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PROTEINS: Structure, Function, and Genetics 36:77–86 (1999)
Molecular Dynamics Simulations of Human ␣-Lactalbumin:
Changes to the Structural and Dynamical Properties of the
Protein at Low pH
Lorna J. Smith,1* Christopher M. Dobson,1 and Wilfred F. van Gunsteren1,2
Centre for Molecular Sciences, New Chemistry Laboratory, University of Oxford, Oxford, England
2Department of Physical Chemistry, Swiss Federal Institute of Technology Zürich, Zürich, Switzerland
1Oxford
ABSTRACT
Two 700-ps molecular dynamics
simulations of human ␣-lactalbumin have been compared. Both were initiated from an X-ray structure
determined at pH 6.5. One simulation was designed
to represent native conditions and the other the
protein in solution at pH 2.0 without a bound calcium ion. The low pH conditions were modelled by
protonating the aspartate, glutamate, and histidine
side chains and the protein C-terminus. Significant
changes were observed for the C-terminal region of
the sequence in the simulation at low pH. Most
notably an ␣-helix, helix D, and the C-terminal 310
helix were substantially disrupted relative to the
simulation at high pH. These perturbations to the
native fold are similar to those observed in an X-ray
structure of ␣-lactalbumin at pH 4.2. In addition,
larger fluctuations about side chain torsion angles
were observed in the low pH simulation than in that
corresponding to the higher pH. These structural
and dynamical changes might be representative of
the early stages of the transition to the moltenglobule state of the protein known to be formed
under low pH conditions in solution. Proteins
1999;36:77–86. r 1999 Wiley-Liss, Inc.
Key words: computer simulation; protein dynamics; protein denaturation; side chain disorder; molten globule; protein folding
INTRODUCTION
Partial or complete denaturation of proteins can be
brought about in vitro by a range of solution conditions.1
These include extremes of temperature or pH, high salt
concentrations, the removal of prosthetic groups or bound
metal ions and the presence of organic solvents or chemical
denaturant such as urea or guanidine hydrochloride.
There is much interest in characterizing the non-native
states formed under such conditions and comparing their
properties with those of globular folded proteins. These
studies can give insight into issues such as protein stability and folding and the relationship between the sequences
of proteins and their three-dimensional structures.2–6 They
also have significance with regard to understanding diseases associated with protein misfolding and the aggregation of non-native protein species. Such diseases include
r 1999 WILEY-LISS, INC.
cystic fibrosis, Alzheimer’s, and the spongiform encephalophies.7
In this work we concentrate on the partial unfolding of
human ␣-lactalbumin under conditions of low pH and in
the absence of a bound calcium ion. Experimental studies
have shown that the behavior of this protein as a function
of pH is particularly interesting. The native fold of human
␣-lactalbumin, defined in X-ray structures determined at
pH 6.5,8,9 contains a helical ␣ domain (four ␣-helices, A–D,
and a short C-terminal 310 helix) and a ␤ domain with a
triple-stranded antiparallel ␤-sheet, a long loop and a
short 310 helix (Fig. 1a). One calcium ion is bound in a site
involving the carbonyl groups of Lys 79 and Asp 84, the
carboxylate groups of Asp 82, Asp 87, and Asp 88, and two
water molecules (Fig. 1b). Comparisons of this structure
with an X-ray structure determined at pH 4.29 (with the
calcium ion still bound) demonstrate that on lowering the
pH there are changes in the C-terminal region of the
sequence (residues 96–123). The most significant of these
are a local unfolding of helix D (involving residues 104–
111) and a movement of the side chain of His 107 from a
buried position in the native structure to a conformation
where it is fully exposed to solvent.
At even lower pH (pH 2.0) and in the absence of calcium
human ␣-lactalbumin in solution forms a molten-globule
state (the A-state)10 consisting of an ensemble of interconverting conformers. The ␣-lactalbumin A-state is compact11 and much of the native secondary structure persists,
particularly the A, B, and C helices in the ␣ domain.12 The
␣ domain also retains an overall native fold.13,14 However,
the packing of amino acid side chains is disordered across
the conformational ensemble. This is particularly clearly
evident in a loss of the near-uv CD signal15 and a significant reduction in the chemical shift dispersion of the NMR
resonances for the molten-globule A-state compared to the
native protein.16,17
Abbreviations: CD, circular dichroism; MD, molecular dynamics; NMR,
nuclear magnetic resonance; RMSD, root-mean-square difference.
Grant sponsors: U.K. Biotechnology and Biological Sciences Research Council; Engineering and Physical Sciences Research Council;
Medical Research Council; Wellcome Trust; Schweizerischer National
Fonds; and the Underwood Fund.
*Correspondence to: L.J. Smith, New Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QT UK. E-mail:
lorna.smith@chemistry.oxford.ac.uk
Received 5 November 1998; Accepted 12 March 1999
78
L.J. SMITH ET AL.
