Lorna J Smith1, Wilfred F van Gunsteren2, Niels Hansen3. 1. Department of Chemistry, University of Oxford, Inorganic Chemistry Laboratory, South Parks Road, Oxford, OX1 3QR, UK. 2. Laboratory of Physical Chemistry, Swiss Federal Institute of Technology, ETH, 8093, Zurich, Switzerland. 3. Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, 70569, Stuttgart, Germany.
Abstract
Values of S 2 CH and S 2 NH order parameters derived from NMR relaxation measurements on proteins cannot be used straightforwardly to determine protein structure because they cannot be related to a single protein structure, but are defined in terms of an average over a conformational ensemble. Molecular dynamics simulation can generate a conformational ensemble and thus can be used to restrain S 2 CH and S 2 NH order parameters towards experimentally derived target values S 2 CH (exp) and S 2 NH (exp). Application of S 2 CH and S 2 NH order-parameter restraining MD simulation to bond vectors in 63 side chains of the protein hen egg white lysozyme using 51 S 2 CH (exp) target values and 28 S 2 NH (exp) target values shows that a conformational ensemble compatible with the experimentally derived data can be obtained by using this technique. It is observed that S 2 CH order-parameter restraining of C-H bonds in methyl groups is less reliable than S 2 NH order-parameter restraining because of the possibly less valid assumptions and approximations used to derive experimental S 2 CH (exp) values from NMR relaxation measurements and the necessity to adopt the assumption of uniform rotational motion of methyl C-H bonds around their symmetry axis and of the independence of these motions from each other. The restrained simulations demonstrate that side chains on the protein surface are highly dynamic. Any hydrogen bonds they form and that appear in any of four different crystal structures, are fluctuating with short lifetimes in solution.
Values of S 2 CH and S 2 NH order parameters derived from NMR relaxation measurements on proteins cannot be used straightforwardly to determine protein structure because they cannot be related to a single protein structure, but are defined in terms of an average over a conformational ensemble. Molecular dynamics simulation can generate a conformational ensemble and thus can be used to restrain S 2 CH and S 2 NH order parameters towards experimentally derived target values S 2 CH (exp) and S 2 NH (exp). Application of S 2 CH and S 2 NH order-parameter restraining MD simulation to bond vectors in 63 side chains of the protein hen egg white lysozyme using 51 S 2 CH (exp) target values and 28 S 2 NH (exp) target values shows that a conformational ensemble compatible with the experimentally derived data can be obtained by using this technique. It is observed that S 2 CH order-parameter restraining of C-H bonds in methyl groups is less reliable than S 2 NH order-parameter restraining because of the possibly less valid assumptions and approximations used to derive experimental S 2 CH (exp) values from NMR relaxation measurements and the necessity to adopt the assumption of uniform rotational motion of methyl C-H bonds around their symmetry axis and of the independence of these motions from each other. The restrained simulations demonstrate that side chains on the protein surface are highly dynamic. Any hydrogen bonds they form and that appear in any of four different crystal structures, are fluctuating with short lifetimes in solution.
During the past 50 years, the determination of structure of proteins in crystal based on the reflections of X‐rays has become a standard procedure to obtain information on proteins at the atomic level of resolution. Over the past 30 years NMR measurement of proteins in solution has also become a standard technique, not only to obtain information on protein structure, but also on dynamics at the atomic level of resolution. Several quantities that are observable by NMR, such as nuclear Overhauser enhancements (NOEs), 3
J couplings or chemical shifts, only provide local structural information. Only residual dipolar couplings (RDCs) do provide longer‐range information in terms of the average (relative) directions of bond vectors throughout a molecule. In contrast, X‐ray diffraction of crystals yields non‐local information and, in addition, its information density, that is, the ratio of the number of independent measured n class="Chemical">values of observable quantities for a molecule and the number of independent molecular degrees of freedom, is much higher than that of NMR experiments on proteins in solution. On the other hand, NMR measurements may provide dynamic information in the form of relaxation data, for example, expressed as S
2 order parameters, and of all techniques available to obtain information on proteins in solution, NMR shows the highest information density.
All techniques to derive structural information from the measurement of observable quantities Q make use of a relation of Q to structure r, a function Q(r).
Since virtually all experimental techniques measure an average ⟨Q⟩space,time of Q over the molecules (space) in the test tube and over a time window determined by the type of experiment, the derivation of structural information from a set of ⟨Q⟩ values should account for the averaging involved in the measurement. Tn class="Chemical">his can be done by applying multi‐molecule averaging
or by time‐averaging
structure refinement instead of the commonly used single‐structure refinement technique. Application of time‐averaging structure refinement to proteins based on X‐ray data,[
,
] NMR NOE[
,
] or 3
J coupling
data showed the protein structural variation to be much larger than that observed using single‐structure refinement techniques.
For observable quantities Q, such as X‐ray reflection intensities I, NOEs (when represented as atom‐atom distance bounds), 3
J couplings or chemical shifts, it is possible to formulate a function Q(r) relating a Q value to a particular structure r. RDCs may be directly related to structure by assuming a single alignment tensor representing the anisotropic rotational distribution of the molecule, which is, unfortunately, unknown. For other observable quantities, such as S
2 order parameters, the function relating Q to r involves some average over the Boltzmann ensemble of structures in solution, Q(⟨f(r)⟩), where f denotes the function of r that is being averaged.
Tn class="Chemical">his means that structure refinement based on such quantities must involve the averaging ⟨f(r)⟩ in addition to the averaging ⟨Q(⟨f(r)⟩)⟩.
S
2 order parameters are commonly derived from an analysis of NMR relaxation data using a so‐called “model free” model
and can be calculated as an ensemble‐ or time‐average of a function of the three Cartesian coordinate components of the n class="Chemical">13C−1H or 15N−1H bond vector.
They are commonly interpreted as a measure of the geometrical restriction (S
2=0: no restriction; S
2=1: complete restriction) of the directions of the mentioned bond vectors on a time scale faster than the stochastic rotational tumbling of the molecule in solution, for proteins of the order of nanoseconds. For relatively stable proteins, order parameters involving backbone atoms lie generally in the range 0.75values as low as 0.5) and for thermodynamic conditions, such as low pH, that are known to often destabilise proteins. For bond vectors in side chains, values as low as 0.05 can be found.
MD simulations have reproduced experimentally derived order‐parameter values for bond vectors involving backbone atoms with some success.[
,
] For side chains, tn class="Chemical">his is more challenging,[
,
,
,
] because of the flexibility of side chains and of the multiple hydrogens bound to the 13C atom in a CH3 ‐group or bound to the 15N atom in a NH2− group. This suggests the use of S
2 order‐parameter structure refinement using time averaging in order to obtain a conformational ensemble compatible with the order‐parameter data. The technique of time‐averaging order‐parameter structure refinement has been tested on the backbone 15N−1H order parameters of the B3 domain of protein G,
and subsequently applied to backbone 15N−1H order parameters of the protein IL‐4 at pH 6 to detect inconsistencies and model flaws regarding complementary sets of NMR data,
and applied to backbone 15N−1H order parameters of the protein hGH at pH 2.7 in order to explain the occurrence of low order‐parameter values in the middle of stable helices.
The application of S
2 order‐parameter restraining to CH3 and NH2 moieties in protein side chains is more challenging than to backbone NH groups. The multiple hydrogens cause ambiguity regarding peak assignments, which requires additional assumptions. The directional variability of bond vectors in side chains is generally ln class="Chemical">arger than for backbone N−H or Cα−H vectors, leading to a greater variety of and smaller order‐parameter values. Third, averaging over side‐chain motions may take longer to converge than over limited backbone motion in a stable protein.
Here the application of S
2 order‐parameter restraining to side‐chain NH, NH2 and CH3 moieties of the protein hen egg white lysozyme (HEWL)[
,
] is investigated. An earlier comparison of the experimentally derived S
2 n class="Chemical">values with those obtained from short, 1 ns unrestrained MD simulations showed a poor relation between simulation and experiment,
which could be due to the short simulation time period or force‐field deficiencies, assuming no flaws in the experimental data. Use of an improved force field, of much longer sampling, and of S
2 order‐parameter restraining might generate a conformational ensemble compatible with these and other experimental data on HEWL.
HEWL is one of the proteins most studied. Several X‐ray crystal structures are available, and sets of NOE data,
of 3
J couplings,
RDC values,
and of S
2 order parameters,[
,
] measured at a variety of thermodynamic conditions. Here the configurational ensembles, generated in unrestrained and in order‐parameter restrained MD simulations, will be used to calculate side‐chainn class="Chemical">13C−1H and 15N−1H order‐parameter values, which are compared to values obtained from NMR measurements at pH 3.5.[
,
]
The side‐chain S
2 values were separated into two groups, one of C−H n class="Chemical">values and another of N−H values. By separately restraining these subsets of S
2 values, it could be investigated whether restraining one subset would improve the agreement with values derived from experiment for the other subset of S
2 values. Four X‐ray crystal structures were used in the simulations and for comparison, in order to delineate the influence of a particular starting structure on the generated configurational ensemble.
The simulated configurational ensembles were also used to calculate NOE atom‐atom distances that were compared to a set of NOE atom‐atom distance bounds derived from experiment at pH 3.8.
A set of side‐chain 3
J
HαHβ couplings derived from experiment is available.[
,
] The 26 3
J
HαHβ couplings in side chains for which S
2 order‐parameter values derived from experiment are available, were used for comparison. They regard χ
1 torsional angles close to the backbone. A comparison of simulated with experimentally derived 3
J
HαHβ coupling n class="Chemical">values is not straightforward though, because the Karplus relation 3
J(θ) that connects a torsional angle θ to a 3
J coupling, possesses a rather large uncertainty of 1–2 Hz,
small 3
J coupling values (≈4 Hz) are difficult to determine precisely from spectra, and 3
J couplings in the range 5–8 Hz may result from averaging over long time periods (microseconds). The set of RDCs for side chains of HEWL
was not used for comparison, because they strongly depend on the solvent environment in the measurement.
Computational Methods
Energy minimisations and molecular dynamics simulations were performed using the GROMOS bio‐molecular simulation software.[
,
,
]
Molecular model
The protein was modelled using the GROMOS bio‐molecular force field 54 A7.[
,
] In view of the pH used in the experimental NMR measurements, pH 3.5, only Glu35 was protonated and n class="Chemical">His was doubly protonated.
The simple point charge (SPC) model
was used to describe the solvent molecules in the rectangular periodic box. To compensate for the overall positive charge of the protein, 10 Cl− ions were included in the solution. All bond lengths and the bond angle of the water molecules were kept rigid with a relative geometric precision of 10−4 using the SHAKE algorithm,
allowing for a 2 fs MD time step in the leap‐frog algorithm
used to integrate the equations of motion. For the non‐bonded interactions a triple‐range method
with cut‐off radii of 0.8/1.4 nm was used. Short‐range van der Waals and electrostatic interactions were evaluated every time step based on a charge‐group pair list.
Medium‐range van der Waals and electrostatic interactions, between pairs at a distance larger than 0.8 nm and shorter than 1.4 nm, were evaluated every fifth time step (10 fs), at which time point the pair list was updated, and kept constant between updates. Outside the larger cut‐off radius a reaction‐field approximation[
,
] with a relative dielectric permittivity of 61
was used. Minimum‐image periodic boundary conditions were applied.
Simulation set‐up
Four X‐ray crystal structures were used as initial structures for the energy minimisations followed by MD simulations.Structure 2VB1 from the Protein Data Bank (PDB),
derived from a triclinic unit cell at 0.065 nm resolution at T=100 K. It contains multiple side‐chain conformations for 46 residues.Structure 4LZT from the PDB, derived from a triclinic unit cell at 0.095 nm resolution at T=295 K. It contains multiple side‐chain conformations for 8 residues.Structure 1IEE from the PDB, derived from a tetragonal unit cell at 0.094 nm resolution at T=110 K. It contains multiple side‐chain conformations for 33 residues.Structure 1AKI from the PDB, derived from a orthorhombic unit cell at 0.15 nm resolution at T=298 K. It contains no multiple side‐chain conformations.For the initial structures the side‐chain conformation with the highest occupancy was chosen.An initial structure was first energy minimised in vacuo to release possible strain induced by small differences in bond lengths, bond angles, improper dihedral angles, and short non‐bonded contacts between the force‐field parameters and the X‐ray structure. Subsequently, the protein was put into a rectangular box filled with water molecules, such that the minimum solute‐wall distance was 1.0 nm, and n class="Chemical">water molecules closer than 0.23 nm from the solute were removed. This resulted in boxes with 12157 water molecules for the initial protein structures. In order to relax unfavourable contacts between atoms of the solute and the solvent, a second energy minimisation was performed for the protein in the periodic box with water while keeping the atoms of the solute harmonically position‐restrained
with a force constant of 25 000 kJ mol−1 nm−2.
The resulting protein‐water configuration (i. e., coordinates) was used as initial configuration for the MD simulation. In order to avoid artificial deformations in the protein structure due to relatively high‐energy atomic interactions still present in the system, the MD simulation was started at T=60 K and then the temperature was slowly raised to T=308 K. Initial atomic velocities were sampled from a Maxwell distribution at T=60 K. The equilibration scheme consisted of five short 20 ps simulations at temperatures 60, 120, 180, 240 and 308 K at constant volume. During the first four of the equilibration periods, the solute atoms were harmonically restrained to their positions in the initial structures with force constants of 25 000, 2500, 250, and 25 kJ mol−1 nm−2. The temperature was kept constant using the weak coupling algorithm
with a relaxation or coupling time τ
Τ=0.1 ps. Solute and solvent were separately coupled to the heat bath. Following tn class="Chemical">his equilibration procedure, the simulations were performed at a reference temperature of 308 K and a reference pressure of 1 atm. The pressure was kept constant using the weak coupling algorithm
with a coupling time τ
p=0.5 ps and an isothermal compressibility κ
T=4.575×10−4 (kJ mol−1 nm−3)−1. The centre of mass motion of the system was removed every 1000 time steps (2 ps).
