Stephen Quirk1, Mandi M Hopkins2, Hailey Bureau3, Ryan J Lusk2, Caley Allen4, Rigoberto Hernandez3,4, David L Bain2. 1. Archeus Bioscience, 7094 Peachtree Industrial Blvd., Norcross, Georgia 30071, United States. 2. Department of Pharmaceutical Sciences, University of Colorado Anschutz Medical Campus, 12850 E Montview Blvd., Aurora, Colorado 80045, United States. 3. Center for Computational and Molecular Science and Technology, School of Chemistry and Biochemistry, Georgia Institute of Technology, 901 Atlantic Dr, Atlanta, Georgia 30332, United States. 4. Department of Chemistry, Johns Hopkins University, 3400 N Charles Street, Baltimore, Maryland 21218, United States.
Abstract
Neuropeptide Y (NPY) is a 36-residue peptide, abundant in the central and peripheral nervous system. The peptide interacts with membrane-bound receptors to control processes such as food intake, vasoconstriction, and memory retention. The N-terminal polyproline sequence of NPY folds back onto a C-terminal α-helix to form a hairpin structure. The hairpin undergoes transient unfolding to allow the monomer to interact with its target membranes and receptors and to form reversible dimers in solution. Using computational, functional, and biophysical approaches, we characterized the role of two conserved tyrosines (Y20 and Y27) located within the hydrophobic core of the hairpin fold. Successive mutation of the tyrosines to more hydrophobic phenylalanines increased the thermal stability of NPY and reduced functional activity, consistent with computational studies predicting a more stable hairpin structure. However, mutant stability was high relative to wild-type: melting temperatures increased by approximately 20 °C for the single mutants (Y20F and Y27F) and by 30 °C for the double mutant (Y20F + Y27F). These findings suggested that the mutations were not just simply enhancing hairpin structure stability, but might also be driving self-association to dimer. Using analytical ultracentrifugation, we determined that the mutations indeed increased self-association, but shifted the equilibrium toward hexamer-like species. Notably, these latter species were not unique to the NPY mutants, but were found to preexist at low levels in the wild-type population. Collectively, the findings indicate that NPY self-association is more complex than previously recognized and that the ensemble of NPY quaternary states is tunable by modulating hairpin hydrophobicity.
Neuropeptide Y (NPY) is a 36-residue peptide, abundant in the central and peripheral nervous system. The peptide interacts with membrane-bound receptors to control processes such as food intake, vasoconstriction, and memory retention. The N-terminal polyproline sequence of NPY folds back onto a C-terminal α-helix to form a hairpin structure. The hairpin undergoes transient unfolding to allow the monomer to interact with its target membranes and receptors and to form reversible dimers in solution. Using computational, functional, and biophysical approaches, we characterized the role of two conserved tyrosines (Y20 and Y27) located within the hydrophobic core of the hairpin fold. Successive mutation of the tyrosines to more hydrophobic phenylalanines increased the thermal stability of NPY and reduced functional activity, consistent with computational studies predicting a more stable hairpin structure. However, mutant stability was high relative to wild-type: melting temperatures increased by approximately 20 °C for the single mutants (Y20F and Y27F) and by 30 °C for the double mutant (Y20F + Y27F). These findings suggested that the mutations were not just simply enhancing hairpin structure stability, but might also be driving self-association to dimer. Using analytical ultracentrifugation, we determined that the mutations indeed increased self-association, but shifted the equilibrium toward hexamer-like species. Notably, these latter species were not unique to the NPY mutants, but were found to preexist at low levels in the wild-type population. Collectively, the findings indicate that NPY self-association is more complex than previously recognized and that the ensemble of NPY quaternary states is tunable by modulating hairpin hydrophobicity.
Neuropeptide Y (NPY)
is a 36-residue, amidated peptide found in
abundance in the central and peripheral nervous systems.[1] NPY interacts with membrane-bound, G-protein-coupled
receptors (GPCRs) to control regulation of food intake, vasoconstriction,
memory retention, sleep regulation, and energy homeostasis.[2−4] As such, GPCRs have been identified as potential drug targets for
treating diseases such as epilepsy, obesity, neurodegenerative, and
psychiatric disorders. Similarly, the NPY peptide has served as a
platform for the development of various agonists and antagonists toward
its receptors.[5,6]As shown in Figure , NPY is characterized by an
N-terminal polyproline II helix (residues
1–10), a short β turn (residues 11–13), and a
C-terminal α-helix (residues 14–31). Residues 32 through
36 are unstructured based on an inspection of all of the NMR and X-ray
crystal structures available in the Protein Data Bank. Also seen is
the pancreatic polypeptide fold found in NPY and its homologs, in
which the N-terminal residues fold back onto the C-terminal α-helix
to form a hairpin.[7] Because of the dynamical
properties of the N-terminal sequence, the hairpin undergoes transient
unfolding,[8] allowing NPY to bind to cell
surface membranes and to its receptors.[9] Transient unfolding is also coupled to reversible dimerization of
NPY, which occurs with micromolar affinity and via the parallel or
antiparallel orientation of α-helices from each protomer.[10] Although the role of NPY dimerization is not
entirely clear, it may serve to regulate the concentration of the
functionally active monomer species.[11−13]
Figure 1
Ribbon cartoon diagram
of NPY (based on PDB 1RON). Tyrosines 20 and
27 are depicted as sticks. Prolines contributing to the core pancreatic
polyproline fold are as noted (Pro 2, 5, and 8).
Ribbon cartoon diagram
of NPY (based on PDB 1RON). Tyrosines 20 and
27 are depicted as sticks. Prolines contributing to the core pancreaticpolyproline fold are as noted (Pro 2, 5, and 8).To better understand the role of individual residues in the
structural
stability, self-association, and function of NPY, we carried out a
mutational analysis of two conserved tyrosines located within the
hairpin core (Y20 and Y27; see Figure ). The core is hydrophobic in character, in part via
conserved prolines 2, 5, and 8.[14] The tyrosines
are known to contribute to stability of the hairpin,[15] and inspection of the three-dimensional structure shows
that they make contacts with prolines 5 and 8. However, their contribution
to stability would seem to be modest relative to a more hydrophobic
residue, such as phenylalanine. This could suggest that Y20 and Y27
play a regulatory role in the stability of the hairpin, resulting
in modulation of NPY dimerization, membrane interactions, or signaling
with GPCRs. Thus, we initially hypothesized that substitution of the
two tyrosines with phenylalanine should lead to an increase in NPY
hairpin stability and therefore a decrease in functional activity,
specifically by increasing the hydrophobicity of the core to allow
more optimal packing.Using computational and experimental approaches,
we examined the
consequences of mutating Y20 and Y27 to phenylalanine. We found that
NPY thermal stability was indeed increased and function was reduced,
consistent with molecular dynamics simulations that predicted a more
stable hairpin. However, the increase in thermal stability of the
mutants was unusually high relative to wild-type: melting temperatures
increased by roughly 20 °C for Y20F and Y27F, and by 30 °C
for the double mutant, Y20F + Y27F. These findings suggested that
the mutations were not just simply enhancing the stability of the
hairpin, but might also be driving higher-order self-association.