Fig. 1. The X-ray structure from Acharya
et al.8 of human ␣-lactalbumin. In a) the full
structure is shown. The positions of the calcium ion and aspartate ligands are indicated
by black spheres and the regions of secondary structure are labelled (Helix A 5–15, Helix
B 24–33, ␤-sheet 41–56, 310(1) 77–80, Helix
C 86–98, Helix D 106–110, 310(2) 116–118). In
b) the details of the calcium-binding site are
shown, a circle representing the calcium ion
and crosses indicating bound water molecules. The program MOLSCRIPT42 was used
to generate part a.
We have been investigating strategies through which
theoretical studies can be used in conjunction with experimental data to extend our understanding of the conformational properties of human ␣-lactalbumin at low pH. In
particular we have previously reported a model for the
A-state of the protein generated using a molecular dynamics (MD) protocol based on insight from experimental
data.18 The molten globule must be described in terms of
an ensemble of slowly interconverting conformers and the
protocol adopted provides models for individual structures
within this ensemble. These differ in the packing of the
amino acid side chains but have essentially the same
native-like secondary structure and fold in accord with
experimental observations.
In this paper we report a complementary study in which
we use MD techniques to probe possible initial stages in
the denaturation of human ␣-lactalbumin under conditions of low pH. In particular we have run and analyzed
two MD simulations of ␣-lactalbumin, one of the native
protein at pH 8.0 (referred to as the high pH simulation)
and the other starting from the native structure but
modelling conditions of pH 2.0 and the absence of calcium
(low pH simulation). Both simulations have been run for
700 ps in the presence of explicit solvent water molecules.
Experimental interconversion between the native state
and the A-state is slow (the average rate of this interconversion for guinea pig ␣-lactalbumin at pH 7.4 and 65°C has
been estimated to be less than 10 s⫺1).19 Therefore within
the low pH MD simulation we do not expect to equilibrate
to the molten globule. Instead the work is intended to
provide insight into the structural and dynamical properties of the native state and how these initially change when
the protein is introduced into an environment at low pH.
METHODS
Human ␣-lactalbumin simulations and analysis were
carried out using the GROMOS96 package of programs.20
The simulations were performed in the presence of explicit
solvent (simple point charge water molecules21), using the
GROMOS96 force field20 for solvent simulations, parameter set 43A1. Two simulations were run, modeling conditions of high (pH 8.0) and low pH (pH 2.0) respectively by
changing the protonation of aspartate, glutamate, and
histidine side chain groups in the protein and the Cterminus. Full details are given in Table I. In each case the
TABLE I. Differences Between the Systems Used
for the Simulations of Human ␣-Lactalbumin
at High and Low pH
Aspartate side chainsa
Glutamate side chainsb
Histidine side chainsc
C-terminus
Overall protein charge
Calcium ion
Crystallographic waters
Box dimensions (initial)
Total numbers of:
Protein atoms
Water molecules
High pH (pH 8)
Low pH (pH 2)
Not protonated
Not protonated
Not protonated
Not protonated
⫺8
Present
Used
7.1832 nm
Protonated
Protonated
Protonated
Protonated
⫹16
Absent
Not used
7.1832 nm
1,243 ⫹ Ca2⫹
5,574
1,267
5,582
aAspartate
residues are 14, 16, 37, 45, 74, 78, 82, 83, 84, 87, 88, 97, 102.
residues are 7, 25, 43, 46, 49, 113, 116, 121.
cHistidine residues are 32, 107.
bGlutamate
starting protein coordinates were taken from the crystal
structure of human ␣-lactalbumin determined at pH 6.5 by
Acharya et al.8 There are discrepancies in the literature
regarding the pKa values of the two histidine side chains;
the pKa values are 5.8 and 7.2 but the assignment of these
to His 32 or His 107 is not clear.9,22 The simulation of the
native protein was therefore run under conditions where
both the histidine side chains were deprotonated, rather
than at the pH of the X-ray structure. The calcium ion was
included in the high pH simulation but was removed for
the simulation at low pH. Truncated octahedron periodic
boundary conditions were used in both simulations, the
initial dimensions of the periodic box being chosen so that
all non-hydrogen solute atoms lie further than 1.0 nm from
the square box walls. Details of the box lengths used and
sizes of the simulation systems are given in Table I.