Order‐parameter restraining
Two sets of 13C−1H and 15N−1H side‐chain order‐parameter target values
(exp)[
,
] for restraining
were used, see Tables 1, 2–3.
Table 1
values (51) derived from relaxation measurements and from four unrestrained MD simulations starting from four X‐ray crystal structures, and the mean of the latter four values and the root‐mean‐square deviation (RMSD) from it. Order‐parameter target values larger than 0.95 were set to 0.95 (second column between brackets). Values differing more than 0.2 from the experimental value (0.95 in case the experimental value is 1) are denoted using italics.
Residue and methyl group
Experimental value[21]
MD simulation
2VB1
4LZT
1IEE
1AKI
Mean
RMSD
Val2 CG2
0.598
0.39
0.51
0.50
0.43
0.46
0.05
Leu8 CD1
0.767
0.58
0.60
0.61
0.53
0.58
0.03
Leu8 CD2
0.803
0.63
0.60
0.64
0.57
0.61
0.03
Ala9 CB
1.0 (0.95)
0.93
0.93
0.93
0.93
0.93
0.003
Ala10 CB
0.901
0.91
0.92
0.92
0.92
0.92
0.003
Ala11 CB
0.861
0.91
0.93
0.92
0.92
0.92
0.01
Met12 CE
0.812
0.33
0.47
0.26
0.58
0.41
0.12
Leu17 CD1
0.630
0.46
0.61
0.33
0.52
0.48
0.10
Leu17 CD2
0.632
0.49
0.58
0.37
0.55
0.50
0.08
Leu25 CD1
1.0 (0.95)
0.40
0.57
0.30
0.41
0.42
0.10
Leu25 CD2
0.609
0.42
0.56
0.32
0.37
0.42
0.09
Val29 CG1
0.871
0.57
0.66
0.61
0.58
0.61
0.03
Val29 CG2
0.791
0.57
0.65
0.60
0.57
0.60
0.03
Ala31 CB
0.98 (0.95)
0.94
0.94
0.93
0.93
0.94
0.004
Thr43 CG2
0.361
0.68
0.78
0.79
0.62
0.72
0.07
Thr47 CG2
0.327
0.73
0.71
0.67
0.68
0.70
0.02
Thr51 CG2
0.778
0.49
0.58
0.64
0.46
0.54
0.07
Ile55 CG2
0.739
0.49
0.70
0.61
0.71
0.63
0.09
Ile55 CD
0.323
0.55
0.57
0.58
0.72
0.61
0.07
Leu56 CD1
0.734
0.79
0.76
0.80
0.77
0.78
0.02
Leu56 CD2
0.681
0.75
0.72
0.76
0.71
0.74
0.02
Ile58 CG2
1.0 (0.95)
0.84
0.86
0.86
0.88
0.86
0.01
Ile58 CD
0.160
0.81
0.76
0.75
0.82
0.78
0.03
Thr69 CG2
0.98 (0.95)
0.72
0.77
0.71
0.74
0.73
0.02
Leu75 CD1
0.590
0.62
0.73
0.62
0.37
0.58
0.13
Ile78 CG2
0.810
0.85
0.72
0.70
0.52
0.70
0.12
Ile78 CD
0.416
0.43
0.36
0.42
0.35
0.39
0.03
Leu83 CD1
0.884
0.68
0.65
0.77
0.53
0.66
0.09
Leu83 CD2
0.783
0.66
0.61
0.74
0.52
0.63
0.08
Leu84 CD1
1.0 (0.95)
0.46
0.66
0.66
0.63
0.60
0.08
Leu84 CD2
0.879
0.45
0.63
0.64
0.60
0.58
0.08
Ile88 CG2
0.697
0.55
0.81
0.62
0.80
0.70
0.11
Ile88 CD
0.722
0.27
0.45
0.34
0.37
0.36
0.06
Thr89 CG2
1.0 (0.95)
0.71
0.64
0.66
0.72
0.68
0.03
Ala90 CB
0.919
0.91
0.92
0.91
0.92
0.92
0.004
Val92 CG1
0.764
0.63
0.83
0.75
0.85
0.76
0.09
Val92 CG2
0.707
0.61
0.81
0.74
0.83
0.75
0.09
Ala95 CB
0.680
0.94
0.93
0.94
0.94
0.94
0.01
Ile98 CG2
0.740
0.90
0.83
0.87
0.85
0.86
0.02
Ile98 CD
0.815
0.89
0.85
0.82
0.85
0.85
0.03
Val99 CG1
0.487
0.85
0.78
0.68
0.52
0.71
0.12
Val99 CG2
0.517
0.85
0.80
0.68
0.53
0.71
0.12
Met105 CE
0.630
0.80
0.36
0.56
0.39
0.52
0.18
Ala107 CB
0.832
0.88
0.88
0.87
0.80
0.86
0.03
Val109 CG2
0.354
0.36
0.38
0.38
0.51
0.41
0.06
Val120 CG1
0.660
0.69
0.55
0.61
0.55
0.60
0.06
Ala122 CB
0.879
0.78
0.85
0.75
0.82
0.80
0.03
Ile124 CG2
0.753
0.75
0.56
0.67
0.72
0.68
0.07
Ile124 CD
0.351
0.48
0.39
0.55
0.56
0.50
0.07
Leu129 CD1
0.525
0.12
0.15
0.16
0.20
0.16
0.03
Leu129 CD2
0.507
0.11
0.12
0.11
0.19
0.13
0.03
Table 2
values (11) for Trp (NE1‐HE1) and Arg (NE‐HE) side chains derived from relaxation measurements and from four unrestrained MD simulations starting from four X‐ray crystal structures, and the mean of the latter four values and the root‐mean‐square deviation (RMSD) from it. Values differing more than 0.2 from the experimental value are denoted using italics.
Residue
Experimental
MD simulation
value[20]
2VB1
4LZT
1IEE
1AKI
Mean
RMSD
Trp28
0.90
0.88
0.84
0.85
0.87
0.86
0.02
Trp62
0.41
0.73
0.66
0.75
0.57
0.68
0.07
Trp63
0.88
0.83
0.81
0.85
0.78
0.82
0.03
Trp108
0.87
0.87
0.80
0.89
0.61
0.79
0.11
Trp111
0.88
0.83
0.78
0.78
0.80
0.80
0.02
Trp123
0.85
0.70
0.68
0.61
0.66
0.66
0.03
Arg61
0.28
0.22
0.30
0.33
0.32
0.29
0.04
Arg73
0.12
0.24
0.17
0.40
0.19
0.25
0.09
Arg112
0.31
0.28
0.16
0.23
0.18
0.21
0.05
Arg114
0.27
0.13
0.32
0.19
0.19
0.21
0.07
Arg125
0.05
0.12
0.14
0.10
0.14
0.13
0.02
Table 3
values (17) for Asn (ND2‐HD21, ‐HD22) and Gln (NE2‐HE21, ‐HE22) side chains derived from relaxation measurements and from four unrestrained MD simulations starting from four X‐ray crystal structures, and the mean of the latter four values and the root‐mean‐square deviation (RMSD) from it. The experimental values correspond to either HD/E21 or HD/E22.
The assignment in the second column is based on the best agreement with the values of the MD_2VB1 simulation (third column). Values differing more than 0.2 from the experimental value are denoted using italics.
Residue
Experimental value[20]
MD simulation
2VB1
4LZT
1IEE
1AKI
Mean
RMSD
Asn19 HD21
0.43
0.49
0.46
0.34
0.42
0.43
0.06
Asn19 HD22
0.24
0.31
0.23
0.23
0.25
0.03
Asn27 HD21
0.86
0.78
0.79
0.82
0.81
0.03
Asn27 HD22
0.72
0.82
0.60
0.62
0.70
0.69
0.09
Asn37 HD21
0.51
0.37
0.36
0.41
0.43
0.39
0.06
Asn37 HD22
0.21
0.21
0.16
0.25
0.21
0.03
Asn39 HD21
0.74
0.80
0.79
0.74
0.79
0.78
0.02
Asn39 HD22
0.61
0.59
0.54
0.59
0.58
0.03
Gln41 HE21
0.31
0.42
0.26
0.39
0.35
0.06
Gln41 HE22
0.19
0.21
0.21
0.16
0.24
0.21
0.03
Asn44 HD21
0.75
0.75
0.58
0.68
0.69
0.07
Asn44 HD22
0.51
0.71
0.68
0.60
0.62
0.65
0.04
Asn46 HD21
0.85
0.84
0.86
0.80
0.84
0.02
Asn46 HD22
0.62
0.82
0.68
0.58
0.74
0.71
0.09
Gln57 HE21
0.82
0.79
0.74
0.72
0.67
0.73
0.04
Gln57 HE22
0.76
0.54
0.64
0.37
0.58
0.14
Asn59 HD21
0.92
0.92
0.90
0.91
0.91
0.01
Asn59 HD22
0.78
0.90
0.89
0.86
0.87
0.88
0.02
Asn65 HD21
0.76
0.64
0.66
0.73
0.70
0.05
Asn65 HD22
0.57
0.42
0.28
0.33
0.25
0.32
0.06
Asn74 HD21
0.74
0.66
0.52
0.60
0.54
0.58
0.05
Asn74 HD22
0.41
0.31
0.36
0.37
0.36
0.04
Asn77 HD21
0.54
0.48
0.47
0.34
0.46
0.07
Asn77 HD22
0.24
0.31
0.22
0.28
0.22
0.26
0.04
Asn93 HD21
0.59
0.53
0.63
0.52
0.72
0.60
0.08
Asn93 HD22
0.34
0.32
0.30
0.40
0.34
0.04
Asn103 HD21
0.72
0.33
0.49
0.36
0.48
0.15
Asn103 HD22
0.26
0.61
0.18
0.33
0.20
0.33
0.17
Asn106 HD21
0.58
0.68
0.44
0.67
0.47
0.57
0.11
Asn106 HD22
0.46
0.24
0.47
0.29
0.37
0.10
Asn113 HD21
0.47
0.40
0.65
0.79
0.58
0.61
0.14
Asn113 HD22
0.21
0.31
0.55
0.45
0.38
0.13
Gln121 HE21
0.36
0.34
0.31
0.50
0.39
0.39
0.07
Gln121 HE22
0.18
0.09
0.36
0.21
0.21
0.10
values (51) derived from relaxation measurements and from four unrestrained MD simulations starting from four X‐ray crystal structures, and the mean of the latter four n class="Chemical">values and the root‐mean‐square deviation (RMSD) from it. Order‐parameter target values larger than 0.95 were set to 0.95 (second column between brackets). Values differing more than 0.2 from the experimental value (0.95 in case the experimental value is 1) are denoted using italics.
Residue and methyl groupExperimental valueMD simulation2VB14LZT1IEE1AKIMeanRMSDVal2 CG20.5980.390.510.500.430.460.05Leu8 CD10.7670.580.600.610.530.580.03Leu8 CD20.8030.630.600.640.570.610.03Ala9 CB1.0 (0.95)0.930.930.930.930.930.003Ala10 CB0.9010.910.920.920.920.920.003Ala11 CB0.8610.910.930.920.920.920.01Met12 CE0.8120.330.470.260.580.410.12Leu17 CD10.6300.460.610.330.520.480.10Leu17 CD20.6320.490.580.370.550.500.08Leu25CD11.0 (0.95)0.400.570.300.410.420.10Leu25CD20.6090.420.560.320.370.420.09Val29 CG10.8710.570.660.610.580.610.03Val29CG20.7910.570.650.600.570.600.03Ala31 CB0.98 (0.95)0.940.940.930.930.940.004Thr43CG20.3610.680.780.790.620.720.07Thr47CG20.3270.730.710.670.680.700.02Thr51CG20.7780.490.580.640.460.540.07Ile55CG20.7390.490.700.610.710.630.09Ile55CD0.3230.550.570.580.720.610.07Leu56CD10.7340.790.760.800.770.780.02Leu56CD20.6810.750.720.760.710.740.02Ile58CG21.0 (0.95)0.840.860.860.880.860.01Ile58CD0.1600.810.760.750.820.780.03Thr69CG20.98 (0.95)0.720.770.710.740.730.02Leu75 CD10.5900.620.730.620.370.580.13Ile78 CG20.8100.850.720.700.520.700.12Ile78 CD0.4160.430.360.420.350.390.03Leu83 CD10.8840.680.650.770.530.660.09Leu83 CD20.7830.660.610.740.520.630.08Leu84 CD11.0 (0.95)0.460.660.660.630.600.08Leu84 CD20.8790.450.630.640.600.580.08Ile88 CG20.6970.550.810.620.800.700.11Ile88 CD0.7220.270.450.340.370.360.06Thr89CG21.0 (0.95)0.710.640.660.720.680.03Ala90 CB0.9190.910.920.910.920.920.004Val92 CG10.7640.630.830.750.850.760.09Val92 CG20.7070.610.810.740.830.750.09Ala95 CB0.6800.940.930.940.940.940.01Ile98CG20.7400.900.830.870.850.860.02Ile98CD0.8150.890.850.820.850.850.03Val99 CG10.4870.850.780.680.520.710.12Val99CG20.5170.850.800.680.530.710.12Met105 CE0.6300.800.360.560.390.520.18Ala107 CB0.8320.880.880.870.800.860.03Val109 CG20.3540.360.380.380.510.410.06Val120 CG10.6600.690.550.610.550.600.06Ala122 CB0.8790.780.850.750.820.800.03Ile124 CG20.7530.750.560.670.720.680.07Ile124 CD0.3510.480.390.550.560.500.07Leu129CD10.5250.120.150.160.200.160.03Leu129CD20.5070.110.120.110.190.130.03values (11) for n class="Chemical">Trp (NE1‐HE1) and Arg (NE‐HE) side chains derived from relaxation measurements and from four unrestrained MD simulations starting from four X‐ray crystal structures, and the mean of the latter four values and the root‐mean‐square deviation (RMSD) from it. Values differing more than 0.2 from the experimental value are denoted using italics.
