 |
BACKGROUND |
A persuasive argument has been made to support
the hypothesis that amyloid peptide deposition is "a necessary but
not sufficient factor for the pathogenesis" of Alzheimer's disease
(Selkoe, 1991
). From the analysis of experimental
studies of amyloidogenesis, several distinct scenarios for fibril
formation and elongation have evolved (Lansbury, 1996;
Maggio and Mantyh, 1996; Teplow, 1998;
Rochet and Lansbury, 2000). In one scenario, largely
unstructured peptide monomers in solution cluster and form nuclei
(Lansbury, 1996). When the cluster reaches a critical
"nucleus," that nucleus then grows to form full length fibrils by
the addition of monomers to the existing fibril ends (Lomakin et
al., 1996, 1997). In a second scenario, there is first the
formation of peptide "protofibrils" of intermediate length
(Harper, 1997a; Walsh, 1997). Such
protofibrils then associate to form full length fibrils (Walsh,
1997; Harper, 1997b). Once the full length
fibrils are formed, additional amyloid peptide may add directly to
existing fibrils (Esler, 1996a; Kusumoto, 1998). Finally, monomers may associate to form micelles. Those micelles may convert to fibril nuclei upon reaching a critical size
(Lansbury, 1996; Lomakin et al., 1996,
1997). The relative importance of each of these possible
pathways has not yet been established.
Once the fibrils are formed, it has been clearly demonstrated that the
process of elongation of those existing fibrils occurs through the
process of monomeric peptide binding to fiber ends (Esler,
1996a) and that the kinetics are first order in the
concentration of monomeric peptide. This key observation has motivated
studies of the simple first order kinetics of fibril elongation
(Teplow, 1997; Kusumoto, 1998).
In such a mechanistic theory of fibril elongation an important question
is raised. How does the peptide's solution phase structure influence
the rate of fibril elongation? The wild-type (WT) peptide congener has
been shown to exist in a loosely formed collapsed coil state in aqueous
solution (Lee et al., 1995; Zhang et al., 1998). The structure of the collapsed coil is characterized by a central hydrophobic cluster (CHC) in the LVFFA (17-21) region. There
is also a dominant turn in the VGSN (24-27) region that is observed in
both the aqueous solution structure and the trifluoroethanol (TFE)-water solution structure, which shows two short
-helical regions (Barrow et al., 1992). This
has been supported by H
chemical shift measurements
taken as a function of temperature (Zhang, 1999), which
have shown very small changes in the chemical shift over a range of
temperature from 5 to 35°C in the VGSN region. Analysis of the
exposed hydrophobic surface area of the collapsed coil structure shows
that the peptide presents a large hydrophobic patch that could play an
important role in the initial deposition of the peptide monomer on the
fibril surface.
Experimental analysis of the E22Q Dutch mutant of the amyloid peptide
has shown it to be significantly more active than the WT peptide with a
twofold increase in the rate of fibril elongation and deposition
competence. Experimental measurement of the H proton
chemical shift in the wild type and Dutch mutant indicates that the
structures of the monomeric peptides in solution are similar
(Esler et al., 2000). The increased deposition rate
observed for the Dutch mutant has been explained in terms of a more
disordered solution state relative to the WT peptide (Esler et
al., 2000). The looser structure is believed to lower the
entropic barrier for opening of the peptide, which is necessary in the
deposition process.
Experimental studies of A
(10-35)-NH2-cycloH14K-E22, an
engineered cyclic peptide congener, has demonstrated that the
covalently locked structure is similar to the structure of the WT
peptide (Esler et al., 2000). However, the structurally
locked cyclic congener is found to be inactive in deposition. This has
been interpreted as a demonstration that the peptide must be allowed to
adopt an extended conformation in order to add to an amyloid template.
Nuclear magnetic resonance spectroscopy (NMR) structural analysis of
the F19T congener of the amyloid peptide congener in aqueous solution
indicates that there is a serious disruption of peptide structure in
the CHC region of the mutant peptide (Esler et al.,
1996b). This disruption of the CHC is correlated with a
diminished ability of the peptide to add to well-formed amyloid deposits. Therefore, in both the F19T congener and the E22Q Dutch mutant, the amyloid peptide monomer in solution is found to be less
constrained in the coil state. In the case of the E22Q Dutch mutant and
the WT peptide, the structure of the CHC is preserved and peptide
activity is normal or increased. In the case of the cyclic congener,
the CHC is preserved and the peptide initially adheres to the fibril.
However, the restricted peptide cannot undergo the necessary
conformational transition required to add to the fibril. In the case of
the F19T congener, the CHC and hydrophobic patch are disrupted and
activity is diminished (Esler et al., 1996b).
The scenario that emerges from these studies is one in which a
partially structured collapsed coil state encounters the fibril end
through diffusion and adheres to the fibril end to bury its hydrophobic
patch. The peptide deposits itself on the fibril end, resulting in a
loosely formed complex. The peptide/fibril complex then undergoes
reorganization to accommodate the peptide in a more fully deposited
(product) state. The reorganization step may involve conformational
changes in the peptide and/or the fibril end. The activation energy for
the fibril elongation is associated with peptide/fibril reorganization.
All of this evidence clearly points to a central role of the structure
and dynamics of the peptide monomer in the mechanism of fibril
elongation. There is evidence that the structure of the monomer in
solution is intimately related to the process of monomer deposition and
reorganization on the preexisting fibril surface. Therefore, knowledge
of the structure of the monomer is essential in understanding the rate
of diffusion of the monomer in solution.
In this study, we develop a model of the WT peptide congener in aqueous
solution and use that model to simulate the peptide dynamics on a
nanosecond time scale. Our focus is on validating our model by direct
comparison with experimental studies and augmenting the existing body
of experimentally derived information regarding the peptide's
structure and dynamics. Specifically, we pose the following questions.