Each simulation was run for 700 ps. In order to allow
relaxation of the water around the protein, a temperature
of 100 K was used for the first 2 ps and 200 K for the next 2
ps; the positions of all the protein atoms were restrained to
the X-ray ones during this initial 4 ps. The simulations
were then continued at 293 K without any positional
restraints and with a constant pressure of 1atm throughout. The temperature and pressure were maintained by
weak coupling to an external bath23 (temperature coupling
MD SIMULATIONS OF ␣-LACTALBUMIN
79
Fig. 2. Variations in the total potential energy of the
system (a) and the protein covalent, electrostatic, and
van der Waals energy (b, c and d respectively) as a
function of time for the ␣-lactalbumin simulations at high
(filled circles) and low pH (open circles). All energies are
given in kJmol⫺1 and are averages over 10 ps periods.
The average temperature of the protein in simulations
over the time period 300–700 ps was 289.3 K (high pH)
and 293.1 K (low pH). The overall differences between
the protein energies observed in the simulations at low
and high pH reflect the different total charges of the
protein molecule in the two simulations (⫺8 at high pH
and ⫹16 at low pH) and the absence of the calcium ion at
low pH.
relaxation time 0.1 ps; pressure coupling relaxation time
0.5 ps; isothermal compressibility ␬T 4.575 10⫺4(kJ mol⫺1
nm⫺3) ⫺1). Throughout the simulations bond lengths were
constrained to equilibrium values using the SHAKE procedure with a geometric accuracy of 10⫺4.24 Nonbonded
interactions were treated using a twin range method.25
Within a short-range cutoff of 0.8 nm all interactions were
determined at every step. Longer range (electrostatic and
van der Waals) interactions within a cutoff range of 1.4 nm
were updated at the same time as the pair list was
generated (every 10 fs). A reaction field was applied (⑀
54.0)26 beyond a cutoff of 1.4 nm. A time step of 2 fs was
used. The analysis was performed using trajectory coordinates and energies that were written to disk every 0.1 ps.
The solvent-accessible surface areas of individual structures taken from the simulation trajectories were calculated using the program NACCESS.27 Regions of secondary structure were identified using the program DSSP.28
The hydrophobic contacts present in structures taken from
the simulations were analyzed using the program
NAOMI.29
RESULTS AND DISCUSSION
Characteristics of the Native Protein
Figures 2 and 3 show the changes in the energy of the
system, the protein radius of gyration, solvent-accessible
surface area and positional root mean square differences
(RMSD) with respect to the X-ray structure through the
simulations. Looking first at the simulation of the protein
at high pH, after initial rapid changes in most of these
parameters the values plateau within 200–300 ps reflecting the equilibration of the system. The C␣ and all atom
positional RMSD values with respect to the X-ray structure stabilize at values of approximately 0.18 and 0.26 nm
respectively. Overall the values reflect changes to the
crystal structure as it adapts to the simulation solution
80
L.J. SMITH ET AL.
Fig. 3. Variations in the protein radius of gyration (a,
in nm), the total protein solvent-accessible surface area
(b, in nm2) and the C␣ atom (c, in nm) and all-atom (d, in
nm) positional root-mean-square differences from the
X-ray structure of native ␣-lactalbumin. The values are
for instantaneous structures taken at 10 ps intervals
through the simulation; high pH (filled circles), low pH
(open circles). The protons only present at low pH and
the calcium ion have been excluded in the RMSD
calculations.
environment. The secondary and tertiary structure of the
protein identified in the X-ray structure at pH 6.5 is
retained throughout the high pH simulation. The populations of the hydrogen bonds defining the secondary structure (over the simulation time of 300–700 ps) are summarized in Table II. Lack of regularity in secondary structure
elements has been recognized previously in the X-ray
structure at the C-terminus of helix A (Leu 11-Ile 15 form a
310 rather than an ␣-helix) and in the D helix region (Ala
106-Leu 110).8,9 These irregularities are reflected in the
simulation as populations of a variety of medium range
main chain hydrogen bonds by these residues. For example, for residues at the C-terminus of helix A there is a
31% and a 13% population of 13NH-11CO and 16NH-12CO
hydrogen bonds respectively in addition to the i,i⫹3 hydrogen bonds which define the 310 helix in the X-ray structure.
For helix D there are significant populations of 108NH104CO (92%) and 111NH-106CO (51%) hydrogen bonds in
the simulation that are not observed in the X-ray structure
(Figure 4a and Table II).
