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Keywords:

  • hen egg white lysozyme;
  • carbohydrate binding;
  • conformational entropy;
  • NMR relaxation;
  • backbone and methyl side chain dynamics

Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. Results and Discussion
  5. Materials and Methods
  6. Acknowledgements
  7. References

It has become clear that the binding of small and large ligands to proteins can invoke significant changes in side chain and main chain motion in the fast picosecond to nanosecond timescale. Recently, the use of a “dynamical proxy” has indicated that changes in these motions often reflect significant changes in conformational entropy. These entropic contributions are sometimes of the same order as the total entropy of binding. Thus, it is important to understand the connections amongst motion between the manifold of states accessible to the native state of proteins, the corresponding entropy, and how this impacts the overall energetics of protein function. The interaction of proteins with carbohydrate ligands is central to a range of biological functions. Here, we examine a classic carbohydrate interaction with an enzyme: the binding of wild-type hen egg white lysozyme (HEWL) to the natural, competitive inhibitor chitotriose. Using NMR relaxation experiments, backbone amide and side chain methyl axial order parameters were obtained across apo and chitotriose-bound HEWL. Upon binding, changes in the apparent amplitude of picosecond to nanosecond main chain and side chain motions are seen across the protein. Indeed, binding of chitotriose renders a large contiguous fraction of HEWL effectively completely rigid. Changes in methyl flexibility are most pronounced closest to the binding site, but average to only a small overall change in the dynamics across the protein. The corresponding change in conformational entropy is unfavorable and estimated to be a significant fraction of the total binding entropy.


Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. Results and Discussion
  5. Materials and Methods
  6. Acknowledgements
  7. References

The interaction of proteins with small-molecule ligands and other macromolecules is a central feature of biochemical function. A fundamental goal of modern biophysical chemistry is to establish the principles underlying these generally high-affinity interactions. The formation of protein complexes involves a complicated manifold of interactions that often includes dozens of amino acids and a significant contact area.1 The origins of high-affinity interactions are quite diverse and complex, presenting a significant computational and analytical challenge.2 Indeed, structure-based design of pharmaceuticals has been largely impeded by this barrier.3 Over the past decade, there has been increasing recognition that significant changes in protein conformational entropy can accompany the interaction of folded proteins with both small molecule and macromolecular ligands.4 Decomposition of the total binding free energy emphasizes that the entropy of binding is composed of contributions from the protein, the ligand, and the solvent:

  • equation image(1)

Historically, the contributions by solvent entropy (ΔSsolvent) have taken center stage and are usually framed in terms of the so-called hydrophobic effect.5 Indeed, hydrophobic solvation of proteins by water continues to be the subject of extensive analysis.6, 7 In principle, however, contributions from conformation entropy of the structured protein (ΔSconf), conformation entropy of the ligand (ΔSligand), and rotational and translational entropy of both the ligand and the protein (ΔSRT) supplement the contribution of solvent entropy (ΔSsolvent) to the overall change in entropy (ΔStot) in a system upon ligand binding.8

Experimental access to changes in conformational entropy of proteins upon association with ligands has been difficult. Recently, solution NMR spectroscopy has emerged as a viable method to obtain quantitative estimates of protein motion4, 9 and to use this information as a proxy for conformational entropy.10–13 Although the direct model-dependent approach originally used11, 12 is fraught with qualifications,4 a recent empirical calibration of the dynamical proxy for conformational entropy provides a more general foundation.13 Here, we use these methods to focus on the interaction of a protein with a small carbohydrate ligand. Recently, several NMR-based studies have indicated that the interaction of non-catalytic proteins with carbohydrate ligands may involve favorable changes in the internal dynamics of the proteins and the corresponding conformational entropy,14–16 which is in distinct contrast to most protein–protein interactions.4 To determine the generality of this observation, we examine the influence of a short carbohydrate inhibitor binding to the classical hydrolase, hen egg white lysozyme (HEWL).

