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Keywords:

  • (bio)molecular simulation;
  • compact fold;
  • experimental observables;
  • hydrogen bonding;
  • secondary structure

Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. Results and Discussion
  5. Materials and methods
  6. Conclusions
  7. Acknowledgements
  8. References
  9. Supporting Information

Prediction and understanding of the folding and stability of the 3D structure of proteins is still a challenge. The different atomic interactions, such as non polar contacts and hydrogen bonding, are known but their exact relative weights and roles when contributing to protein folding and stability are not identified. Initiated by a previous molecular dynamics simulation of fully ester-linked hen egg white lysozyme (HEWL), which showed a more compact fold of the ester-linked molecule compared to the native one, three variants of this protein are analyzed in the present study. These are 129-residue native HEWL, partly ester-linked HEWL, in which only 34 peptide linkages that are not involved in the helical or β-strand parts of native HEWL were replaced by ester linkages, and fully (126 residues) ester-linked HEWL. Native and partly ester-linked HEWL showed comparable behaviour, whereas fully ester-linked HEWL could not maintain the native secondary structure of HEWL in the simulation and adopted a more compact fold. The conformational changes were analyzed by comparing simulation averaged values of quantities that can be measured by NMR, such as 1H–15N backbone order parameters, residual dipolar couplings, proton–proton NOE distances and 3J-couplings with the corresponding values derived from experimental NMR data for native HEWL. The information content of the latter appeared to be insufficient to detect the local conformational rearrangements upon esterification of the loop regions of the protein. For fully ester-linked HEWL, a significantly reduced agreement was observed. Upon esterification, the backbone–side chain and side chain–side chain hydrogen-bonding pattern of HEWL changes to maintain its compactness and thus the structural stability of the ester-linked lysozymes.


Abbreviations
HEWL

hen egg white lysozyme

MD

molecular dynamics

RDC

residual dipolar coupling

rmsd

root-mean-square deviation

rmsf

root-mean-square fluctuation

Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. Results and Discussion
  5. Materials and methods
  6. Conclusions
  7. Acknowledgements
  8. References
  9. Supporting Information

Proteins and the stability of their specific active fold play an important role in molecular biology and have been extensively studied for decades. Early studies of protein denaturation reported in the 1930s and 1940s by Wu and Yang [1] and Anson [2] explain the stability of a native protein conformation as being a result of electrostatic intra-molecular interactions (e.g. hydrogen bonding). The reversibility of protein denaturation, ionic bonding and the restoration of enzymatic activity was described and discussed by Lumry and Eyring [3]. Other causes for protein stability were considered and, in 1959, Kauzmann [4] proposed the ‘hydrophobic effect’. In 1972, the issue achieved a wide audience when Anfinsen received the Nobel prize ‘for his work on ribonuclease, especially concerning the connection between the amino acid sequence and the biologically active conformation’. He had shown that this protein could be reversibly denaturated in a test tube [5]. Anfinsen explained this observation by identifying that the protein would adapt its conformation such as to minimize its Gibbs free energy in a given environment defining the thermodynamic state point: physiological conditions favour a native fold of the protein, whereas the unfolded conformation is preferred under different, non physiological solvents or temperatures.

The past four decades revealed the major factors in protein folding energetics, namely the hydrophobic effect, van der Waals interactions together with peptide hydrogen bonds and solvent composition. These are accompanied by several auxiliary factors, including salt bridges, side-chain hydrogen bonds, disulfide bridges and propensities to form α-helices and β-structures, as reviewed by Baldwin [6]. The primary structure of a protein together with knowledge about the relative weights of these factors and the actual thermodynamic state should in theory allow a prediction of the 3D structure of a protein. However, prediction of protein folding and stability remain unmet challenges because the different weights, the exact roles and the corresponding mechanisms of each factor remain largely unknown [7,8].

A systematic investigation of the contributions of each of these types of interactions to a native protein structure would involve separately eliminating each of them and observing the subsequent changes in protein structure. Such an approach is experimentally largely impossible as a result of physical and chemical limitations. Even computationally, it is rather challenging to eliminate some of the mentioned interactions without interfering with other interactions. However, one possibility with minimal interference is the removal of backbone hydrogen bonds (i.e. hydrogen bonds involving the NH atoms as hydrogen donor). These can be eliminated by replacing the amide bond by an ester bond, a so-called A-to-E replacement (Fig. 1). This eliminates one hydrogen-bond donor by replacing an NH group by an O atom, and reduces the hydrogen-bond acceptor ability of the carbonyl [9]. Inevitably, the backbone properties are also modified by an A-to-E replacement. The peptide Cα–C–Oα–Cα torsional angle is less restricted to planar configurations than the Cα–C–N–Cα one [10] and the dipole of the CO–Oα–Cα group is smaller and differently directed than that of a CO–NH–Cα group, which will induce long-range effects. A-to-E replacements are experimentally feasible using a nonsense suppression technique first reported by Schultz and colleagues [11]. The chemical synthesis is straightforward and, besides the fact that a hydroxy amino acid is inserted, is very similar to the synthesis of native polypeptides. Therefore, a few studies of proteins with A-to-E replacements have been carried out with the aim of obtaining further insight into protein folding and stability and/or biological activity [12–26]. Theoretical approaches of A-to-E replaced peptides or proteins are far less abundant but not absent. A study of a coiled coil system showed that the largest structural changes observed were a result of missing hydrogen bonds of the protein within the hydrophobic core [27].

image

Figure 1.  Partial atomic charges in e and charge groups (dashed boxes, adding up to a total charge of zero) for (A) the peptide linkage of the 45A3 force field [40] and (B) the corresponding ester linkage after an A-to-E replacement. The Oα atom has integer atom type OA (IAC = 3).