During the simulation the calcium ion was not restrained to its X-ray structure position. All the features of
the binding site persist, however, throughout the simulation (Fig. 5a), though the calcium ion does move slightly
away from the protein (distances from the ion to the ligand
binding sites on the protein increase on average by 0.02
nm compared to those present in the X-ray structure;
Table III). The calcium ion continues to be essentially
buried in the protein (solvent-accessible surface area of
0.04 nm2 at the end of the simulation, compared to 0.002
nm2 in the X-ray structure). This is of interest as recent
experimental results suggest that the interconversion of
MD SIMULATIONS OF ␣-LACTALBUMIN
TABLE II. Populations of Main-chain Hydrogen Bonds
(Indicated by Residue Numbers) in Regions of Secondary
Structure in the Human ␣-Lactalbumin Simulations†
A) Hydrogen bonds present in the X-ray structure
NH-CO
Helix A
8-4
9-5
10-6
11-7
12-8
13-10
15-12
16-13
Helix B
27-23
28-24
29-25
30-26
31-27
32-28
33-29
34-30
␤-sheet
42-49
44-47
49-42
51-40
50-55
54-51
55-50
High pH Low pH
83
93
63
95
91
2
7
44
99
97
57
92
90
5
63
62
99
82
99
78
98
90
92
72
99
96
88
86
98
75
35
0
72
53
98
59
98
54
98
56
86
97
54
98
77
99
NH-CO
57-48
310 helix 1
79-76
80-77
81-78
Helix C
89-85
90-86
91-87
92-88
93-89
94-90
95-91
96-92
97-93
98-94
99-95
Helix D
107-104
109-105
110-106
111-107
310 helix 2
118-115
119-116
High pH Low pH
56
86
38
97
68
61
13
14
98
95
93
99
98
86
92
68
94
94
60
49
91
98
99
96
57
98
98
91
74
87
13
95
43
40
40
0
1
7
72
65
0
0
B) Additional hydrogen bonds with significant populations
(ⱖ10%) in one or both of the simulations
NH-CO
Helix A
13-11
16-12
Helix B
26-22
32-29
␤-sheet
47-44
310 helix 1
81-77
High pH Low pH NH-CO
31
13
23
13
96
7
60
14
36
52
0
45
82-78
82-79
84-79
Helix C
98-95
Helix D
108-104
108-105
110-105
111-106
High pH Low pH
0
0
0
49
31
21
0
12
92
0
18
51
23
46
0
65
†The
populations listed are percentages over the simulation time
300–700 ps.
holo bovine ␣-lactalbumin into the native apo form does
not occur directly but via a molten-globule state (V. Forge
et al., unpublished results). Presumably partial unfolding
of the protein is required to liberate the calcium.
Previous studies have shown that isotropic B factors
calculated using protein simulation trajectories may be
unreliable even if simulation lengths of approximately 500
ps (after equilibration) are used.30 This reflects the fact
that atomic fluctuations may not converge fully within this
time scale. In addition, experimental crystallographically
refined B factors reflect atomic positional disorder and are
sensitive to the details of the refinement protocol. A
detailed comparison of the B factors calculated from the
81
␣-lactalbumin simulation with experimental values is
therefore not warranted. Indeed the calculated B factors
for ␣-lactalbumin (mean for C␣ 0.12 nm2 using 300–700 ps
simulation time) are considerably lower on average that
those in the X-ray structure of Acharya et al.8 (mean 0.22
nm2). This suggests that a longer simulation time would be
required to sample fully the internal motions of the
protein. However, various trends can be identified regarding the mobility of human ␣-lactalbumin from the magnitude of the fluctuations in the simulation over the 700 ps
time scale covered. Looking first at the main chain, from
300–700 ps the largest fluctuations in the simulation are
for Asp 45, Glu 46, Thr 112, Glu 113, Lys 114 (C␣ RMS
position fluctuations 0.13–0.14 nm; calculated B factors
0.44–0.52 nm2) and Leu 123 (C␣ RMS position fluctuation
0.22 nm2; B factor 1.27 nm2). All these residues are in
exposed positions where atomic motions will be more
readily allowed because of the absence of close packing.
Asp 45 and Glu 46 form a turn between the first two
strands of the ␤-sheet, Thr 112-Lys 114 are located in a
surface loop linking helix D and the C-terminal 310 helix,
and Leu 123 is the C-terminal residue of the polypeptide
chain. It is of interest that these residues correlate very
well with those that have the highest B factors experimentally although the experimental values of the latter are
larger, in general, than those calculated from the trajectory; in the X-ray structure the highest C␣ atom B factors
(0.55–0.86nm2) are observed for Asp 45, Glu 46, Glu 113,
Lys 114, Glu 121, Lys 122, and Leu 123.
In the X-ray structure determined at pH 6.5 by Acharya
et al.8 which was used as the starting structure for the
simulations, no residues are defined as having multiple
conformations. However, there are seven residues with
multiple side chain conformations in a human ␣-lactalbumin structure determined by Harata and Muraki9 at pH
6.5. (Harata and Muraki have determined structures of
human ␣-lactalbumin at both pH 6.5 and pH 4.2. The
structure at pH 6.5 is closely similar to that of Acharya et
al. with the exception of the C-terminus; the C␣ atom
positional RMSD between the two structures for residues
1–120 is 0.02 nm.) All but one of the residues with multiple
side chain conformations occupy exposed positions on the
protein surface. Therefore it might be expected that these
residues have mobile side chains in solution. Indeed NMR
studies have suggested that in general more than 60% of
residues on the surfaces of proteins populate multiple ␹1
conformations in solution.31 Met 30, however, has two
different side chain conformations in the ␣-lactalbumin
structure of Harata and Muraki (differing in the ␹2 and ␹3
torsion angles; Fig. 6a) but is completely buried (zero
solvent accessibility). This residue is situated in one of the
hydrophobic clusters in the core of the protein. This side
chain also has elevated B factors in the X-ray structure of
Acharya et al. (particularly for the S␦ atom 0.31nm2
compared with a mean of 0.14nm2 for other buried residues) and the ␹2 torsion angle observed in this structure
(21°) differs from either of those in the structure of Harata
and Muraki (␹2 angles 176° and ⫺42°; Fig. 6a).