Using analytical ultracentrifugation, we determined that the mutations
indeed increased self-association, but shifted the equilibrium toward
hexamer-like species. Notably, these latter species were not unique
to the NPY mutants, but were found to preexist at low levels in the
wild-type population. Collectively, the results indicate that NPY
self-association is more complex than previously recognized and that
the ensemble of NPY quaternary states can be tuned by modulating the
hydrophobicity of the hairpin core.
Results
Molecular Dynamics-Predicted
Y to F Mutations Increase Stability of the Hairpin Fold
To
examine the potential contributions of Y20 and Y27 to NPY hairpin
stability, we first carried out molecular dynamic studies. The potential
of mean force (PMF) of hairpin unfolding was calculated for the wild-type
peptide, Y20F, Y27F, and Y20F + Y27F. To compare trends among the
peptides, we reference specific regions of the reaction coordinate, ree (the pull distance in angstroms). As shown
in Figure A, at an ree of 20 Å, the substitution of phenylalanine
creates a pronounced minimum in the PMF for the Y20F and Y27F peptides
in comparison to wild-type. Moreover, the minimum for Y20F + Y27F
is shifted to the right of Y20F and Y27F minima. Collectively, this
indicates that the local structure of the double mutant is calculated
to be more stable than either of the single mutants, which in turn
are more stable than wild-type peptide. In the region of PMFs between
30 and 70 Å, the clearest trend is the similarity between the
Y20F and Y27F curves relative to WT and Y20F + Y27F, suggesting that
the location of the individual mutations does not influence hairpin
stability. Finally, from 70 to 80 Å, the PMFs begin to increase
significantly, and this is the point at which the hydrophobic pocket
of the hairpin begins to open. The wild-type pocket opens at approximately
70 Å, the single-mutant pockets open at 75 Å, and the double-mutant
pocket opens at 80 Å. Representative structures associated with
the PMF curves over these distances for each peptide are shown in Figure B.
Figure 2
PMF calculations and
representative structures for wild-type NPY
and mutants. (A) PMFs obtained for all 4 peptides using a sampling
size of 100 trajectories per stage at a pulling velocity of 10 Å/ns;
wild-type NPY (black), Y20F (blue), Y27F (green), and Y20F + Y27F
(red). Only the first 70 Å of the pull are shown for clarity.
(B) Representative structures for each peptide at 20, 40, and 60 Å.
PMF calculations and
representative structures for wild-type NPY
and mutants. (A) PMFs obtained for all 4 peptides using a sampling
size of 100 trajectories per stage at a pulling velocity of 10 Å/ns;
wild-type NPY (black), Y20F (blue), Y27F (green), and Y20F + Y27F
(red). Only the first 70 Å of the pull are shown for clarity.
(B) Representative structures for each peptide at 20, 40, and 60 Å.To probe the origins of the stability
differences observed among
the peptides, we next carried out an analysis of interactions between
hydrophobic core residues and solvent. Plotted in Figure A is the interaction energy
between the hydrophobic residues of each peptide and water, over a
range of pull distances. This was determined using the weighted averaging
scheme for calculating the residue pair interaction energies and hydrogen-bonding
patterns (see Materials and Methods). Each
curve represents the results of the weighted average of all of the
trajectories. The region marked by ree between 60 and 80 Å represents the range of end-to-end distances
at which the hydrophobic pocket opens. In each case, after the pocket
opens, the interaction of amino acid residues and backbone moieties
in the pocket with water increases substantially: the more stable
the peptide, the more shifted is the increase in interaction energy
and hence opening of the pocket. For example, the wild-type pocket
opens at ree approximately equal to 60
Å, whereas the single mutants open at approximately 75 Å.
Finally, the double mutant exhibits the most shifted opening of the
pocket at an ree of 80 Å. Taken together
with the results of the PMF calculations (Figure A), the results reveal a clear peptide-specific
trend for the opening of the hydrophobic pocket, and therefore peptide
stability, as follows: wild-type < Y20F/Y27F < Y20F + Y27F.
Figure 3
Adaptive
steered molecular dynamics (ASMD)-based analysis of peptide
mechanical unfolding. (A) Comparison of the opening of the hydrophobic
core across all peptides. The energies for each curve are obtained
using a weighted average of 100 trajectories per stage at a velocity
of 10 Å/ns; wild-type NPY (black), Y20F (blue), Y27F (green),
and Y20F + Y27F (red). (B) Weighted average intrapeptide hydrogen
bonds of wild-type NPY (black), Y20F (blue), Y27F (green), and Y20F
+ Y27F (red). The average is of 100 trajectories per stage at a pulling
velocity of 10 Å/ns. (C) Weighted average hydrogen bonds formed
between the peptide and explicit water solvent for the wild-type NPY
(black), Y20F (blue), Y27F (green), and Y20F + Y27F (red). The average
is of 100 trajectories per stage at a pulling velocity of 10 Å/ns.
Adaptive
steered molecular dynamics (ASMD)-based analysis of peptide
mechanical unfolding. (A) Comparison of the opening of the hydrophobic
core across all peptides. The energies for each curve are obtained
using a weighted average of 100 trajectories per stage at a velocity
of 10 Å/ns; wild-type NPY (black), Y20F (blue), Y27F (green),
and Y20F + Y27F (red). (B) Weighted average intrapeptide hydrogen
bonds of wild-type NPY (black), Y20F (blue), Y27F (green), and Y20F
+ Y27F (red). The average is of 100 trajectories per stage at a pulling
velocity of 10 Å/ns. (C) Weighted average hydrogen bonds formed
between the peptide and explicit water solvent for the wild-type NPY
(black), Y20F (blue), Y27F (green), and Y20F + Y27F (red). The average
is of 100 trajectories per stage at a pulling velocity of 10 Å/ns.In addition to hydrophobic interactions,
differences in hydrogen-bonding
patterns (either intrapeptide or with solvent) may also play a role
in influencing stability among the peptides. Shown in Figure B is the average number of
intrapeptide hydrogen bonds formed and broken over the course of mechanical
unfolding for each peptide. Prior to unfolding, the peptides exhibit
a similar trend in the number of hydrogen bond contacts, with the
initial structures containing 5–10 bonds. Between the regions
of 20 and 60 Å, the average number of intrapeptide bonds increases
to a range of 20–25. The wild-type, Y20F, and Y27F peptides
all have a maximum of approximately 20 bonds at an ree of 70 Å. Y20F + Y27F forms the most contacts at
an ree of 80 Å, after which the number
of bonds formed begins to decrease significantly. This ordering in
the onset of the maximum number of hydrogen bond contacts coincides
with the trend in the opening of the hydrophobic pocket presented
in Figure A. Finally,
we note that the reorganization of intrapeptide hydrogen bonds under
the strain is consistent with i → i + 4 (α-helical) bonding patterns observed for model
helical peptides.[16]To further investigate
the role of hydrogen-bonding patterns, hydrogen
bonds formed between the peptide and the explicit water solvent were
examined. As shown in Figure C, the wild-type and double mutant both begin with a slightly
elevated number of hydrogen bond contacts with solvent at 85 contacts.