ResidueExperimentalMD simulationvalue2VB14LZT1IEE1AKIMeanRMSDTrp280.900.880.840.850.870.860.02Trp620.410.730.660.750.570.680.07Trp630.880.830.810.850.780.820.03Trp1080.870.870.800.890.610.790.11Trp1110.880.830.780.780.800.800.02Trp1230.850.700.680.610.660.660.03Arg610.280.220.300.330.320.290.04Arg730.120.240.170.400.190.250.09Arg1120.310.280.160.230.180.210.05Arg1140.270.130.320.190.190.210.07Arg1250.050.120.140.100.140.130.02values (17) for n class="Chemical">Asn (ND2‐HD21, ‐HD22) and Gln (NE2‐HE21, ‐HE22) side chains derived from relaxation measurements and from four unrestrained MD simulations starting from four X‐ray crystal structures, and the mean of the latter four values and the root‐mean‐square deviation (RMSD) from it. The experimental values correspond to either HD/E21 or HD/E22.
The assignment in the second column is based on the best agreement with the values of the MD_2VB1 simulation (third column). Values differing more than 0.2 from the experimental value are denoted using italics.
ResidueExperimental valueMD simulation2VB14LZT1IEE1AKIMeanRMSDAsn19 HD210.430.490.460.340.420.430.06Asn19 HD220.240.310.230.230.250.03Asn27 HD210.860.780.790.820.810.03Asn27 HD220.720.820.600.620.700.690.09Asn37 HD210.510.370.360.410.430.390.06Asn37 HD220.210.210.160.250.210.03Asn39 HD210.740.800.790.740.790.780.02Asn39 HD220.610.590.540.590.580.03Gln41 HE210.310.420.260.390.350.06Gln41 HE220.190.210.210.160.240.210.03Asn44HD210.750.750.580.680.690.07Asn44HD220.510.710.680.600.620.650.04Asn46HD210.850.840.860.800.840.02Asn46HD220.620.820.680.580.740.710.09Gln57 HE210.820.790.740.720.670.730.04Gln57 HE220.760.540.640.370.580.14Asn59 HD210.920.920.900.910.910.01Asn59 HD220.780.900.890.860.870.880.02Asn65HD210.760.640.660.730.700.05Asn65HD220.570.420.280.330.250.320.06Asn74 HD210.740.660.520.600.540.580.05Asn74 HD220.410.310.360.370.360.04Asn77 HD210.540.480.470.340.460.07Asn77 HD220.240.310.220.280.220.260.04Asn93 HD210.590.530.630.520.720.600.08Asn93 HD220.340.320.300.400.340.04Asn103HD210.720.330.490.360.480.15Asn103HD220.260.610.180.330.200.330.17Asn106 HD210.580.680.440.670.470.570.11Asn106 HD220.460.240.470.290.370.10Asn113 HD210.470.400.650.790.580.610.14Asn113 HD220.210.310.550.450.380.13Gln121 HE210.360.340.310.500.390.390.07Gln121 HE220.180.090.360.210.210.10A set of 51
(exp) values for CH3 moieties in 30 residues,A set of 28
(exp) values for NH and NH2 moieties in six Trp, five Arg, fourteen Asn and three Gln residues.The distribution of these S
2 values over the protein is shown in Figure 1.
Figure 1
Ribbon pictures of the structure of HEWL with explicit side chains for which S
2(exp) order‐parameter values derived from relaxation measurements are available. Left: Ala, Ile, Leu, Met, Thr and Val side chains; middle: Arg and Trp side chains; right: Asn and Gln side chains.
Ribbon pictures of the structure of HEWL with explicit side chains for which S
2(exp) order‐parameter values derived from relaxation measurements are available. Left: Ala, Ile, Leu, Met, Thr and Val side chains; middle: Arg and Trp side chains; right: Asn and Gln side chains.For the Asn and n class="Chemical">Gln residues, one
(exp) value per NH2 group was available. This required the assignment to one of the two NH1 and NH2 bond vectors. This was done by calculating
(MD) and
(MD) values from the unrestrained simulation MD_2VB1 starting from the 2VB1 X‐ray structure and then selecting the N−H vector with its
(MD) value closest to
(exp) for restraining. A corresponding procedure was used to assign experimentally unassigned
and
values for Val residues and
and
values for Leu residues.
For an ideal methyl group with equal and fixed C−H bond lengths and H−C−H bond angles in which rotation around the symmetry axis occurs uniformly, the order parameter for the C−H bond vector is given bywhere β is the angle between a C−H vector and the symmetry axis, which can be considered equal to the C−C bond vector of the bond to the C‐atom adjacent to the CH3 group. When in addition the rotational motion around the C−C axis is independent of the motion of the C‐axis itself, one may factorise their contributions,When β=109.5°, one has
=0.111. Thus the methyl group restraining is applied to the C−C bond vector and the target value isFor the NH2 groups in Asn and n class="Chemical">Gln approximation (2) does not hold, because the rotation around the C−N axis is not uniform. There is a large barrier for the 180° rotation and the rotational motion need not be decoupled from other motions. Experimentally, the two hydrogens are in slow exchange.
Order‐parameter target values greater than 0.95 were set to 0.95. The restraining force constant K
sr was set to 300 kJmol−1, the memory relaxation time to τ
sr=200 ps, and the flat‐bottom parameter of the restraining potential‐energy term to ΔS
2=0.1, which means a flat bottom of 0.2 width.
MD simulations performed
Four unrestrained MD simulations, starting from the four mentioned X‐ray crystal structures, were performed:MD_2VB1,MD_4LZT,MD_1IEE,MD_1AKI,each 20 ns long. The average solute temperatures were 311 K and the solvent temperatures 312 K.Starting from the 2VB1 X‐ray crystal structure, three S
2‐restraining MD simulations were performed:MD_2VB1_Cres, applying
restraining,MD_2VB1_Nres, applying
restraining,MD_2VB1_C+Nres, applying
and
restraining,again each 20 ns long. The average solute temperatures were 311 K and the solvent temperatures 312 K. When restraining an order parameter for a bond vector to a target n class="Chemical">value derived from experiment, the length of the simulation does not play a significant role. It is the restraining force that has to overcome the resistance originating from the particular local protein structure, for example.
Analysis of atomic trajectories
Trajectory energies and atomic coordinates were stored at 5 ps intervals and used for analysis.
S
2 order parameters were calculated using the ensemble averaging expressionwhere τ indicates the time‐averaging window, here 1 ns, shorter than the rotational correlation time of 5.7 ns of HEWL in solution,are the components of the vector ≡− connecting atoms X and Y, and r≡|| its length.
To obtain a dimensionless quantity the term in curly brackets is multiplied with the 6th power of the effective length (
) of the vector
XY. Because in the present work bond length constraints are used, the length of
XY is essentially constant over time and thus equal to its effective value
.Before calculating
, the protein trajectory structures are superimposed using the backbone atoms (N, Cα, C) of residues 3–126 in the fit in order to eliminate the effect of overall rotation of the protein upon the
values. Use of only the backbone atoms of four of the five α‐helices and two β‐strands in HEWL (residues 4–15, 24–36, 41–45, 50–53, 89–99, and 108–115) did not lead to significantly different
n class="Chemical">values.
In the S
2 order‐parameter restraining simulations, the S
2 order parameter is calculated at every time step (2 fs) using an exponential damping factor in the average
with a memory relaxation time τ
sr=200 ps, and no rotational fit of the protein structures is carried out, which means that the calculated order parameters in the biased simulation are influenced by the stochastic tumbling of the protein. These S
2 order‐parameter values will thus differ slightly from the ones calculated from the saved trajectory structures, because in the averages in Equation (4) trajectory structures 5 ps apart are used, the exponential damping factor is not used, the averaging period is 1 ns and a rotational fit of the protein structures is carried out. However, to analyse all trajectories in the same way Equation (4) was used for both the unrestrained and restrained trajectories.In view of the uncertainty inherent to the derivation of
(exp) values from relaxation experiments and inherent to the calculation of
(MD) n class="Chemical">values from MD simulation, a deviation of less than 0.2 between simulation and experiment is considered insignificant.
The GROMOS force fields treat aliphatic carbons as united CH, CH2 and CH3 atoms. So inter‐n class="Chemical">hydrogen distances involving the aliphatic hydrogen atoms were calculated using virtual atomic positions for CH and pro‐chiral CH2
and pseudo‐atomic positions for CH3
for those hydrogen atoms.
The pseudo‐atom NOE distance bound corrections of ref. [44] were used.
The set of NOE distance bounds can be found in Table S1 in the Supporting Information, together with values obtained from the seven simulations. The NOE between Trp28 HZ3 and Leu56 HG was reassigned as between Trp28 HZ3 and Leu56HD* following reassessment of the experimental spectra. Inter‐hydrogen distances were calculated as ⟨r
−3⟩−1/3, that is, using r
−3 averaging over the trajectory structures, where r indicates the actual hydrogen‐hydrogen distance.
In view of the uncertainty inherent to the calculation of NOE bounds and r
−3 averaged distances, deviations from experiment of less than 0.1 nm are considered insignificant.
For the calculation of the side‐chain 3
J
Hα‐Hβ couplings, the Karplus relation[
,
] was used with the parameter values a=9.5 Hz, b=−1.6 Hz and c=1.8 Hz.
In view of the various factors contributing to an uncertainty of about 2 Hz inherent to the Karplus relation linking structure and 3
J couplings, a deviation of less than 2 Hz between 3
J
Hα‐Hβ coupling n class="Chemical">values calculated from MD trajectory structures and 3
J
Hα‐Hβ coupling values derived from experiment is considered insignificant.
Atom‐positional root‐mean‐square differences RMSD(t) between trajectory structures and the X‐ray crystal structures and atom‐positional root‐mean‐square fluctuations (RMSF), i. e. around their average positions, in the MD trajectories were calculated after superimposing the backbone atoms (N, Cα, C) of residues 3–126 to eliminate the contribution of overall translation and rotation of the protein.The secondary structure assignment was done with the program DSSP, based on the Kabsch‐Sander rules.Hydrogen bonds were identified according to a geometric criterion: a n class="Chemical">hydrogen bond was assumed to exist if the hydrogen‐acceptor distance was smaller than 0.25 nm and the donor‐hydrogen‐acceptor angle was larger than 135°.
Results and Discussion
Comparison of S
2 order‐parameter values calculated from unrestrained MD trajectories with NMR derived values
Table 1 lists 51
values derived from relaxation measurements and from four unrestrained MD simulations starting from four X‐ray crystal structures. The mean of the four MD n class="Chemical">values and the root‐mean‐square deviation (RMSD) from it are also presented. As order parameters in an MD simulation can only be equal to 1 if there is no motion at all, order‐parameter target values larger than 0.95 were set to 0.95. Deviations from the experimentally derived values of more than 0.2 are denoted in italics. The mean values of the MD simulations show 18 deviations larger than 0.2, 12 are smaller and six are larger than the experimentally derived value. Some large (>0.8) experimentally derived values, for example, for Met12 CE (0.812), Leu25CD1 (1.0), Val29 CG1 (0.871), Thr69CG2 (0.98), Leu84 CD1 (1.0) and CD2 (0.879), Thr89CG2 (1.0), are not reproduced within 0.2 in any of the four MD simulations. Some small (<0.4) experimentally derived values, for example, for Thr43CG2 (0.361), Thr47CG2 (0.327), Ile55CD (0.323), and Ile58CD (0.160), are also not reproduced within 0.2 in any of the four MD simulations. Large order parameters are expected for side chains buried inside the protein, while small order parameters are expected for side chains at the protein surface. Yet, this seems not always true. Val99 has in the 2VB1 X‐ray structure a solvent accessible area of only 7 % and its side chain is surrounded by the side chains of Tyr20, Trp28, Ile98, and Tyr108. This leads to simulated
values of about 0.71 to be compared to the experimentally derived value of 0.5. Thr89 has in the 2VB1 X‐ray structure a solvent accessible area of 76 %. This leads to simulated
values of about 0.68 to be compared to the experimentally derived value of 1.0. A larger variation (RMSD≥0.12) of
values between the four MD simulations is observed for Met12 CE, Leu75 CD1, Ile78 CG2, Val99 CG1 and CG2, and Met105 CE.
Table 2 lists the 11
values for n class="Chemical">Trp (NE1‐HE1) and Arg (NE‐HE) side chains derived from relaxation measurements and from four unrestrained MD simulations starting from four X‐ray crystal structures. Three simulations show only one deviation from the experimentally derived value larger than 0.2. Both, large and small values are well reproduced.