(1) How well can simulation represent the computed NMR structural order
parameters for the peptide in solution, the rate of peptide diffusion,
and the observed hydrodynamic radius? (2) Are there structural motifs
that characterize the conformations of the monomer in solution? (3)
What interactions stabilize the monomer structure and what role
do those interactions play in the peptide's "activity"?
To answer these questions, multiple trajectories were run originating
from independent starting conformations of the peptide. From these
trajectories, the peptide structure, intramolecular fluctuations, and
overall peptide dynamics were analyzed. Direct comparison is made with
a variety of experimental observables. The analysis points to specific,
key interactions that stabilize the structure of the peptide monomer.
The role of these interactions in the process of peptide deposition and
fibril elongation is discussed.
| |
METHODS |
The WT peptide congener is depicted in Fig.
1. The structure was derived using NMR by
Lee and coworkers (Zhang et al., 2000) from distance geometry
calculations employing NMR-derived NOE restraints. The colored regions
are Tyr10-Glu11-Val12 (purple), His13-His14 (gray), Gln15-Lys16
(purple), Leu17-Val18-Phe19-Phe20-Ala21 (red), Glu22 (green), Asp23
(pink), Val24-Gly25-Ser26-Asn27 (yellow), Lys28-Gly29-Ala30-Ile31-Ile32-Gly33-Leu34-Met35 (purple). Of primary interest in this work is the 17-21 LVFFA segment (red) that forms the
central hydrophobic cluster and the 24-27 VGSN (yellow) segment that
forms a stable turn.
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FIGURE 1
This master figure identifies the important groups of
residues that compose the wild-type congener amyloid
(10-35)-NH2 peptide. From the N-terminus the groups are
Tyr10-Glu11-Val12 (blue), His13-His14 (gray), Gln15-Lys16 (blue),
Leu17-Val18-Phe19-Phe20-Ala21 (red), Glu22 (green), Asp23 (purple),
Val24-Gly25-Ser26-Asn27(yellow),
Lys28-Gly29-Ala30-Ile31-Ile32-Gly33-Leu34-Met35 (blue).
|
|
Our simulations each originated from one of a set of four initial
peptide structures that were chosen from two families of C-terminus
conformers. Those structures resulted from a distance geometry
refinement combined with a molecular dynamics annealing/minimization procedure employing experimentally derived NOE restraints. NMR heteronuclear relaxation data was also used to successfully compute S2 order parameters for a number of the backbone
amide H-N vectors. Further fitting of the relaxation data together with
estimation of the shape factors and hydrodynamic radii from NMR based
translational diffusion measurements allowed for two independent
estimates of the rotational correlation time which were in good
agreement. For completeness, in this section we provide a brief
description of the experimental approach used to determine the set of
initial structures, order parameters and peptide diffusion constants
employed in our study. Further details may be found elsewhere
(Lee et al., 1995; Zhang, 1999;
Zhang et al., 2000).
In the remainder of this section we describe the simulation model
employed in our study. The standard methods used to determine the
peptide's structure, NMR order parameters, time dependent structural
changes, and rates of self-diffusion are briefly summarized.
Experimental methods
NMR sample preparation
A Merrifield solid phase synthesis was used to build the
A(10-35)-NH2 peptide that was subsequently purified to
greater than 98% homogeneity by HPLC. A first sample was uniformly
labeled with 2H at Val12, Leu17, Val18, Phe19, Ile32, and
Leu34, 15N in the backbone position of Phe19, Val24, Gly25,
and Gly29, and 13C uniformly at Val24, in the -methyl
groups of Ala21 and Ala30 and the 
-methyl group of Met35. A second
sample was uniformly labeled with 2H at Val12, Leu17,
Phe19, Val24, Ile31, and Leu34, 15N in the backbone
position of Val18, Phe20, Gly25, and Gly29, and Gly33, and
13C uniformly at Val24, in the -methyl groups of Ala21
and Ala30 and the -methyl group of Met35. The use of
15N- and 13C-labeled samples resulted in the
unambiguous identification of a larger number of
1H-1H NOEs, thereby increasing the
number of restraints that could be subsequently employed in the
structural refinement. The use of extensive 2H labeling of
Leu, Val and Ile residues aided in the identification of cross peaks in
the Leu, Val, Ile CH3 fingerprint region. This effort was
only partially successful in resolving the methyl resonances of Ile31,
Ile32, and Leu34. The 2H labeling of the Phe19 and Phe20
residues aided in the unique assignment of these key residues of the
central hydrophobic core in the crowded aromatic region.
Dried samples were used to make an approximately 250 µM concentration
of peptide in either 100% D2O or a 90:10 ratio of
H2O:D2O with 0.5 mM sodium
3-(trimethylsilyl)propionate-2,2,3,3,-d4 (TSP) where
the pH was adjusted to approximately 5.6 using hydrochloric acid or
ammonium hydroxide (deuterated when appropriate). The resulting
solutions were immediately centrifuged for 10 min at 100,000 × g and then, the centrifugation was continued to achieve a
sedimentation of particles greater than 0.5 s. That criterion would demand, depending on the centrifuge, ultra-centrifugation for 100 to 200 hours. The intensive centrifugation is an essential step in the
preparation of the samples of predominately monomeric peptide required
for structural analysis. Intensive centrifugation has been shown to
lead to samples 200-300 µM in peptide that are stable and show no
signs of aggregation for periods in excess of 3 years.
NMR experiments
Data for 1H spectra were collected for samples
maintained at 10°C on 11.7 T (located at Boston University)
and 17.6 T (located at Oxford Instruments, Oxford, UK) Varian
UNITYplus NMR machines employing pulse field gradient probes. The
design of the structural work, presented in detail elsewhere
(Lee et al., 1995; Zhang et al., 2000),
is the following. The chemical shifts, referenced to internal TSP at
0.00 ppm, were detected using two-dimensional waveform gradient
suppression total correlation spectroscopy (TOCSY) with
frequency discrimination achieved through the time-proportional phase-incrementation (TPPI-States) method. 1H detected
heteronuclear multiple quantum coherence nuclear Overhauser enhancement
spectroscopy (NOESY) spectra were taken to determine the isotope
filtered 15N edited spectra.