The single mutants both begin with 80 contacts. For each peptide,
the number of bonds formed to solvent remains constant over the first
half of the unfolding process. The number of bonds begins to increase
at an ree of 80 Å and peaks at 110
bonds at an ree of 110 Å. The number
of bonds remains constant at 110 for the remainder of the reaction
coordinate. Thus, the overall solvation of all of the mutants is similar
to that of the wild-type at the maximum extension. This suggests that
all four open chains have similar entropic contributions, which are
consequently not the drivers of the peptide-specific trends observed
experimentally.
Spectroscopic Analyses Confirm That NPY Mutants
Have Increased
Thermal Stability
To experimentally determine if mutations
at Y20 and Y27 influenced overall peptide stability, we carried out
melting studies using circular dichroism (CD) spectroscopy. Far-UV
CD spectra are shown in Figure A. For all peptides, the spectrum is predominantly α-helical
in character, exhibiting minima at 208 and 222 nm. Helicity is presumably
arising from C-terminal residues 14–31 and is consistent with
the NMR structure in Figure . Interestingly, the Y27F peptide shows evidence of additional
helicity, as evidenced by a larger mean molar ellipticity at 222 nm.
This is possibly due to the induced structure of residues 32–34
at the C-terminus.[17]
Figure 4
CD analysis of NPY thermal
stability. (A) Far-UV CD spectra of
NPY and NPY mutants. All peptides were at 20 μM in 15 mM NaPO4 (pH 7.0); wild-type NPY (closed circles), Y20F (closed squares),
Y27F (open squares), and Y20F + Y27F (open circles). The data presented
represent the average of three independent experiments, all of which
were superimposable to within ±0.75 deg cm2/dmol at
a given wavelength. (B) Thermal denaturation of NPY and NPY mutants
as measured by CD spectroscopy at 222 nm. Mean molar ellipticity values
are converted to fraction unfolded peptide as described in Materials and Methods section; wild-type NPY (closed
circles), Y20F (closed squares), Y27F (open squares), and Y20F + Y27F
(open circles).
CD analysis of NPY thermal
stability. (A) Far-UV CD spectra of
NPY and NPY mutants. All peptides were at 20 μM in 15 mM NaPO4 (pH 7.0); wild-type NPY (closed circles), Y20F (closed squares),
Y27F (open squares), and Y20F + Y27F (open circles). The data presented
represent the average of three independent experiments, all of which
were superimposable to within ±0.75 deg cm2/dmol at
a given wavelength. (B) Thermal denaturation of NPY and NPY mutants
as measured by CD spectroscopy at 222 nm. Mean molar ellipticity values
are converted to fraction unfolded peptide as described in Materials and Methods section; wild-type NPY (closed
circles), Y20F (closed squares), Y27F (open squares), and Y20F + Y27F
(open circles).Shown in Figure B are thermal unfolding curves
for wild-type NPY and the three mutants,
collected at 222 nm. Wild-type unfolding is characterized by a broad
transition from 15 to 65 °C and with a melting temperature (Tm) of 38.6 ± 0.4 °C. By contrast,
Y20F and Y27F have the same Tm value of
58 ± 0.3 °C and Y20F + Y27F has a Tm of 68.9 ± 0.5 °C. Interestingly, the thermal transitions
for at least the Y20F and Y20F + Y27F mutants show evidence of multiple
transitions, suggesting that difference in their Tm values is due to more than just differences in hairpin
stability.
NPY Mutants Have Reduced Affinity toward
Membranes and GPCRs
The above results indicate that both
computationally and experimentally,
mutations at Y20 and Y27 have a significant impact on hairpin and
peptide stability. To determine the functional impact of these mutations,
we measured the affinity of the peptides toward lipid membrane vesicles
and the ability of the peptides to displace wild-type peptide from
GPCRs. Surface plasmon resonance (SPR) was used for measuring NPY–membrane
interactions, and a competition–displacement assay was used
to measure NPY interactions with GPCRs.Representative SPR data
for interactions of each of the peptides with unilamellar vesicles
are shown in Figure A, and the observed kinetics and apparent affinities of the peptides
toward the vesicles are summarized in Table . Following the trends seen for the thermal
stability measurements, all mutants show weaker affinities relative
to wild-type, with the double mutant having the weakest affinity.
With regard to the kinetics of the interactions, we find that the
observed dissociation rate constants are similar, in the range of
(1.1–1.5) × 10–2 s–1, indicating that differences in NPY–membrane binding affinity
are driven by changes in the association rate constant (Table ).
Figure 5
Functional analysis of
NPY membrane and receptor interactions.
(A) SPR response of wild-type and mutant NPY peptides interacting
with a 4:1 DMPC/DMPG lipid bilayer surface. Plotted is the SPR signal
in response units (RU) as a function of time in seconds for peptide
at 10 μM. Curves from top to bottom: wild-type NPY, Y20F, Y27F,
Y20F + Y27F, and control. Association phase was from 10 to 210 s,
and the dissociation phase was from 210 to 450 s. Overlaid on the
raw sensograms are the curve fits, shown in red. (B) Release of receptor-bound
Pacific Blue-labeled wild-type NPY upon the addition of unlabeled
competitor peptide. Plotted is the percent fluorescence in the supernatant
as a function of competitor peptide concentration; wild-type NPY (closed
circles), Y20F (closed squares), Y27F (open squares), and Y20F + Y27F
(open circles).