Table 3 lists the 17
values for n class="Chemical">Asn (ND2‐HD21, ‐HD22) and Gln (NE2‐HE21, ‐HE22) side chains derived from relaxation measurements and from four unrestrained MD simulations starting from four X‐ray crystal structures. The simulations show one or two deviations from the experimentally derived value larger than 0.2, four simulated values, for Asn65 and 74, smaller than the experimentally derived values, and two simulated values, for Asn103 and 113, larger than the experimentally derived ones.
Table 4 shows the occurrence (%) of hydrogen bonds involving the side chains of n class="Chemical">Arg, Asn, Gln and Trp residues in the four X‐ray structures and in the four unrestrained MD simulations starting from the four respective X‐ray structures. The four hydrogen bonds present in all four X‐ray structures are also observed in the MD simulations, but with widely different occurrences (0–85 %). For the seven hydrogen bonds observed in only three of the four X‐ray structures the occurrences vary from 0 to 99 %. Considering the different thermodynamic conditions under which the X‐ray diffraction of the different crystals was measured and the pH of the NMR measurement in aqueous solution, the observed differences are not surprising.
Table 4
Occurrence (%) of hydrogen bonds (52) involving the side chains of Arg, Asn, Gln and Trp residues in four X‐ray structures and in the four unrestrained MD simulations starting from the four X‐ray structures. Only hydrogen bonds present in one of the X‐ray structures or with a population of at least 20 % in any of the restrained or unrestrained MD simulations are included. Only hydrogen bond populations of 1 % or greater are shown.
Hydrogen bond
X‐ray structure
MD simulation
Donor‐acceptor
2VB1
4LZT
1IEE
1AKI
2VB1
4LZT
1IEE
1AKI
Arg5 NE‐HE‐Trp123 O
15
21
10
1
Arg5 NH1/2‐HH1/2‐Arg125 O*
100
100
100
100
9
3
5
3
Arg5 NH1‐HH12‐Trp123 O
100
100
100
100
22
17
24
13
Asn19 ND2‐HD22‐Asp18 OD1/2*
11
10
10
19
Asn27 ND2‐HD22‐Trp111 O
–
2
–
–
Asn27 ND2‐HD22‐Ser24 O
100
–
13
1
1
Asn27 ND2‐HD22‐Ser24 OG
–
11
2
–
Asn27 ND2‐HD22‐Cys115 O
–
19
1
78
Trp28 NE1‐HE1‐Leu17 O
–
2
–
29
Trp28 NE1‐HE1‐Tyr23 O
100
–
32
8
–
Gln41 NE2‐HE22‐Leu84 O
100
2
3
1
–
Asn44 ND2‐HD22‐Asp52 OD1/2*
100
100
61
43
34
34
Asn44 ND2‐HD22‐Gln57 OE1
100
14
2
27
5
Arg45 NH1‐HH12‐Gly49 O
100
8
2
–
4
Asn46 ND2‐HD21‐Ala107 O
56
–
4
–
Asn46 ND2‐HD1/2‐Asp52 OD1/2*
100
100
100
75
40
61
55
Asn46 ND2‐HD22‐Ser50 OG
100
100
100
1
24
35
10
Asn46 ND2‐HD22‐Ser50 O
2
24
36
10
Gln57 NE2‐HE21‐Glu35 OE1
1
–
–
36
Gln57 NE2‐HE21‐Ala42 O
66
7
21
–
Gln57 NE2‐HE22‐Ser36 OG
6
46
2
23
Gln57 NE2‐HE22‐Gly54 O
100
100
100
100
85
16
49
–
Asn59 ND2‐HD21‐Ser50 OG
100
100
100
99
94
79
96
Asn59 ND2‐HD1/2‐Asp52 OD1/2*
100
100
100
70
54
50
50
Arg61 NH2‐HH22‐Asp48 OD2
100
100
100
1
–
–
–
Arg61 NH2‐HH21‐Asp48 O
100
–
–
1
–
Arg61 NE‐HE‐Thr69 OG1
6
16
13
28
Trp63 NE1‐HE1‐Asn106 OD1
11
–
28
–
Asn65 ND2‐HD22‐Asn74 OD1
52
15
35
14
Arg68 NH2‐HH22‐Thr51 OG1
100
–
2
–
–
Arg73 NH1‐HH12‐Arg61 O
13
11
28
13
Asn74 ND2‐HD21‐Asn77 O
–
3
–
22
Asn103 ND2‐HD22‐Ile98 O
100
100
–
–
–
–
Asn103 ND2‐HD22‐Asp101 OD1/2*
42
3
23
–
Asn106 ND2‐HD22‐Gly102 O
–
21
–
–
Asn106 ND2‐HD22‐Asn103 O
100
100
3
–
–
3
Asn106 ND2‐HD22‐Asn103 OD1
22
–
4
1
Trp108 NE1‐HE1‐Leu56 O
100
91
59
94
45
Trp111 NE1‐HE1‐Asn27 OD1
100
100
100
100
1
16
2
1
Trp111 NE1‐HE1‐Asn27 O
–
–
–
–
Arg112 NE‐HE‐Asn106 O
20
8
1
27
Arg112 NH1‐HH12‐Asn106 O
100
100
100
19
28
2
4
Asn113 ND2‐HD21‐Val109 O
2
–
66
1
Arg114 NH1‐HH12‐Glu35 OE1
–
25
–
–
Arg114 NE‐HE‐Asn113 OD1
9
3
26
26
Gln121 NE2‐HE22‐Asp119 OD1/2*
22
10
34
27
Trp123 NE1‐HE1‐Gly117 O
14
–
20
49
Trp123 NE1‐HE1‐Thr118 OG1
14
48
–
3
Arg125 NE‐HE‐Gln121 OE1
100
2
5
–
1
Arg125 NH2‐HH22‐Asp119 OD2
100
100
100
–
–
–
–
Arg125 NH2‐HH22‐Gln121 OE1
100
100
1
4
1
1
Arg125 NH1‐HH12‐Ala122 O
100
–
–
1
1
* Some hydrogen bonds involving aspartic acid side chains are present in the simulations with either OD1 or OD2 acting as the acceptor. In these cases (marked OD1/2) the highest population of the hydrogen bond involving either OD1 or OD2 is listed. Similarly for hydrogen bonds involving asparagine NH2 groups in some cases (marked ND2‐HD1/2) the highest population of a hydrogen bond where the donor is either ND2‐HD21 or ND2‐HD22 is listed while for arginine NH2 groups in some cases (marked NH1/2‐HH1/2) the highest population of a hydrogen bond where the donor is either NH1‐HH11, NH1‐HH12, NH2‐HH21 or NH2‐HH22 is listed.
Occurrence (%) of hydrogen bonds (52) involving the side chains of n class="Chemical">Arg, Asn, Gln and Trp residues in four X‐ray structures and in the four unrestrained MD simulations starting from the four X‐ray structures. Only hydrogen bonds present in one of the X‐ray structures or with a population of at least 20 % in any of the restrained or unrestrained MD simulations are included. Only hydrogen bond populations of 1 % or greater are shown.
Hydrogen bondX‐ray structureMD simulationDonor‐acceptor2VB14LZT1IEE1AKI2VB14LZT1IEE1AKIArg5 NE‐HE‐Trp123 O1521101Arg5 NH1/2‐HH1/2‐Arg125 O*1001001001009353Arg5 NH1‐HH12‐Trp123 O10010010010022172413Asn19 ND2‐HD22‐Asp18 OD1/2*11101019Asn27 ND2‐HD22‐Trp111 O–2––Asn27 ND2‐HD22‐Ser24 O100–1311Asn27 ND2‐HD22‐Ser24 OG–112–Asn27 ND2‐HD22‐Cys115 O–19178Trp28 NE1‐HE1‐Leu17 O–2–29Trp28 NE1‐HE1‐Tyr23 O100–328–Gln41 NE2‐HE22‐Leu84 O100231–Asn44 ND2‐HD22‐Asp52 OD1/2*10010061433434Asn44 ND2‐HD22‐Gln57 OE1100142275Arg45 NH1‐HH12‐Gly49 O10082–4Asn46 ND2‐HD21‐Ala107 O56–4–Asn46 ND2‐HD1/2‐Asp52 OD1/2*10010010075406155Asn46 ND2‐HD22‐Ser50 OG1001001001243510Asn46 ND2‐HD22‐Ser50 O2243610Gln57 NE2‐HE21‐Glu35 OE11––36Gln57 NE2‐HE21‐Ala42 O66721–Gln57 NE2‐HE22‐Ser36 OG646223Gln57 NE2‐HE22‐Gly54 O100100100100851649–Asn59 ND2‐HD21‐Ser50 OG10010010099947996Asn59 ND2‐HD1/2‐Asp52 OD1/2*10010010070545050Arg61 NH2‐HH22‐Asp48 OD21001001001–––Arg61 NH2‐HH21‐Asp48 O100––1–Arg61 NE‐HE‐Thr69 OG16161328Trp63 NE1‐HE1‐Asn106 OD111–28–Asn65 ND2‐HD22‐Asn74 OD152153514Arg68 NH2‐HH22‐Thr51 OG1100–2––Arg73 NH1‐HH12‐Arg61 O13112813Asn74 ND2‐HD21‐Asn77 O–3–22Asn103 ND2‐HD22‐Ile98 O100100––––Asn103 ND2‐HD22‐Asp101 OD1/2*42323–Asn106 ND2‐HD22‐Gly102 O–21––Asn106 ND2‐HD22‐Asn103 O1001003––3Asn106 ND2‐HD22‐Asn103 OD122–41Trp108 NE1‐HE1‐Leu56 O10091599445Trp111 NE1‐HE1‐Asn27 OD110010010010011621Trp111 NE1‐HE1‐Asn27 O––––Arg112 NE‐HE‐Asn106 O208127Arg112 NH1‐HH12‐Asn106 O100100100192824Asn113 ND2‐HD21‐Val109 O2–661Arg114 NH1‐HH12‐Glu35 OE1–25––Arg114 NE‐HE‐Asn113 OD1932626Gln121 NE2‐HE22‐Asp119 OD1/2*22103427Trp123 NE1‐HE1‐Gly117 O14–2049Trp123 NE1‐HE1‐Thr118 OG11448–3Arg125 NE‐HE‐Gln121 OE110025–1Arg125 NH2‐HH22‐Asp119 OD2100100100––––Arg125 NH2‐HH22‐Gln121 OE11001001411Arg125 NH1‐HH12‐Ala122 O100––11* Some hydrogen bonds involving n class="Chemical">aspartic acid side chains are present in the simulations with either OD1 or OD2 acting as the acceptor. In these cases (marked OD1/2) the highest population of the hydrogen bond involving either OD1 or OD2 is listed. Similarly for hydrogen bonds involving asparagine NH2 groups in some cases (marked ND2‐HD1/2) the highest population of a hydrogen bond where the donor is either ND2‐HD21 or ND2‐HD22 is listed while for arginine NH2 groups in some cases (marked NH1/2‐HH1/2) the highest population of a hydrogen bond where the donor is either NH1‐HH11, NH1‐HH12, NH2‐HH21 or NH2‐HH22 is listed.
Figures 2 and S1–S3 show the secondary structure elements
of HEWL as a function of time calculated for the four unrestrained MD simulations. Five α‐helices (red; residues 4–15, 24–36, 89–99, 108–115 and 121–125) and three β‐strands (blue; residues 41–45, 50–53 and 58–59) are ln class="Chemical">argely maintained, but the α‐helix at residues 108–115 turns into two β‐bridges (yellow) after 3 ns in the MD_1IEE simulation (Figure S2). All four simulations show a helix of alternating α‐helical (red) and 310‐helical (black) character at residues 80–85. At residues 21–24, simulation MD_1AKI (Figure S3) shows a 310‐helix, which is lost after about 6 ns in the MD_2VB1 (Figure 2) and MD_1IEE (Figure S2) simulations, and within 1 ns in the MD_4LZT simulation (Figure S1).
Figure 2
Secondary structure elements
as a function of time calculated for the unrestrained MD simulation MD_2VB1 starting from the 2VB1 X‐ray structure. Red: α‐helix; green: π‐helix; black: 310‐helix; blue: β‐strand; yellow: β‐bridge; brown: bend; grey: turn.
Secondary structure elements
as a function of time calculated for the unrestrained MD simulation MD_2VB1 starting from the 2VB1 X‐ray structure. Red: α‐helix; green: π‐helix; black: 310‐helix; blue: β‐strand; yellow: β‐bridge; brown: bend; grey: turn.Figure 3 shows the backbone Cα atom‐positional root‐mean‐square fluctuations (RMSF) as function of residue sequence number in the four unrestrained MD simulations MD_2VB1 (black), MD_4LZT (red), MD_1IEE (green) and MD_1AKI (blue) starting from the respective four X‐ray structures. Apart from the residues beyond residue sequence number 100 at the C‐terminal part of the polypeptide chain, the motional patterns in the four simulations are rather similar, except for residues 21–24 in the MD_4LZT (red) simulation that become very mobile, their initial 310‐helical character being lost.
Figure 3
Backbone Cα atom‐positional root‐mean‐square fluctuations (RMSF) as function of residue sequence number in the four unrestrained MD simulations MD_2VB1 (black), MD_4LZT (red), MD_1IEE (green) and MD_1AKI (blue) starting from the respective four X‐ray structures. The trajectory structures are translationally and rotationally superimposed using the backbone atoms (N, Cα, C) of residues 3–126. The black bars at the top indicate secondary structure elements of HEWL (thick bars: α‐helix; thin bars, β‐strand).