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The present study was suggested by a previous molecular dynamics (MD) simulation of fully ester-linked hen egg white lysozyme (HEWL) (i.e. a protein built of 126 hydroxy amino acids, all but the inline image head group and the two prolines) [10]. It was shown that, in aqueous solution (i.e. in contrast to what might be expected), the ester analogue does not unfold but shows a different, more compact fold compared to native HEWL. The pattern of backbone–side chain and side chain–side chain hydrogen bonds did change upon replacement of the peptide linkages by ester linkages: only ∼ 25% of the hydrogen bonds in the native simulation were also observed in the ester-linked simulation and vice versa. Despite the fact that fully ester-linked HEWL lost all its helices and β-strands, an unexpected 85% of 1630 NMR NOE distance bounds derived from experiment for native HEWL were still fulfilled within 0.1 nm when calculated based on the ester-linked HEWL simulation trajectory. These two intriguing suggested the need for a further investigation of the effect of A-to-E replacements in HEWL on various quantities that are observable in NMR experiments.

In the present study, we not only consider the two extreme cases of native HEWL (no A-to-E replacements) and fully ester-linked HEWL (126 A-to-E replacements, as many as possible) that were considered previously, but also report a simulation of partly ester-linked HEWL. Here, there are 34 A-to-E replacements for amino acids not involved in helices or β-strands (Figs 2 and 3). In addition, more quantities were analyzed in more depth than previously reported [10], using longer MD trajectories. The focus of the present study is: (a) which experimentally observable quantities are sensitive to the structural changes that maintain a compact fold and (b) why is the fold of ester-linked lysozymes still compact? Accordingly, different observables that can be experimentally measured by NMR techniques, i.e. NH-order parameters, backbone 15N-1H, 13Cα13C and 13C−15N residual dipolar couplings (RDCs), NOE proton–proton distances, as well as 3JHNHα -and 3Jαβ-coupling constants, have been calculated from the MD simulation trajectories of native, partly and fully ester-linked HEWL and compared with the values for native HEWL obtained experimentally. Because these observables contain only short-distance or rather local information regarding pairs of atoms, it is of interest to investigate how sensitive these measurable quantities are to configurational rearrangements that maintain a compact fold of the protein. In addition, hydrogen-bond patterns have been analyzed in simulations that search for stabilization effects in the non-native fold of ester-linked HEWL.

image

Figure 2.  Distribution of ester bonds in partly ester-linked HEWL. White numbers on black boxes indicate a hydroxy amino acid (i.e. the connection to the previous amino acid is established by an ester bond and not by a peptide bond as in native HEWL).

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image

Figure 3.  (A) The main secondary structure elements of native HEWL, as they were used in the hydrogen bonding analysis. The four α-helices are drawn in red (A, residues 5–14; B, residues 25–34; C, residues 89–100; D, residues 109–114); the two 310-helices in black (a, residues 80–83; b, residues 120–123); and the three β-strands in blue (β1, residues 43–45; β2, residues 51–53; β3, residues 58–59). (B) Side-chain atoms of the residues involved in the hydrophobic box (residues 17, 20, 23, 28, 98, 105, 108 and 111) are represented by green balls. Not all of the atoms in these residues are involved in the hydrophobic box of HEWL, a more precise definition is provided elsewhere [54].

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Results and Discussion

  1. Top of page
  2. Abstract
  3. Introduction
  4. Results and Discussion
  5. Materials and methods
  6. Conclusions
  7. Acknowledgements
  8. References
  9. Supporting Information

Structural properties and flexibility

The positional rmsd of the backbone atoms from the X-ray structure for the simulation trajectories of native, partly ester-linked and fully ester-linked HEWL are shown in Fig. 4 (upper panel). For all three proteins, the values increase during the first period of the simulation and level off at a constant value of ∼ 0.3 nm for native and partly ester-linked HEWL and ∼ 0.5 nm for fully ester-linked HEWL after a few nanoseconds. Native and fully ester-linked HEWL reach these values after 2 and 3 ns, respectively, whereas the rmsd value for partly ester-linked HEWL stays constant at ∼0.2 nm after 1 ns but jumps up to the same value as that observed for native HEWL (0.3 nm) after 7 ns, where partly ester-linked HEWL lost its α-helix D (see below). Fully ester-linked HEWL deviates much more from the X-ray crystal structure than native and partly ester-linked HEWL. Yet, fully ester-linked HEWL becomes more compact than the other two proteins, as indicated by the radius of gyration in Fig. 4 (lower panel). It appears that the loss of secondary structure in fully ester-linked HEWL allows it to become more spherically compact. When the secondary structure is maintained, as in partly ester-linked HEWL, the compaction is less than for native HEWL.

image

Figure 4.  Positional rmsd from the initial X-ray structure [35] of the backbone atoms (N/Oα, Cα, C and O) and the radius of gyration (lower panel) for the three simulations of native, partly ester-linked and fully ester-linked HEWL. Black solid lines, native HEWL; grey solid lines, partly ester-linked HEWL; black dotted lines, fully ester-linked HEWL.

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Fully ester-linked HEWL is more flexible than native and partly ester-linked HEWL, as seen from the rmsf of the Cα atoms in Fig. 5. Partly ester-linked HEWL shows somewhat larger fluctuations than native HEWL, in particular for residues where the amide bond has been replaced by an ester bond, whereas the fluctuations for the other residues are more comparable. The increased flexibility is likely to be a product of a loosened hydrogen-bond network throughout the molecule.

image

Figure 5.  rmsf of the Cα-atoms of native, partly ester-linked and fully ester-linked HEWL calculated from the last 2 ns of the corresponding MD simulations (8–10 ns). The grey bars at the bottom indicate secondary structure elements of native HEWL (compare Fig. 3), (i.e. thick bars, α-helix; medium bars, 310-helix; thin bars, β-strand). The state of the peptide linkage in partly ester-linked HEWL [i.e. native (open circle) versus ester bond (filled circle)] is indicated below the secondary structure bars.

