that the cleavage reaction supported by the action of the general acid is rate limited by the closing motion of the WPD loop (Whittier et al. Reference Whittier, Hengge and Loria2013). The actual chemical reaction, i.e. bond breaking and bond making in the transition state, is much faster (occurring on a femtosecond time scale) than the loop motions that were detected by NMR.

5.4.1 Coupled folding/binding

Coupled folding and binding pathways directly link protein folding and biological function; in such cases, the folding and functional energy landscapes overlap (Olsson & Wolf-Watz, Reference Olsson and Wolf-Watz2010). Proteins that are unfolded in solution in vitro are often found to be folded in their functional context (i.e. under cellular conditions) because they fully or partially fold on binding to another molecule, which may be another protein, a nucleic acid, a membrane, or a small molecule. Two major pathways for coupled binding and folding have been proposed: folding after binding (which corresponds to an induced fit) and conformational selection. In the folding after binding pathway, the unfolded protein binds to the target and then folds into the final structure, thus utilizing the target molecule as a folding template (Sugase et al. Reference Sugase, Dyson and Wright2007). On the other hand, in the conformational selection pathway a small fraction of the protein is folded when unbound and binding selects the folded form. Intermediate pathways between these two extremes also exist where a small amount of preformed structure might be required for the initial encounter complex. In the following sections we highlight cases where NMR has been used to describe coupled folding and binding processes between proteins and different target molecules such as proteins, lipids, small molecules and nucleic acids.

5.4.1.1 Phosphorylated kinase inducible activation domain (pKID)-KIX

One protein that follows the folding after binding pathway is the pKID of the transcription factor CREB. pKID exists as an unfolded protein in solution in vitro (Radhakrishnan et al. Reference Radhakrishnan, Perez-Alvarado, Parker, Dyson, Montminy and Wright1997) but folds upon binding to the KIX domain of the CREB binding protein (Parker et al. Reference Parker, Ferreri, Nakajima, Morte, Evans, Koerber, Hoeger and Montminy1996). The structure of the pKID-KIX complex has been solved by NMR (Radhakrishnan et al. Reference Radhakrishnan, Perez-Alvarado, Parker, Dyson, Montminy and Wright1997), revealing that the pKID forms two helices and that the C-terminal helix in particular is very well-defined, interacting specifically with KIX (Fig. 5). The binding process was studied using a combination of ¹⁵N-relaxation dispersion and chemical shift analysis of the pKID-KIX complex (Sugase et al. Reference Sugase, Dyson and Wright2007). An analysis of chemical shifts of pKID as a function of the relative concentration of KIX showed that most of its amino acid residues experience slow exchange (Sugase et al. Reference Sugase, Dyson and Wright2007) while a subset of residues experience fast exchange at sub stoichiometric KIX concentrations. Relaxation dispersion experiments showed that the protein was present in three different conformations: free protein, an intermediate, and the fully folded complex. This three-state model was chosen instead of a two-state model even though the latter yielded an estimated K _D value that agreed well with ITC data (Zor et al. Reference Zor, De Guzman, Dyson and Wright2004). These observations led to the conclusion that an encounter complex is in fast exchange with unbound pKID leading to a folding process that occurs via an intermediate state and in which KIX serves as a folding template (Sugase et al. Reference Sugase, Dyson and Wright2007).

Fig. 5. Coupled folding and binding illustrated with the NMR solution structure of the pKID:KIX complex. The structure of KIX is colored in gray, whereas the two helices of pKID are colored in light- and bright orange, respectively. The location of the phosphorylation site Serine 133 is shown in blue in a side chain representation. This figure was adapted from reference Radhakrishnan et al. (Reference Radhakrishnan, Perez-Alvarado, Parker, Dyson, Montminy and Wright1997).