Backbone Cα atom‐positional root‐mean‐square fluctuations (RMSF) as function of residue sequence number in the four unrestrained MD simulations MD_2VB1 (black), MD_4LZT (red), MD_1IEE (green) and MD_1AKI (blue) starting from the respective four X‐ray structures. The trajectory structures are translationally and rotationally superimposed using the backbone atoms (N, Cα, C) of residues 3–126. The black bars at the top indicate secondary structure elements of HEWL (thick bars: α‐helix; thin bars, β‐strand).
Comparison of S
2 order‐parameter values calculated from S
2 order‐parameter restraining MD trajectories with NMR derived values
Table 5 lists the 51
values derived from relaxation measurements and from the unrestrained and order‐parameter restrained MD simulations starting from the 2VB1 X‐ray crystal structure using n class="Chemical">three different sets of S
2 order‐parameter restraints. The unrestrained MD simulation shows 22 S
2 order‐parameter values (in italics) that deviate more than 0.2 from the experimentally derived values (in 17 residues: 2, 12, 25, 29, 43, 47, 51, 55, 58, 69, 83, 84, 88, 89, 95, 99 and 129). S
2 order‐parameter restraining towards the set Cres of 51 target
(exp) values leads, as expected, to good agreement between simulation and experiment for the 51
order parameters. Only three deviations larger than 0.2 are observed, for Ala95 CB and for Leu129CD1 and CD2. Tables 6 and 7 show that restraining towards the set Cres of 51 target
(exp) values very slightly worsens the agreement between simulation and experiment for the
(exp) values. Worsening by more than 0.1 is observed for Trp108, Trp111, and Arg112 (Table 6), and for Gln57 HE21 and Asn65HD22 (Table 7). Yet, also some improvement by 0.1 of the agreement between simulation and experiment for the
values is observed, for example, for Asn44HD22, Asn46HD22 and Asn103HD22 (Table 7).
Table 5
values (51) derived from relaxation measurements and from the unrestrained and order‐parameter restrained MD simulations starting from the 2VB1 X‐ray crystal structure. Order‐parameter target values larger than 0.95 were set to 0.95 (second column between brackets). Values differing more than 0.2 from the experimental value (0.95 in case the experimental value is 1) are denoted using italics.
Residue and methyl group
Experimental value[21]
Unrestrained MD
Order‐parameter restrained MD
2VB1
2VB1_Cres
2VB1_Nres
2VB1_C+Nres
Val2 CG2
0.598
0.39
0.42
0.46
0.44
Leu8 CD1
0.767
0.58
0.64
0.65
0.67
Leu8 CD2
0.803
0.63
0.72
0.66
0.71
Ala9 CB
1.0 (0.95)
0.93
0.93
0.93
0.93
Ala10 CB
0.901
0.91
0.92
0.92
0.92
Ala11 CB
0.861
0.91
0.92
0.92
0.92
Met12 CE
0.812
0.33
0.90
0.46
0.87
Leu17 CD1
0.630
0.46
0.51
0.78
0.56
Leu17 CD2
0.632
0.49
0.58
0.77
0.61
Leu25 CD1
1.0 (0.95)
0.40
0.81
0.64
0.81
Leu25 CD2
0.609
0.42
0.69
0.69
0.75
Val29 CG1
0.871
0.57
0.85
0.62
0.82
Val29 CG2
0.791
0.57
0.84
0.61
0.81
Ala31 CB
0.98 (0.95)
0.94
0.95
0.93
0.94
Thr43 CG2
0.361
0.68
0.43
0.74
0.35
Thr47 CG2
0.327
0.73
0.40
0.73
0.42
Thr51 CG2
0.778
0.49
0.85
0.54
0.79
Ile55 CG2
0.739
0.49
0.63
0.53
0.69
Ile55 CD
0.323
0.55
0.41
0.56
0.40
Leu56 CD1
0.734
0.79
0.63
0.56
0.74
Leu56 CD2
0.681
0.75
0.66
0.53
0.68
Ile58 CG2
1.0 (0.95)
0.84
0.87
0.72
0.88
Ile58 CD
0.160
0.81
0.20
0.78
0.22
Thr69 CG2
0.98 (0.95)
0.72
0.89
0.84
0.88
Leu75 CD1
0.590
0.62
0.69
0.52
0.56
Ile78 CG2
0.810
0.85
0.83
0.59
0.80
Ile78 CD
0.416
0.43
0.45
0.29
0.40
Leu83 CD1
0.884
0.68
0.79
0.35
0.77
Leu83 CD2
0.783
0.66
0.72
0.41
0.71
Leu84 CD1
1.0 (0.95)
0.46
0.86
0.60
0.86
Leu84 CD2
0.879
0.45
0.83
0.58
0.84
Ile88 CG2
0.697
0.55
0.66
0.81
0.66
Ile88 CD
0.722
0.27
0.64
0.49
0.58
Thr89 CG2
1.0 (0.95)
0.71
0.87
0.69
0.85
Ala90 CB
0.919
0.91
0.92
0.92
0.91
Val92 CG1
0.764
0.63
0.80
0.89
0.86
Val92 CG2
0.707
0.61
0.79
0.87
0.83
Ala95 CB
0.680
0.94
0.91
0.94
0.91
Ile98 CG2
0.740
0.90
0.87
0.73
0.83
Ile98 CD
0.815
0.89
0.86
0.82
0.85
Val99 CG1
0.487
0.85
0.38
0.53
0.45
Val99 CG2
0.517
0.85
0.37
0.52
0.42
Met105 CE
0.630
0.80
0.76
0.37
0.79
Ala107 CB
0.832
0.88
0.87
0.82
0.85
Val109 CG2
0.354
0.36
0.22
0.32
0.25
Val120 CG1
0.660
0.69
0.52
0.52
0.57
Ala122 CB
0.879
0.78
0.86
0.81
0.83
Ile124 CG2
0.753
0.75
0.79
0.50
0.70
Ile124 CD
0.351
0.48
0.49
0.44
0.34
Leu129 CD1
0.525
0.12
0.27
0.12
0.33
Leu129 CD2
0.507
0.11
0.27
0.10
0.31
Table 6
values (11) for Trp (NE1‐HE1) and Arg (NE‐HE) side chains derived from relaxation measurements and from the unrestrained and order‐parameter restrained MD simulations starting from the 2VB1 X‐ray crystal structure.
Residue
Experimental value[20]
Unrestrained MD
Order‐parameter restrained MD
2VB1
2VB1_Cres
2VB1_Nres
2VB1_C+Nres
Trp28
0.90
0.88
0.84
0.85
0.89
Trp62
0.41
0.73
0.72
0.48
0.54
Trp63
0.88
0.83
0.81
0.87
0.85
Trp108
0.87
0.87
0.70
0.81
0.83
Trp111
0.88
0.83
0.59
0.81
0.78
Trp123
0.85
0.70
0.67
0.82
0.78
Arg61
0.28
0.22
0.30
0.26
0.29
Arg73
0.12
0.24
0.21
0.13
0.13
Arg112
0.31
0.28
0.13
0.23
0.22
Arg114
0.27
0.13
0.18
0.13
0.19
Arg125
0.05
0.12
0.13
0.11
0.10
Table 7
values (17) for Asn (ND2‐HD21, ‐HD22) and Gln (NE2‐HE21, ‐HE22) side chains derived from relaxation measurements and from the unrestrained and order‐parameter restrained MD simulations starting from the 2VB1 X‐ray crystal structure. The experimental values correspond to either HD/E21 or HD/E22.
The assignment in the second column is based on the best agreement with the values of the MD_2VB1 simulation (third column). The N−H vectors used as restraint are indicated by * . Values differing more than 0.2 from the experimental value are denoted using italics.
Residue
Experimental value[20]
Unrestrained MD
Order‐parameter restrained MD
2VB1
2VB1_Cres
2VB1_Nres
2VB1_C+Nres
Asn19 HD21*
0.43
0.49
0.56
0.43
0.39
Asn19 HD22
0.24
0.45
0.28
0.25
Asn27 HD21
0.86
0.79
0.76
0.82
Asn27 HD22*
0.72
0.82
0.57
0.71
0.66
Asn37 HD21*
0.51
0.37
0.32
0.50
0.51
Asn37 HD22
0.21
0.20
0.21
0.20
Asn39 HD21*
0.74
0.80
0.77
0.80
0.79
Asn39 HD22
0.61
0.57
0.59
0.57
Gln41 HE21
0.31
0.45
0.42
0.35
Gln41 HE22*
0.19
0.21
0.22
0.21
0.20
Asn44 HD21
0.75
0.66
0.63
0.65
Asn44 HD22*
0.51
0.71
0.56
0.57
0.58
Asn46 HD21
0.85
0.85
0.84
0.75
Asn46 HD22*
0.62
0.82
0.52
0.69
0.56
Gln57 HE21*
0.82
0.79
0.56
0.80
0.76
Gln57 HE22
0.76
0.23
0.66
0.48
Asn59 HD21
0.92
0.89
0.91
0.91
Asn59 HD22*
0.78
0.90
0.87
0.88
0.87
Asn65 HD21
0.76
0.78
0.50
0.55
Asn65 HD22*
0.57
0.42
0.30
0.43
0.43
Asn74 HD21*
0.74
0.66
0.65
0.71
0.75
Asn74 HD22
0.41
0.38
0.30
0.46
Asn77 HD21
0.54
0.50
0.45
0.47
Asn77 HD22*
0.24
0.31
0.28
0.24
0.24
Asn93 HD21*
0.59
0.53
0.63
0.61
0.58
Asn93 HD22
0.34
0.39
0.30
0.29
Asn103 HD21
0.72
0.33
0.31
0.29
Asn103 HD22*
0.26
0.61
0.21
0.17
0.17
Asn106 HD21*
0.58
0.68
0.40
0.48
0.47
Asn106 HD22
0.46
0.23
0.21
0.20
Asn113 HD21*
0.47
0.40
0.41
0.39
0.41
Asn113 HD22
0.21
0.24
0.18
0.21
Gln121 HE21*
0.36
0.34
0.37
0.28
0.31
Gln121 HE22
0.18
0.17
0.15
0.14
values (51) derived from relaxation measurements and from the unrestrained and order‐parameter restrained MD simulations starting from the 2VB1 X‐ray crystal structure. Order‐parameter target values larger than 0.95 were set to 0.95 (second column between brackets). Values differing more than 0.2 from the experimental value (0.95 in case the experimental value is 1) are denoted using italics.Residue and methyl groupExperimental valueUnrestrained MDOrder‐parameter restrained MD2VB12VB1_Cres2VB1_Nres2VB1_C+NresVal2 CG20.5980.390.420.460.44Leu8 CD10.7670.580.640.650.67Leu8 CD20.8030.630.720.660.71Ala9 CB1.0 (0.95)0.930.930.930.93Ala10 CB0.9010.910.920.920.92Ala11 CB0.8610.910.920.920.92Met12 CE0.8120.330.900.460.87Leu17 CD10.6300.460.510.780.56Leu17 CD20.6320.490.580.770.61Leu25CD11.0 (0.95)0.400.810.640.81Leu25CD20.6090.420.690.690.75Val29 CG10.8710.570.850.620.82Val29CG20.7910.570.840.610.81Ala31 CB0.98 (0.95)0.940.950.930.94Thr43CG20.3610.680.430.740.35Thr47CG20.3270.730.400.730.42Thr51CG20.7780.490.850.540.79Ile55CG20.7390.490.630.530.69Ile55CD0.3230.550.410.560.40Leu56CD10.7340.790.630.560.74Leu56CD20.6810.750.660.530.68Ile58CG21.0 (0.95)0.840.870.720.88Ile58CD0.1600.810.200.780.22Thr69CG20.98 (0.95)0.720.890.840.88Leu75 CD10.5900.620.690.520.56Ile78 CG20.8100.850.830.590.80Ile78 CD0.4160.430.450.290.40Leu83 CD10.8840.680.790.350.77Leu83 CD20.7830.660.720.410.71Leu84 CD11.0 (0.95)0.460.860.600.86Leu84 CD20.8790.450.830.580.84Ile88 CG20.6970.550.660.810.66Ile88 CD0.7220.270.640.490.58Thr89CG21.0 (0.95)0.710.870.690.85Ala90 CB0.9190.910.920.920.91Val92 CG10.7640.630.800.890.86Val92 CG20.7070.610.790.870.83Ala95 CB0.6800.940.910.940.91Ile98CG20.7400.900.870.730.83Ile98CD0.8150.890.860.820.85Val99 CG10.4870.850.380.530.45Val99CG20.5170.850.370.520.42Met105 CE0.6300.800.760.370.79Ala107 CB0.8320.880.870.820.85Val109 CG20.3540.360.220.320.25Val120 CG10.6600.690.520.520.57Ala122 CB0.8790.780.860.810.83Ile124 CG20.7530.750.790.500.70Ile124 CD0.3510.480.490.440.34Leu129CD10.5250.120.270.120.33Leu129CD20.5070.110.270.100.31values (11) for Trp (NE1‐HE1) and Arg (NE‐HE) side chains derived from relaxation measurements and from the unrestrained and order‐parameter restrained MD simulations starting from the 2VB1 X‐ray crystal structure.ResidueExperimental valueUnrestrained MDOrder‐parameter restrained MD2VB12VB1_Cres2VB1_Nres2VB1_C+NresTrp280.900.880.840.850.89Trp620.410.730.720.480.54Trp630.880.830.810.870.85Trp1080.870.870.700.810.83Trp1110.880.830.590.810.78Trp1230.850.700.670.820.78Arg610.280.220.300.260.29Arg730.120.240.210.130.13Arg1120.310.280.130.230.22Arg1140.270.130.180.130.19Arg1250.050.120.130.110.10values (17) for n class="Chemical">Asn (ND2‐HD21, ‐HD22) and Gln (NE2‐HE21, ‐HE22) side chains derived from relaxation measurements and from the unrestrained and order‐parameter restrained MD simulations starting from the 2VB1 X‐ray crystal structure. The experimental values correspond to either HD/E21 or HD/E22.