Table 1
Average
NPY–1,2-Dimyristoyl-sn-glycero-3-phosphocholine
(DMPC)/1,2-Dimyristoyl-sn-glycero-3-phospho-(1′-rac-glycerol)
(DMPG) (4:1 w/w) Membrane Interaction Rate Constants and Equilibrium
Constants Determined by SPR
peptide
ka (M–1 s–1)
kd (s–1)
Ka (M–1)
χ2
WT
1.2 × 103 (110)a
1.1 × 10–2 (0.003)
1.1 × 105 (2.1 × 104)
4.3 (0.4)
Y20F
8.5 × 102 (22)
1.5 × 10–2 (0.004)
5.6 × 104 (1.2 × 104)
6.7 (0.5)
Y27F
6.7 × 102 (31)
1.4 × 10–2 (0.002)
4.8 × 104 (1.3 × 104)
5.4 (0.5)
Y20F + Y27F
2.7 × 102 (16)
1.3 × 10–2 (0.002)
2.1 × 104 (2.3 × 103)
8.2 (0.7)
Values in parentheses represent
the standard deviation. Average of three trials.
Functional analysis of
NPY membrane and receptor interactions.
(A) SPR response of wild-type and mutant NPY peptides interacting
with a 4:1 DMPC/DMPGlipid bilayer surface. Plotted is the SPR signal
in response units (RU) as a function of time in seconds for peptide
at 10 μM. Curves from top to bottom: wild-type NPY, Y20F, Y27F,
Y20F + Y27F, and control. Association phase was from 10 to 210 s,
and the dissociation phase was from 210 to 450 s. Overlaid on the
raw sensograms are the curve fits, shown in red. (B) Release of receptor-bound
Pacific Blue-labeled wild-type NPY upon the addition of unlabeled
competitor peptide. Plotted is the percent fluorescence in the supernatant
as a function of competitor peptide concentration; wild-type NPY (closed
circles), Y20F (closed squares), Y27F (open squares), and Y20F + Y27F
(open circles).Values in parentheses represent
the standard deviation. Average of three trials.Shown in Figure B are competition–displacement curves
for measuring NPY interactions
with rat brain GPCRs. This assay measures the ability of each peptide
to displace wild-type, fluorescently labeled NPY from its receptors.
It is evident that all mutants displace bound peptide, but less effectively
so compared to wild-type. Once again, the trend in peptide displacement
mirrors the trend seen in the thermal unfolding studies (and the lipid
binding experiments). The calculated IC50 values for the
displacement reaction are shown in Table . The IC50 values in the nanomolar
range are comparable to previously reported affinities for NPY–GPCR
binding,[18,19] thus indicative of receptor-specific interactions.
Table 2
Half-Maximal Inhibitory Concentration
(IC50) for Wild-Type NPY Receptor Displacementa
peptide
IC50 (nM)
WT
1.9 ± 0.5
Y20F
4.6 ± 0.2
Y27F
7.6 ± 0.3
Y20F + Y27F
14.2 ± 0.2
Average of three
experiments ±
standard deviation.
Average of three
experiments ±
standard deviation.
NPY Mutants
Perturb a Preexisting Equilibrium of Monomers, Dimers,
and Higher-Order Species
The above results indicate that
the mutations at Y20 and Y27 enhance NPY hairpin stability (as shown
by the simulations) and overall peptide stability (that is, the unfolding
of both the hairpin and the C-terminal α-helix, as shown by
the CD thermal melt experiments). The thermal melt experiments measure
overall peptide stability, but cannot partition that stability at
the mechanistic level that the simulations reveal. Taken together,
however, the simulations and melts indicate that the phenylalanine
substitutions stabilize the hairpin (e.g., polyproline fold) and contribute
to the stability of the α-helix. The changes in stability also
reduce functional interactions with membranes (SPR experiments, Figure A) and receptors
(receptor competition assay, Figure B). These findings are in line with our initial hypothesis
that substitution of the tyrosines with more hydrophobic phenylalanines
should lead to more efficient packing of the hydrophobic core. However,
we found that the increases in thermal stability were unusually large,
for example, model systems, such as lysozyme, reveal that single amino
acid substitutions increase Tm by no more
than 5 °C.[20] Moreover, the melting
curves for at least a subset of peptides showed multiple transitions,
suggesting that other factors might be in play. Noting that NPY reversibly
dimerizes via its hydrophobic core, we speculated that the unusual
thermal stabilities might also be linked to higher-order self-association.
The self-association properties of wild-type NPY and the three mutants
were therefore assessed via sedimentation velocity and sedimentation
equilibrium.The sedimentation coefficient distribution of wild-type
NPY collected over a 30-fold concentration range is shown in Figure A. At 10 and 30 μM,
NPY sediments as a single, concentration-independent peak with a sedimentation
coefficient of 0.80 S and an estimated molecular weight of 4.3 kDa.
Noting that the calculated molecular weight of the NPY monomer is
4.27 kDa and that bead modeling predicts that the folded monomer in Figure A should have a sedimentation
coefficient of 0.74 S,[21] this peak is suggestive
of monomeric NPY. As peptide concentration is increased to 100 μM,
the distribution shifts rightward, with a second peak appearing at
∼1.5 S. This concentration-dependent change in the distribution
is indicative of a reversibly interacting system, although the second
peak cannot be assigned a specific stoichiometry.[22] Nonetheless, the results are qualitatively consistent with
previous reports indicating that NPY reversibly dimerizes in the micromolar
range.[23] Unexpectedly, however, as peptide
concentration is increased to 300 μM, the second peak continues
to shift and broaden to ∼2.5 S. Again, it is not possible to
assign specific stoichiometries to this peak or within the distribution.
However, for perspective, a spherical shape approximation for an NPY
dimer predicts that it sediments at ca. 1.2–1.3 S. Thus, overall,
the results suggest that NPY is self-associating past dimer. We address
this possibility in more detail using sedimentation equilibrium studies
below.
Figure 6
Analytical ultracentrifugation analysis of wild-type NPY. (A) c(s) analysis of 10, 30, 100, and 300 μM
NPY using Sedfit software. Scans were collected at 50 000 rpm
and 20 °C in phosphate-buffered saline (PBS), pH 7.4. (B) Global
fitting of data using SedAnal software to a monomer–dimer–hexamer
model. Scans were collected under identical buffer conditions as the
sedimentation velocity data, using NPY concentrations of 10, 30, 100,
200, 300, and 400 μM. Rotor speeds were 30 500 rpm (blue),
36 600 rpm (red), 42 900 rpm (green), and 52 800
(purple) rpm. The open circles represent observed data, the solid
black lines represent the model fit, and the solid black circles are
the residuals. The root-mean-square deviation (RMSD) of the fit was
6.78 × 10–3 absorbance units.
