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Article
Oligomerization of a Glucagon-like Peptide 1 Analog: Bridging Experiment
and Simulations
Tine M. Frederiksen,
1
Pernille Sønderby,
1
Line A. Ryberg,
1
Pernille Harris,
1,
*Jens T. Bukrinski,
2
Anne M. Scharff-Poulsen,
2
Maria N. Elf-Lind,
1
and Gu
¨nther H. Peters
1,
*
1
Department of Chemistry, Technical University of Denmark, Kongens Lyngby, Denmark; and
2
Novozymes A/S, Bagsværd, Denmark
ABSTRACT The glucagon-like peptide 1 (GLP-1) analog, liraglutide, is a GLP-1 agonist and is used in the treatment of type-2
diabetes mellitus and obesity. From a pharmaceutical perspective, it is important to know the oligomerization state of liraglutide
with respect to stability. Compared to GLP-1, liraglutide has an added fatty acid (FA) moiety that causes oligomerization of lir-
aglutide as suggested by small-angle x-ray scattering (SAXS) and multiangle static light scattering (MALS) results. SAXS data
suggested a global shape of a hollow elliptical cylinder of size hexa-, hepta-, or octamer, whereas MALS data indicate a hex-
amer. To elaborate further on the stability of these oligomers and the role of the FA chains, a series of molecular-dynamics sim-
ulations were carried out on 11 different hexa-, hepta-, and octameric systems. Our results indicate that interactions of the fatty
acid chains contribute noticeably to the stabilization. The simulation results indicate that the heptamer with paired FA chains is
the most stable oligomer when compared to the 10 other investigated structures. Theoretical SAXS curves extracted from the
simulations qualitatively agree with the experimentally determined SAXS curves supporting the view that liraglutide forms hep-
tamers in solution. In agreement with the SAXS data, the heptamer forms a water-filled oligomer of elliptical cylindrical shape.
INTRODUCTION
The glucagon-like peptide 1 (GLP-1) receptor is a well-es-
tablished therapeutic target for the treatment of type-2
diabetes mellitus (1–3), and extensive research has estab-
lished the physiologic roles of GLP-1 and its endogenous
receptor in regulating glucose homeostasis and energy
metabolism (4,5). GLP-1-(7-37) is a 31-amino-acid incretin
hormone secreted by the endocrine L cells in the gut wall
upon glucose intake (6), and the peptide is secreted in
response to the nutrient content of the gastrointestinal tract
and thus potentiates insulin exocytosis from pancreatic b-
cells in a glucose-dependent manner (6,7). Additionally,
GLP-1 suppresses appetite, glucagon secretion, and gastric
emptying, all of which contribute to inhibition of the post-
prandial rise in plasma glucose concentrations (8). GLP-1
is responsible for up to 60% of the postprandial insulin
response (9). Recent studies show that GLP-1 is not only
a key factor in type-2 diabetes mellitus treatment, but also
has potential in the treatment of obesity (1,10) and has
shown positive effects on neuroprotection in animal models
(11), which can potentially be used for the treatment of Par-
kinson’s and Alzheimer’s disease (12–15).
While GLP-1 is interesting for a pharmaceutical applica-
tion, it cannot be used for routine treatment, because its
biological half-life is only a few minutes (16,17). The short
insulinotropic action of GLP-1 results from the degradation
of the peptide by dipeptidyl-peptidase IV (DPP IV) and
rapid renal clearance due to its relatively small size (18–
20). DPP IV degrades GLP-1 at the N-terminus by cleaving
off the first two amino acids, generating the biologically
inactive fragment, GLP-1-(9-37) (9,21). To overcome this
shortcoming, different strategies have been used. Those
include: 1) incorporation of the peptides in injectable micro-
spheres; 2) fusion with larger carrier molecules like albumin
or fragment crystallizable region of immunoglobulin G
or polyethylene glycol; and 3) attachment of a fatty acid
(FA) directing oligomerization and promoting reversible
binding to endogenous human serum albumin (20). All three
approaches result in an increased half-life partly due to the
increased size of the drug minimizing the renal clearance
mechanism. The latter approach, for instance, has been uti-
lized in designing the GLP-1 analog: liraglutide (Victoza;
Novo Nordisk A/S, Bagsværd, Denmark) (22,23). An in-
depth understanding of the oligomerization state of liraglu-
tide is not only instrumental in the understanding of the
increased half-life observed for this molecule but also to
ensure a stable oligomeric state, because uncontrolled and
extensive oligomerization can drive fibrillation (24). The
amino acid sequence of liraglutide is shown in Fig. 1.