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Figure 6 shows the evolution of secondary structure elements of native, partly and fully ester-linked HEWL. Partly ester-linked HEWL largely maintains the major secondary structure elements (Fig. 3) visible in native HEWL: α-helices A–C remain stable, whereas helix D is lost after 7 ns, although it shows much less π-character instead of α-character than in native HEWL. The two 310 helices a and b are present in both simulations but mostly in the form of an α-helix. It is known that the 45A3 force field tends to favour α over 310-helices [28]. The three main β-strands are stable in native and partly ester-linked HEWL, although less so in the latter case. Partly ester-linked HEWL displays more structural variation than native HEWL and this higher flexibility is also reflected in the rmsf (Fig. 5). Fully ester-linked HEWL shows different behaviour. All helices are lost within the first 4 ns and the β-strands are disrupted even earlier.

image

Figure 6.  Secondary structure elements as a function of time calculated for the three MD simulation trajectories of native, partly ester-linked and fully ester-linked HEWL (from left to right). Colour code: black (310-helix); red (α-helix); green (π-helix); blue (β-strand); yellow (β-bridge); brown (bend); grey (turn). The labelling of the secondary structure elements in native lysozyme as defined in Fig. 3 is shown on the right.

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Comparison with experimental NMR data

1H−15N order parameters

A comparison of the 1H-15N order parameters S2 derived from experiments [29] to with those calculated for native, partly ester-linked and fully ester-linked HEWL is provided in Fig. 7. The order parameters calculated from the simulations are generally smaller than those derived using the so-called model-free analysis [30] of the experimental relaxation times. The largest order parameters are found for residues in helices. The simulation of native HEWL produces a pattern of 1H-15N S2-values along the backbone that is approximately similar to that of the S2-values derived from experiment, with the correlation coefficient being 0.41. Partial esterification does enlarge the deviation between calculated and experimental order parameters, as illustrated by a lower correlation coefficient of 0.38, although the general pattern as a function of residue number is still similar. However, full esterification largely destroys the pattern, which is reflected by the correlation coefficient of 0.16.

image

Figure 7. 1H–15N order parameters of HEWL derived from experiment on native HEWL (dotted line with crosses) [29] compared to calculated 1H–15N order parameters for the MD simulations of native, partly ester-linked and fully ester-linked HEWL (from top to bottom). 1H–15N order parameters are calculated using Eqn (6) over the whole 10 ns of simulation time but averaged over a 1-ns time window. The grey bars on top of each graph indicate the secondary structure elements of native HEWL (compare Fig. 3) (i.e. thick bars, α-helix; medium bars, 310-helix; thin bars, β-strand). The state of the peptide bond in partly ester-linked HEWL, native versus ester bond, is indicated by open and filled circles, respectively, above the secondary structure bars in the plot of partly ester-linked HEWL.

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NOE proton–proton distances

One way to measure the quality of a molecular structure from an MD simulation is a comparison of simulated with experimentally derived NMR NOE proton–proton distances. This is generally achieved by evaluating whether simulated proton–proton distances exceed an upper limit, the NOE bound, as determined based on the experimental NMR data.

A total of 1630 distance bounds, including 392 long-range NOE bounds (i.e. from residue i to residue j with |i − j| ≥ 4) is available from NMR experiments [31] and the corresponding r−3 averaged distances were calculated from each of the three simulations and compared with the NOE distance upper bounds. The number of bound violations is given in Table 1, whereas the distribution of NOE distance bound violations for the long-range NOE atom pairs is shown in Fig. 8. There are less NOE bound violations in the simulation of partly ester-linked HEWL than in that of native HEWL, except for the time window from 8–10 ns.

Table 1.   NMR NOE proton–proton distance bound violations in the MD simulations of native, partly ester-linked and fully ester-linked HEWL with respect to the upper NOE distance bounds derived experimentally [31]. The calculations were performed using a r−3-averaging for 1630 NOE bounds including 392 long-range NOE bounds (i.e. from residue i to residue j with |i − j | ≥ 4).
SystemNumber of violations (all/long-range)
> 0.1 nm> 0.3 nm> 0.5 nm
Time window: 0–3.5 ns
 Native64/446/51/1
 Partly ester-linked58/365/50/0
 Fully ester-linked192/13360/5323/20
Time window: 1.5–3.5 ns
 Native84/5221/185/5
 Partly ester-linked70/466/60/0
 Fully ester-linked250/15994/8242/37
Time window: 8–10 ns
 Native92/5421/164/4
 Partly ester-linked107/7023/207/7
 Fully ester-linked327/201165/13282/70
Time window: 0–10 ns
 Native69/4411/103/3
 Partly ester-linked66/427/70/0
 Fully ester-linked237/15882/7030/25
image

Figure 8.  Distribution of all 392 long-range NOE bound violations (from residue i to j with | i − j | ≥ 4) for native, partly ester-linked and fully ester-linked HEWL (from top to bottom) calculated from 10-ns trajectories. NOE bound violations are coloured black, whereas the fulfilled NOE bounds appear in grey.

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Interestingly, a large majority of all 1630 NOE distances calculated over the whole time frame of 10 ns is within 0.1 nm of the bounds in all three simulations: all/long-range: 96%/89%, 96%/89% and 85%/60% for native, partly ester-linked and fully ester-linked HEWL, respectively. Thus, the loss of secondary structure in the fully ester-linked HEWL simulation (Fig. 6) increases the number of NOE bound violations larger than 0.1 nm by only 11%/29% (all/long-range), a number that was expected to be much higher for a protein with a high proportion of its residues (54 of 129 residues; 42%) involved in the main secondary structure elements (Fig. 3). This result is particularly unexpected because the atoms involved in the 1630 experimental NOE atom pairs are widely distributed over the 129 amino acid residues.

A closer look at the large (> 0.5 nm) long-range NOE distance bound violations shows that most of them involve residues of the hydrophobic box region in the core of the protein (Fig. 3B). Table 2 shows that 21 of 25 NOE bound violations larger than 0.5 nm in the 10 ns simulation of fully ester-linked HEWL involve hydrogens of the hydrophobic box residues. The hydrophobic box must be disrupted almost immediately in the fully ester-linked HEWL simulation because 19 of 20 of the long-range NOE bound violations larger than 0.5 nm already involve hydrophobic box residues during the first time window of 0–3.5 ns. This is in agreement with experimental results for A-to-E replaced peptides where the biggest structural changes as a result of missing hydrogen bonds were observed within the hydrophobic core [27]. Larger changes in other parts of the molecule begin to happen later in the simulation. This is reflected by the numbers of violations during the last 2 ns of the simulation: the number of long-range NOE bound violations involving hydrophobic box residues increased to 27, whereas the total number of long-range NOE bound violations rose to 70.