5.4.2 Cracking or ‘order-disorder-order’ transitions

It has been postulated that one way of increasing the rate constants of functional transitions in proteins is by ‘cracking’, i.e. the unfolding of localized polypeptide segments in the transition state structure (Hyeon & Onuchic, Reference Hyeon and Onuchic2007; Miyashita et al. Reference Miyashita, Onuchic and Wolynes2003). This postulate builds on a notion from energy landscape theory (Frauenfelder et al. Reference Frauenfelder, Sligar and Wolynes1991, Reference Frauenfelder, Chen, Berendzen, Fenimore, Jansson, Mcmahon, Stroe, Swenson and Young2009; Onuchic & Wolynes, Reference Onuchic and Wolynes1993) that proteins constantly fluctuate between states in a stochastic way. During a functional transition, a protein may build up strain that is released through partial unfolding once it has exceeded a certain threshold. This unfolding event may then cause a gain in conformational entropy that can reduce the free energy barrier for the transition (Whitford, Reference Whitford2013). In essence the idea is that a protein that populates two different and completely folded structural states in inactive and active conformations can transiently populate a partially disordered state in the transition state. In analogy to such ‘disorder-order’ transitions, cracking models can be formulated in terms of an ‘order-disorder-order’ event (Olsson & Wolf-Watz, Reference Olsson and Wolf-Watz2010). Cracking is inherently difficult to probe experimentally but there are cases when its occurrence has been inferred from simulations. Proteins suggested to undergo cracking include Adk (Whitford et al. Reference Whitford, Miyashita, Levy and Onuchic2007, Reference Whitford, Onuchic and Wolynes2008), epidermal growth factor receptor (Shan et al. Reference Shan, Arkhipov, Kim, Pan and Shaw2013), calmodulin (Tripathi & Portman, Reference Tripathi and Portman2009) and influenza hemagglutinin (Lin et al. Reference Lin, Eddy, Noel, Whitford, Wang, Ma and Onuchic2014). Here we will briefly summarize the computational results for Adk and cracking in relation to a reaction coordinate linking open (inactive) and closed (active) states. Cracking was inferred from simulations in which the system was allowed to follow low frequency collective modes (Miyashita et al. Reference Miyashita, Onuchic and Wolynes2003) and from coarse grained simulations using structure-based potentials (Taketomi et al. Reference Taketomi, Ueda and Go1975; Whitford et al. Reference Whitford, Miyashita, Levy and Onuchic2007). A converging picture emerged from these studies which suggested that, segments in which cracking were likely could be found in both of the nucleotide-binding domains of Adk. A fundamental requirement for cracking to occur is that the local stabilities of the relevant polypeptide sequences must be low enough to allow strain release via local unfolding. This appears to be the case for Adk, for which NMR-based H/D exchange experiments have clearly demonstrated that the flexible nucleotide binding domains are significantly less stable than the protein is globally (Rundqvist et al. Reference Rundqvist, Ådén, Sparrman, Wallgren, Olsson and Wolf-Watz2009). Thus, the underlying energetics required to enable cracking are present in Adk. In an experimental approach designed to test the cracking model (Olsson & Wolf-Watz, Reference Olsson and Wolf-Watz2010) point mutations in Adk were designed to destabilize a segment of the ATPlid that was suggested to crack during the enzyme's functional transition. NMR monitoring revealed that the mutants were folded and adopted the correct structural motifs at the extremes of the reaction coordinate (i.e. in the open and closed states). However, the equilibrium constant for the folding/unfolding reaction was shifted more towards the unfolded state in the mutated variants. The mutants’ functionality was evaluated and benchmarked against the wild type in two experiments: (i) an ATP binding affinity assay probed by ITC, and (ii) an enzymatic activity assay probed using a coupled ATPase assay (Rhoads & Lowenstein, Reference Rhoads and Lowenstein1968). Notably the mutated and destabilized Adk variants displayed a fifty fold improved ATP binding affinity (K _D values decreased from 50 to 1 µM). This is a remarkable result since in general destabilization of a protein is expected to impair functionality. The result is fully consistent with the idea that the mutations act to push the enzyme along the free energy surface in a way that is coupled to conformational change, and that the transition state structure is more disordered than the stable ground states. A related increase in binding affinity in response to a perturbation of native contacts has been observed for the binding of a peptide to the fibronectin extradomain B via a local unfolding mechanism (Yu et al. Reference Yu, Shin, Kim, Kim, Ryu, Cheong, Ahn, Jon and Suh2014). Since Adk is rate limited by the opening of its substrate binding domains, these mutations should in fact reduce the enzyme's catalytic efficiency (with the assumption that the free energy surfaces are robust to the mutations). This matches experimental observations: the variants retain only approximately 3% of wild type activity. Taken together, the experimental observations are fully consistent with the cracking model but do not provide definite evidence of its validity.