Compared to GLP-1, two structural modifications have
been introduced. A C-16 acyl chain (palmitoyl), is linked
to Lys
26
via a g-glutamic acid spacer, and the lysine in po-
sition 34 of the native GLP-1 sequence is exchanged with
arginine to ensure homogenous palmitoylation at position
26 (25,26). The general understanding is that the acyl chain
allows a noncovalent binding to albumin, which delays both
proteolytic inactivation by DPP IV and renal clearance,
Submitted March 3, 2015, and accepted for publication July 30, 2015.
*Correspondence: ghp@kemi.dtu.dk or ph@kemi.dtu.dk
Editor: Ivet Bahar.
Ó2015 by the Biophysical Society
0006-3495/15/09/1202/12 http://dx.doi.org/10.1016/j.bpj.2015.07.051
1202 Biophysical Journal Volume 109 September 2015 1202–1213
resulting in a biological half-life of ~13–14 h and allowing
once-daily administration (2,23). A further prolongation
may also be caused by the fatty acid chain that may steri-
cally hinder DPP IV from degrading liraglutide (5). Further-
more, studies have shown that one way to stabilize GLP-1 is
to add a clustering agent that causes the peptide to oligomer-
ize (2), thus, the FA chain in liraglutide could act as a clus-
tering agent.
Although the pharmacological efficiency of liraglutide
has been established (23,27), there is a lack of a molecular
understanding of the solution structure of liraglutide. Using
analytical ultracentrifugation, Steensgaard et al. (28) could
show that liraglutide oligomerizes in a concentration-inde-
pendent manner forming, predominately, heptamers in the
concentration range of 0.004–4.501 mg/mL. Recently,
Wang et al. (29) studied the pH dependence of the size
and secondary structure of liraglutide oligomers using
light-scattering and circular dichroism, respectively. The
authors report a transformation from an octamer to a
dodecamer at pH 6.4 and 6.9 with subsequent partial loss
of the a-helical structure of liraglutide. Furthermore, it
has been shown that the oligomerization of GLP-1 and
similar peptide analogs is dependent on the pH and ionic
strength (30), and thus different solution structures may
exist (3,31).
To get further insight in the solution structure of liraglu-
tide, we have performed a series of molecular-dynamics
(MD) simulations, and the simulation results are compared
with results from small-angle x-ray scattering (SAXS) and
multiangle static light-scattering (MALS) experiments.
MATERIALS AND METHODS
SAXS
A quantity of 3 mL commercial Victoza (contains 18 mg liraglutide (free-
base, anhydrous); Novo Nordisk A/S)) and the inactive ingredients diso-
dium phosphate dihydrate, 1.42 mg; propylene glycol, 14 mg; and phenol,
5.5 mg in aqueous solution (32) were dialyzed against 3 1 L buffer con-
taining ~0.47 mg/mL (0.376 mM) Na
2
HPO
4
2H
2
O, pH 8.1, over 3 days.
Concentration determinations were performed with the NanoDrop 1000
Spectrophotometer (Thermo Fisher Scientific, Waltham, MA) at 280 nm.
The extinction coefficient was calculated to be 6990 cm
1
M
1
with the
PROTPARAM (33) tool from ExPASy.org (34) using the primary sequence
of the protein.