Structural refinements using NOE restraints
Structures of the peptide that were consistent with the
experimentally derived NOE restraints were computed using the Distance Geometry II module of the Insight II computational software package (Molecular Simulations, San Diego, CA). There were 55 inter-residue and 24 intra-residue NOEs observed for the peptide's
N-terminal (Tyr10-Lys16) region; 86 inter-residue and 31 intra-residue
NOEs were detected for the central hydrophobic cluster (Leu17-Ala21); 46 inter-residue and 22 intra-residue NOEs were measured for the extended core (Glu22-Lys28); for the C-terminal peptide region (Gly29-Met35) 28 inter-residue and 24 intra-residue NOEs were observed.
The measured NOEs resulted in the total of 84 sequential, 66 medium
range (i,i + 2 or i,i + 3), and 32 long-range restraints used in the distance geometry calculations.
A set of 40 peptide structures resulted from the distance geometry
calculations. A subset of those structures was then used as input in a
series of molecular dynamics (MD) calculations performed using
the DISCOVER program of the Insight II computational software program.
The MD calculations employed loose harmonic restraints of atoms about
their initial positions and consisted of 1 ps of dynamics at 1000 K
followed by a stepwise cooling to 200 K at a rate of 100 K/ps. The
energy of the final "annealed" structure was then minimized using
the conjugate gradient algorithm. Of the starting set of 40 peptide
structures, following the MD annealing and minimization procedure, 15 structures with the lowest potential energy (in the absence of solvent)
were selected to represent the solution state ensemble of monomeric
peptide. The 15 final structures can be grouped in two main structural
families depending upon the orientation of the C-terminus. The root
mean square deviation (RMSD) of the backbone atoms
(N-C-C) has been calculated for both families
separately. It showed consistently smaller values for one of the two
families in every region of the peptide. The RMSD in the region of the
central hydrophobic cluster and extended core (Lys 16-Lys28) was 0.47 Å and 0.58 Å respectively for the two families of structures. This
result is different from the one reported by Lee (Zhang et al.,
2000), since a different definition of the RMSD has been used
(Molecular Simulations). Outside of the peptide's core region, the
C-terminal residues (Gly29-Met35) were relatively well-structured in
one of the two families with a backbone RMSD of 0.57 Å, and less well
structured in the other with an RMSD of 1.00 Å. However, the
N-terminal region was significantly less structured in solution
resulting in an absence of medium- and long-range NOE restraints with
RMSD values of 1.01 and 1.20 Å. The four initial structures employed
in our MD simulations were taken to be the two lowest-energy structures
from each family.
Diffusion
Diffusion constants for the peptide were measured as described
elsewhere (Tseng et al., 1999). Briefly, the pulse field
gradient probe was used to tailor a trapezoidal spatial gradient, the
amplitude of which could then be arrayed. The NMR gradient amplitude
dependence of the signal intensity was then measured and fitted to an
exponential function of the squared gradient amplitude. The decay rate
of the exponential was assumed to be proportional to the peptide diffusion constant. Ten values of the gradient amplitude were used in
each of three complete measurements.
Measurement of 15N relaxation times
One approach to the determination of the amide bond vector order
parameters, S2 is known as spectral density mapping
(Peng and Wagner, 1992, 1995). In that approach, a
series of rates for (1) longitudinal 15N magnetization
relaxation, RN(Nz); (2)
in-phase 15N single quantum coherence relaxation,
RN(Nx); (3) antiphase
15N single quantum coherence relaxation,
RHN(2HzN
Nx); (4) longitudinal heteronuclear two-spin
order relaxation, RH(2HzN
Nz); (5) amide proton longitudinal relaxation,
RH(HzN); and (6)
longitudinal cross-relaxation between the amide proton and nitrogen,
RN(HzN 
Nz), were measured. A set of constraint
equations relaters the set of relaxation rates to the spectral density
J(
) at five frequencies 0, H,
N, and |H| ± |N|,
and the sum of the proton longitudinal relaxation rate constants. The
spectral density may then be fit using a model free approach to derive
the S2 order parameters (Cavanagh et al.,
1996).
In this work, the reduced spectral density mapping protocol was
followed (Peng and Wagner, 1995). It is assumed that at
high magnetic fields J(H) 
J(N + H) J(H 
N), i.e., the
differences are less than the typical error in measuring relaxation
rates. This assumption eliminates two of the six (relaxation)
equations, reducing the set of equations to four. However, the sum of
the proton longitudinal relaxation rate constants is, under this
assumption, decoupled, thereby resulting in three equations relating
three values of the spectral density J(0),
J(N), and J(H) to
RN(Nz), RN(Nx), and
RN(HzN Nz) or equivalently T1,
T2, and the NOE where the steady-state heteronuclear NOE, 
, is defined (Peng and Wagner,
1992):
|
(1)
|
The relaxation rates measured at B0 field
strength of 11.74 T were then used to solve for the spectral density at
the three specified frequencies. The spectral density was, in turn,
fitted using the Lipari-Szabo model free formalism, which incorporates overall molecular reorientation with a time constant 
c
(the mean time required for the molecule to rotate by one radian) and
intramolecular or "internal" motions with a time constant
int (Lipari and Szabo, 1982a,b). By
fitting the spectral density to the prescribed functional form, it was
possible to derive the squared generalized order parameters,
S2, for the individual amide bond vectors. In
that procedure, J(0) was ignored and
J(N) and J(H) were
fit to determine values of S2 and
int using a value of c = 1.3 ns/rad.