HEWL was the first enzyme to have its three-dimensional structure determined by X-ray diffraction17 and has since served as a paradigm for a wide range of biochemical and biophysical studies. The double-displacement catalytic mechanism proposed initially by Koshland,18 involving a covalent intermediate with the substrate, has supplanted19 the long-held Philips mechanism that centered on a long-lived oxocarbenium ion intermediate.17 Here, we are pursuing the thermodynamics of the interaction of an inhibitory carbohydrate with HEWL. Lysozymes catalyze the hydrolysis of β-(1,4)-linkages between N-acetylmuramic acid (MurNAc) and N-acetyl-D-glucosamine (GlcNAc) in peptidoglycans. Additionally, some lysozymes, including that from hen egg whites, can cleave between GlcNAc residues in chitodextrins such as chitin.20 HEWL can accommodate up to six GlcNAc residues of a chitin polymer, each binding in six subsites along a cleft of the protein. Cleavage occurs at the linkage between the GlcNAc residues occupying the third and fourth subsites19, 21 and thus does not readily occur with molecules consisting of only one (GlcNAc), two (chitobiose), or three (chitotriose) GlcNAc residues.22, 23 These smaller molecules do, however, bind with reasonable affinity (Kd ∼ 10−4–10−6M)23, 24 and therefore act as natural competitive inhibitors. Using isothermal titration calorimetry, the binding of both chitobiose and chitotriose to HEWL has been found to be enthalpically driven over a wide range of temperatures.23 The extent of the contribution from conformational entropy manifested as fast internal motion of the protein, however, is unclear, as indicated by Eq. (1). To examine this issue, we have carried out a comprehensive characterization of the subnanosecond timescale dynamics of the backbone and of the methyl-bearing side chains of HEWL in the apo state and in complex with chitotriose.

Results and Discussion

  1. Top of page
  2. Abstract
  3. Introduction
  4. Results and Discussion
  5. Materials and Methods
  6. Acknowledgements
  7. References

Backbone dynamics

The analysis of 15N backbone amide T1, T2, and nuclear overhauser effect (NOE) relaxation measurements determined that both the apo and chitotriose-bound states tumble isotropically with essentially the same overall molecular correlation time: 5.3 ± 0.1 ns. The average backbone amide N[BOND]H-squared generalized order parameter (O2NH) of the apo state is determined here to be 0.838 ± 0.001. Previously determined average backbone amide order parameters of apo-HEWL in slightly more acidic environments were marginally more rigid (0.865 ± 0.00125 and 0.871 ± 0.00326), but individual order parameters from both studies followed similar trends to the data measured here. The average backbone amide N[BOND]H-squared generalized order parameter (Omath image) of the chitotriose-bound state is determined to be 0.853 ± 0.001 (compared with the previously determined26 0.845 ± 0.004). The difference of the averages indicates only a slight decrease in motion at the backbone upon binding a ligand, compared with a slight increase seen previously.26 The overall trends in order parameters are conserved between the two states, indicating that there is no large overall effect of chitotriose binding on the fast motions of the backbone of HEWL.

Methyl-bearing side chain dynamics

Of the 61 methyl groups in HEWL, Lipari–Szabo-squared generalized methyl axis order parameters (Omath image) were obtained for 52 in both states. The apo state had Omath image parameters ranging from 0.16 to 1 (average of 0.714 ± 0.019), whereas the chitotriose-bound state had order parameters ranging from 0.20 to 1 (average of 0.733 ± 0.026). Histograms of the distribution of Omath image parameters of the apo protein and the HEWL–chitotriose binary complex are shown in Figure 1. Three types or classes of motion of methyl-bearing side chains can be revealed by NMR relaxation.4 The so-called J-class is centered around an Omath image value of ∼0.35 and involves motion of the methyl group between rotameric wells, leading to averaging of the associated J-coupling. The α-class is centered around an Omath image value of ∼0.65 and has a smaller contribution from motions that lead to rotameric interconversion and generally reflects large amplitude motion within a single rotameric well. The ω-class is centered around an Omath image value of ∼0.85 and has highly restricted motion within a single rotameric well that is somewhat reminiscent of the uniform rigidity of most backbone sites. Both the apo and binary states of HEWL have, relative to most proteins, low populations of the J-class, somewhat diminished α-classes and enriched contributions from the ω-class. Thus, from the point of view of fast methyl-bearing side chain dynamics, HEWL is an unusually rigid protein in both its free and complexed states. Of proteins that have been examined in this way, only those having high-affinity cofactors (flavodoxin) or covalently attached prosthetic groups (cytochrome c and c2) have comparable general rigidity.27–29 There is no obvious spatial clustering of rigidity or flexibility in the molecular structure of either state (Fig. 2).