SAXS measurements were performed at the MAX IV laboratories at
beamline I911-SAXS, MAX IV Laboratory, Lund, Sweden (35). The sam-
ple detector distance and the direct beam position were calibrated
using AgBe (silver behenate). Parameters are shown in Table S2 in the
Supporting Material. Measurements on pure water were used to get the
data on an absolute scale. Buffers were measured both before and
after each sample and averaged before subtraction. The sample size was
~50 mL injected manually in a flow cell. Measurements were performed
on a series of liraglutide samples at the approximate concentrations of
1, 2, and 4.7 mg/mL.
All calibrations and corrections of the SAXS data were done using the
in-house software BLI911-4 (35). Buffer averaging and subsequent subtrac-
tion before data analysis was done in the program PRIMUS (36). The
software package ATSAS, Ver. 2.4 (37), was used for further data analysis.
Evaluation of the Guinier region was performed within PRIMUS. The pair
distribution function, p(r), was evaluated using the interactive program
GNOM (38).
Asymmetric flow field flow
fractionation-UV-MALS
Asymmetric flow field flow fractionation (AF4) separation was performed
using a Dionex UltiMate 3000 autosampler and pump (Thermo Fisher
Scientific, Waltham, MA) connected to an Eclipse AF4 separation system
(Wyatt Technology Europe, Dernbach, Germany) followed by a Dionex
UltiMate 3000 RS variable wavelength UV detector (Thermo Fisher Scien-
tific) set at 280 nm, and a Dawn Heleos-II 18-angle MALS detector (Wyatt
Technology Europe). Separations were performed using a 10-kDa molecu-
lar-mass cutoff PES (polyethersulfone) membrane in a 17.5 cm separation
channel with an S-350 mm spacer. Samples were introduced to the channel
at 0.2 mL/min and subsequently focused at the head of the channel at a
focus flow rate of 1.5 mL/min. Samples were eluted over 15 min with
a channel flow rate of 1 mL/min and a cross flow gradient of 4.0–
2.5 mL/min. Undiluted Victoza (6 mg/mL liraglutide) and 10diluted Vic-
toza (diluted with eluent) were injected and eluted with 20 mM phosphate,
100 mM NaCl, and 0.05% NaN
3
, pH 8.1, filtrated through a 0.1 mm filter.
Different injection volumes of undiluted and diluted Victoza were used, and
the resulting mass loads were 6, 12, and 18 mg liraglutide. The molecular
mass of liraglutide was calculated using the software ASTRA, Ver. 6.1.2
(Wyatt Technology Europe) with dn/dc¼0.185 mL/g and UV extinction
coefficient (280 nm) ¼6990 cm
1
M
1
.
MD simulations
Several orientations and oligomers of liraglutide have been investigated.
All are based on the solution NMR structure of liraglutide (PDB: 4APD)
obtained from the Protein Data Bank (39). The coordinates from the
PDB file were copied, translated, and rotated in a circle with a radius
of 20 A
˚, corresponding to the results from SAXS experiments. This re-
sulted in several oligomers containing six, seven, or eight monomers,
respectively. A set of oligomers was created where the monomers were
oriented so that two FA chains were paired in the direction of the ellip-
tical cylinder arrangement, which hereafter will be referred to as hexa-,
hepta-, and octamer systems (Fig. 2). In the heptamer, one monomer
was oriented with the FA chain pointing outward of the elliptical
arrangement.
Furthermore, another set of oligomers were created where some of the
monomers were flipped upside down to see if interactions between the C-
and N-terminal charges would stabilize the structures. For this set of olig-
omers, the hexa- and one octamer were made with every second monomer
FIGURE 1 Amino-acid sequence of liraglutide. To see this figure in
color, go online.