The assignment in the second column is based on the best agreement with the values of the MD_2VB1 simulation (third column). The N−H vectors used as restraint are indicated by * . Values differing more than 0.2 from the experimental value are denoted using italics.
ResidueExperimental valueUnrestrained MDOrder‐parameter restrained MD2VB12VB1_Cres2VB1_Nres2VB1_C+NresAsn19 HD21*0.430.490.560.430.39Asn19 HD220.240.450.280.25Asn27 HD210.860.790.760.82Asn27 HD22*0.720.820.570.710.66Asn37 HD21*0.510.370.320.500.51Asn37 HD220.210.200.210.20Asn39 HD21*0.740.800.770.800.79Asn39 HD220.610.570.590.57Gln41 HE210.310.450.420.35Gln41 HE22*0.190.210.220.210.20Asn44HD210.750.660.630.65Asn44HD22*0.510.710.560.570.58Asn46HD210.850.850.840.75Asn46HD22*0.620.820.520.690.56Gln57 HE21*0.820.790.560.800.76Gln57 HE220.760.230.660.48Asn59 HD210.920.890.910.91Asn59 HD22*0.780.900.870.880.87Asn65HD210.760.780.500.55Asn65HD22*0.570.420.300.430.43Asn74 HD21*0.740.660.650.710.75Asn74 HD220.410.380.300.46Asn77 HD210.540.500.450.47Asn77 HD22*0.240.310.280.240.24Asn93 HD21*0.590.530.630.610.58Asn93 HD220.340.390.300.29Asn103HD210.720.330.310.29Asn103HD22*0.260.610.210.170.17Asn106 HD21*0.580.680.400.480.47Asn106 HD220.460.230.210.20Asn113 HD21*0.470.400.410.390.41Asn113 HD220.210.240.180.21Gln121 HE21*0.360.340.370.280.31Gln121 HE220.180.170.150.14Tables 6 and 7 show that in the unrestrained MD simulation only two
order‐parameter values (in italics) deviate more than 0.2 from the experimentally derived n class="Chemical">values, for Trp62 (Table 6) and for Asn103HD22 (Table 7). S
2 order‐parameter restraining towards the set Nres of 28 target
(exp) values leads, as expected, to good agreement between simulation and experiment for the 28
order parameters. No deviations larger than 0.2 are observed.
S
2 order‐parameter restraining towards the set C+Nres of 79 target
(exp) and
(exp) n class="Chemical">values leads, as expected, to good agreement between simulation and experiment for 78 S
2 order parameters (Figure S4), only one deviation larger than 0.2 is observed, for the
value of Ala95 CB (Table 5). The S
2 order‐parameter restraining is not able to reduce the
(MD) value from 0.94 in the unrestrained simulation to the target
(exp) value of 0.68. Enhancing the mobility of the CA–CB vector that is close to the polypeptide backbone and in a residue that is in the centre of a helix seems impossible with the parameters applied here.
Table 5 shows that for the 51
order parameters restraining towards the set Nres of 28 target
(exp) n class="Chemical">values yields 21 deviations larger than 0.2. Restraining towards the
(exp) values does not improve the overall agreement between simulation and experiment for the
values. Yet, for some
order parameters the agreement improves (Met12 CE, Leu25CD1 and CD2, Thr69CG2, Leu84 CD1 and CD2, Ile88 CD2, Ile98CG2, Val99 CG1 and CG2) by more than 0.1, and for some
order parameters the agreement worsens (Leu56CD1 and CD2, Ile58CG2, Ile78 CG2 and CD, Leu83 CD1 and CD2, Met105 CE, Val120 CG1 and Ile124 CG2) by more than 0.1.
Table 8 shows the occurrence (%) of hydrogen bonds involving the side chains of n class="Chemical">Arg, Asn, Gln and Trp residues in the MD_2VB1 unrestrained MD simulation and in the three S
2 order‐parameter restraining MD simulations starting from the 2VB1 X‐ray structure. The unrestrained simulation shows nine hydrogen bonds with an occurrence larger than 50 %. S
2 order‐parameter restraining MD simulation reduces this number to 5, 3 and 3 for the three S
2 order‐parameter restraining MD simulations using the Cres, Nres or C+Nres sets of restraints, respectively. All but one of the occurrences of the mentioned 9 hydrogen bonds are reduced by the S
2 order‐parameter restraining. In contrast, only one hydrogen‐bond occurrence is raised above 50 % by restraining, the hydrogen bond Asn46 ND2‐HD22–Ser50 O, from 2 % to 51, 27 and 17 %, respectively. Of the 52 hydrogen bonds listed (i. e., observed in either the four X‐ray structures or for at least 20 % in the seven MD simulations), 38 are observed in the unrestrained simulation, 39, 37 and 42 are observed in the three S
2 order‐parameter restraining MD simulations using the Cres, Nres or C+Nres sets of restraints, respectively.
Table 8
Occurrence (%) of hydrogen bonds (52) involving the side chains of Arg, Asn, Gln and Trp residues in the MD_2VB1 unrestrained MD simulation and in the three S
2 order‐parameter restraining MD simulations starting from the 2VB1 X‐ray structure. Only hydrogen bonds present in one of the X‐ray structures or with a population of at least 20 % in any of the restrained or unrestrained MD simulations are included. Only hydrogen bond populations of 1 % or greater are shown.
Hydrogen bond
MD simulation
Unrestrained
Order‐parameter restrained
Donor‐acceptor
2VB1
2VB1_Cres
2VB1_Nres
2VB1_C+Nres
Arg5 NE‐HE‐Trp123 O
15
6
14
9
Arg5 NH1/2‐HH1/2‐Arg125 O*
9
4
7
8
Arg5 NH1‐HH12‐Trp123 O
22
27
10
12
Asn19 ND2‐HD22‐Asp18 OD1/2*
11
35
30
24
Asn27 ND2‐HD22‐Trp111 O
–
–
26
4
Asn27 ND2‐HD22‐Ser24 O
–
2
9
1
Asn27 ND2‐HD22‐Ser24 OG
–
3
21
–
Asn27 ND2‐HD22‐Cys115 O
–
24
7
6
Trp28 NE1‐HE1‐Leu17 O
–
30
30
7
Trp28 NE1‐HE1‐Tyr23 O
–
15
23
4
Gln41 NE2‐HE22‐Leu84 O
2
2
2
3
Asn44 ND2‐HD22‐Asp52 OD1/2*
61
41
30
33
Asn44 ND2‐HD22‐Gln57 OE1
14
3
6
3
Arg45 NH1‐HH12‐Gly49 O
8
2
4
3
Asn46 ND2‐HD21‐Ala107 O
56
–
–
–
Asn46 ND2‐HD1/2‐Asp52 OD1/2*
75
68
41
40
Asn46 ND2‐HD22‐Ser50 OG
1
25
23
23
Asn46 ND2‐HD22‐Ser50 O
2
51
27
17
Gln57 NE2‐HE21‐Glu35 OE1
1
–
–
1
Gln57 NE2‐HE21‐Ala42 O
66
5
24
4
Gln57 NE2‐HE22‐Ser36 OG
6
9
4
17
Gln57 NE2‐HE22‐Gly54 O
85
18
71
8
Asn59 ND2‐HD21‐Ser50 OG
99
84
95
93
Asn59 ND2‐HD1/2‐Ser52 OD1/2*
70
60
52
52
Arg61 NH2‐HH22‐Asp48 OD2
1
–
–
9
Arg61 NH2‐HH21‐Asp48 O
–
–
–
–
Arg61 NE‐HE‐Thr69 OG1
6
–
–
–
Trp63 NE1‐HE1‐Asn106 OD1
11
–
–
–
Asn65 ND2‐HD22‐Asn74 OD1
52
56
3
2
Arg68 NH2‐HH22‐Thr51 OG1
–
2
–
3
Arg73 NH1‐HH12‐Arg61 O
13
10
6
11
Asn74 ND2‐HD21‐Asn77 O
1
1
7
8
Asn103 ND2‐HD22‐Ile98 O
–
–
–
–
Asn103 ND2‐HD22‐Asp101 OD1/2
42
5
1
4
Asn106 ND2‐HD22‐Gly102 O
–
5
1
1
Asn106 ND2‐HD22‐Asn103 O
3
3
–
1
Asn106 ND2‐HD22‐Asn103 OD1
22
–
–
1
Trp108 NE1‐HE1‐Leu56 O
91
9
24
54
Trp111 NE1‐HE1‐Asn27 OD1
1
17
22
1
Trp111 NE1‐HE1‐Asn27 O
–
–
23
19
Arg112 NE‐HE‐Asn106 O
20
3
4
4
Arg112 NH1‐HH12‐Asn106 O
19
9
16
6
Asn113 ND2‐HD21‐Val109 O
2
–
8
–
Arg114 NH1‐HH12‐Glu35 OE1
–
2
–
11
Arg114 NE‐H‐Asn113 OD1
9
2
–
–
Gln121 NE2‐HE22‐Asp119 OD1/2*
22
12
20
16
Trp123 NE1‐HE1‐Gly117 O
14
1
–
1
Trp123 NE1‐HE1‐Thr118 OG1
14
5
45
11
Arg125 NE‐HE‐Gln121 OE1
2
4
5
4
Arg125 NH2‐HH22‐Asp119 OD2
–
–
–
–
Arg125 NH2‐HH22‐Gln121 OE1
1
3
3
3
Arg125 NH1‐HH12‐Ala122 O
–
–
–
–
* Some hydrogen bonds involving aspartic acid side chains are present in the simulations with either OD1 or OD2 acting as the acceptor. In these cases (marked OD1/2) the highest population of the hydrogen bond involving either OD1 or OD2 is listed. Similarly for hydrogen bonds involving asparagine NH2 groups in some cases (marked ND2‐HD1/2) the highest population of a hydrogen bond where the donor is either ND2‐HD21 or ND2‐HD22 is listed while for arginine NH2 groups in some cases (marked NH1/2‐HH1/2) the highest population of a hydrogen bond where the donor is either NH1‐HH11, NH1‐HH12, NH2‐HH21 or NH2‐HH22 is listed.
Occurrence (%) of hydrogen bonds (52) involving the side chains of n class="Chemical">Arg, Asn, Gln and Trp residues in the MD_2VB1 unrestrained MD simulation and in the three S
2 order‐parameter restraining MD simulations starting from the 2VB1 X‐ray structure. Only hydrogen bonds present in one of the X‐ray structures or with a population of at least 20 % in any of the restrained or unrestrained MD simulations are included. Only hydrogen bond populations of 1 % or greater are shown.
Hydrogen bondMD simulationUnrestrainedOrder‐parameter restrainedDonor‐acceptor2VB12VB1_Cres2VB1_Nres2VB1_C+NresArg5 NE‐HE‐Trp123 O156149Arg5 NH1/2‐HH1/2‐Arg125 O*9478Arg5 NH1‐HH12‐Trp123 O22271012Asn19 ND2‐HD22‐Asp18 OD1/2*11353024Asn27 ND2‐HD22‐Trp111 O––264Asn27 ND2‐HD22‐Ser24 O–291Asn27 ND2‐HD22‐Ser24 OG–321–Asn27 ND2‐HD22‐Cys115 O–2476Trp28 NE1‐HE1‐Leu17 O–30307Trp28 NE1‐HE1‐Tyr23 O–15234Gln41 NE2‐HE22‐Leu84 O2223Asn44 ND2‐HD22‐Asp52 OD1/2*61413033Asn44 ND2‐HD22‐Gln57 OE114363Arg45 NH1‐HH12‐Gly49 O8243Asn46 ND2‐HD21‐Ala107 O56–––Asn46 ND2‐HD1/2‐Asp52 OD1/2*75684140Asn46 ND2‐HD22‐Ser50 OG1252323Asn46 ND2‐HD22‐Ser50 O2512717Gln57 NE2‐HE21‐Glu35 OE11––1Gln57 NE2‐HE21‐Ala42 O665244Gln57 NE2‐HE22‐Ser36 OG69417Gln57 NE2‐HE22‐Gly54 O8518718Asn59 ND2‐HD21‐Ser50 OG99849593Asn59 ND2‐HD1/2‐Ser52 OD1/2*70605252Arg61 NH2‐HH22‐Asp48 OD21––9Arg61 NH2‐HH21‐Asp48 O––––Arg61 NE‐HE‐Thr69 OG16–––Trp63 NE1‐HE1‐Asn106 OD111–––Asn65 ND2‐HD22‐Asn74 OD1525632Arg68 NH2‐HH22‐Thr51 OG1–2–3Arg73 NH1‐HH12‐Arg61 O1310611Asn74 ND2‐HD21‐Asn77 O1178Asn103 ND2‐HD22‐Ile98 O––––Asn103 ND2‐HD22‐Asp101 OD1/242514Asn106 ND2‐HD22‐Gly102 O–511Asn106 ND2‐HD22‐Asn103 O33–1Asn106 ND2‐HD22‐Asn103 OD122––1Trp108 NE1‐HE1‐Leu56 O9192454Trp111 NE1‐HE1‐Asn27 OD1117221Trp111 NE1‐HE1‐Asn27 O––2319Arg112 NE‐HE‐Asn106 O20344Arg112 NH1‐HH12‐Asn106 O199166Asn113 ND2‐HD21‐Val109 O2–8–Arg114 NH1‐HH12‐Glu35 OE1–2–11Arg114 NE‐H‐Asn113 OD192––Gln121 NE2‐HE22‐Asp119 OD1/2*22122016Trp123 NE1‐HE1‐Gly117 O141–1Trp123 NE1‐HE1‐Thr118 OG11454511Arg125 NE‐HE‐Gln121 OE12454Arg125 NH2‐HH22‐Asp119 OD2––––Arg125 NH2‐HH22‐Gln121 OE11333Arg125 NH1‐HH12‐Ala122 O––––* Some hydrogen bonds involving n class="Chemical">aspartic acid side chains are present in the simulations with either OD1 or OD2 acting as the acceptor. In these cases (marked OD1/2) the highest population of the hydrogen bond involving either OD1 or OD2 is listed. Similarly for hydrogen bonds involving asparagine NH2 groups in some cases (marked ND2‐HD1/2) the highest population of a hydrogen bond where the donor is either ND2‐HD21 or ND2‐HD22 is listed while for arginine NH2 groups in some cases (marked NH1/2‐HH1/2) the highest population of a hydrogen bond where the donor is either NH1‐HH11, NH1‐HH12, NH2‐HH21 or NH2‐HH22 is listed.