Table 2.   Number of violations for the 124 long-range NOE distance bounds involving residues of the hydrophobic box in the MD simulations of native, partly ester-linked and fully ester-linked HEWL with respect to the experimental NMR NOE distance bounds [31]. The values are compared to the total number of the 392 long-range NOE distance bound violations in the whole protein (numbers in parenthesis). A detailed list of the NOE violations is found in Tables S1–S3.
SystemHydrophobic box (all)
> 0.1 nm> 0.3 nm> 0.5 nm
Time window: 0–3.5 ns
 Native19 (44)1 (5)0 (1)
 Partly ester-linked17 (36)5 (5)0 (0)
 Fully ester-linked49 (133)29 (53)19 (20)
Time window: 1.5–3.5 ns
 Native22 (52)9 (18)0 (5)
 Partly ester-linked22 (46)5 (6)0 (0)
 Fully ester-linked57 (159)33 (82)27 (37)
Time window: 8–10 ns
 Native28 (54)7 (16)0 (4)
 Partly ester-linked25 (70)7 (20)2 (7)
 Fully ester-linked77 (201)51 (132)27 (70)
Time window: 0–10 ns
 Native21 (44)3 (10)0 (3)
 Partly ester-linked20 (42)5 (7)0 (0)
 Fully ester-linked60 (158)35 (70)21 (25)
Proton–proton 3J-coupling constants

Different sets of experimental proton-proton 3J-coupling constants, 3JHNHα and 3Jαβ, for native HEWL [32] were compared with values calculated from the simulation trajectories (Fig. 9). The 3Jαβ-coupling constants were calculated only if the stereospecific Hβ assignments were available from experiment.

image

Figure 9.  Comparison of simulated (0–10 ns) 3J-coupling constants of native (upper panels), partly ester-linked (middle panels) and fully ester-linked HEWL (lower panels) with the experimental coupling constants of native HEWL [32]. The left column shows the 3JHNHα-coupling constants, whereas the right column contains the values of the 3Jαβ-coupling constants. Colours indicate the secondary structure of the corresponding amino acid: red (α-helix); green (π-helix); blue (β-strand); yellow (β-bridge); orange (turn); brown (bend); grey (other).

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For native HEWL both, the 3JHNHα- and 3Jαβ-coupling constants show a difference of 1–2 Hz between simulated and measured values. The rmsd of the calculated coupling constants from the experimental values for native HEWL is 1.7, 1.4 and 2.4 Hz for native, partly and fully ester-linked HEWL, respectively. Unexpectedly, partial esterification improves the agreement of the calculated 3JHNHα-couplings with those measured for native HEWL. The most apparent changes going from native or partly ester-linked HEWL to fully ester-linked HEWL are observed for residues involved in a native α-helix (Fig. 9, left panels, red dots). For the 3Jαβ-coupling constants, the corresponding rmsd values are 2.3, 3.0 and 3.9 Hz, showing a rise with increasing esterification.

The quality of the simulated 3J-couplings suffers from limited sampling compared to the experimental time scale and from inaccuracy induced by the empirical nature of the parameters of the Karplus relation used to obtain 3J-couplings from a configuration [33]. In addition, force-field induced inaccuracies may play a role. Yet, the approximate correlation between simulated and measured 3J-couplings for native HEWL is completely lost when comparing values from the fully ester-linked HEWL simulation to those measured for native HEWL.

Backbone 15N-1H, 13Cα-13C, and 13C-15N residual dipolar couplings

The quality, as represented by a so-called Q-value (Eqn 10) of the backbone 15N-1H, 13Cα-13C and 13C−15N RDCs calculated from the simulation trajectories of native, partly ester-linked and fully ester-linked HEWL with respect to the experimental RDCs of native HEWL [34] is shown in Fig. 10. The calculations from the three simulations all result in a much higher Q-value than that calculated from the X-ray crystal structure [35]. Interestingly, the simulation of partly ester-linked HEWL shows a better (Cα-C and C-N RDCs) or similar (N-H RDCs) agreement with the experimental values for native HEWL than the values obtained from the native HEWL simulation trajectory. By contrast, the Q-values obtained from the RDCs based on the fully ester-linked HEWL simulation trajectory are much higher.

image

Figure 10. Q-value distribution of the calculated backbone N–H, Cα–C and C–N RDCs of native (solid line), partly ester-linked (dashed line) and fully ester-linked (dotted line) HEWL when fitting the calculated RDCs of each configuration to the experimentally derived RDCs of native HEWL [34]. The quality of the fits from the X-ray crystal structure [35] is indicated by a vertical dashed-dotted line.

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Hydrogen bonding

The analysis of atom-positional rmsd and rmsf, radius of gyration and NMR NOE atom–atom distances showed that even fully ester-linked HEWL did not completely unfold as might be expected. An explanation could be the four disulfide bridges holding the protein together. Therefore, we repeated the simulations of the native, partly- and fully ester-linked HEWL without the four disulfide bridges (i.e. only the covalent interactions across the disulfide bridges were omitted [36,37]). These trajectories did not show a different picture of the effect of esterification upon the properties analyzed than the one presented here (see Fig. S1 for the corresponding radius of gyration). Thus, the presence of disulfide bridges does not explain why 85% of all 1630 experimental NMR NOE distance bounds of native HEWL are satisfied within 0.1 nm in the simulation of fully ester-linked HEWL. What other factors or forces could keep the ester-linked protein compact?

A possible cause might be hydrogen bonding. Replacing amide by ester linkages, the number of backbone–backbone and backbone–side chain hydrogen-bonds is massively reduced as a result of the missing hydrogen-bond donor and reduced acceptor ability of esters compared to amides. Therefore, numerous non hydrogen-bonded hydrogen-bond acceptors were present in the beginning of the partly ester-linked and particularly in the fully ester-linked HEWL simulations, which would be able to find donor partners by local conformational rearrangement.