Biophysical Journal 109(6) 1202–1213
Oligomerization of a GLP1 Analog 1203
flipped upside down. In the case of the heptamer, only the monomer
with the FA chain pointing outward was flipped upside down. Also,
another octameric structure was prepared where every second monomer
pair was flipped upside down. These configurations are hereafter referred
to as the AA6_3ud, AA7_1ud, AA8_4udp, and AA8_4uds systems where
ud,p, and sare short for upside-down, pair, and single, respectively
(Fig. 2). To clarify the extent of the stabilizing effect of the FA chain
on the structures, another set of oligomers were created. One oligomer
is constructed according to the rotation and translation of the first
heptamer, but it does not contain any FA chains (hereafter referred to as
‘‘AA7_glp1’’ and represented in Fig. 2). Three other oligomers were
also created, namely, a hexa-, hepta-, and octamer where all the monomers
are rotated so that the FA chains are pointing outward of the elliptical
arrangement. These will hereafter be referred to as the AA6_FAout,
AA7_FAout, and AA8_FAout systems (Fig. 2). This gives a total of 11
oligomeric structures.
The structures were solvated using the program SOLVATE from
Grubmu
¨ller and Groll (40). Water molecules were described by the TIP3
water model (41). Next, the systems were neutralized by adding 3 Na
þ
ions per monomer. Simulations were performed at an ionic strength of
0.1 M NaCl (see details in Table 1). All simulations were performed using
the computer program NAMD (42) with the CHARMM36 force field (43).
The same simulation parameters were used as described by Madsen et al.
(44). (See the Supporting Material for a detailed description.) Analyses
of the trajectories were carried out in the software VMD (45).
Theoretical SAXS curves
The program CRYSOL (46), which is part of the program package ATSAS,
Ver. 2.6 (37), was used to compare the SAXS curves of the structures ex-
tracted from the MD simulations with the experimental measured SAXS
curve of the oligomer. CRYSOL calculates the scattering intensity based
on the atomic coordinates of the protein and adds a hydration layer simpli-
fied as a continuous outer envelope (37).
FIGURE 2 Representation of the start structures
for the 11 oligomeric structures. All structures are
shown from a top view. (Red line) Orientation of
the FA chain on each monomer; (ellipses) size
and shape of the oligomers. To see this figure in
color, go online.
TABLE 1 System and simulation details of the 11 oligomeric
systems
Structure
No. of
Atoms
No. of
Waters
No. of
NaCl
Initial Box
Size (A
˚)
Simulation
Time (ns)
Hexamer 140,203 45,615 86 113 118 115 69
Heptamer 53,774 16,665 31 83 88 89 129
Octamer 136,414 44,000 83 113 115 115 71
AA6_3ud 57,419 18,055 34 91 88 85 34
AA7_1ud 57,090 17,769 33 91 87 87 39
AA8_4udp 54,814 16,834 32 91 85 85 41
AA8_4uds 54,928 16,872 32 91 85 85 43
AA6_FAout 52,289 16,247 31 83 90 85 21
AA7_FAout 53,114 16,445 31 83 88 89 51
AA8_FAout 54,937 16,875 32 83 90 90 21
AA7_glp1 51,729 16,131 30 83 87 87 69
Biophysical Journal 109(6) 1202–1213
1204 Frederiksen et al.
RESULTS
In this section, experimental results from SAXS and AF4-
UV-MALS are presented, followed by the computational
results.
SAXS
SAXS intensity curves of liraglutide measured at different
concentrations are shown in Fig. 3. Repulsion is observed
already at 1 mg/mL, while the shape of the curve is consis-
tent over the concentration range, reflecting a similar shape
of molecule. This is also reflected in the Kratky plots shown
in Fig. S1. Corresponding pair distribution functions are
provided in Fig. S2.
Table 2 summarizes the parameters extracted from the
SAXS measurements. The radius of gyration (R
g
), maximum
particle diameter (D
max
) and I(0)/cshow a slight decrease
with concentration, as expected from the repulsive behavior.
The partial specific volume, n, used for calculating the
molecular mass is chosen to match pure protein and is set
to the average value of 0.73 cm
3
/g. To compare the experi-
mental results with the model structures extracted from the
simulations, the experimental data were extrapolated to q¼
0 to avoid interparticle repulsion.
AF4-UV-MALS
Analysis of liraglutide showed a single peak and a uniform
molecular weight across the peak in all analyses (Fig. 4,left)
indicating that repulsive behavior is negligible at the con-
centration range found in the detector. The average molecu-
lar mass across the peak was 22 kDa, which corresponds to a
hexamer assuming a monomer molecular mass of 3.7 kDa.