Those parameters were then used to predict J(0). The
experimentally derived values of J(0) were somewhat higher
than the back-predicted values, suggesting the presence of
conformational exchange. The back-predicted values are nonetheless in
reasonable agreement with the experimental values. This suggests
that the resulting values of S2 are reliable.
Simulation model of the WT peptide congener in aqueous solution
The NMR structure of the amyloid -peptide served as the
starting configuration of the simulation. The peptide was centered in a
rhombic dodecahedron cell that was carved from a cubic box of 50 Å on
a side and filled with 2113 water molecules (for a 31 mM concentration
of peptide). Periodic boundary conditions were applied to avoid edge
effects. The energetics of the A peptide in water was simulated
using the version 22 potential energy function of the CHARMM program
(Mackerell et al., 1998). The potential energy cutoff
distance for the nonbonding interactions was 12.0 Å. Ewald summation
was used to evaluate the electrostatic interactions. The use of the
SHAKE constraint algorithm throughout the simulation, to keep the
lengths of the bonds involving hydrogen atoms fixed at their
equilibrium values, allowed for the use of a time step of integration
of 2 fs using the CHARMM program (Brooks et al., 1983).
After the equilibration period of 200 ps, a production run of 1 ns was
completed with an average temperature of 300K. Coordinates and
energetic data were collected every 200 fs.
The starting configurations for our peptide simulations were taken from
a set of coordinates derived from distance geometry calculations and
modeling with NMR derived NOE restraints. The four structures are
depicted as ribbons in Fig. 2. The four
1-ns trajectories are denoted T1, T2, T3, and T4. What is in common to
the four structures is the conformation of the 17-27 region containing
the LVFFA and VGSN substructures. Outside of that core structure there
is considerable disorder. In those regions, the experimentally derived
restraints are fewer, but nonetheless consistent with some residual
structure.
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FIGURE 2
The four initial configurations of the peptide
superimposed to best overlap the 17-21 LVFFA regions of the peptides.
Each initial structure was generated through a refinement procedure
using NOE restraints derived from NMR experiments on the wild-type
congener amyloid (10-35)-NH2 peptide by Lee and
coworkers. Note the significant disorder outside of the central core
region.
|
|
Measures of peptide dynamics and reorganization
We employ a number of useful measures of the peptide dynamics,
including the rate of translational diffusion of the peptide and
variations in the compactness of the peptide as measured by the radius
of gyration and peptide end-to-end distance. Comparisons are made with
the theoretical estimates for a freely jointed linear chain.
Self-diffusion constant for the peptide
The mean-square displacement of the center-of-mass of the
peptide was computed as a function of time for the trajectories T1, T2,
T3, and T4. The diffusion constant of the peptide monomer was estimated
using the Einstein relation
|
(2)
|
which is expected to hold in the limit of long times. The mean
square displacement was computed over the length of the trajectory and
the slope was measured to determine the diffusion constant.
The magnitude of the diffusion constant was also estimated using the
Kubo relation,
|
(3)
|
where
vCOM(t)vCOM(0)
is the velocity autocorrelation function for the center-of-mass of the
peptide. The velocity autocorrelation function was computed and fitted
to an exponential function to estimate the time integral and
D.
Peptide end-to-end distance
The end-to-end distance of the peptide was defined by the
distance separating the first N atom of the N-terminus of Tyr10 and the
second end N atom attached to the carbonyl oxygen of the C-terminal
residue Met35. This is equivalent to a sum along the backbone according
to
|
(4)
|
where li is the vector connecting the
consecutive N atoms along the back-bone between the N- and C-termini.
This distance was computed for each simulation. We write the
ensemble-averaged value re2, which is
computed by averaging over the MD trajectories. Large changes indicate
significant reorganization in the global structure of the peptide.
Radius of gyration
The radius of gyration for the peptide was computed using all of
the peptide atoms in the standard formula (Berne and Pecora, 1976)
|
(5)
|
where rCOM is the peptide's center of
mass, rk is the position of the kth
atom in the peptide, and mk is its mass. When
the masses are all equal, this expression is equivalent to a sum over all atom pair distances rij as
|
(6)
|
In our computations, rg was computed
using (1) all atoms and (2) only the heavy (non-hydrogen) atoms. Each
computation was carried out over many configurations of the peptide
generated over the trajectory to determine the ensemble-averaged value
rg2.
Characterizing the peptide structure in solution
Direct visualization of the peptide structure's time evolution
was used as part of the analysis of the peptide dynamics. In addition,
we analyzed the intramolecular hydrogen bond network by computing a
measure of persistence for all possible hydrogen bonds. We also
analyzed the evolution of the peptide structure by computing the
solvent exposed surface area of the total peptide and the hydrophobic
patch centered about the LVFFA region. These methods are defined below.
Recognizing intramolecular hydrogen bonds
In each stored configuration, the peptide was analyzed for
hydrogen bonding groups for all possible donors and acceptors. The
hydrogen bonding frequency was then computed for the full simulation by
dividing the number of snapshots showing hydrogen bonds by the total
number of snapshots. The approximate definition of the hydrogen bond
that was used is that the donor and acceptor atoms must be at a
distance shorter than or equal to 2.5 Å and the angle between the
donor and acceptor diatomic groups is in the range 113-180°
(Simmerling et al., 1995).
Solvent exposed surface area of the LVFFA region
The atomic exposed surface area was computed by the method
described by Wesson and Eisenberg (1992) and originally
developed by Lee and Richards (1971). Essentially, the
solvent exposed surface area of each atom was defined as the area
exposed to contact by a water probe of diameter 2.8 Å. The total
surface area for the peptide in a modeled extended configuration was
computed to represent an upper bound on the surface area of the
peptide. Each trajectory was then analyzed by computing the total
solvent exposed surface area of the whole peptide molecule and the
atoms composing the LVFFA region.