5.4.3 Coupled unfolding/binding

As discussed above, coupled folding and binding appears to be a fundamental concept in molecular recognition. Having established this model, it is not farfetched to assume that coupled unfolding and binding reactions may also be relevant in biological recognition processes. This has indeed recently been shown in an elegant paper by Suh and co-workers (Yu et al. Reference Yu, Shin, Kim, Kim, Ryu, Cheong, Ahn, Jon and Suh2014). The authors show in a very convincing manner that a β-strand in the fibronectin extra domain B (EDB) detaches from the core of the protein structure upon binding of a class of high-affinity peptides called aptides (Kim et al. Reference Kim, Kim, Jung, Lee, Kim, Suh and Jon2012). In the bound complex, the detached β-strand is replaced with a strand from the aptide. The work rests on a firm structural basis and the structures of both ligand-free EDB and a complex between EDB and an aptide were solved by NMR spectroscopy. Perhaps the most notable result is that the fast ps-to-ns mobility is significantly increased in the complex with the detached β-strand. The mechanism put forward by the authors thus involves a coupled local unfolding and binding event. The final result, i.e. a β-strand donation from the ligand to the protein, is fundamentally related to the ‘donor strand complementation’ model that was discovered for chaperone-adhesin complexes in bacterial pili (Choudhury et al. Reference Choudhury, Thompson, Stojanoff, Langermann, Pinkner, Hultgren and Knight1999; Sauer et al. Reference Sauer, Futterer, Pinkner, Dodson, Hultgren and Waksman1999). In a broader sense, it seems that cooperative folding reactions are fundamental in molecular recognition and that several flavors of folding are utilized, as exemplified by systems making use of ‘coupled folding-binding’, ‘coupled unfolding-binding’ and ‘cracking’ mechanisms for recognition of their respective targets. Since the cooperative folding reaction is evolutionarily robust, it comes as no surprise that it is used to add functionality to proteins.

5.4.4 Folding by phosphorylation

Most binding events leading to folding are driven by binding energetics arising from non-covalent interactions. The intrinsically disordered protein 4E-BP2 represents a notable exception in that its folding is induced by phosphorylation. The phosphorylation-driven folding of 4E-BP2 was detected on the basis of differences in ¹⁵N-hNOEs and the dispersion of chemical shifts observed in a ¹H-¹⁵N-HSQC spectrum for phosphorylated and non-phosphorylated versions of the protein (Bah et al. Reference Bah, Vernon, Siddiqui, Krzeminski, Muhandiram, Zhao, Sonenberg, Kay and Forman-Kay2015). Since the protein's role is to bind to eIF4E in order to suppress cap-dependent translational initiation, the strength of the interaction between 4E-BP2 and eIF4E was evaluated using ITC. These titration experiments showed a significant decrease in binding affinity for the phosphorylated form, with K _D increasing from 3 to 12 320 nM. This suggests that the phosphorylation event suppresses binding and thereby activates cap-dependent translation (Bah et al. Reference Bah, Vernon, Siddiqui, Krzeminski, Muhandiram, Zhao, Sonenberg, Kay and Forman-Kay2015).