Undiluted Victoza (6 mg/mL liraglutide) and 10diluted
Victoza were analyzed and different injection volumes
were used, which resulted in mass loads of 6, 12, and
18 mg liraglutide. Liraglutide is diluted during analysis by
the eluate, and the resulting liraglutide concentration was
quantified in the eluate passing the UV detector (Fig. 4,
right). Peak liraglutide concentrations of 0.012, 0.024, and
0.036 mg/mL were observed.
MD simulations
Simulations were performed on several sets consisting of
hexa-, hepta-, and octamer oligomers, to study the structural
arrangement and stability of the oligomers including the
role of the FA in promoting the stability of the oligomers.
The last structures taken from the simulations are shown
in Figs. S3–S5.
Figs. S3–S5 show that although the internal structures for
all 11 oligomers are highly distorted compared to the start
structures, all of them but AA6_3ud (Fig. S4 a) maintain
a tunnel-like structure which is, however, more or less flat-
tened and resembling an elliptical shape.
The solvent-accessible surface area (SASA) of the oligo-
mers seen in Figs. 5,S6, and S7 relates to the packing of the
monomers.
Overall, the packing of the heptamers appears to be more
prominent than the octamers throughout the simulations,
indicated by the lower SASA. The AA6_3ud structure has
a significant lower packing than the AA7_1ud, AA8_4udp,
and AA8_4uds structures, which most likely is a result of a
complete opening of the elliptical structure as seen in Fig
S4 a. The relatively high SASA for the AA6_FAout olig-
omer could be due to the elongation of some of the mono-
mers, which appear to unfold from the helix structure
(Fig. S5 a).
The time evolution of the root-mean-square deviation
(RMSD) is shown for the 11 structures in Figs. 6,S8, and S9.
From the initial steep increase in RMSD, it is evident that
the oligomers rearrange to some extent within the first 6 ns.
RMSD converges for the hexamer, AA6_3ud and heptamer,
AA7_1ud, AA8_4udp, AA8_4uds, AA8_FAout, and
AA7_glp1 conformations. These structures appear to be sta-
ble when it comes to the overall movement of the systems.
The octamer, AA6_FAout and AA7_FAout, however, do not
converge. Furthermore, the three hexameric systems and
AA7_FAout present a significantly higher RMSD value
compared to the other systems.
To further monitor the movement of the monomers, the
two-dimensional positions of the a-carbon in the FA-Lys
linker (Fig. S11) for all 11 oligomer conformations, pro-
jected onto the yz plane (the monomers are translated and
rotated around the xaxis), are shown as a function of simu-
lation time in Figs. 7,8, and 9.
From Fig. 7, we can conclude that the spread of the
hexamer is larger than for the heptamer and the octamer
throughout the simulation. Furthermore, the hexamer is
squeezed to give a more flattened shape. For the octamer,
it appears that the elliptical structure is unstable because
one monomer seems to migrate from the oligomeric
FIGURE 3 Scattering curves normalized for concentration. Plots at con-
centrations 1, 2, and 4.7 mg/mL. (Inset) Scattering over entire measured
scattering range. (Lir is liraglutide.) To see this figure in color, go online.
Biophysical Journal 109(6) 1202–1213
Oligomerization of a GLP1 Analog 1205
structure. In the case of the heptamer, Fig. 7 b,itis
evident that the position of the a-carbon is rather dense
throughout the simulation and that the structure resembles
an ellipse.
Fig. 8 ashows that the AA6_3ud structure flattens drasti-
cally, which corresponds to the more open structure seen in
Fig. S4 a. The AA8_4udp structure maintains a more ellip-
tical arrangement, even though one monomer seems to be
leaving the structure (indicated by the circumference). The
AA8_4uds structure is rather mobile and gains a squared
shape. The AA7_1ud structure is, like the hexamer in
Fig. 7 a, squeezed so that the elliptical structure is
destroyed.