Characterizing internal motions: Lipari-Szabo NMR order parameters
We follow the standard "model free" analysis of
Lipari and Szabo (1982a,b). The motion of the peptide
can be described by a correlation function C(t) for the
orientation of a peptide backbone amide bond vector. Assuming that the
internal motions are uncorrelated with the overall molecular tumbling,
C(t) can be separated into two contributions: one for the
internal motions, Cint(t), and the
other for the overall molecular rotation,
Ctumb(t).
|
(7)
|
Cint(t) is given by
|
(8)
|
where Y2m(
, 
) are the second order
spherical harmonics and and are the spherical polar angles that
specify the orientation of the internuclear NH amide bond vector in the
molecule-fixed coordinate frame.
The internal motions of the peptide can be characterized by the two
parameters S2, a generalized order parameter,
and int, an effective correlation time, defined through
|
(9)
|
and
|
(10)
|
where T is the time after which
Cint(t) = S2.
Cint(0) is the value of the internal
correlation function at time zero.
S2 is a measure of the degree of freedom of the
motion of the intermolecular amide bond vector;
S2 is equal to 1 if the motion is completely
restricted and is equal to 0 for isotropic motion. In order to separate
the overall molecular rotation from the internal motion, every
coordinate frame of the 1 ns trajectory was translated and rotated
until the root mean square displacement with respect to a reference
configuration (t = 0) was minimized
(Philippopoulos and Lim, 1994).
| |
RESULTS |
This section summarizes the analysis of the four nanosecond
trajectories of the solvated A-peptide congener dynamics. The peptide dynamics is described and connection with experiment is made
through the computation of NMR order parameters and rates of peptide
self-diffusion and reorganization.
Peptide structure in solution
The structural dynamics of the peptide is depicted for the four
trajectories in Fig. 3. In each
"movie" the peptide is rendered every 100 ps during the nanosecond
duration of the run. In trajectories T1, T2, and T4 the core of the
peptide structure is seen to be maintained. The N- and C-terminal
peptide regions are less well structured.
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FIGURE 3
A "movie" composed of snapshot configurations taken
every 100ps along the nanosecond trajectories T1, T2, T3, and T4,
respectively.
|
|
The character of the global peptide fluctuation is even more apparent
in Fig. 4, in which the snapshots of the
peptide depicted in Fig. 3 are reoriented so as to best fit the LVFFA
(17-21) region for all structures. A striking feature is the strong
structural integrity of the central core of the peptide, in particular
the LVFFA (17-21) region and the VGSN (24-27) turn region. This is the case in all trajectories. A slight difference in simulation T3 is
that the core of the structure is disrupted and the end-to-end distance
in the peptide is significantly decreased over the simulation run. This
transition will be discussed in detail below.
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FIGURE 4
A "collage" composed of snapshot configurations
taken every 100ps along the nanosecond trajectories T1, T2, T3, and T4,
respectively. The peptide backbone structures are overlapped to best
fit the 17-21 LVFFA regions of the peptide.
|
|
Hydrogen bond formation
A plot of the hydrogen bond frequency, computed as the fraction of
time a hydrogen bond is well-formed during the trajectory, is shown in
Fig. 5. In simulation T1, the hydrogen
bonds that are most persistent include Glu11(O)-His13(HN), seen in all
four runs, Val18(O)-Lys28(HN), Ser26(hydroxylic H)-Asn27(HN), and
Lys16(O)-Val18(HN). Other hydrogen bonds that are formed in this
trajectory include Leu17(O)-Phe19(HN), Ala21(O)-Asp23(HN), and
Lys28(O)-Val18(HN). We find that for this run, amino acids in the VGSN
turn region do not form hydrogen bonds with the LVFFA region. During
this run, the only hydrogen bonds to form in either region are those internal to the region.
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FIGURE 5
Plot of the hydrogen bonding probabilities for
simulations T1, T2, T3, and T4, respectively. Hydrogen bond acceptors
are noted along the x-axis and donors are indicated along the y-axis.
The acceptors indicated with single letters are side chain groups;
those that follow are backbone carbonyl oxygen atoms. Similarly, the
donors indicated with single letters are side chain groups; the
remaining donors are backbone amide hydrogen atoms. On all four plots,
different styles of boxes have been used to identify atoms from
different regions on the peptide: rectangular solid line boxes for the
LVFFA and oval solid line boxes for the VGSN region. Hydrogen bonds
common to at least two different trajectories are indicated with an
additional box, whose shape and line type are common among the
trajectories.
|
|
In simulation T2 we find Asn27 (side chain acyl oxygen)-Ala30(HN),
Glu11(O)-His13(HN), and Ile32(O)-Asn27 (sidechain HN) to be persistent
hydrogen bonds. In addition to those hydrogen bonds, also seen in the
T2 run are hydrogen bonds between Phe20(O)-Ser26(hydroxylic H),
Ala21(O)-Gly25(HN), Leu17(O)-Phe19(HN), and
Ala21(O)-Asp23(HN), all of which involve at least one atom of
the LVFFA region. Two of these bonds are between the LVFFA and the VGSN
regions. The last two bonds listed above are also present in the T1
run. In simulations T2 and T4, there is a hydrogen bond between
Asp23(O)-Gln15(HN).
In simulation T3, the peptide structure appears to be more open.
Persistent hydrogen bonds are formed between Ser26(hydroxylic O)-Asn27(HN), His14(O)-Val18(HN), and His13(O)-Gln15(HN). The backbone
oxygen of the Phe19 residue interacts with both Gly25(HN) and
Val24(HN). Those interactions involve residues from the LVFFA and VGSN
regions. A hydrogen bond between Ala30(O)-Ile32(HN) is also seen.
Hydrogen bonds involving Ala21 and Leu17 occur infrequently. This run
presents the smallest number of common hydrogen bonds of all the trajectories.