When analyzing such a hydrogen-bond rearrangement effect, three types of hydrogen-bonds were distinguished in the hydrogen-bond analysis: backbone–backbone hydrogen bonds to show the reduction of hydrogen bonding with an increasing number of ester linkages in the backbone, as well as backbone–side chain and side chain–side chain hydrogen bonds. The number of bb–sc hydrogen bonds is given excluding the amide as hydrogen-bond donor. This is to separate the effect as a result of the change in the number of donors from that as a result of configurational rearrangement. An increasing number of backbone–side chain and side chain–side chain hydrogen bonds upon esterification would indicate a stabilization of the observed compact fold by them.

Table 3 shows that the number of backbone–backbone and backbone–side chain hydrogen bonds with a total occurrence > 10% is comparable or smaller in partly ester-linked HEWL than in native HEWL, and even smaller in fully ester-linked HEWL over the whole time range of the simulation (0–10 ns). The same is true for the cumulative sums of the corresponding hydrogen-bond occurrences for all hydrogen-bond types. However, the number of side chain-side chain hydrogen bonds is increasing from native over partly ester-linked to fully ester-linked HEWL. A similar behaviour is seen for the three other time windows. The picture for backbone–side chain and side chain–side chain hydrogen bonds changes when looking at hydrogen bonds with any occurrence (Table 3). The total occurrence of backbone–side chain and side chain–side chain hydrogen bonds is still smaller for ester-linked HEWL compared to native HEWL, except for backbone–side chain hydrogen bonds during the first part of the simulation where they stay rather constant. By contrast, the number of hydrogen bonds from native to partly ester-linked to fully ester-linked HEWL grows massively, independent of the time window.

Table 3.   Number of hydrogen bonds as well as the cumulative sum over the corresponding occurrence for the simulations of native, partly ester-linked and fully ester-linked HEWL. The numbers are sorted with respect to the hydrogen bond type: backbone–backbone (bb–bb), backbone–side chain (bb–sc) and side chain–side chain (sc–sc) hydrogen bonds. Hydrogen bonds of type bb–sc involving an amide hydrogen were not considered. Upper part: only hydrogen bonds with an occurrence > 10%, during the indicated time window, are considered whereas the lower part contains all hydrogen bonds with any occurrence.
Proteinbb–bbbb–scsc–sc
nOccurrence/%nOccurrence/%nOccurrence/%
Hydrogen bonds with an occurrence >10%
 Time window: 0–3.5 ns
  Native90497221469291041
  Partly ester-linked7941571751127780
  Fully ester-linked001835833647
 Time window: 1.5–3.5 ns
  Native8249702255124917
  Partly ester-linked7841452265529825
  Fully ester-linked002550033652
 Time window: 8–10 ns
  Native85502225773261205
  Partly ester-linked7442322255332919
  Fully ester-linked002348834817
 Time window: 0–10 ns
  Native8949792359324995
  Partly ester-linked8041292047626656
  Fully ester-linked001831231651
All hydrogen bonds with any occurrence
 Time window: 0–3.5 ns
  Native22052573078782741326
  Partly ester-linked18643665209084341108
  Fully ester-linked008608885971132
 Time window: 1.5–3.5 ns
  Native18652352319091981195
  Partly ester-linked17343384079813531101
  Fully ester-linked005639554071091
 Time window: 8–10 ns
  Native175519221411211711416
  Partly ester-linked18544133628843381240
  Fully ester-linked005419544201200
 Time window: 0–10 ns
  Native243524339610173781327
  Partly ester-linked21843347529256241102
  Fully ester-linked0013599389211184

To obtain a simple picture of the changed pattern of hydrogen bonding, the hydrogen bonds between secondary structure elements have been analyzed. Table 4 shows the number and occurrence of hydrogen bonds connecting two secondary structure elements in native, partly ester-linked and fully ester-linked HEWL. Only hydrogen bonds linking two helices or two β-strands (A, B, C, D, a, b, β1, β2 or β3; Fig. 3) are considered. The connection may be intra or inter two secondary structure elements. Analyzing the whole time window of 10 ns shows a higher amount of backbone–side chain and side chain–side chain hydrogen bonding (i.e. number and occurrence) for partly ester-linked and fully ester-linked HEWL than for native HEWL. Therefore, longer-living backbone–side chain hydrogen bonds are connecting pairs of secondary structure elements, holding the protein together. This additional hydrogen bonding might not fully compensate for the loss of backbone–backbone and backbone–side chain hydrogen bonding involving the amide hydrogen atoms of native HEWL. Nevertheless, this backbone–side chain and side chain–side chain stabilization appears to help to keep the molecule in a slightly different and more flexible compact form than displayed by native HEWL.

Table 4.   Number of hydrogen bonds involving residues in helices or β-strands as well as the cumulative sum over the corresponding occurrence for the simulations of native, partly ester-linked and fully ester-linked HEWL. Hydrogen bonds with any occurrence have been considered but only if the hydrogen bond bridges any of the main helices or β-strands, A–D, a,b or β1–β3 (Fig. 3), inter- or intra-structural. The numbers are sorted with respect to the hydrogen bond type: backbone–backbone (bb–bb), backbone–side chain (bb–sc) and side chain–side chain (sc–sc) hydrogen bonds. Hydrogen bonds of type bb–sc involving an amide hydrogen were not considered.
Proteinbb–bbbb–scsc–sc
nOccurrence/%nOccurrence/%nOccurrence/%
Helix–helix
 Time window: 0–3.5 ns
  Native55189139732144
  Partly ester-linked54198262553774
  Fully ester-linked001361185266
 Time window: 1.5–3.5 ns
  Native55194250972740
  Partly ester-linked59191383614662
  Fully ester-linked002471449934
 Time window: 8–10 ns
  Native471972241151632
  Partly ester-linked56184046742056
  Fully ester-linked0097114317
 Time window: 0–10 ns
  Native52193026721825
  Partly ester-linked54198348582962
  Fully ester-linked00921183969
β-strand–β-strand
 Time window: 0–3.5 ns
  Native635071013160
  Partly ester-linked7336141318190
  Fully ester-linked00194718151
 Time window: 1.5–3.5 ns
  Native633591016140
  Partly ester-linked7316241527177
  Fully ester-linked00362928103
 Time window: 8–10 ns
  Native52876118136
  Partly ester-linked6321161117181
  Fully ester-linked0023362385
 Time window: 0–10 ns
  Native635361110136
  Partly ester-linked8337111614198
  Fully ester-linked00144412160

A similar backbone–side chain stabilization of the hydrophobic box residues (Fig. 3B) could be detected in an equivalent hydrogen-bond analysis considering residues involved in the hydrophobic box (Table 5). The changing extent of hydrogen bonding in ester-linked HEWL observed through the simulations hints at a rapid, structural change in this part of the protein.