In AA7_glp1, Fig. 9 d, monomers are more mobile than
compared with the other structures resulting in a disordered
(unstable) structure. In Fig. 9 b, the AA7_FAout structure
appears to maintain an elliptical structure, but the move-
ment of the a-carbons is very spread out. Fig. 9 cshows
that the a-carbon movement of the AA8_FAout system is
rather centered on the starting position throughout the
simulation, which indicates a stable system. However, as
seen for the octamer and AA8_4udp systems, one mono-
mer escapes from the elliptical arrangement. The AA6_FA-
out system (Fig. 9 a) moves significantly throughout
the simulation, and this movement results in a flattened
structure.
Mean energies based on the structures taken at every
50 ps throughout the simulations are given in Table 3.
The energies calculated for the oligomeric system (pep-
tide-peptide, P-P) and the oligomer-water interactions
(P-W) are normalized to the number of monomers in
each oligomer to make comparison of the different systems
possible. From these, it can be seen that the total P-P van
der Waals (vdW) energy for the heptamer is lower than
for any of the other oligomers. Considering the P-W inter-
actions, the energy for the heptamer system is less nega-
tive than found for the other systems. In general, all
the hexameric systems of liraglutide (hexamer, AA6_3ud,
AA6_FAout) are higher in P-P vdW energy, which might
indicate that these structures are less stable than the hepta-
and octameric liraglutide oligomers. The energies show
relatively large fluctuations (data not shown) which is
also reflected by the relatively large standard deviations.
This indicates that internally the 11 oligomeric systems
are flexible structures.
The analyses were done for segment-segment interac-
tions where FA chains are facing each other (S-S FA), no
FA chains are between them (S-S), one FA chain pointing
outward (S-S FA out), and all FA chains pointing outward
(S-S all FA out). See Figs. 10 and 2for illustration of S-S,
S-S FA, S-S FA out, and S-S all FA out (AA6/7/8_FAout
structures). The two last analyses were only done for the
heptamer, AA7_1ud, and for the oligomer, AA6_FAout,
AA7_FAout, and AA8_FAout because these were the
only conformations relevant for such investigation. Results
for the AA7_glp1 structure (with no Fa chains attached)
are also reported since the monomers in the AA7_glp1
structure are rotated the same way as those in the heptamer
with paired FA chains. It can be seen that for the structures
with FA pairs, the energies are significantly lower for the
TABLE 2 Parameter overview extracted from SAXS measurements
Concentration (mg/mL) R
g
Guinier (A
˚)R
g
p(r)(A
˚)D
max
(A
˚)I(0) Guinier I(0) p(r)I(0)/cMolecular Mass (kDa)
1 23.1 23.8 82.0 0.021 0.021 0.021 26
2 21.7 22.3 75.9 0.040 0.041 0.020 25
4.7 22.2 22.2 74.2 0.096 0.096 0.020 25
FIGURE 4 AF4-UV-MALS analysis of undiluted Victoza (6 mg/mL lir-
aglutide) and 10diluted Victoza (F10). Different injection volumes were
tested. All analyses showed a single peak in the UV chromatogram and a
uniform molar mass of ~22 kDa across the peak (left). No other peaks
were observed in the chromatogram. The liraglutide concentration in the
eluate passing the UV detector is shown in the right graph. To see this figure
in color, go online.
FIGURE 5 SASA as a function of time for the hexamer, heptamer, and
octamer. The area has been normalized according to the number of mono-
mers. SASA was calculated every 50 ps along the trajectory using a van der
Waals radius of 1.4 A
˚. To see this figure in color, go online.
Biophysical Journal 109(6) 1202–1213
1206 Frederiksen et al.
monomer pairs that have FA chains facing each other than
for those where no FA chains are between them. This sup-
ports the view that interactions of the FA chains contribute
to the stabilization of the oligomers of liraglutide (2,5).
DISCUSSION
The experimental SAXS curves (Fig. 3) show that even
at the lowest measured concentration of 1 mg/mL, repul-
sive interactions between liraglutide oligomers are pre-
sent, which increases with increasing concentration.