5.4.5 Conformational entropy

The energetics underlying molecular recognition are described by the standard Gibbs free energy, ΔG° = ΔH°-TΔS°, and the relationship between the standard free energy and the equilibrium constant, ΔG° = −RTlnK _D. Both the enthalpic (ΔH°) and entropic (ΔS°) components can be obtained from ITC experiments. However, these components reflect total changes in the energetics of the protein, the ligand and the solvent (including any co-solvents such as ions). Thus a fundamental problem in understanding energetics data obtained by ITC is the difficulty of deconvoluting the individual components of the system of interest. The entropic component is of particular interest and since the overall entropy contains a large desolvation term it is challenging to quantify the contribution from protein conformational entropy to a binding event. However, there are NMR approaches that can be used to estimate changes in a protein's conformational entropy based on analyses of order parameters (Akke et al. Reference Akke, Brüschweiler and Palmer1993a; Li & Bruschweiler, Reference Li and Bruschweiler2009; Wand, Reference Wand2001; Yang & Kay, Reference Yang and Kay1996). In the following section we describe some cases where estimates of protein conformational entropy provided new insight into molecular recognition.

5.4.6 Encounter complexes

The rapid and specific association of protein complexes is a central component of many biological processes. For diffusion-controlled binding, the basal association rate constants are restricted by diffusion and the geometric constraints of binding surfaces. The binding process can be further slowed down through isomerization reactions on the protein (such as conformational changes) that occur after the initial encounter (Schreiber, Reference Schreiber2002). A minimal reaction for the association between two proteins, A and B, is then:

(13) $$A + B_{\mathop \leftarrow \limits_{{k_{ - 1}}}} ^{\mathop \to \limits^{{k_1}}} A{B^{\rm *}}{}_{\mathop \leftarrow \limits_{{k_{ - 2}}}} ^{\mathop \to \limits^{{k_2}}} A{B^{{\rm **}}}{}_{\mathop \leftarrow \limits_{{k_{ - 3}}}} ^{\mathop \to \limits^{{k_3}}} AB$$

where AB* is an encounter complex, AB** is an intermediate that is obtained following the isomerization of AB*, and AB is the stereospecific complex. Typical association rate constants (k ₁ in the above equation) are in the range of 10⁵–10⁹ M⁻¹ s⁻¹ and the absolute value can be strongly dependent on electrostatic interactions and ionic strength (Schreiber & Fersht, Reference Schreiber and Fersht1996). When a non-specific encounter complex has been formed, a protein can engage in a 2D diffusion process that will eventually lead to the formation of the stereospecific complex. Since encounter complexes consist of several transient and weakly bound conformations, they are silent to many structural biology techniques. However, they can be studied using NMR because weak binding (K _D values on the order of mM) are readily detected. A fundamental question relates to the structure of the encounter complex (AB*); as expected, it is most adequately described as an ensemble of conformers. Below we briefly review two cases in which NMR has been used to obtain detailed information on encounter complexes.

5.5.1 GroEL

Chaperonins, a sub-class of the larger group of molecular chaperones, are assembled into cylindrical, stacked ring structures with large internal cavities that can encapsulate substrate or client proteins (Braig et al. Reference Braig, Otwinowski, Hegde, Boisvert, Joachimiak, Horwich and Sigler1994). These proteins are found in all cell types in all organisms where they facilitate folding, assembly and transport. The most extensively studied chaperonin, both structurally and mechanistically, is the GroEL-GroES machinery (Horwich & Fenton, Reference Horwich and Fenton2009). GroEL is a 780-kDA assembly consisting of two stacked cylindrical units, each of which is built up from seven identical 56-kDa subunits. Encapsulation and release of substrate proteins is accomplished through a series of ATP-driven conformational changes to GroEL together with recruitment of the co-chaperone GroES (Horwich & Fenton, Reference Horwich and Fenton2009). Questions under considerable debate in the scientific literature are: (1) how GroEL interacts with substrate proteins and (2) the mechanism of GroEL-mediated protein folding. As discussed below, NMR has provided important insights into these challenging questions.