82
L.J. SMITH ET AL.
Fig. 4. The main chain conformation of residues Trp 104 to Leu 119 in
human ␣-lactalbumin. Examples of instantaneous structures are shown
taken from the simulations of the protein (after 600 ps) at high pH (a) and
low pH (b). Main-chain hydrogen bonds are indicated by dashed lines, the
residues involved being labelled with the residue number. To provide the
same orientation for panels a) and b) the two structures shown were
superimposed using the backbone atoms of residues 104–119.
Fig. 5. Residues involved in the calcium-binding site
of human ␣-lactalbumin. Examples of instantaneous
structures are shown taken from the simulations of the
protein (after 600 ps) at high pH (a) and low pH (b). In
each case the main chain is drawn together with the
aspartate side chains that form the calcium-binding
ligands. Hydrogen bonds are shown by dashed lines, and
in the high pH structure a circle and crosses indicate the
position of the calcium ion and bound water molecules
respectively. To provide the same orientation for panels
a) and b) the two structures shown were superimposed
using the backbone atoms of residues 76–88.
TABLE III. Distances (in nm) Between the Calcium Ion
and the Protein Atom and Water Ligands in the X-Ray
Structure8 and the High pH Human ␣-Lactalbumin
Simulation (Average for 300–700 ps)
Distance
X-Ray
Simulation
Ca2⫹-79O
Ca2⫹-82OD1
Ca2⫹-84O
Ca2⫹-87OD1
Ca2⫹-88OD1
Ca2⫹-OW1
Ca2⫹-OW2
0.234
0.235
0.224
0.239
0.242
0.230
0.250
0.245 ⫾ 0.008
0.266 ⫾ 0.010
0.246 ⫾ 0.009
0.262 ⫾ 0.008
0.260 ⫾ 0.008
0.247 ⫾ 0.008
0.246 ⫾ 0.008
Analysis of the conformation of Met 30 in the simulation
shows that there are considerable fluctuations about the
side chain torsion angles for this residue. In particular, two
␹2 and seven ␹3 transitions of 120° or greater are observed
during the high pH simulation (Fig. 6b). This contrasts
with the behavior in the simulation of the majority of other
buried side chains in ␣-lactalbumin. For 20 of the 24
residues in the protein which have side chain accessibilities of less than 1%, no dihedral angle transitions are
Fig. 6. The conformation of Met 30. a) The X-ray structures of Acharya
et al.8 and Harata and Muraki9 at pH 6.5. b) Instantaneous structures
taken at 100 ps intervals through the ␣-lactalbumin simulation at high pH.
The structures are superimposed using the main chain atoms of Met 30
(positioned at the top of the figure), the same orientation being used in a)
and b).
MD SIMULATIONS OF ␣-LACTALBUMIN
observed during the simulation. The buried residues in
addition to Met 30 for which dihedral transitions of 120° or
greater are seen are Leu 12 (2 transitions), Leu 52 (9
transitions) and Ile 55 (14 transitions). In the ␣-lactalbumin structure Met 30 is adjacent to the aromatic rings of
Phe 53 and Tyr 104. Interestingly, Leu 52 and Ile 55 also
cluster together beside these two aromatic rings. Longer
simulations times would be required to characterize the
side chain motions in detail. However the current results
show that within this hydrophobic core there is some
flexibility in the native protein. This is clearly in agreement with the experimentally observed multiple conformations for Met 30. Multiple side chain conformations are not
observed for Leu 52 or Ile 55 in either of the X-ray
structures determined at pH 6.5 but two different conformations are defined for the side chain of Ile 55 in the pH
4.2 X-ray structure of human ␣-lactalbumin.9 The C␦1
atom B factor of Leu 52 is also elevated in the pH 6.5 X-ray
structure of Harata and Muraki (0.28 nm2 compared with
a mean for the buried residues of 0.15 nm2).