In the T4 simulation, there is a high degree of structure. The H-bonds
involve many residues; with the exception of Phe20, all of the amino
acids between His13 and Asp27 are involved in hydrogen bonds within the
region. The residues of the LVFFA region form many hydrogen bonds in
the T4 run and many of those hydrogen bonds are formed with atoms in
the VGSN region. Examples of such hydrogen bonds include Asp23 (side
chain O)-Val18(HN), Asp23 (side chain O)-Leu17(HN), Phe19(O)-Asn27(HN),
Val18(O)-Ala21(HN), Val18(O)-Val24(HN), Ala21(O)-Ser26(HN), and
Ala21(O)-Gly25(HN). The backbone oxygen atom of the Asp23 residue also
interacts with the backbone amide hydrogens of Gln15 and Lys16.
Hydrogen bonds between Val24(O)-Gln25(HN), His13(O)-Lys16 (sidechain
HN) and Glu22(O)-His14 (sidechain HN) are also seen. These extensive
hydrogen bond networks are important to the stabilization of the core
peptide structure.
Solvent-exposed surface area
The exposed hydrophobic surface area is thought to be crucial to
the peptide's ability to recognize and adhere to the fibril end. The
solvent-exposed surface area of the peptide is depicted in Fig.
6 for both the total peptide and the
LVFFA central hydrophobic cluster region. Averaging over fluctuations,
the LVFFA hydrophobic patch is approximately 400 Å2 in
extent, compared with the surface area of approximately 2600 Å2 of the peptide as a whole.
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FIGURE 6
The atomic solvent exposed surface area contributed by
the central hydrophobic cluster LVFFA (top) and the total
peptide (bottom) over the length of the four simulation
runs.
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There is a relatively high contribution of hydrophobic residues to the
solvent-exposed surface area of the peptide in solution. It is
interesting to notice that the nonpolar surface area is not evenly
distributed on the peptide molecule, but is localized in a continuous
patch on about one-third of the surface (Zhang et al.,
2000).
In the T3 and T4 simulations, as the total solvent-exposed surface area
of the peptide increases, the radius of gyration also increases. Note
also that the T4 simulation shows the smallest values for the
solvent-exposed surface area. That simulated structure is also the most
rigid with small root-mean-square (RMS) atomic fluctuations and
S2 values.
Measures of peptide dynamics and reorganization
The most commonly used measure of the fluctuation in a peptide
structure during a dynamic simulation is the RMS deviation in the
position of each atom from its average value computed over the full
simulation run. Those RMS deviations are plotted in Fig. 7 for the four runs. The magnitude of the
RMS fluctuations provides the general description of the large scale
motion of the N- and C-terminal regions. Large fluctuations also occur
in the loop region centered about residue Glu22. The overall
fluctuations in T4 are significantly lower than in the other three
runs. In fact, the fluctuations in T4 are on the order of 1 Å, similar in magnitude to fluctuations observed in simulations of larger, globular proteins. Fluctuations in runs T1, T2, and T3 are
significantly larger, on the order of 2 Å. In the T3 simulation there
are very small values of S2 for Ala21 and for
residues 26-35. This is in agreement with the large RMS values for
those regions.
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FIGURE 7
The averaged root-mean-square atomic coordinate
deviation from the average peptide structure computed over the each of
the four simulation runs.
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Various NMR studies such as the proton chemical shifts show these
regions to be particularly well structured in aqueous solution and
reasonably insensitive to changes in temperature in the 5-35°C range
(Zhang, 1999; see Fig.
8). In general, it can be seen that regions of small differential chemical shift correspond to regions of
small RMS fluctuations. The overall picture is one of the peptide as a
collapsed coil with significant structure imposed by the stable
structure of the CHC LVFFA (17-21) and VGSN (24-27) turn regions and
stabilized by their interactions (Zhang et al., 1998).
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FIGURE 8
The difference between the values of the experimentally
measured H proton chemical shift at temperature
T and at temperature T = 5°C
( H = H(T) H(5°C)) as a
function of the temperature over a range of 5 to 35°C. Small values
indicate regions of the peptide where the average structure is stable
over the measured temperature range (Zhang, 1999).
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Peptide self-diffusion
The translational self-diffusion constant for the amyloid peptide
was computed using the Einstein relation for the mean-square displacement of the peptide's center of mass. The results are depicted
in Fig. 9, which shows the fits to the
initial linear regions of the mean-square displacement and the
resulting estimates of the diffusion constant. The average diffusion
constant is approximately D = 1.4 × 10
6 cm2/s.
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FIGURE 9
The mean square atomic displacement as a function of
time for each of the four trajectories T1, T2, T3, and T4. The slope of
the mean square displacement is equal to 6D where
D is the self-diffusion constant. From this data were
derived four estimates of the diffusion constant of the peptide.
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The magnitude of the diffusion constant was also estimated by
integrating over the velocity autocorrelation function depicted in Fig.
10. For the cases of trajectories
T1, T3, and T4, the initial decay up to 2.0 ps is well approximated by
an exponential function of the form C(t) = v2 exp(t/) where the mean square
velocity v2 = 0.235 Å2/ps2 = 2,350 m2/s2 for a root mean square velocity of 47 m/s
as expected from kinetic theory for a peptide of mass M = 2902 g/mol. Using a simple fit to the exponential model where
= 0.27 ps, the estimate for the diffusion constant is
D = 2.1 × 106 cm2/s.
This value is slightly larger than, but in reasonable agreement with,
D values derived from fits to the mean-square displacement data. The experimentally measured value of the diffusion constant for
the peptide in aqueous solution at this temperature is
Dexp = 1.4 × 106
cm2/s (Tseng et al., 1999). (A previous
estimate of the diffusion constant was 1.6 × 107
cm2/s, Kusumoto et al., 1998)
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FIGURE 10
The velocity autocorrelation function for the center
of mass motion of the peptide as a function of time for each of the
four trajectories T1, T2, T3, and T4. For trajectories T1, T3, and T4,
the decay is well approximated by an exponential function.