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Figure 1. Distribution of methyl symmetry axis-squared generalized order parameters of HEWL in two states. The apo state is shown in gray, and the binary or chitotriose-bound state is shown in orange.

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Figure 2. Spatial distribution of fast methyl-bearing side chain dynamics of HEWL in the (A) apo and (B) chitotriose-bound states (using PDB codes 1LZA30 and 1LZB,30 respectively). The protein backbone is rendered as a gray ribbon and in (B) the chitotriose is shown in orange. Each methyl site is depicted as a sphere and colored according to its methyl symmetry axis order parameter (Omath image) in the given state where blue indicates sites that are largely rigid (and thus have high Omath image values) and red indicates sites that are largely flexible (and thus have low Omath image values).

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The response of the side chain motion to chitotriose binding is complex and hetergeneous, with some sites increasing the amplitude of their motion while others are decreased. The changes in methyl axis-squared generalized order parameters across the molecule average to nearly zero ( equation image = 0.019 ± 0.004). Additionally, a single Gaussian curve fit to a histogram of ΔOmath image values has a center of nearly zero (0.037 ± 0.011) and a fitted width of 0.163 ± 0.015 (Fig. 3). An iterative implementation of the interquartile range method31 identified only a single outlier, the I98δ1, which is located at the interface with chitotriose. Although the average dynamics of the molecule, which will determine the overall thermodynamic impact (see below), changed only slightly, there is considerable variance in the dynamical response to ligand binding to the protein [Figs. 3 and 4(A)].

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Figure 3. Distribution of changes in fast internal dynamics of HEWL methyl-bearing side chains upon binding chitotriose. The solid line corresponds to the best fit to a single Gaussian (R = 0.972) centered at 0.037 ± 0.011 with a width of 0.163 ± 0.015.

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Figure 4. Site-to-site comparison of fast methyl-bearing side chain dynamics in the apo state and binary complex of HEWL with chitotriose. Colored boxes span regions of the three classes of motion observed for methyl-bearing side chains.4 The dashed line along the diagonal is shown to guide the eye. Panel A shows all available pairwise comparisons. Only a few side chains change motional class, that is, fall well outside the boxed areas. Panel B is an expansion of the ω-class region. Labeled are those sites that become effectively completely rigid upon the binding of chitotriose. These residues form a core in the protein (Fig. 6). Also labeled are sites that are effectively completely rigid in the apo state and become dynamic in the complex.

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Binding of chitotriose results in a few side chains changing motional class (Fig. 4). The probes include I78δ1, which goes from the highly dynamic rotamer averaging J-class to the rotamer restricted α-class upon binding chitotriose and I98δ1, which moves from the highly restricted ω-class in the apo state to the highly dynamic J-class in the complex. Other examples of class conversion are evident and are labeled in Figure 4(A). The distribution of the Omath image parameters across the apo and binary states of the HEWL protein does not show the presence of a statistically significant spatial clustering of motional changes within the protein (Fig. 5). Nevertheless, a most remarkable redistribution within the ω-class occurs upon binding of chitotriose. A significant number of relatively rigid methyl-bearing side chains of the apo state become effectively completely immobile upon binding of the ligand [Fig. 4(B)]. These residues form a contiguous grouping that spans the core of the protein including the two catalytic residues. Interestingly, this core of rigidification is capped by residues that are released from an effectively rigid state in the apo state to become more dynamic upon binding chitotriose (Fig. 6). This study appears to shed light on a cooperatively formed rigidified core contacting HEWL's catalytic residues and capped by two sites that become markedly more flexible on either end.

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Figure 5. Spatial distribution of perturbations of fast internal motion in HEWL upon binding of chitotriose. The backbone of the HEWL crystal structure30 (using PDB code 1LZB) is rendered as a gray ribbon and the chitotriose is shown in orange. Amide N[BOND]H and methyl motional probes with data available in both the apo and complexed states are depicted as spheres and colored according to the change in Omath image or Omath image parameters, respectively. Large spheres represent methyl groups and small spheres represent backbone amide. Blue indicates sites that become more rigid upon binding chitotriose, and red indicates sites that become more flexible on the subnanosecond timescale. Sites with the largest changes in dynamics are located near the binding surface. Additionally, a general restriction of motion (stiffening) in the central core is noted from the swath of blue across the central domain.