Analytical ultracentrifugation analysis of wild-type NPY. (A) c(s) analysis of 10, 30, 100, and 300 μM
NPY using Sedfit software. Scans were collected at 50 000 rpm
and 20 °C in phosphate-buffered saline (PBS), pH 7.4. (B) Global
fitting of data using SedAnal software to a monomer–dimer–hexamer
model. Scans were collected under identical buffer conditions as the
sedimentation velocity data, using NPY concentrations of 10, 30, 100,
200, 300, and 400 μM. Rotor speeds were 30 500 rpm (blue),
36 600 rpm (red), 42 900 rpm (green), and 52 800
(purple) rpm. The open circles represent observed data, the solid
black lines represent the model fit, and the solid black circles are
the residuals. The root-mean-square deviation (RMSD) of the fit was
6.78 × 10–3 absorbance units.To determine the affinities and stoichiometry of
assembly for wild-type
NPY, we carried out sedimentation equilibrium studies under buffer
conditions identical to the sedimentation velocity experiments using
multiple rotor speeds and a range of protein concentrations. The data
were then globally fit to various self-association models, with the
molecular weight of the monomer fixed at the known value of 4272.72
Da. On the basis of previous studies and the results in Figure A, we tested a variety of interaction
models, including monomer–dimer, monomer–trimer, monomer–dimer–tetramer,
etc. Only two models described the data to an acceptable level as
determined by the RMSD of the fit: these were monomer–dimer–hexamer
and monomer–trimer–hexamer. Shown in Figure B is a global fit to the monomer–dimer–hexamer
model. This fit resolved a monomer–dimer association constant
of 3620 (1740, 7576) M–1, corresponding to a Kd of ∼270 μM. The dimer–hexamer
association constant was determined to be 6.64 × 107 (4.10 × 107, 1.15 × 108) M–2, corresponding to a Kd of ∼123
μM on a per dimer basis. The RMSD of the fit was 6.78 ×
10–3 absorbance units. A global fit to a monomer–trimer–hexamer
model resolved a comparable RMSD of 6.26 × 10–3 absorbance units (not shown).By contrast, a simple monomer–dimer
interaction model did
not describe the data well, generating obvious systematic residuals
and an increased RMSD of 1.59 × 10–2 (see Figure S1, Supporting Information). Other models
generated similarly poor fits or resolved nonsensical interaction
parameters. Although additional studies will be necessary to determine
the precise stoichiometries and affinities of NPY self-association,
both the sedimentation velocity and sedimentation equilibrium results
indicate that wild-type NPY reversibly assembles to species greater
than dimer.To assess whether the Y20 and Y27 mutations influence
the distribution
seen for wild-type NPY, we carried out sedimentation velocity studies
on each of the mutants (Figure ). As seen for Y20F, a broad distribution of species, ranging
from ∼0.8 to nearly 3 S, is already present even at the lowest
peptide concentration. As concentration is increased, a 3 S species
eventually dominates the distribution. This is again indicative of
an interacting system, but based on our interpretation for wild-type
NPY, one that also associates well past dimer and with greater affinity.
A similar result is seen for Y27F, with differences in the distributions
likely arising from differences in the kinetics and/or energetics
of self-association.[22] Finally, Y20F +
Y27F exhibits the greatest enhancement in self-association, to the
point that only a single, rapidly sedimenting peak at ∼2.3
S is observed at nearly all NPY concentrations. This concentration-independent
peak has an estimated molecular weight of 25.2 kD and is thus suggestive
of hexamer. Therefore, the introduction of phenylalanines at Y20 and
Y27 results in a redistribution of a complex and preexisting equilibrium
to higher-order assembly states.
Figure 7
Sedimentation velocity results for NPY
mutants. Columns 1 through
3 represent Y20F, Y27F, and Y20F + Y27F, respectively. Data were analyzed
by c(s) analysis using NPY concentrations
of 10, 30, 100, and 300 μM. Scans were collected at 50 000
rpm and 20 °C in PBS, pH 7.4.
Sedimentation velocity results for NPY
mutants. Columns 1 through
3 represent Y20F, Y27F, and Y20F + Y27F, respectively. Data were analyzed
by c(s) analysis using NPY concentrations
of 10, 30, 100, and 300 μM. Scans were collected at 50 000
rpm and 20 °C in PBS, pH 7.4.
Discussion
Computational Insight into NPY Hairpin Stability
Previous
work by Hernandez and co-workers used ASMD to examine unfolding pathways
for the hairpin structure of wild-type NPY.[24] Here, we employ this simulation approach to determine how Y20F,
Y27F, and Y20F + Y27F influence hairpin unfolding and stability. The
results suggest that there may be two possible unfolding pathways
that differ slightly but are discernable from each other. The single
mutants result in PMFs that fall within the range of thermal fluctuation
of one another and are different from the PMFs obtained for WT and
Y20F + Y27F. Additionally, from our analysis, we gained insight into
the stability of the hydrophobic core and helical region. Through
the calculation of the interaction energy between the hydrophobic
residues within the peptide and the water solvent, we can determine
that mutations do effect the ree at which
the hydrophobic core opens. As expected, the wild-type hydrophobic
core opens at a relatively small ree of
60 Å, which indicates that it has the least stabilized core.
This is followed by Y20F and Y27F, which both open at 75 Å, and
finally by Y20F + Y27F opening at 80 Å. The analysis of the hydrogen
bond patterns that emerge during the unfolding, either between peptide
and solvent or between intrapeptide bonds, indicates that residues
normally associated with a folded hydrophobic core do not participate
in the formation of new hydrogen bonds, concomitant with core opening
and exposure to solvent. Hence, the simulations presented here support
the hypothesis that tyrosine to phenylalanine mutations serve to increase
the hydrophobic character and packing of the core, and it is this
optimization that leads to the computationally observed increases
in peptide monomer stability. Additional computational and experimental
studies probing the role of alanine, leucine, and tryptophan substitutions
should provide further support for this hypothesis.The ASMD
simulation results are completely consistent with the experimental
results discussed below, but do not account for the magnitude of the
observed increase in thermal stability. They also cannot shed light
on the contributions of higher-order structure to the observed increase
in thermal stability. However, taken together with the analytical
ultracentrifugation results, they show that thermal stability increases
are due in part to monomer stabilization and/or stabilization brought
about by higher-order structure formation. Future studies will be
necessary to address the relative contributions of these two effects.Similarly, the thermal CD experiments cannot distinguish between
monomer unfolding and subunit dissociation. This may be because both
processes occur simultaneously at the melting temperature or because
subunit dissociation that may occur prior to the melting temperature
is spectroscopically silent. The unfolding curves are broad and may
therefore be indicative of a more complex process than a simple dissociation/unfolding
reaction. We are in the process of harnessing other biophysical methods
that can help dissect out the contributions of monomers and quaternary
structure in the observed increase in thermal stability.