Table 5.   Number of hydrogen bonds between residues of the hydrophobic box as well as the cumulative sum over the corresponding occurrence for the simulations of native, partly ester-linked and fully ester-linked HEWL. Hydrogen bonds with any occurrence have been considered but only if the hydrogen bond bridges two residues involved in the hydrophobic box. The numbers are sorted with respect to the hydrogen bond type: backbone–backbone (bb–bb), backbone–side chain (bb–sc) and side chain–side chain (sc–sc) hydrogen bonds. Hydrogen bonds of type bb–sc involving an amide hydrogen were not considered.
ProteinHydrophobic box–hydrophobic box
bb–bbbb–scsc–sc
nOccurrence/%nOccurrence/%nOccurrence/%
Time window: 0–3.5 ns
 Native33672641915193
 Partly ester-linked34610812095790
 Fully ester-linked0018213384115
Time window: 1.5–3.5 ns
 Native34610842556762
 Partly ester-linked356351141877486
 Fully ester-linked0028020315071
Time window: 8–10 ns
 Native24588462822434
 Partly ester-linked29702521674093
 Fully ester-linked001142288149
Time window: 0–10 ns
 Native29642512253457
 Partly ester-linked28580692025175
 Fully ester-linked0013014367110

Hydrogen bonding from the protein backbone to the solvent or vice versa is reported in Table 6 in terms of the number and occurrence of amide to water NH-OW, water to amide or water to ester HW1/2-O and water to ester HW1/2-Oα bonds (Fig. 1). Although the total number of hydrogen bonds in the ester substituted proteins is somewhat larger than in native HEWL, the corresponding occurrence decreases with increasing amount of ester-linkages within the backbone. Interestingly, the number and occurrence of protein-solvent hydrogen-bonds involving the ester Oα atoms of the protein backbone is larger for partly ester-linked HEWL than for fully ester-linked HEWL. Apparently, the hydrogen-bond acceptors in the protein that are released from hydrogen bonding by the A-to-E replacements do prefer hydrogen bonding to other hydrogen bond donors in the protein over hydrogen bonding to water. The replacement also allows for an increase of the number of protein–protein hydrogen bonds involving backbone atoms.

Table 6.   Number and summed-up occurrence of hydrogen bonds from a backbone atom of the protein (HN, N, Oα, Cα, C and O) to a water molecule (OW, HW1, HW2) from the 10-ns simulations of native, partly ester-linked and fully ester-linked HEWL. All values are normalized [i.e. divided by the corresponding number of donor (HN) or acceptor (N, Oα and O) atoms present in the protein backbone for the indicated protein-solvent hydrogen bond]. Note that the NHinline image head group has not been considered in these calculations.
ProteinHN⋯OWHW1/2⋯NHW1/2⋯OαHW1/2⋯OTotal
nOccurrence/%nOccurrence/%nOccurrence/%nOccurrence/%nOccurrence/%
Native HEWL1991820007774097857
Partly ester-linked HEWL1521490353394734146050
Fully ester-linked HEWL001014328482799229

The complete lists of all protein–protein hydrogen bonds during the simulation of native, partly ester-linked and fully ester-linked HEWL is given in Tables S4–S6.

Materials and methods

  1. Top of page
  2. Abstract
  3. Introduction
  4. Results and Discussion
  5. Materials and methods
  6. Conclusions
  7. Acknowledgements
  8. References
  9. Supporting Information

Simulation program and force-field parameters

The molecular dynamics simulations of all three systems, native HEWL, fully ester-linked HEWL and partly ester-linked HEWL in SPC [38] water, were carried out using gromos simulation software [39], and the 45A3 force-field parameter set [40,41]. The introduction of ester bonds in the backbone of the protein required some force-field changes affecting partial charges and charge groups (Fig. 1), as well as bonded interactions (Table 7). No A-to-E replacements were carried out for the simulation of native HEWL, whereas fully ester-linked HEWL contained 126 A-to-E replacements, all but the head amino acid and the two prolines. For the partly ester-linked HEWL simulation, 34 A-to-E replacements were carried out (Fig. 2). The selection of peptide bonds to be replaced by an ester bond was based on the assignment of 310- and α-helices, as well as β-strands/bridges in the native protein, as reported by Oostenbrink et al. [28] (Table 1). The aim was to preserve the main secondary structure elements of native HEWL, namely the three β-strands, four α-helices and two 310-helices (Fig. 3).

Table 7.   Comparison of the force-field parameters used for the native peptidic bonds (gromos 45A3 [40] parameters) and for the ester bonds. All force-field changes are included that were made because of the ester bonds, except the changes of the charges and charge groups specified in Fig. 1.
Bondb0/nmKb / 106 kJ·mol−1· nm−4
C–N0.13311.80
N–Cα0.1478.71
C–Oα0.13610.20
Oα–Cα0.1438.18
Bond angleΘ0 / degreesK  / 102 kJ·mol−1
C–N–Cα122.0700
C–Oα–Cα109.5450
Dihedral angle cos (δ)mKΦ / kJ ·mol−1
Cα–C–N–Cα−1233.50
C–N–Cα–C−161.00
N–Cα–C–N161.00
Cα–C–Oα–Cα−1216.70
C–Oα–Cα–C131.26
Oα–Cα–C–Oα135.29

Simulation set-up and protocol

The initial coordinates of the lysozyme atoms for native, fully ester-linked and partly ester-linked HEWL were derived from the native X-ray crystal structure (Protein Data Bank code: 1AKI) [35]. The protonation states of all amino acids corresponding to pH 7 were used, leading to a total protein charge of 8 e. Each protein was separately solvated in a cubic box of edge lengths 7.73, 8.54 and 8.54 nm with 14 378, 19 644 and 19 675 SPC [38] water molecules, respectively. The overall neutrality of the box was preserved by adding eight chloride counter ions.