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Figure 6. Apparent cooperative rigidification of HEWL upon binding chitotriose. The backbone of the HEWL crystal structure30 (PDB code 1LZB) is rendered as a gray ribbon and the chitotriose is shown in orange. Atoms are shown as spheres for residues whose methyl groups are effectively rigid in both the apo and complexed states (light blue) or become effectively rigid in the complexed state (dark blue). The atoms of residues whose methyl groups are effectively rigid in the apo state and become dynamic in the complex are shown in red and effectively cap the residues that are rigid in the bound state. The catalytic amino acids E35 and D52 are shown in yellow.

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The dominant feature of the overall perturbation in motion by binding of chitotriose is an inverse correlation of the variance of the perturbation with the closest distance of the probe to the binding interface (Fig. 7), which seems to reflect the dissipation of motional coupling initiated at the interface with chitotriose. It is important to emphasize that binding of chitotriose does not produce a general rigidification of residues of HEWL at the interface. Both relatively large increases and decreases in Omath image are seen near to the chitotriose.

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Figure 7. Distance dependence of the dynamic perturbation of fast internal dynamics of HEWL due to the binding of chitotriose. Amide probes are colored gray, whereas methyl probes are colored black. Error bars are determined by Monte Carlo sampling of the relaxation data.

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The backbone N[BOND]H-squared generalized order parameters and methyl-squared generalized axial order parameters have been deposited to the BMRB under accession codes 18304 and 18305 for the apo and bound states, respectively.

Binding entropy

The thermodynamics of the interaction of HEWL with its natural saccharide inhibitors, chitobiose and chitotriose, have been studied extensively by isothermal titration calorimetry.23 The binding of chitotriose is enthalpically driven. The overall binding entropy is highly unfavorable. Attribution to solvent-related contributions was the focus of that study with the aim of understanding the unique features of the protein–carbohydrate interaction. To solve for the various entropies listed in Eq. (1), Garcia-Hernandez et al.23 used a statistical analysis of the structural variation across the family of structural models determined by solution NMR methods32 to estimate the contributions from conformational entropy of the protein and, after adjusting to the temperature used here, arrived at a value for –TΔSconf of +42 kJ mol−1.

Recently, the “dynamical proxy” of using changes in NMR-derived parameters of disorder as an indirect measure of local residual entropy has been quantitatively calibrated for complexes between calcium-saturated calmodulin and a series of peptides representing calmodulin-binding domains.13 This empirical approach attempts to overcome many of the objections presented by the simple “oscillator inventory” approach used previously.11, 12 That calmodulin study suggested an empirical scaling between perturbation of motion over the energy landscape and changes in the corresponding conformational entropy, but the generality of the scaling constant is uncertain. However, if it is assumed that it is universally applicable, then by averaging over the entire lysozyme protein and scaling the resulting average change in ΔOmath image with the empirical constant13 of −0.037 ± 0.007 kJ (mol res)−1 K−1, one obtains an estimate for the corresponding change in conformational entropy. The response of lysozyme upon binding chitotriose then corresponds to +28 ± 8 kJ mol−1 of unfavorable energy change at 308 K. The change in solvent entropy estimated from changes in accessible hydrophobic and polar surface area yields a favorable change of −10 kJ mol−1. An upper limit for the change in translational/rotational entropy from the rigid docking of a relatively rigid chitotriose and HEWL can be gauged from the calculations of Luo and Sharp33 as ∼+30 kJ mol−1. The sum of these contributions is somewhat more than the unfavorable binding entropy at 308 K determined by isothermal titration calorimetry23 (48 ± 8 vs. 35 kJ mol−1), suggesting the presence of residual motion in the complex, unusual solvation of the free chitotriose and/or a smaller “dynamical proxy” scaling constant for HEWL than for the calmodulin system.