Functional
Implications of Increased NPY Stability and Higher-Order
Structure
The membrane- and GPCR binding studies indicate
that the Y20F and Y27F mutations reduce NPY biological activity. Although
we report only apparent binding affinities for the peptide–lipid
interactions, previous studies have shown that NPY binds DMPC or DMPC/DMPG
bilayers in a multistep process.[25] These
studies found that there is an initial interaction between NPY and
the lipid surface that is characterized by distinct sets of rate constants.
In the first phase of binding, it is thought that NPY undergoes a
structural transformation while optimally orienting to the bilayer
surface.[10,25] This is then followed by two-dimensional
translocation to the receptor.[10,25] Receptor selection
is thus more efficient, with NPY movement along the membrane rather
than via three-dimensional (3D) diffusional binding (i.e., directly
from solvent to receptor). Interestingly, our SPR analysis indicates
a good fit via a single set of rate constants and a rather poor fit
to the more complex lipid binding model described above (data not
shown). Moreover, porcine NPY had a relatively poor fit to the multistep
model in the study relative to other homologues.[25] This could suggest that the kinetic mechanisms for NPY–family
interactions with lipid membranes (or micelles) are species-dependent.
Although there is still debate regarding the exact nature of this
process (e.g., whether hairpin unfolding is prerequisite for receptor
binding[10,26]), current thinking suggests that the active
binding species is the monomer[27] and that
Y20 and Y27 are critical for NPY–lipid interactions.[10] In fact, these studies[10,27] suggest that the monomeric NPY form is not in the PP-fold conformation
at the moment of lipid binding, in contrast to other studies.[26] Our results suggest that the higher-order quaternary
structures of Y20F, Y27F, and Y20F + Y27F must dissociate to monomer
sometime prior to either lipid or receptor binding. This interpretation
may also explain why the apparent binding affinities of the mutants
in this work are controlled by on-rate rather than off-rate: dissociation
of higher-order species may be a kinetically limiting step in NPY
function. We note that this interpretation does not preclude the possibility
of hairpin unfolding as part of membrane and receptor binding.
NPY Higher-Order
Structure
Previous studies have shown
that wild-type NPY undergoes reversible self-association to dimer,
with an affinity ranging from 0.2 to 3 μM (reviewed in ref (23)). Here, we find that dimerization
affinity is considerably weaker, occurring in the hundreds of micromolar
range. Although the exact basis of this difference will require further
study, we note that a subset of previous studies was carried out under
considerably different solution conditions. These include differences
in pH and temperature, both of which are known to influence NPY dimerization
affinity.[9] For those studies carried out
under similar conditions, a key difference may have been in the use
of porcine NPY, rather than the humanNPY examined here. The two peptides
differ by a single M (human) to L (porcine) substitution at position
17, potentially implicating this position as a regulator of NPY self-association.
An additional difference between earlier studies and the current work
is our observation of a hexamer-like assembly state. This species
was seen at low levels for wild-type NPY and is likely to exist in
the mutant peptide populations. Although such a species has not been
reported previously, it is worth speculating that observations of
“higher aggregates” in spectroscopic studies of NPY
dimerization may be reflective of the hexamers seen here.[28]Regarding the mechanism of NPY self-association,
it is well established that association is dependent on whether the
N-terminal polyproline sequence is packed against the C-terminal α-helix.
In fact, fully stabilized and folded, NPY is prevented from forming
higher oligomeric structures.[29] Conversely,
if the polyproline sequence is removed, the remaining α-helix
forms trimeric or tetrameric structures.[30] Both of these interactions are driven by the hydrophobic character
of the C-terminal and N-terminal sequences. In the current study,
replacing one or both tyrosines increases the hydrophobic character
of the α-helix and promotes the formation of distinct and stable
higher-order quaternary states. The mechanism for this is presumably
through better core packing among interpeptide C-terminal helices,
even as the intrapeptide hairpin is also stabilized. From a thermodynamic
perspective, the free energy of higher-order self-association must
therefore be greater than the free energy of hairpin stabilization.
In summary, these results suggest that Y20 and Y27 play a modulatory
role in maintaining hairpin stability and that the ensemble of NPY
quaternary states is “tunable” by modulating the hydrophobicity
of the hairpin core. This possibility may have implications for the
development of new NPY-based therapeutics,[31] possibly by regulating the population of the functionally active
monomers and/or the ability of the hairpin to unfold for membrane
binding. Overall, this study highlights how computational and biophysical
methodologies bring increased insight into traditional biochemical
functional studies. Our future work is focused on fully elucidating
the self-association pathways for each of the four peptides.
Materials
and Methods
Peptide Synthesis
HumanNPY sequences were synthesized
using standard solid-phase synthetic techniques by New England Peptide,
Inc. Each peptide had a standard N-terminal structure and contained
either a carboxy or amidated C-terminus. For all solution studies
presented here, the nature of the C-terminus had no impact on the
results (data not shown). Molecular weight and purity were confirmed
by mass spectroscopy and reversed-phase chromatography. Typical peptide
purity was >95%. Sequences were as follows, with mutated residue(s)
bold/underlined:WT: NH2-YPSKPDNPGEDAPAEDMARYYSALRHYINLITRQRY-COOHY20F: NH2-YPSKPDNPGEDAPAEDMARYSALRHYINLITRQRY-COOHY27F: NH2-YPSKPDNPGEDAPAEDMARYYSALRHINLITRQRY-COOHY20F + Y27F:
NH2-YPSKPDNPGEDAPAEDMARYSALRHINLITRQRY-COOH
Circular
Dichroism Studies and Thermal Melts
Peptides
were dissolved to a final concentration of 20 μM in 15 mM NaPO4 (pH 7.0) for far-UV (190–250 nm) measurements. Spectra
were obtained as a function of temperature on an Applied Photophysics
Chirascan spectrophotometer utilizing a 1 mm path length quartz cuvette.
Melting curves were obtained at 1 °C intervals after a 5 min
incubation at the new temperature with an averaging time of 5 s. Thermal
denaturation was fully reversible as evidenced by recovering ∼99%
of the CD signal upon cooling and by the observation that reverse
and forward melting curves were superimposable. Raw CD data were converted
to mean molar ellipticity according towhere mD is the raw CD
reading in millidegrees,
PL is the cell path length in millimeters, n is the
number of amino acids in the peptide, and C is the
micromolar concentration.CD signal at 222 nm was fit to a two-state
equilibrium unfolding model (after a linear fit of the folded and
unfolded baselines) according towhere Fu is the
fraction folded; θf, θu, and θ are the CD signals of the native, unfolded,
and ith temperature state, respectively. Finally,
the data presented represent the average of three independent experiments,
all of which were superimposable to within 0.25 °C of Tm.