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Suppose that we interpret the magnitude of the diffusion constant using
a Langevin model. What is the value of the friction constant, 
, that
results? Taking
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(11)
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we find that = 1.9 × 1011 kg/s. Now
suppose that we use the Stokes-Einstein relation
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(12)
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where = 0.01 poise is the viscosity of the water solvent.
We estimate that the hydrodynamic radius of the peptide is
rH = 10 Å, which is in reasonable
agreement with the estimates of the peptide radius computed over our
simulated dynamics discussed in the following section.
In Fig. 11 we plot the dependence of
the logarithm of the diffusion constant for a number of molecules
(glycine, sucrose, ribonuclease, lysozyme, bovine serum albumin, and
hemoglobin) along with the computed value for the A peptide as a
function of the logarithm of the molecular mass. Two fits are shown.
The first fit is based on an approximation that the hydrodynamic radius
aH scales as M1/3 where
M is the mass of the molecule. The result is
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(13)
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This fit should work well if the molecule is closely packed.
However, as we have seen, the peptide structure is somewhat extended in
solution. A better fit to the mass scaling of the diffusion constant is
achieved with
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(14)
|
although the mass scaling is less well founded. If the peptide was
a linear chain we might expect rH to scale as
the peptide radius of gyration which is expected to scale as
M3/5 in agreement with Flory theory (where
excluded volume is considered). However, the peptide is a branched
polymer that is well structured in a way that the ensemble of linear
chains is not. The measured result is a mass scaling that lies between
the close-packed scaling and the expectations of the linear chain
model. Although the calculation of the diffusion constant of the
peptide does not provide a precise measure of the structure of the
peptide, it certainly gives an indication that the peptide in solution
is not in a completely extended conformation but is rather structured
in a more compact way.
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FIGURE 11
The log-log plot of the diffusion constant as a
function of the molecular mass for a series of macromolecules (from
experiment) and the -amyloid peptide congener (from this work).
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End-to-end distance fluctuations
The end-to-end distance in the peptide computed over the four
dynamical trajectories is depicted in Fig.
12. The results clearly indicate that
the global structure of the peptide is largely intact throughout
simulations T1, T2, and T4. This is true in spite of the fact that by a
number of measures, including the magnitude of mean-square atomic
fluctuations and NMR order parameters, the terminal ends of the peptide
are largely disordered. In simulation T3 the behavior is quite
different, as there is a strong drift in the end-to-end distance
towards shorter distances.
To create a point of reference for our simulation results, it is useful
to compare them with a standard of a simple solvable model of an ideal
linear polymer. For that model, the end-to-end distribution
W(re) is a expected to be a Gaussian
function
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(15)
|
where re2 is the square of the
end-to-end distance averaged over all configurations. For an ideal
freely jointed chain, where external forces and hydrodynamic effects
are ignored, we expect that re2 = Nl2 where l2 is the
mean-square bond length along the chain and N is the number of bonds. Taking the C C distance to be 3.84 Å and N = 25
the predicted value is Re = re21/2 = 19.2 Å. That
value sits slightly above the computed values shown in Fig. 12
indicating that the effect of intramolecular interactions and solvation
is to reduce the end-to-end distance somewhat relative to the
predictions of the freely jointed chain.
Of course, the difference is greater than the deviation of the mean
value indicates. This is clearly demonstrated by Fig. 13, which shows the distribution of
re values computed for the simulated peptide
dynamics. In the distribution of re the
difference is even more pronounced. Unlike a freely jointed chain, the
peptide is structured and the range of values of the
re is severely restricted. The distribution is
well approximated by a Gaussian function
|
(16)
|
where µ and 
are the average and the standard deviation,
respectively, calculated from the set of data. The parameters of the
fits are listed in Table 1.
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FIGURE 13
The distribution of the instantaneous values of the
end-to-end distance of the peptide computed for the trajectories T1,
T2, T3, and T4.
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TABLE 1
The parameters (in Å) of the Gaussian fits to the
distribution of end-to-end distances computed over the four
trajectories
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A point of comparison with experiment is found in the quasielastic
light scattering data of Teplow and coworkers (Lomakin, 1997). They measured diffusion constants, which were then
interpreted using a Stokes-Einstein analysis (see Eqs. 11 and 12) to
derive a distribution of values of the hydrodynamic radius
rH for the peptide. The distribution of radii
attributed to the peptide monomer was shown to be spread between 10 and
20 Å. That distribution is in good agreement with the distribution of
peptide end-to-end distances derived from our simulations (see Fig.
13).
Radius of gyration
The radius of gyration is a convenient measure of the spatial
extent of the peptide during the simulated dynamics. The time dependence of this quantity is depicted in Fig.
14 for the four dynamical simulations.
The resulting values provide an estimate of the spatial extent of the
molecule that is in good agreement with the estimate of the molecule's
hydrodynamic radius.
The time average of the radius of gyration is approximately 9.2 Å,
which is in close correspondence with the estimate of the hydrodynamic
radius rH = 10 Å computed from the
diffusion constant using the Stokes-Einstein relation.
In the simplest approximation of an ideal polymer where excluded volume
is ignored, the radius of gyration distribution
W(rg) is a expected to be strongly
weighted Gaussian
|
(17)
|
The radius of gyration was binned over the four simulations and
the distributions are plotted in Fig.
15. A fit to the data using the
computed values of rg2 is shown for
comparison and a Gaussian distribution function (using Eq. 16). This
fit approximates the actual distribution satisfactorily over most of
its range. The parameters of the fits are listed in Table
2.
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FIGURE 15
The distribution of the instantaneous values of the
radius of gyration of the peptide computed for the trajectories T1, T2,
T3, and T4.