The conformational heterogeneity of side chains in a
hydrophobic core of human ␣-lactalbumin identified here
is of interest with respect to the substantially poorer
quality of the NMR spectra of human ␣-lactalbumin
compared with those of the homologous hen lysozyme.22
Although many factors contribute to this difference in
spectral quality, it in a large part reflects the broader line
widths of resonances in the ␣-lactalbumin spectra. Line
broadening can result from conformational exchange due
to mobility within the protein structure.32 Analysis of 15N
relaxation data for the ␣-lactalbumin main chain provides
evidence for conformational exchange for a significant
number of residues in the ␣ domain of the protein (C.
Redfield and C.M. Dobson, unpublished data). The effects
are most extreme for Gly 19 and Phe 31; the ratios of T1 to
T2 relaxation times for the 15N nuclei of these residues are
more than a factor of two greater than those for residues in
the ␤ domain of the protein (data recorded at a 1H
frequency of 750 MHz). In addition, the NMR resonances
of Leu 105 and Lys 108 cannot be identified, this being
thought to be due to extreme broadening of these resonances (C. Redfield and C.M. Dobson, unpublished data).
Two of the residues with the largest conformational exchange effects (Phe 31 and Leu 105) are adjacent in the
polypeptide chain to Met 30 or Tyr 104 within the region of
the protein core where there are significant side chain
fluctuations within the simulation. The time scale of
motions required for conformational averaging to be observed experimentally is much longer than the 700 ps
probed within the MD simulation. However, the conformational flexibility which allows fluctuations within the
interior of the structure in the ␣-lactalbumin simulation is
likely to permit slower motions to occur which are revealed
in the experimental NMR relaxation behavior.
Changes to the Structure and Dynamics at Low pH
As with the high pH simulation, analysis of the variations in the energies and structural parameters shown in
Figures 2 and 3 for the low pH simulation suggests that
83
the system has substantially equilibrated within 200–300
ps. After equilibration there are essentially no differences
between the radius of gyration or the solvent-accessible
surface area of the high and low pH structures in the
simulations. The C␣ and all atom-positional RMSD’s with
respect to the X-ray structure for the low pH simulation
stabilize at values slightly higher than those for the high
pH simulation (0.22nm for C␣ atoms, 0.30nm for all
atoms). These values are similar to the positional RMSD’s
between the structures in the low and high pH simulations
after 700 ps (0.20nm for C␣ atoms, 0.29 nm for all atoms).
In the simulation of the protein at low pH there are some
changes to the secondary structure of the protein (Table
II). There are minor differences in the hydrogen bonds
populated at the termini of the A and B helices but the
most significant changes are to the D helix and the two 310
helices in the protein. Concentrating first on the D helix
(Ala 106-Leu 110), there are no main chain hydrogen
bonds involving these residues that are populated for more
than 70% of the simulation time (from 300–700 ps). For
this region at low pH the hydrogen bonds with the greatest
population are between residues with an i,i⫹3 or i,i⫹5
separation rather than the ␣-helical i,i⫹4 separation. In
particular the hydrogen bonds 107NH-104CO, 108NH105CO and 111NH-106CO are observed (40, 46, and 65%
populations over 300–700 ps). In the region corresponding
to the native C-terminal 310 helix (116–118) no main chain
hydrogen bonds with a population greater than 5% (over
300–700 ps) are observed in the low pH simulation (Fig.
4b).
The conditions of low pH have disrupted the conformation of the C-terminal region of the polypeptide chain. The
simulation has been able to reproduce the local unfolding
of helix D, the major change observed experimentally
between the X-ray structures of ␣-lactalbumin determined
at pH 6.5 and pH 4.2 (see above).9 In the X-ray structure,
however, the loss of helix D is associated with a substantial
movement of the side chain of His 107. No significant
changes to this side chain are seen in the simulation. A
movement to an exposed position such as that observed in
the X-ray structure at pH 4.2 would, however, be likely to
occur over a much longer time scale than the 700 ps
monitored here. There are some changes observed in the
side chain contacts for the C-terminal region in the low pH
simulation. These are related to the loss of the main chain
helical hydrogen bonds and the protonation of glutamate,
aspartate, and histidine side chains. For example, hydrogen bonds between the side chain oxygen atoms of Glu 116
and the main chain amide groups of Leu 115, Glu 116 and
Gln 117 (30%, 56%, and 86% populations at high pH
respectively) are completely absent in the low pH simulation. These atoms are brought into close proximity at high
pH by the main chain 310 helical hydrogen bonds.
Although the secondary structure in the C-terminal
region of the protein sequence is retained in the simulation
at high pH it is interesting that even in this simulation
helix D has more variation in its main chain hydrogen
bonding than the other ␣-helices. At high pH four non
␣-helical main chain hydrogen bonds (107NH-104CO,
84
L.J. SMITH ET AL.