Small unilamellar vesicles (SUVs) were prepared essentially
as described[32] and consisted of a 4:1 w/w
ratio of 1,2-dimyristoyl-sn-glycero-3-phosphocholine
(DMPC) to 1,2-dimyristoyl-sn-glycero-3-phospho-(1′-rac-glycerol)
(DMPG) in 20 mM phosphate buffer (pH 7.0) and 125 mM NaCl (buffer
I). Final SUV concentration was 60 nM. SPR experiments were conducted
as described by Lerch et al.[25] with several
modifications. The L1 sensor chip was utilized in a Biacore-X to produce
a lipid bilayer sensor surface. The bare chip was washed with 10 μL
of 20 mM 3-[(3-cholamidopropyl)dimethylammonio]-1-propanesulfonate
at a flow rate of 5 μL/min. The SUV prepared was then injected
over the surface at a flow rate of 2 μL/min for a total of 50
min (100 μL of total SUV load). Next, 50 μL of 10 mM NaOH
was passed over the surface at a flow rate of 50 μL/min to remove
loosely bound vesicles from the chip surface. Finally, the surface
was washed with 20 μL of buffer I at a flow rate of 15 μL/min.
Peptide solutions in buffer I were flowed over the membrane chip surface
at concentrations between 5 and 25 μM, to determine the concentration
affording optimal signal (10 μM), at a flow rate of 15 μL/min
at 25 °C for the 200 s association phase, during which, flow
was switched to buffer I only for an additional 250 s for the disassociation
phase.Raw SPR curves were processed using Scrubber2 (BioLogic
Software, Inc.). Final peptide–membrane SPR-binding isotherms
were evaluated against multiple binding models using CLAMP,[33] where it was ultimately determined that the
NPY peptide–membrane binding data were best fit by simultaneously
fitting the forward (ka) and reverse (kd) rate constants towhere R is the SPR signal
(in response units, RU) at time t, Rmax is the maximum binding capacity in RU, and C is the peptide concentration. SPR-binding isotherms are
presented in Results for peptide at 10 μM.
Because the exact binding model is not known, we fit the data to obtain
an apparent equilibrium affinity constant (Kapp) that is defined as
Receptor Binding
Assays
Peptide Labeling
A competition assay was developed
to measure the relative affinities of the peptides toward receptors
that were prebound with a fluorophore-modified wild-type NPY peptide.
First, N-terminal acetylated wild-type NPY was labeled with the fluorophore,
Pacific Blue (Molecular Probes, Inc.), by reacting the succinimidyl
ester derivative of the dye with the single NPYlysine residue. Briefly,
lyophilized wild-type NPY peptide was brought to 1 mg/mL in 0.1 M
Na bicarbonate, and 100 μL of this solution was added to a vial
of Pacific Blue succinimidyl ester. Reactions were run in quadruplicate.
Samples were gently agitated until the dye dissolved, and the reactions
were incubated at 20 °C for 3 h with gentle agitation. The reaction mixtures were pooled and were loaded onto a Biogel P-2 column (10
cm × 0.78 cc2) in buffer I. Under these conditions,
labeled NPY elutes in the void volume and dye/buffer components are
in the latter included volume. Fractions containing peptide fluorescence
(excitation wavelength = 410 nm, emission wavelength = 455 nm) were
pooled and used for receptor binding without further modification.
Receptor Interactions
The brain is highly enriched
with membrane-bound NPY receptors. The membrane fraction was isolated
as described in ref (34) from Brown Norway rats purchased from BioreclamationIVT. Brain membranes
(20 μg) were placed in a siliconized Eppendorf tube, to which
was added 1.0 μg of Pacific Blue-labeled NPY in buffer I plus
15 mM MgCl2, 10 mM CaCl2, 0.5% bovine serum
albumin, 0.2% Tween-20, and 0.2 mM phenylmethylsulfonyl fluoride (buffer
II, all chemicals from Sigma-Aldrich Chemical Co.) in a final assay
volume of 200 μL. After incubation at 30 °C for 1 h, the
membrane fraction was pelleted by centrifugation at 20 000g for 15 min, the supernatant was discarded, and the membranes
were washed in buffer II, recentrifuged, and brought up into 200 μL
of buffer II supplemented with various concentrations of unlabeled
NPY peptides (from 10–4 to 10–10 M). The reaction was incubated and processed as above. However,
at this last stage, the entire decanted supernatant was measured for
fluorescence (excitation wavelength = 410 nm; emission wavelength
= 455 nm). The fluorescence in the supernatant of a control reaction
(labeled NPY bound to membrane receptors but without added peptide
in step 2) was subtracted from each reaction to account for bound
labeled NPY that disassociates from membrane receptors on its own
during the assay. Fluorescence in the final supernatant represents
receptor-bound Pacific Blue-labeled NPY that has been competed off
brain NPY receptor-containing membranes by the addition of unlabeled
peptide. Maximum fluorescence is arbitrarily defined as 100%. Data
are presented as a plot of percent fluorescence in the supernatant
against the log of the concentration of competing peptide.
Lyophilized
peptide samples were reconstituted in phosphate-buffered
saline (PBS) at pH 7.4 and to a concentration of ∼800 μM.
Samples were then prepared at concentrations ranging from 10 to 300
μM. Sedimentation velocity studies were carried out using a
Beckman XL-A analytical ultracentrifuge equipped with absorbance optics
and an An-50 Ti rotor. Two-channel, 12 or 3 mm path length centerpieces
were used throughout, depending on peptide concentration. Data were
collected at 20 °C and at 50 000 rpm, with scans taken
as frequently as the instrument allowed. Data were collected at either
230 or 280 nm depending on peptide concentration. Scans were analyzed
using Sedfit, version 14.81,[22] to determine
sedimentation coefficient distributions at each peptide concentration.
Solvent density and peptide partial specific volumes were calculated
using Sednterp (http://www.jphilo.mailway.com).
NPY concentrations ranging from 10 to 400 μM were allowed to
reach sedimentation equilibrium at 30 500, 36 600, 42 900,
and 52 800 rpm on a Beckman XL-A analytical ultracentrifuge.
Rotor speeds were chosen on the basis of guidelines laid out by Laue,[35] with the approach to equilibrium monitored by
acquiring scans 30 min to 2 h apart and verified using the match algorithm
in HeteroAnalysis (https://core.uconn.edu/resources/biophysics).[36] Data were collected at 230 and 280
nm. Global fits were performed using SedAnal (http://www.sedanal.org), version
6.54.[37] Buffer conditions were identical
to the sedimentation velocity studies.