There are a number of examples where the MD_2VB1 unrestrained simulation yields a S
2 value ln class="Chemical">arger than experiment. When restraining reduces the S
2 value, a reduction or change in the populations of hydrogen bonds involving that side chain is observed. For example, Asn44 (experimental
value 0.51 compared to 0.71 and 0.58 in the MD_2VB1 and MD_2VB1_C+Nres simulations, respectively, Table 7) shows a reduction in the populations of hydrogen bonds to the side chains of Asp52 and Gln57 (Table 8) and Asn46 (experimental
value 0.62 compared to 0.82 and 0.56 in the MD_2VB1 and MD_2VB1_C+Nres simulations, respectively) shows a reduction in the population of the hydrogen bond to the side chain of Asp52, but an increase in the population of hydrogen bonds to both the main chain and side chain oxygens of Ser50 in the restrained simulations. Similarly, for Asn103 (experimental
value 0.26 compared to 0.61 and 0.17 in the MD_2VB1 and MD_2VB1_C+Nres simulations, respectively), the hydrogen bond to the side chain of Asp101 is almost completely lost in the restrained simulations.
Figures 4 to 6 show the secondary structure elements
of HEWL as a function of time calculated for the three S
2 order‐parameter restraining MD simulations starting from the 2VB1 X‐ray structure. Compared to the MD_2VB1 unrestrained simulation (Figure 2),
order‐parameter restraining towards the
(exp) n class="Chemical">values of set Cres induces some changes in secondary structure (Figure 4). Residues 19–21 become 310‐helical, the second α‐helix (residues 24–36) is slightly more stable at its C‐terminal end, the helix of alternating α‐helical and 310‐helical character at residues 80–85 gains 310‐helical character, residues 103–108 become α‐helical after 4 ns, and the α‐helix 108–115 gains π‐helical character. Generally, the 310‐helical character is increased.
order‐parameter restraining towards the
(exp) values of set Nres shows similar changes in the secondary structure (Figure 5). The same observation holds for the MD_2VB1_C+Nres simulation (Figure 6).
Figure 4
Secondary structure elements
as a function of time calculated for the
order‐parameter restraining MD simulation MD_2VB1_Cres starting from the 2VB1 X‐ray structure. Red: α‐helix; green: π‐helix; black: 310‐helix; blue: β‐strand; yellow: β‐bridge; brown: bend; grey: turn.
Figure 5
Secondary structure elements
as a function of time calculated for the
order‐parameter restraining MD simulation MD_2VB1_Nres starting from the 2VB1 X‐ray structure. Red: α‐helix; green: π‐helix; black: 310‐helix; blue: β‐strand; yellow: β‐bridge; brown: bend; grey: turn.
Figure 6
Secondary structure elements
as a function of time calculated for the
and
order‐parameter restraining MD simulation MD_2VB1_N+Cres starting from the 2VB1 X‐ray structure. Red: α‐helix; green: π‐helix; black: 310‐helix; blue: β‐strand; yellow: β‐bridge; brown: bend; grey: turn.
Secondary structure elements
as a function of time calculated for the
order‐parameter restraining MD simulation MD_2VB1_Cres starting from the 2VB1 X‐ray structure. Red: α‐helix; green: π‐helix; black: 310‐helix; blue: β‐strand; yellow: β‐bridge; brown: bend; grey: turn.Secondary structure elements
as a function of time calculated for the
order‐parameter restraining MD simulation MD_2VB1_Nres starting from the 2VB1 X‐ray structure. Red: α‐helix; green: π‐helix; black: 310‐helix; blue: β‐strand; yellow: β‐bridge; brown: bend; grey: turn.Secondary structure elements
as a function of time calculated for the
and
order‐parameter restraining MD simulation MD_2VB1_N+Cres starting from the 2VB1 X‐ray structure. Red: α‐helix; green: π‐helix; black: 310‐helix; blue: β‐strand; yellow: β‐bridge; brown: bend; grey: turn.Figure 7 shows the backbone Cα atom‐positional root‐mean‐square fluctuations (RMSF) as function of residue sequence number in the unrestrained MD simulation MD_2VB1 (black) and in the S
2 order‐parameter restraining simulations MD_2VB1_Cres (magenta), MD_2VB1_Nres (cyan) and MD_2VB1_C+Nres (orange) all starting from the 2VB1 X‐ray structure.
order‐parameter restraining induces mobility for residues 1–17, residues 85–105 and residues 109–112. Restraining
order parameters shows increased mobility for residues 100–105. Restraining to both sets of order parameters shows increased mobility for residues 100–104 and 109–110.
Figure 7
Backbone Cα atom‐positional root‐mean‐square fluctuations (RMSF) as function of residue sequence number for the unrestrained MD simulation MD_2VB1 (black) and for the three S
2 order‐parameter restraining MD simulations MD_2VB1_Cres (magenta), MD_2VB1_Nres (cyan) and MD_2VB1_C+Nres (orange) all starting from the 2VB1 X‐ray structure. The trajectory structures are translationally and rotationally superimposed using the backbone atoms (N, Cα, C) of residues 3–126. The black bars at the top indicate secondary structure elements of HEWL (thick bars: α‐helix; thin bars, β‐strand).
Backbone Cα atom‐positional root‐mean‐square fluctuations (RMSF) as function of residue sequence number for the unrestrained MD simulation MD_2VB1 (black) and for the three S
2 order‐parameter restraining MD simulations MD_2VB1_Cres (magenta), MD_2VB1_Nres (cyan) and MD_2VB1_C+Nres (orange) all starting from the 2VB1 X‐ray structure. The trajectory structures are translationally and rotationally superimposed using the backbone atoms (N, Cα, C) of residues 3–126. The black bars at the top indicate secondary structure elements of HEWL (thick bars: α‐helix; thin bars, β‐strand).
Discussion
Table 9 summarises the deviations of
(MD) values from
(exp) n class="Chemical">values for the 51
order parameters in the seven MD simulations. Of course,
order‐parameter restraining reduces the number of larger deviations.
order‐parameter restraining increases the number of deviations larger than 0.1 from 33 in the unrestrained MD_2VB1 simulation to 35 in the MD_2VB1_Nres simulation. S
2 order‐parameter restraining to all 79 experimentally derived S
2 order‐parameter values yields even less deviations larger than 0.1 (12) than restraining only to the 51
order‐parameter values (16).
Table 9
Number of deviations, |S
2(exp) ‐ S
2(MD)|, for the 51
values in the seven MD simulations.
Simulation
Size of S2 deviation
0.05–0.1
0.1–0.2
0.2–0.3
0.3–0.4
0.4–0.5
>0.5
MD_2VB1
7
12
9
6
5
1
MD_4LZT
6
11
8
7
1
1
MD_1IEE
9
11
9
5
1
3
MD_1AKI
7
6
16
8
0
2
MD_2VB1_Cres
19
13
3
0
0
0
MD_2VB1_Nres
6
13
11
7
2
2
MD_2VB1_C+Nres
17
11
1
0
0
0
Number of deviations, |S
2(exp) ‐ S
2(MD)|, for the 51
values in the seven MD simulations.SimulationSize of S
2 deviation0.05–0.10.1–0.20.2–0.30.3–0.40.4–0.5>0.5MD_2VB17129651MD_4LZT6118711MD_1IEE9119513MD_1AKI7616802MD_2VB1_Cres19133000MD_2VB1_Nres61311722MD_2VB1_C+Nres17111000Tables 10 and 11 summarise the deviations of
(MD) values from
(exp) n class="Chemical">values for the 28
order parameters in the seven MD simulations. Of course,
order‐parameter restraining marginally improves the agreement with experiment.
order‐parameter restraining does not improve the agreement with experiment for the 28
order parameters, from 12 deviations larger than 0.1 in the MD_2VB1 simulation to 11 deviations in the MD_2VB1_Nres simulation. Combining
and
order‐parameter restraining yields almost equally good agreement.
Table 10
Number of deviations, |S
2(exp)−S
2(MD)|, for the 11
values of Trp and Arg residues in the seven MD simulations.
Simulation
Size of S2 deviation
0.05–0.1
0.1–0.2
0.2–0.3
0.3–0.4
0.4–0.5
>0.5
MD_2VB1
2
3
0
1
0
0
MD_4LZT
5
3
1
0
0
0
MD_1IEE
3
1
2
1
0
0
MD_1AKI
4
4
1
0
0
0
MD_2VB1_Cres
5
3
1
1
0
0
MD_2VB1_Nres
5
1
0
0
0
0
MD_2VB1_C+Nres
4
1
0
0
0
0
Table 11
Number of deviations, |S
2(exp)−S
2(MD)|, for the 17
values of Asnand Gln residues in the seven MD simulations.
Simulation
Size of S2 deviation
0.05–0.1
0.1–0.2
0.2–0.3
0.3–0.4
0.4–0.5
>0.5
MD_2VB1
6
5
2
1
0
0
MD_4LZT
5
6
2
0
0
0
MD_1IEE
6
5
1
1
0
0
MD_1AKI
5
6
1
1
0
0
MD_2VB1_Cres
5
4
2
0
0
0
MD_2VB1_Nres
8
1
0
0
0
0
MD_2VB1_C+Nres
8
2
0
0
0
0
Number of deviations, |S
2(exp)−S
2(MD)|, for the 11
values of Trp and Arg residues in the seven MD simulations.SimulationSize of S
2 deviation0.05–0.10.1–0.20.2–0.30.3–0.40.4–0.5>0.5MD_2VB1230100MD_4LZT531000MD_1IEE312100MD_1AKI441000MD_2VB1_Cres531100MD_2VB1_Nres510000MD_2VB1_C+Nres410000Number of deviations, |S
2(exp)−S
2(MD)|, for the 17
values of Asnand Gln residues in the seven MD simulations.SimulationSize of S
2 deviation0.05–0.10.1–0.20.2–0.30.3–0.40.4–0.5>0.5MD_2VB1652100MD_4LZT562000MD_1IEE651100MD_1AKI561100MD_2VB1_Cres542000MD_2VB1_Nres810000MD_2VB1_C+Nres820000The data in Tables 5 and 7 and 9–11 indicate some unreliability of
order‐parameter restraining, which may have different experimental or computational sources: 1) Some
(exp) values (Table 5) are very different for two vectors in the same side chain, for example, for n class="Chemical">Ile58 CG2 and CD (1.0 and 0.16) and less so for Leu25CD1 and CD2 (1.0 and 0.609) and Ile55CG2 and CD (0.739 and 0.323). This suggests an unlikely large difference in mobility for nearby C−H vectors. 2) Some residues in the protein interior show unexpectedly low
(exp) values, indicating high mobility, for example Val99 (CG1 0.487 and CG2 0.517) with a solvent accessible area in the 2VB1 X‐ray structure of only 7 %. 3) Some residues at the surface of the protein show unexpectedly high
(exp) values, indicating low mobility, for example Thr89CG2 with
(exp)=1.0 and a solvent accessible area in the 2VB1 X‐ray structure of 76 %. 4) As discussed in section 2.3, the
order‐parameter restraining algorithm restrains the C−C vector adjacent to the three C−H vectors of a methyl group, of which the relaxation is measured experimentally. This procedure is based on the assumption that the rotational motion of the C−H vectors around the axis of symmetry of the CH3 group is uniform and decoupled from the motion of the symmetry axis itself (the C−CH3 vector). These assumptions need not be true. This suggests that
order‐parameter restraining is less reliable than
order‐parameter restraining, for which the latter assumptions are not invoked.
Table 12 shows the number of NOE distance bound violations in the four X‐ray crystal structures and the seven MD simulations for the 1630 NOE distance bounds specified in Table S1.
order‐parameter restraining decreases the number of NOE bound violations larger than 0.1 nm from 42 in the unrestrained 2VB1 simulation to 34 in the MD_2VB1_Cres simulation.
order‐parameter restraining reduces the number of NOE bound violations larger than 0.1 nm from 42 in the unrestrained MD_2VB1 simulation to 36 in the MD_2VB1_Nres simulation, halving the number of violations larger than 0.2 nm from 13 to 7. Combining
and
order‐parameter restraining yields better agreement, with 30 violations larger than 0.1 nm, as well as worse agreement, with nine violations larger than 0.2 nm. S
2 order‐parameter restraining in MD simulation improves agreement with experimentally derived NOE atom‐atom distance bounds.