108NH-105CO, 110NH-105CO, 111NH-106CO) have significant populations in this region of the sequence and
three of these have increased populations in the low pH
simulation (Table II). This could reflect sampling a low
population of conformers characteristic of the low pH
ensemble even at the higher pH. This hypothesis is
supported by previous observations of elevated main chain
B factors for the C-terminal residues in the X-ray structures of ␣-lactalbumin at pH 6.5 compared to those at pH
4.2.9 It is also consistent with the exchange broadening,
particular for Leu 105 and Lys 108, identified by the 15N
relaxation studies discussed above.
This proposed sampling of a low population of conformers with a disordered C-terminal sequence at high pH is of
significance with respect to understanding data from
experimental studies of the exchange rates of main chain
amide hydrogens in native ␣-lactalbumin (at pH 6.3).12 No
protection from exchange is observed for residues in either
the D helix or the C-terminal 310 helix in the native
protein. Interestingly, despite the fast amide proton exchange rates in the C-terminal sequence, this region of the
structure is most resistant to unfolding on the addition of
urea to the molten-globule A-state of the protein.33 The
results therefore suggest that the resistance to denaturation reflects stabilization from hydrophobic contacts rather
than from secondary structure. Evidence in support of this
comes from an observed close similarity the hydrophobic
contacts present in the C-terminal sequence in the X-ray
structure and at the end of the low pH simulation (average
structure from the final 100 ps). Considering contacts
between the side chains of aromatic residues in this region
(Tyr 103, Trp 104, His 107, and Trp 118) and other
hydrophobic side chains within the protein, contacts between 17 residue pairs are observed in the X-ray structure
and 15 of these pairs retain hydrophobic contacts in the
low pH conformer.
The other 310 helix in human ␣-lactalbumin is adjacent
to the calcium-binding site. In the low pH simulation in the
absence of calcium this helix is elongated compared with
that present in the X-ray structure but has an irregular
pattern of hydrogen bonds (Fig. 5b and Table II). In this
region several main chain i,i⫹3, i,i⫹4 and i,i⫹5 hydrogen
bonds are populated. Two of these hydrogen bonds involve
the carbonyl oxygen atom of Lys 79 (82NH-79CO and
84NH-79CO) which is one of the ligands in the calciumbinding site. In addition the amide of Asp 83, which
because of the irregular hydrogen-bonding pattern is not
involved in a main chain hydrogen bond, makes a hydrogen bond with the side chain of Asp 82. This side chain is
also a ligand in the native calcium-binding site. The
features of the calcium-binding site are therefore substantially disrupted in the low pH simulation.
The RMS fluctuations about dihedral angles and the
total number of dihedral angle transitions have also been
compared in the two simulations (Table IV). As with the
structural parameters, the fluctuations are initially larger
in each simulation as the system equilibrates, but the
extent of the motions stabilizes within the first 300 ps of
the simulations. The fluctuations about the main chain ␾
and ␺ torsion angles are very similar in the two simulations. For example, the RMS fluctuations about ␾ from
300–700 ps are 15.6° and 15.7° in the high and low pH
simulations respectively. Differences are seen however in
the motions of the side chains. In particular the fluctuations about the ␹1, ␹2, and ␹3 torsion angles are greater in
the low pH simulation. The RMS fluctuations from 300–
700 ps are 21.3° (␹1), 52.8° (␹2), and 67.3° (␹3) at high pH
compared to 30.0° (␹;1), 59.0° (␹2), and 122.9° (␹3) at low
pH. In addition, there are significantly more dihedral
angle transitions for the side chains at low pH (563
transitions of 120° or greater at low pH compared to 380 at
high pH). These differences may reflect in part the smaller
number of hydrogen bonds involving side chains present
during the low pH simulation. Counting only hydrogen
bonds with a population greater than 10% in the simulations between 300–700 ps, there are 81 hydrogen bonds in
the high pH simulation compared with 56 at low pH. The
observed increase in fluctuations at low pH is of considerable interest as it indicates an increased flexibility and
disorder in the protein interior under these conditions. If
the simulation were to be run for much longer times, one
would be able to sample more fully this disorder in the side
chain packing within the protein core in equilibrium at low
pH. Such results would correlate with the experimentally
observed formation of the molten-globule state under
conditions of low pH in which the side chain packing is
disordered across the conformational ensemble.16,17,19 They
are also in agreement with MD simulations that have
shown that the packing of amino acid side chains in the
native human ␣-lactalbumin structure can be substantially disrupted whilst retaining a low-energy native-like
fold.18
CONCLUSIONS
Despite increasing interest in non-native protein conformations2–7 our understanding of their structural and dynamical properties at an atomic level is still limited. This
is primarily because of the considerable conformational
disorder associated with such states and the resulting
difficulties in their study and description. In general
non-native states must be described explicitly in terms of
ensembles of interconverting conformers.6,34,35 This poses
problems for both experimental and theoretical studies.