Summary

Both backbone amide and side chain methyl bond vectors in HEWL are relatively rigid in both the apo and chitotriose-bound states. Upon binding chitotriose, changes in fast timescale dynamics are observed for many probes across the molecule. The variance in methyl dynamics, as manifested in Omath image values, is greater than that of Omath image, and this variance is dependent on the distance to the chitotriose ligand. Although there are local changes spread across the molecule, the overall effect is only a slight rigidification. Moreover, methyl sites that stay rigid and methyl sites that become rigid upon binding chitotriose form a stiff central core. This in contrast to the changes previously reported in noncatalytic oligosaccharide binders, which on average become more flexible upon ligand binding.14–16

Materials and Methods

  1. Top of page
  2. Abstract
  3. Introduction
  4. Results and Discussion
  5. Materials and Methods
  6. Acknowledgements
  7. References

Sample preparation

The gene encoding HEWL with an N-terminal methionine residue subcloned into the pET11a expression vector (Genscript) was expressed in BL21(DE3) E. coli cells on minimal media. HEWL for the backbone relaxation experiments was expressed using 15NH4Cl (Cambridge Isotope Laboratories) as the sole nitrogen source and unlabeled glucose as the carbon source. HEWL for chemical shift assignment and deuterium relaxation experiments were grown in M9 media containing 15NH4Cl, 13C6-glucose (Cambridge Isotope Laboratories), and 55% D2O. HEWL was purified and refolded as described.34 NMR samples were prepared from freeze-dried protein in a 100 mM acetate solution (pH 4.7) containing 10% D2O. Protein concentrations were determined spectrophotometrically, and samples used for relaxation were 410 μM. Liganded protein samples were prepared with 1.2 molar equivalents of chitotriose. Complete binding was confirmed by the 15N-HSQC resonance frequencies of residues with distinct chemical shift changes upon binding. The chemical shifts of the free and bound resonances are in slow exchange as predicted by the reasonably tight binding constant (Kd ∼ 14 μM).

Nuclear magnetic resonance experiments and analysis

All NMR experiments were collected at 35°C using Bruker BioSpin Avance III NMR spectrometers equipped with cryogenic probes. A minimal set of resonance assignment experiments were collected using the 15N/13C/55%-2H deuterium relaxation sample at 750 MHz (1H) because extensive resonance assignments were available for apo-HEWL25, 35 and there are few structural changes in HEWL upon the addition of chitotriose.30 Standard 15N-HSQC, 13C-HSQC, and HNCACB37 spectra were collected. Additionally, deuterium decoupling was added to an (H)CCH3-TOCSY 3D experiment38 via the inclusion of a WALTZ-1636 decoupling scheme during aliphatic carbon evolution and a refocusing 180° pulse during the constant time methyl carbon evolution period. Spectra were referenced to internal DSS,39 and the HNCACB spectra had an additional correction to align the data with resonance assignments corresponding to the CH3 isotopomer.

Relaxation experiments were collected at both 600 and 750 MHz (1H). Nitrogen-15 T1, T2 and NOE relaxation experiments40 were collected on 15N-labeled protein. IZCZDZ, IZCZDY, and IZCZ CH2D methyl relaxation experiments41 were collected on the 15N/13C/55%-2H samples with buffer and protein concentrations matching those used in the 15N relaxation experiments. Each pseudo-3D experiment was collected with nine time points in the variable relaxation time to sample the exponential decay resulting from the specified relaxation mechanism and three duplicate time points to estimate error. DZ and DY rates were obtained by subtracting the IZCZ rate from the IZCZDZ and IZCZDY rates, respectively. The 2D 1H-15N NOE experiments were collected with and without an initial presaturation pulse train, and the ratio of intensities for each probe in these spectra was used to calculate the NOE rate. A grid search approach42 was used to characterize macromolecular tumbling (τm)43 and to determine model-free parameters44 (O2, Omath image, and τe) from the relevant rates and using a 2H quadrupolar coupling constant of 167 kHz, an effective N[BOND]H bond length of 1.04 Å,45 and an 15N chemical shift anisotropy tensor breadth of −170 ppm46 using in-house software.

The change in solvent entropy47 was estimated using solvent accessible surface areas determined using the program Surfcv.48 Distances to chitotriose (Fig. 7) are determined from the probe site to the nearest non-hydrogen chitotriose atom in the binary structure30 (PDB code 1LZB). Images of three-dimensional structures were generated using the program PyMOL (Schrödinger, Portland).

Acknowledgements

  1. Top of page
  2. Abstract
  3. Introduction
  4. Results and Discussion
  5. Materials and Methods
  6. Acknowledgements
  7. References

The authors thank A. Seitz for the preparation of 15N/13C/55%-2H-labeled HEWL and Professor K. A. Sharp for helpful discussion.

References

  1. Top of page
  2. Abstract
  3. Introduction
  4. Results and Discussion
  5. Materials and Methods
  6. Acknowledgements
  7. References