Repulsive interactions can lead to an underestimation
of the molecular weight. The SAXS data suggest that
the solution structure of liraglutide is a hexa-, hepta-,
or octamer. The uncertainty of the structure arises from
uncertainties related to the measured concentration and
the estimated partial specific volume (v) (and hence
the number of monomers in the oligomer). To our
knowledge, there is no value of nfor liraglutide avail-
able in the literature. In this study, v¼0.73 cm
3
/g (cor-
responding to an average value for pure proteins) was
used. The FA chain could contribute to an increase in
the partial specific volume, but to which extent is diffi-
cult to estimate. Using v¼0.74 cm
3
/g as also reported
by Mylonas and Svergun (47), the molecular weight in-
creases to that resembling an octamer. From the SAXS
measurements, it can only be concluded that the solution
structure of liraglutide is an oligomer of approximately
heptameric molecular size, with a consistent shape of
an elliptical cylinder, and that this oligomerization is
concentration-independent within the measured concen-
tration range.
The MALS results indicate a hexameric solution structure
of liraglutide. In contrast to the SAXS data, no repulsion in-
teractions between oligomers were observed in the concen-
tration range of 0.012–0.036 mg/mL. Note that the SAXS
data were measured in the concentration range of 1.0–
4.7 mg/mL, where 1 mg/mL corresponds to the lowest con-
centration that can be measured.
Simulation results suggest that the hexamer is an unfa-
vorable arrangement for the monomers as seen from the
structural deviation of the oligomers, given by the RMSD
(Fig. 6) and the two-dimensional plot of the a-carbon in
the FA-Lys linker (Fig. 7). However, the packing of the
structure is relatively tight with a low SASA (Fig. 5), which
indicates that more interactions are obtainable. This is also
FIGURE 7 Position of a-carbon in the FA-Lys
linker of the hexamer (a), heptamer (b), and oc-
tamer (c), as a function of simulation time. One
monomer is highlighted (circle) in the octamer
(c), to indicate the possible disintegration of this
structure. Coordinates taken from the first 15 ns,
5 ns in the middle of the simulation, and then the
last ~5 ns, are shown. (Circles and dashed lines)
Average structure within the 5-ns intervals (dots).
The yz a-carbon atom coordinates for the FA-Lys
linker were plotted in intervals of 50 ps. To see
this figure in color, go online.
FIGURE 6 RMSD of the entire oligomeric structure for the hexa-, hepta-,
and octamer. Structures were aligned to the first frame (t¼0), and devia-
tions are determined for the backbone chains. To see this figure in color,
go online.
Biophysical Journal 109(6) 1202–1213
Oligomerization of a GLP1 Analog 1207
supported by the relatively low P-P energy of the hexameric
system compared to the others (Table 3). The heptamer
seems to present a very favorable arrangement with a tight
packing as indicated by the low SASA (Fig. 5), little
displacement given by the low and converging RMSD
(Fig. 6), and the overall elliptical shape seen in the two-
dimensional plot of the a-carbon in the FA-Lys linker
(Fig. 7). This is also the structure with the overall lowest
P-P energy of ~200 kcal/mol. The octamer, like the hex-
amer, also appears to present an unfavorable arrangement
with a slight opening and disintegration of the elliptical
structure as seen in the end structure (Fig. S3), the two-
dimensional plot of the a-carbon (Fig. 7), and the high
SASA (Fig. 5). The AA6_3ud presents the worst monomer
arrangement out of the 11 investigated structures based on
the end structure (Fig. S4) that opens completely, resulting
in an unstable conformation as also seen from the relatively
large SASA (Fig. S6), increasing RMSD (Fig. S8), and the
scattered a-carbon position (Fig. 8). The AA7_1ud,
AA8_4udp, and AA8_4uds systems all maintain a relatively
well-arranged end structure (Fig. S4), even though one
monomer appears to be leaving the general elliptical struc-
ture of AA8_4up. In contrast to this, the overall packing of
the three systems is relatively tight (Fig. S6), but the overall
movement is scattered and very spread out as seen in the
two-dimensional plot of the a-carbon (Fig. 8). Thus, it
seems like interactions between the C- and N-termini are
not contributing to the energy, hence, liraglutide is most
likely not to arrange like the flipped structures (AA6_3ud,
AA7_1ud, AA8_4udp, and AA8_4uds). The AA6/7/8_FA-
out structures also present unfavorable arrangements of
the monomers, as can be seen by the large scattering
of the individual monomers in the two-dimensional plot
of the a-carbon (Fig. 9) and large overall displacement rep-
resented by the RMSD (Fig. S9).