Simulations
Mutations
The solution NMR structure of the folded
conformation of the wild-type NPY[28] was
used as the starting structure to make the mutants Y20F, Y27F, and
the double mutant Y20F + Y27F in silico. Amino acid substitutions
were made using the VMD Mutator plugin.[38] Accommodation of the mutations did not alter the backbone structure
as evidenced by a 3D least-squares supposition of the mutant peptide
with the wild-type structure.
Equilibration
All of the simulations use nanoscale
molecular dynamics (NAMD)[39] to integrate
the molecular dynamics equations of motion with respect to the c36
CHARMM all-atom force field.[40,41] The following are the
simulation parameters: the smooth switching function turns on at 8
Å, the van der Waals interaction cutoff distance is 12 Å,
pair list distances are truncated at 13.5 Å, and long-range electrostatic
forces are calculated using the particle-mesh Ewald summation method
with a grid size of <1 Å.Peptides are solvated individually
in a rectangular cuboid box with approximately 19 000 water
molecules initialized using the NAMD solvation package. These explicit
waters are represented by a pairwise TIP3P force field. The solvent
box is built with two equal sides of length L (=30 Å) and a longer side of length L (=150 Å), along which
the peptide ends will be steered apart through adaptive steered molecular
dynamics (ASMD). After solvation, the overall charge of the peptide
and solvent system is neutral. No ions are required to gain neutrality.
The system then undergoes a three-step equilibration protocol:The first step of the protocol is the equilibration of the peptide
side chains and solvent while the backbone of the peptide is restrained.
This step allows the water solvent to reach a density of approximately
0.9998 g/cm3 while simultaneously allowing the peptide
side chains to find favorable conformations. Energy minimization is
performed for 10 000 steps to remove bad contacts using the
conjugate gradient method. The system is then equilibrated for 1 ns
at 300 K under NPT conditions. Pressure is maintained using the Nosé–Hoover
Langevin piston method with a damping coefficient of 5 ps–1, a decay period of 100 fs, and a damping time constant of 50 fs.
Temperature is maintained using a Langevin thermostat.In the
second step of the equilibration protocol, the system undergoes
a constant-volume equilibration under NVT conditions. The backbone
is initially restrained with a harmonic potential of 10 kcal/(mol
Å2). The constraints on the backbone are gradually
released during a series of three 100 ps intervals ending at 5.0,
1.0, and 0 kcal/(mol Å2). The gradual release of the
constraints on the peptide backbone ensures that its atoms do not
shift too quickly in relation to the solvent motion. The entire system
is then allowed to equilibrate for another 500 ps.In the third
step, the peptide is realigned back to the z axis.
This is needed because the free motion of the peptide
during the second step of the equilibration protocol can induce substantial
drift away from the z axis. This is achieved by first
extracting the peptide from solvent, that is, removing the TIP3P waters
from the representation and then translating and rotating the peptide
so that its axis, as defined by the line connecting the Cα atoms
of the 1st and 36th residues, is aligned with the z axis. The transformation of the peptide does not in any way change
the equilibrated structure obtained in the second step. Instead of
applying the transformation to the water molecules, for simplicity,
the peptide is then resolvated using the same procedures as before.
Following the solvation, the Cα atoms of the 1st and 36th residues
are restrained, but all other motions unconstrained. A 1 ns equilibration
of the water and peptide system is then performed to equilibrate the
solvent and side chains. The equilibration is verified through analysis
of the secondary structure and root-mean-square deviations using the
NAMD plugin Timeline.
Unfolding Simulation
In this work,
the PMFs for the
unfolding pathway of the four NPY peptides are obtained computationally
using the ASMD method. This technique was previously used to determine
the mechanism by which wild-type NPY “unhinged” using
a nonlinear pulling pathway.[24] The efficiency
of the algorithm has also been benchmarked for various solvent conditions,
including vacuum,[42] implicit solvent,[43] and explicit solvent.[44]In all of the ASMD simulations, the peptides are stretched,
mimicking unfolding by an external agent, along the long z axis, for which the box can accommodate the extended or stretched
peptide structure. All simulations are carried out at a temperature
of 300 K. The stretching coordinate ree is defined as the distance between the Cα of the
1st and 36th residues. At the start of each simulation, the distance
between the stationary and pulled atom is compressed to 16 Å.
This constraint is used to ensure that the peptide accesses the local
minimum obtained from the equilibration protocol during the driven
unfolding. The peptides are gradually stretched for 120 Å as
the end-to-end distance is extended from 16 to 136 Å. The ASMD
simulations are partitioned across stages with constant separation
in the stretching coordinate at the endpoints ree, for j running from 0
to 40. The separations in each stage are 3 Å and resulted in
changes in the free energy across the stage that never exceeded 3kBT, which was seen in our earlier
work to be an important criterion for satisfying convergence.[42−44] At the end of each stage, the PMF is calculated using the Jarzynski equality,[45−48] as in a typical SMD simulation for computing the average work (W)where ξ( is the ith trajectory in the nonequilibrium
ensemble
stretched from ree,.
A more rigorous description of the algorithm is presented in ref (49).Once the Jarzynski
average is calculated, the trajectory with the
closest final work value to the average is selected for use in the
next stage. In particular, the coordinates and velocities at the end
of the selected trajectory are taken as the initial values for the
beginning of the next stage. The PMFs of the peptides are evaluated
at a stretching velocity of 10 Å/ns with a sampling size of 100
trajectories per stage. Once a PMF is obtained, it is shifted (vertically)
to reset the zero of energy at its minimum. This shifting allows for
a more direct comparison of the PMFs.In addition to the PMFs,
other observable quantities can be calculated
and compared to further reveal the underlying causes of stability
of a peptide. These include hydrogen-bonding patterns and interaction
energies of specific pairs of residues. Expected values of observables
along the unfolding (stretching) pathway are obtained using the weights
for the work associated with the nonequilibrium paths. To calculate
the number of hydrogen bonds between two sets of atoms along the unfolding
pathways, we define the sets S1 and S2 containing the indices of the selected atoms
and/or of collective variables in the overall configuration ξ.
The weighted average number of hydrogen bonds between the two sets
can then be written aswhere the instantaneous number of hydrogen
bonds between the sets isThe average interaction energy between residues
indexed in sets S1 and S2 can be obtained in an analogous form by replacing NH with E.
Authors: Robert B Best; Xiao Zhu; Jihyun Shim; Pedro E M Lopes; Jeetain Mittal; Michael Feig; Alexander D Mackerell Journal: J Chem Theory Comput Date: 2012-07-18 Impact factor: 6.006