Experimental data represent an average over the conformational ensemble and are therefore difficult to interpret in
structural terms.6,36 For theoretical MD studies, currently
accessible simulation times are not nearly long enough
when using conventional procedures to sample the full
conformational ensemble, let alone characterize the process of interconversion between native and non-native
species. A range of MD approaches has however been
developed that attempt to overcome these problems. These
provide an important starting point for interpreting experimental data. The MD approaches include using simplified
force fields or elevated temperatures in the simulations,
running series of simulations from different starting structures, and simulating peptide fragments rather than the
full length polypeptide chain.37,38
MD SIMULATIONS OF ␣-LACTALBUMIN
85
TABLE IV. Root-Mean-Square Fluctuations About Torsion Angles and the Total Number of Torsion Angle Transitions in
the Human ␣-Lactalbumin Simulations†
A. RMS fluctuations (in degrees)a
100–200
200–300
300–400
Time period (ps)
400–500
500–600
600–700
300–700
␾
High pH
Low pH
14.5
15.3
13.8
15.3
14.3
14.0
13.2
14.8
13.8
13.7
13.2
14.6
15.6
15.7
High pH
Low pH
13.6
15.0
13.4
15.3
14.0
13.7
12.6
14.7
13.3
13.5
12.6
14.4
15.7
15.9
High pH
Low pH
20.1
19.9
17.0
21.8
16.7
18.3
13.7
20.5
15.7
21.3
15.6
20.3
21.3
30.0
High pH
Low pH
38.1
44.3
29.4
35.3
31.4
32.8
32.2
39.0
25.9
38.3
27.4
35.0
52.8
59.0
High pH
Low pH
57.1
83.7
47.1
57.9
44.1
61.7
40.9
48.9
38.5
66.6
46.2
56.9
67.3
122.9
Time period (ps)
400–500
500–600
␺
␹1
␹2
␹3
B. Number of torsion angle transitionsb
All main chain
High pH
Low pH
All side chain
High pH
Low pH
ⱖ120° side chainc
High pH
Low pH
100–200
200–300
300–400
600–700
300–700
616
808
670
839
589
749
639
727
627
730
587
631
2416
2806
843
1330
848
1095
677
1063
663
970
684
965
680
1013
2710
4011
149
193
129
160
100
161
70
137
109
153
98
103
380
563
†The
side chains of proline and cysteine residues are excluded from this analysis.
fluctuations for ␹4 are not listed due to the small number of residues with this torsion angle.
bThe total number of torsion angle transitions of 60° or greater (All) and of 120° or greater (ⱖ120°) are listed.
cThere are no main chain torsion angle transitions of 120° or greater in either of the simulations.
aThe
Here we have used a different strategy which does not
attempt to characterize the denaturation of ␣-lactalbumin
directly. Instead we have concentrated on events that
could be related to the very initial steps of the denaturation at acidic pH values. Similar approaches have been
used, for example, in studies of the pH-dependent conformations of a peptide fragment39 and of the denaturation of
barnase under acidic conditions and in 8 M urea.40,41 The
results for ␣-lactalbumin are promising in that a number
of features correlate at least in general terms with experimental data. Most notably, structural changes are seen in
the C-terminal region of the protein at low pH resulting in
a disruption of the D helix and the C-terminal 310 helix. In
addition there are increases in the side chain fluctuations
at low pH which might be related to the experimental
equilibration of the protein, over longer time scales, to the
molten-globule state. The work has also increased our
understanding of the properties of native ␣-lactalbumin.
In particular significant side chain fluctuations involving
Met 30, Leu 52, and Ile 55 in a buried hydrophobic core
were observed in the simulation at high pH. This flexibility
in the protein core correlates with multiple side chain
conformations and elevated B factors observed in X-ray
structures of the protein. It may also be related to the
exchange broadening evident in data from 15N relaxation
studies of the native protein. This work therefore provides
further evidence that, as computing power increases and
longer simulation times become accessible, MD techniques
will provide an increasingly important method for characterizing not only the dynamics of native protein conformations but also of much longer-scale conformational transitions associated with protein denaturation.
ACKNOWLEDGMENTS
This is a contribution from the Oxford Centre for Molecular Sciences which is supported by the U.K. Biotechnology
and Biological Sciences Research Council, the Engineering
and Physical Sciences Research Council, and the Medical
Research Council. The research of C.M.D. is supported in
part by the Wellcome Trust and by an International
Research Scholars award from the Howard Hughes Medical Research Institute. L.J.S. is a Royal Society Research
Fellow. W.F.v.G. gratefully acknowledges financial support
given by the Underwood Fund for his stay as a visiting
86
L.J. SMITH ET AL.
Professor in Oxford and financial support from the Schweizerischer National Fonds (project 21-50929.97). We thank
Christina Redfield for valuable discussions.
22.
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