Table 12
Number of NOE distance bound violations in the four X‐ray crystal structures and the seven MD simulations. Number of NOE distance bounds: 1630.
Structure or
Size of NOE distance bound violation [nm]
simulation
0.05–0.1
0.1–0.15
0.15–0.2
0.2–0.25
0.25–0.3
>0.3
2VB1
21
7
5
0
0
0
4LZT
20
7
4
0
0
0
1IEE
20
7
5
0
0
0
1AKI
15
10
4
0
0
0
MD_2VB1
44
18
11
5
3
5
MD_4LZT
41
13
13
5
3
5
MD_1IEE
43
20
13
8
3
5
MD_1AKI
44
15
14
2
3
8
MD_2VB1_Cres
40
18
8
4
2
2
MD_2VB1_Nres
36
19
10
4
2
1
MD_2VB1_C+Nres
42
14
7
4
4
1
Number of NOE distance bound violations in the four X‐ray crystal structures and the seven MD simulations. Number of NOE distance bounds: 1630.Structure orSize of NOE distance bound violation [nm]simulation0.05–0.10.1–0.150.15–0.20.2–0.250.25–0.3>0.32VB121750004LZT20740001IEE20750001AKI15104000MD_2VB1441811535MD_4LZT411313535MD_1IEE432013835MD_1AKI441514238MD_2VB1_Cres40188422MD_2VB1_Nres361910421MD_2VB1_C+Nres42147441Table 13 shows 26 side‐chain 3
J
HαHβ coupling values for side chains, for which S
2 order‐parameter n class="Chemical">values derived from experiment are available, as derived from NMR measurements
as well as from the unrestrained and S
2 order‐parameter restraining MD simulations starting from the 2VB1 X‐ray crystal structure. In the unrestrained simulation, six 3
J
HαHβ coupling values differ more than 2 Hz from the experimentally derived values, four for side chains for which experimentally derived
order‐parameter values are available and two for side chains for which experimentally derived
order‐parameter values are available.
order‐parameter restraining induces two more deviations of 3
J
HαHβ‐couplings in side chains with
order‐parameter values, while
order‐parameter restraining induces four more deviations of 3
J
HαHβ‐couplings in side chains with
order‐parameter values. Combined
and
order‐parameter restraining also leads to four more deviations of 3
J
HαHβ‐couplings, two in side chains with
order‐parameter values and two in side chains with
order‐parameter values. Overall, S
2 order‐parameter restraining in MD simulation did not improve the agreement with experiment for the 26 side‐chain 3
J
HαHβ coupling values. For some residues, Thr51 for example, the agreement improves, whereas for other residues, Val29 for example, the agreement worsens.
Table 13
Side‐chain 3
J
HαHβ coupling values (26, for side chains for which S
2 order‐parameter values derived from experiment are available), in Hz, derived from NMR measurements and from the unrestrained and order‐parameter restrained MD simulations starting from the 2VB1 X‐ray crystal structure. Experimental data is from Tables III and IV of ref. [23] and consists of values that could be stereo‐specifically assigned based on NMR data as well as of values that could not be stereospecifically assigned in this way (marked with *). For the latter, stereo‐specific assignment of the experimental values for the β2 and β3 hydrogens is based on the 3
J
HαHβ coupling values calculated from the four unrestrained MD simulations starting from the four X‐ray structures in case 4 or 3 of the unrestrained MD simulations suggested the same stereo‐specific assignment. The root‐mean‐square fluctuations (RMSF) of the 3
J
HαHβ couplings in the MD simulations are given within parentheses. MD values differing more than 2 Hz from the experimental value are denoted using italics.
Residue
Experimental
Unrestrained MD
Order‐parameter restrained MD
value
MD_2VB1
2VB1_Cres
2VB1_Nres
2VB1_C+Nres
Val2
10.8
9.3 (4.6)
6.1 (4.6)
10.8 (3.8)
7.4 (4.8)
Asn19 β2
7.3
8.3 (4.6)
8.4 (4.1)
8.9 (3.9)
7.5 (4.3)
β3
6.4
5.9 (4.6)
5.0 (4.5)
4.3 (3.9)
5.1 (4.2)
Val29
11.1
10.1 (4.3)
6.3 (4.6)
9.6 (4.4)
3.0 (1.6)
Asn37* β2
8.1
9.1 (4.6)
6.6 (4.8)
5.2 (4.3)
7.6 (4.8)
β3
4.2
5.1 (3.9)
7.3 (4.6)
8.8 (4.4)
6.7 (4.5)
Thr43
3.7
3.4 (2.6)
4.6 (3.9)
3.1 (2.0)
5.1 (4.2)
Thr47
2.6
3.0 (1.5)
4.0 (3.2)
2.9 (1.4)
3.9 (3.1)
Thr51
9.3
5.6 (4.6)
9.1 (4.6)
8.8 (4.7)
9.4 (4.2)
Asn65* β2
4.5
4.2 (3.1)
3.2 (1.2)
3.3 (2.2)
3.4 (2.4)
β3
11.4
11.3 (3.2)
12.4 (0.9)
10.5 (3.4)
10.4 (3.4)
Thr69
9.3
6.1 (4.6)
12.6 (0.5)
12.4 (0.7)
12.6 (0.5)
Asn74* β2
10.5
11.3 (3.2)
11.9 (2.3)
3.1 (1.4)
2.9 (1.5)
β3
3.9
4.0 (2.2)
3.9 (1.9)
6.0 (3.7)
7.6 (4.2)
Leu75 β2
12.4
11.5 (2.4)
11.7 (2.1)
10.4 (3.3)
10.9 (2.9)
β3
2.1
3.0 (1.8)
2.9 (1.8)
3.3 (2.5)
3.1 (2.1)
Asn77* β2
8.3
10.8 (3.4)
11.0 (3.4)
10.6 (3.7)
10.6 (3.8)
β3
5.9
3.8 (2.6)
4.3 (3.2)
4.4 (3.4)
4.4 (3.4)
Ile88
4.5
4.3 (3.8)
3.2 (2.3)
2.4 (0.9)
4.2 (3.6)
Thr89
9.5
4.8 (3.4)
6.9 (4.9)
3.5 (2.7)
3.0 (1.0)
Val92
10.1
9.6 (4.5)
4.0 (2.7)
12.3 (1.5)
11.8 (2.4)
Asn93* β2
10.8
10.7 (3.6)
9.9 (4.1)
10.6 (3.6)
9.4 (4.4)
β3
3.5
4.1 (3.6)
4.8 (4.2)
4.4 (3.7)
5.4 (4.3)
Val99
6.3
3.0 (1.6)
5.5 (4.3)
6.4 (4.6)
3.7 (3.3)
Val109
8.0
9.0 (4.7)
5.1 (4.3)
6.4 (4.8)
5.9 (4.6)
Ile124
4.6
4.1 (2.7)
3.5 (1.4)
5.2 (3.8)
3.3 (1.6)
Side‐chain 3
J
HαHβ coupling values (26, for side chains for which S
2 order‐parameter n class="Chemical">values derived from experiment are available), in Hz, derived from NMR measurements and from the unrestrained and order‐parameter restrained MD simulations starting from the 2VB1 X‐ray crystal structure. Experimental data is from Tables III and IV of ref. [23] and consists of values that could be stereo‐specifically assigned based on NMR data as well as of values that could not be stereospecifically assigned in this way (marked with *). For the latter, stereo‐specific assignment of the experimental values for the β2 and β3 hydrogens is based on the 3
J
HαHβ coupling values calculated from the four unrestrained MD simulations starting from the four X‐ray structures in case 4 or 3 of the unrestrained MD simulations suggested the same stereo‐specific assignment. The root‐mean‐square fluctuations (RMSF) of the 3
J
HαHβ couplings in the MD simulations are given within parentheses. MD values differing more than 2 Hz from the experimental value are denoted using italics.
ResidueExperimentalUnrestrained MDOrder‐parameter restrained MDvalueMD_2VB12VB1_Cres2VB1_Nres2VB1_C+NresVal210.89.3 (4.6)6.1 (4.6)10.8 (3.8)7.4 (4.8)Asn19 β27.38.3 (4.6)8.4 (4.1)8.9 (3.9)7.5 (4.3)β36.45.9 (4.6)5.0 (4.5)4.3 (3.9)5.1 (4.2)Val2911.110.1 (4.3)6.3 (4.6)9.6 (4.4)3.0 (1.6)Asn37* β28.19.1 (4.6)6.6 (4.8)5.2 (4.3)7.6 (4.8)β34.25.1 (3.9)7.3 (4.6)8.8 (4.4)6.7 (4.5)Thr433.73.4 (2.6)4.6 (3.9)3.1 (2.0)5.1 (4.2)Thr472.63.0 (1.5)4.0 (3.2)2.9 (1.4)3.9 (3.1)Thr519.35.6 (4.6)9.1 (4.6)8.8 (4.7)9.4 (4.2)Asn65* β24.54.2 (3.1)3.2 (1.2)3.3 (2.2)3.4 (2.4)β311.411.3 (3.2)12.4 (0.9)10.5 (3.4)10.4 (3.4)Thr699.36.1 (4.6)12.6 (0.5)12.4 (0.7)12.6 (0.5)Asn74* β210.511.3 (3.2)11.9 (2.3)3.1 (1.4)2.9 (1.5)β33.94.0 (2.2)3.9 (1.9)6.0 (3.7)7.6 (4.2)Leu75 β212.411.5 (2.4)11.7 (2.1)10.4 (3.3)10.9 (2.9)β32.13.0 (1.8)2.9 (1.8)3.3 (2.5)3.1 (2.1)Asn77* β28.310.8 (3.4)11.0 (3.4)10.6 (3.7)10.6 (3.8)β35.93.8 (2.6)4.3 (3.2)4.4 (3.4)4.4 (3.4)Ile884.54.3 (3.8)3.2 (2.3)2.4 (0.9)4.2 (3.6)Thr899.54.8 (3.4)6.9 (4.9)3.5 (2.7)3.0 (1.0)Val9210.19.6 (4.5)4.0 (2.7)12.3 (1.5)11.8 (2.4)Asn93* β210.810.7 (3.6)9.9 (4.1)10.6 (3.6)9.4 (4.4)β33.54.1 (3.6)4.8 (4.2)4.4 (3.7)5.4 (4.3)Val996.33.0 (1.6)5.5 (4.3)6.4 (4.6)3.7 (3.3)Val1098.09.0 (4.7)5.1 (4.3)6.4 (4.8)5.9 (4.6)Ile1244.64.1 (2.7)3.5 (1.4)5.2 (3.8)3.3 (1.6)Overall, the structure of HEWL is maintained in all seven MD simulations, as is indicated in Figures S1 and S2 showing the backbone atom‐positional root‐mean‐square deviation (RMSD) from the 2VB1 X‐ray structure as function of time.
Conclusions
S
2 order parameters for C−H and N−H bonds in proteins derived from NMR relaxation measurements reflect the directional mobility of these bonds. Consequently, they cannot be related to a single protein structure, but to an ensemble of such structures. Therefore, S
2 order parameters are not used as data for standard single‐structure determination of proteins. A comparison of four X‐ray structures of HEWL and four MD simulations starting from these four different X‐ray structures illustrates the need of a conformational ensemble representation of the HEWL protein, in particular for its side chains. MD simulation allows for averaging over an ensemble of trajectory structures, which is used in protein structure determination based on S
2 order parameters.
order‐parameter restraining can be directly applied to the N−H bond vectors in a protein. In contrast,
order‐parameter restraining of C−H bond vectors in methyl groups makes no sense because of the fast rotation of the three C−H bonds around their symmetry axis parallel to the C−CH3 bond. By assuming the above‐mentioned rotation to be uniform and independent from the motion of the symmetry axis itself,
the
order‐parameter restraining algorithm can be applied to the C−CH3 bond. The results for HEWL show that
order‐parameter restraining is more problematic than
order‐parameter restraining, which may be due to less n class="Chemical">valid assumptions and approximations used to derive experimental
(exp) values from NMR relaxation measurements and the assumptions of uniform rotational motion of methyl C−H bonds around their symmetry axis and of the independence of these motions from each other.
The application of S
2 order‐parameter restraining to the protein HEWL shows that this technique is able to produce a conformational ensemble compatible with the experimentally derived
(exp) and
(exp) n class="Chemical">values. S
2 order‐parameter restraining in MD simulation does improve the agreement with 1630 NOE atom‐atom distance bounds for HEWL. It maintains the overall structure of the protein and induces slightly more mobility, reflected in the backbone atom‐positional fluctuations. The unrestrained MD simulations show a high level of conformational disorder for side chains on the protein surface. However, this disorder is increased even further on S
2 order‐parameter restraining. In the MD simulations, which show good agreement with the experimental order parameters, the populations of many of the hydrogen bonds that are seen in all or most of the X‐ray structures are low. This has important implications for the use of X‐ray structure data in areas such as drug design, the interpretation of mutational data and receptor binding studies.
Conflict of interest
The authors declare no conflict of interest.As a service to our authors and readers, this journal provides supporting information supplied by the authors. Such materials are peer reviewed and may be re‐organized for online delivery, but are not copy‐edited or typeset. Technical support issues arising from supporting information (other than missing fn class="Chemical">iles) should be addressed to the authors.
SupplementaryClick here for additional data file.
Authors: H M Berman; J Westbrook; Z Feng; G Gilliland; T N Bhat; H Weissig; I N Shindyalov; P E Bourne Journal: Nucleic Acids Res Date: 2000-01-01 Impact factor: 16.971
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