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TABLE 2
The parameters (in Å) of the Gaussian fits to the
distribution of radii of gyration computed over the four
trajectories
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We can estimate the radius of gyration from the freely jointed chain
model to be
|
(18)
|
where N is the number of bonds in the chain and
l is the root mean square bond length. In the limit of
larger N one finds that rg2 = 
re2. For this molecule,
we find that on average
re21/2 = 16 Å, so
that we would estimate
rg21/2 = 6.5 Å,
which is somewhat less than our computed value in the range of
rg21/2 = 10 Å. This
difference results from the fact that the end-to-end distance does not
fluctuate widely as is expected in the freely jointed chain model. The
peptide has a definite core structure that restricts the range of
probable end-to-end distances in the peptide. In this case, that leads
to values of re21/2 that
are smaller than expected.
Characterizing internal motions: Lipari-Szabo NMR order parameters
In Table 3 are listed the computed
S2 order parameters for the four nanosecond
simulations of the peptide. The experimentally measured values are
listed for comparison. The same data are plotted in Fig.
16 to show better the overall trends
across the peptide's primary structure. Comparing the table of
S2 values with the computed RMS fluctuations
(see Fig. 7), the correlation is quite good: large values of
S2 correspond with small values of the RMS
fluctuation from the average peptide structure.
Simulations T1 and T2 show significant correlations that extend to
include the LVFFA and VGS regions. In the T1 simulation, the N terminal
end of the peptide shows the higher degree of correlation. In the T2
simulation, it is the C terminal end of the peptide that shows the
higher level of correlation.
In the T3 run there is significantly less correlation than in the other
three trajectories. There are two regions (from Gln15 to Phe19 and
Glu22 to Asp23) with larger values of S2. Note
that the FA end of the LVFFA region shows lower values indicating that
the LVFFA cluster is disrupted. The structure of the VGSN turn region
also appears to be disrupted. It would be interesting to know if that
is a consequence of, or reason for, the relatively unstructured nature
of the peptide dynamics over that trajectory. In the T3 run, the
peptide structure is more open or loose. For example, the Phe19 and
Phe20 residues interact with Gly25 and Asp23. Those interactions are
not seen in any other trajectory.
In the T3 simulation, Ala21 forms hydrogen bonds not at all or at a
very low frequency. This is quite different from all other trajectories
in which it is always part of a hydrogen bonding pair. In addition,
Leu17 and Val18 do not form any hydrogen bonds with atoms in the region
LVFFAEDVGSNK. This could explain the disruption of the core and the
fact that S2 = 0.1 for Ala21 in the T3 simulation.
The simulation T4 shows a much higher degree of structure than the
other simulations. Values for S2 exceed 0.5 from
Glu11 to Leu34. There are particularly large values in the LVFFA
region. This is the simulation that presents the highest number of
H-bonds over the entire run. Moreover, the structure of the peptide is
significantly more compact in the T4 run than in the other simulations.
Note that the Glu22 shows large S2 values
throughout all four runs. It is the Glu22 residue that is mutated in
the E22Q Dutch mutant. This observation is in line with the notion that
the WT is less flexible than the E22Q Dutch mutant in the peptide
monomer. The greater flexibility in the mutant form may contribute to
the faster addition of the peptide monomer to the existing fibril and a
larger rate of fibril elongation.
| |
SUMMARY AND CONCLUSIONS |
The simulation of four nanosecond trajectories of the wild-type
congener amyloid (10-35)-NH2 peptide solvated by 2113 water molecules in a rhombic dodecahedral cell was performed. The
analysis of the simulations focused on computing quantities to
characterize the structure and dynamics of the peptide. This
computational study employed a theoretical model of the peptide in
aqueous solution and has provided a number of tests of the model
against the results of experiments probing the peptide structure, rate
of self-diffusion, conformational fluctuations, and key stabilizing
interactions. Particular attention was paid to observables that can be
or have been measured experimentally so as to test and validate the
theoretical model. The results led to the following conclusions.
1. The computed values of the peptide diffusion constant are
consistently on the order of D = 1.4 × 106cm2/s in good agreement with the
experimentally measured value of Dexp = 1.4 × 106cm2/s (Tseng et al.,
1999). If the simulated peptide structure was significantly
different from that of the actual peptide in aqueous solution, the
diffusion constants could have been quite different in magnitude. The
magnitude of D is consistent with a relatively compact
peptide structure.
2. The computed values of the radius of gyration for the peptide, in
three of the four simulations, are consistently in the range of
rg21/2 = 10 Å. The
computed value of the hydrodynamic radius,
rH = 9.2 Å is quite similar to this
value, indicating that the assumptions underlying the use of the
Stokes-Einstein relation are reasonably well satisfied by the
dynamics of the A-peptide congener in aqueous solution.
3. Computed NMR order parameters (S2) are in
good agreement with experimentally measured values for three of the
four simulations. Evidence suggests that the LVFFA cluster and VGSN
turn are cooperatively stabilized through intramotif hydrogen bonds.
4. Simulations suggest that the LVFFA hydrophobic cluster and VGSN turn
are particularly stable in agreement with chemical shift data. The
general trends in the magnitude of the root-mean-square atomic
fluctuations compare well with the trends in the magnitude of the
chemical shift data.
All of these results suggest that the theoretical model employed
provides an accurate representation of the peptide structure and
dynamics in solution.
An understanding of the mechanism of in vivo amyloid fibril formation
and elongation is an important goal that is best reached by a
combination of experimental and computational studies. Our simulation
study indicates that the peptide is somewhat disordered in solution. As
a result, characterization of the peptide structure and dynamics is
difficult using NMR probes alone. The solution structure of the
monomeric peptide is central to the understanding of peptide-peptide
association and aggregation to form amyloid fibrils. To unravel the
mechanism of amyloid fibril formation, it will be necessary to
understand t
TOP
ABSTRACT
BACKGROUND