Initial velocities for all atoms and simulations were assigned from a Maxwell–Boltzmann distribution at 60 K with position restraining of the protein atoms with an initial harmonic force constant of 25 000 kJ·mol−1·nm−2. The temperature was raised stepwise by 60 K and the force constant of the position restraining lowered by a factor of ten, every 20 ps, ending in a non restrained protein simulation of 20 ps at 300 K after 80 ps of simulated time. A 10-ns simulation followed the 100-ps thermalization procedure with the protein configuration being saved every 0.5 ps for analysis.

The temperature and pressure (300 K, 1 atm) were kept constant using the weak coupling algorithm [42] with corresponding coupling times of τT = 0.1 ps and τp = 0.5 ps, respectively, and an estimated isothermal compressibility of 4.575 × 10−4 (kJ·mol−1·nm−3)−1. All bond lengths and the bond angles of the water molecules were kept rigid by applying constraints using the shake algorithm [43] with a relative geometric tolerance of 10−4, allowing for an integration time step of 2 fs when solving the equation of motion using the leap-frog algorithm [44]. Nonbonded (van der Waals and electrostatic) interactions were handled adopting triple-range cut-off radii: interactions within the short-range cut-off of 0.8 nm were calculated every time step from a pair list that was generated every five steps, when interactions in the range 0.8–1.4 nm were computed. The long-range electrostatic forces were represented by a reaction field with a relative permittivity of ɛRF = 61 [45] outside the long-range cut-off of 1.4 nm. The centre of mass translation and rotation were removed every 2 ps to avoid a flying ice cube [46]. All three simulations reported here (i.e. for native, for partly ester-linked and for fully ester-linked HEWL) were carried out at constant pressure, whereas the fully ester-linked HEWL simulation reported previously [10] was performed at constant volume. This explains the slight differences between some of the results, e.g. the rmsd values as function of time in Fig. 4 and those reported previously [10].

Analysis

All analyses of the simulation trajectories were carried out using the tools available in gromos++ [47], which is part of the gromos simulation package [39]. Because the properties calculated, such as NMR NOE proton–proton distance bound violations or 3J-coupling constants, were compared with experimentally measured values for native HEWL, the amide hydrogen positions not present in ester-linked HEWL were generated for each protein configuration of the trajectory.

This ester-to-amide (E-to-A) transformation does nothing else than convert the Oα atom of the ester into an N atom, placing the missing hydrogen atom such that the N–H distance is 0.1 nm and the two angles C–N–H and H–N–Cα have the same value. In addition, the H atom is placed to lie on the bisecting plane of the two planes defined by the C–N–Cα and O–C–N atoms. An E-to-A transformed trajectory looks like a native HEWL simulation trajectory and can thus be used to detect secondary structure elements in the protein using the gromos++ routine dssp, based on the rules of Kabsch and Sander [48], as well as for other analyses that depend on the amide hydrogen positions. E-to-A transformed trajectories were not used for the hydrogen-bonding analysis of ester-linked HEWL.

When comparing or averaging quantities of Q that depend on the position of the centre of mass and the spatial orientation of a particular set of atoms, the centres of mass are superimposed and a rotational least-square fit of the positions of the set of atoms is performed before Q is calculated.

rmsd and rmsf

The atom-positional rmsd between two structures have been evaluated based on all backbone non hydrogen atoms (N/Oα, Cα, C and O) according to the formula:

  • image(1)

where rNa = (r1,r2,…,rNa) represents the positions of the atoms. In Eqn (1), Na is the number of atoms considered, ri is the position of atom i in the first structure and ri,ref is the position of atom i in the second, reference structure. We used the X-ray crystal structure [35] as the reference structure.

The atom-positional rmsf were calculated as:

  • image(2)

where i indicates the Cα-atom of residue i, 〈ri〉 its average position and NT is the number of configuration time frames in the simulation trajectory.

Radius of gyration

The radius of gyration of a protein, a measure of the compactness of the structure that can be related to light-scattering intensity, was calculated using the definition:

  • image(3)

with

  • image(4)

and

  • image(5)

in which ri denotes the Cartesian position of atom i, mi its mass, and Na denotes the number of protein atoms.

Detection of secondary structure elements

The rules of Kabsch and Sander [48] have been applied to detect and monitor secondary structure elements in the native and ester-linked HEWL simulations. In some cases, one residue may be assigned to be part of two different secondary structure elements. To avoid ambiguous assignments in such cases, priority rules were applied: β-strand/β-bridge >α-helix >π-helix > 310-helix > hydrogen-bonded turn > bend.

Calculation of 1H–15N order parameters

The 1H–15N order parameters (S2) were calculated as [49,50]:

  • image(6)

where μα (α = 1, 2, 3) are the x, y and z components of the normalized inter-atomic N–H vector, and compared with the experimental data for native HEWL [29].

NMR NOE proton–proton distances and 3J-coupling constants

A detailed description of the calculation procedures with equations and corrections is provided elsewhere [51]. In total, 1630 experimental NMR proton–proton upper distance bounds were taken from Schwalbe et al. [31], including pseudo-atom distance corrections as given by Wüthrich et al. [52] and the 3J-coupling constants reported by Smith et al. [32] were used for comparison. Proton–proton distances were calculated using 1/r3 averaging, inline image = (〈r−3〉)−1/3.

Calculation of backbone 15N-1H, 13Cα-13C, and 13C-15N residual dipolar couplings

The RDC Dij between two spins i and j is calculated according to:

  • image(7)

where γi and γj are the gyromagnetic ratios of the two spins, μ0 is the magnetic permittivity of vacuum and h is Planck's constant. P2 denotes the second-order Legendre polynomial and θij is the angle between the inter nuclear vector rij and the static magnetic field. Because there is typically only one copy of the molecule in an MD simulation, Eqn (7) is reformulated so that the averaging over different orientations of a given structure of the molecule with respect to the magnetic field is represented by an alignment tensor A

  • image(8)

where ζx is the angle between the inter nuclear vector and the x-axis and ζy, ζz are the angles for the y- and z-axes, respectively. For every configuration in the trajectory, the alignment tensor A is determined by a singular-value decomposition fit, solving the equation:

  • image(9)

where the five dimensional vector a = (Axx,Ayy,Axy,Axz,Ayz) contains the five independent elements of the 3 × 3 alignment tensor, and R contains the ND experimental RDCs used for the fit. A more complete description of RDC calculations using gromos is provided elsewhere [53]. The quality of each SVD fit is assessed by the Q-value:

  • image(10)

which can be displayed as a distribution resulting from all configurations within a simulation trajectory.

Hydrogen bonds

Hydrogen bonds were defined according to a geometric criterion: a minimum donor-hydrogen-acceptor angle of 135° and a maximum hydrogen-acceptor distance of ∼ 0.25 nm. The hbond routine of gromos++ [47] was used to detect and monitor hydrogen bonds in native and ester-linked HEWL.

Conclusions

  1. Top of page
  2. Abstract
  3. Introduction
  4. Results and Discussion
  5. Materials and methods
  6. Conclusions
  7. Acknowledgements
  8. References
  9. Supporting Information

The present study was motivated by a previous study [10] that showed a compaction of fully ester-linked HEWL (i.e. a protein bearing 126 amide-to-ester replacements) compared to native HEWL in 3.5-ns MD simulations. In fully ester-linked HEWL, 85% of all 1630 NOE proton–proton distance bounds derived from NMR experiments were still satisfied within 0.1 nm. The protein mutants showed a shifted hydrogen-bonding pattern: only ∼25% of the hydrogen bonds in the native simulation were also observed in the fully ester-linked HEWL simulation, and vice versa.

In the present study, we repeated the simulations of native and fully ester-linked HEWL but at constant pressure for 10 ns, and added a simulation of partly ester-linked HEWL, an intermediate state with 34 amide-to-ester replacements outside the helical and β-strand secondary structure elements observed in native HEWL.

It is not unexpected that the simulations of native HEWL and partly ester-linked HEWL preserved the secondary structure known from native HEWL during the simulations. By contrast, fully ester-linked HEWL lost all its secondary structure during the first few nanoseconds of the simulation, doubled its structural difference from the native X-ray structure, yet showed a larger compaction during the simulation than native or partly ester-linked HEWL. Because the experimental data obtained in NMR experiments involve local information, it was of interest to investigate how sensitive the observable quantities are to local spatial rearrangements of the protein that maintain its compactness.

Overall, the simulation of partly ester-linked HEWL agreed with the experimental NMR data measured for native HEWL equally well as the simulation of native HEWL itself. 3JHNHα-coupling constants, NOE proton–proton distances and backbone residual dipolar couplings of partly ester-linked HEWL agreed better with the experimental data, whereas the 1H–15N order parameters and the 3Jαβ-coupling constants agreed less well than in the simulation of native HEWL. This indicates that the considered observables cannot be used to distinguish local structural rearrangements. This is not too unexpected considering the many approximations and model assumptions that flow into the conversion of NOE intensities or relaxation rates into distances and order parameters. For the 3J-couplings, the empirical character of the Karplus relation between local structure and 3J-coupling is a source of considerable uncertainty. Only larger structural changes, as observed in the present study for fully ester-linked HEWL, appear to be detectable by the NMR parameters under consideration.

The observed compact fold of ester-linked HEWL can be explained. At the beginning of the simulation, starting from the native X-ray structure, there are numerous non-hydrogen-bonded acceptors in the backbone of ester-linked HEWL. This unfavourable hydrogen-bonding configuration of the Oα and O = C atoms is rearranged during the simulation by forming new hydrogen bonds, preferentially within the protein and not to the solvent, which help to stabilize the protein structure. This rearrangement is reflected by the changed but not reduced hydrogen-bond pattern found previously for fully ester-linked HEWL [10] and by the increasing number and occurrence of backbone–side chain and/or side chain–side chain hydrogen bonds connecting two secondary structure elements (helix–helix or β-strand–β-strand) or two residues involved in the hydrophobic box, respectively. Thus, the compact fold of fully ester-linked HEWL is maintained by hydrogen bonds involving side chains.

It would be of interest to synthesize fully ester-linked HEWL to verify the conclusions reached from the simulations. Until now, ester-linked versions of proteins are only available for shorter polypeptide chains.

Acknowledgements

  1. Top of page
  2. Abstract
  3. Introduction
  4. Results and Discussion
  5. Materials and methods
  6. Conclusions
  7. Acknowledgements
  8. References
  9. Supporting Information

We thank Dr Jane Allison for her gentle and competent help concerning the calculation of the RDCs from the simulation trajectories. This work was financially supported by the National Center of Competence in Research (NCCR) in Structural Biology and by grant number 200020-121913 of the Swiss National Science Foundation, as well as grant number 228076 of the European Research Council, which is gratefully acknowledged.

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  3. Introduction
  4. Results and Discussion
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  6. Conclusions
  7. Acknowledgements
  8. References
  9. Supporting Information
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Supporting Information

  1. Top of page
  2. Abstract
  3. Introduction
  4. Results and Discussion
  5. Materials and methods
  6. Conclusions
  7. Acknowledgements
  8. References
  9. Supporting Information

Fig. S1. Radius of gyration as calculated from the three control simulation trajectories of native, partly ester-linked and fully ester-linked HEWL proteins not having the four native disulfide bridges.

Table S1. The biggest NOE distance bound violations in the simulation of native HEWL during the time windows of 0–3.5, 1.5–3.5, 8–10 and 0–10 ns.

Table S2. The biggest NOE distance bound violations in the simulation of partly ester-linked HEWL during the time windows of 0–3.5, 1.5–3.5, 8–10 and 0–10 ns.

Table S3. The biggest NOE distance bound violations in the simulation of fully ester-linked HEWL during the time windows of 0–3.5, 1.5–3.5, 8–10 and 0–10 ns.

Table S4. List of all hydrogen bonds in the native HEWL simulation (0–10 ns).

Table S5. List of all hydrogen bonds in the partly ester-linked HEWL simulation (0–10 ns).

Table S6. List of all hydrogen bonds in the fully ester-linked HEWL simulation (0–10 ns).

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