The most important analysis result for these structures is,
however, that the S-S all FAout energies for all three
systems are less negative than those of the segment inter-
actions in systems where the FA chains are pointing toward
each other (Table 3). This amplifies the hypothesis of
liraglutide oligomer structures that give rise to FA inter-
actions. However, when the FA chains are pointing out-
ward they could, in theory, wrap around the elliptical
structure in such a manner that they interact. This appears
not to be the case, based on the energy calculations (Table
3) and the fact that all the FA chains in all the three
FIGURE 8 Position of a-carbon in the FA-Lys linker of the AA6_3ud (a), AA7_1ud (b), AA8_4udp (c), and AA8_4uds (d) as a function of simulation
time. One monomer is highlighted in a circumference in AA8_4udp (c), to indicate the possible disintegration of the AA8_4udpsystem. See Fig. 7 legend for
details. To see this figure in color, go online.
Biophysical Journal 109(6) 1202–1213
1208 Frederiksen et al.
structures seem to be randomly laying on the surface of
the oligomers (Fig. S5). This arrangement could promote
clustering of oligomers. However, this is not the case
because SAXS and MALS data indicate the presence of
one defined oligomeric species. The AA7_glp1 was made
as a reference structure when considering the role of the
FA chains. The results show that the movement of the indi-
vidual monomers of this system (Fig. 9) is rather large. This
FIGURE 9 Position of a-carbon in the FA-Lys linker of the AA6_FAout (a), AA7_FAout (b), AA8_FAout (c), and AA7_glp1 (d), as a function of simu-
lation time. See Fig. 7 legend for details. To see this figure in color, go online.
TABLE 3 Mean energies and corresponding standard error of the mean (for P-P and P-W) and standard deviation (for S-S) for the 11
systems are calculated from the simulations
Structure P-P vdW (kcal/mol) P-W vdW (kcal/mol) S-S vdW (kcal/mol) S-S FA vdW (kcal/mol) S-S FA out vdW (kcal/mol)
Hexamer 188 518.9 84.7 521.1 20 54.5 44 56.1 —
Heptamer 200 514.8 68.1 519.3 37 55.6 56 54.7 23 53.8
Octamer 187 513.7 84.4 518.0 21 53.8 62 54.1 —
AA6_3ud 185 516.4 88.1 522.1 4.6 52.2 52 57.1 —
AA7_1ud 191 519.8 83.0 522.4 12 54.6 50 54.7 38 54.8
AA8_4udp 189 515.1 86.8 518.9 18 53.1 55 53.5 —
AA8_4uds 190 516.5 85.3 521.1 24 53.6 54 54.4 —
AA7_glp1 160 515.1 84.9 519.0 23 55.1 26 55.0 29 55.2
Structure P-P vdW (kcal/mol) P-W vdW (kcal/mol) S-S all FA out vdW (kcal/mol)
AA6_FAout 171 513.4 104 521.5 23 53.0
AA7_FAout 187 518.9 86.5 525.3 33 53.0
AA8_FAout 176 513.1 98.6 522.8 35 53.0
The vdW energies for the peptide-peptide (P-P), peptide-water (P-W), segment-segment (seg-seg) with FA pairs (S-S FA), seg-seg without FA pairs inter-
acting (S-S), and—for the heptamer—seg-seg interactions for the monomer pairs including the monomer with the FA pointing outward (S-S FA out), are
calculated. Energies are also calculated for the systems where all FA chains are pointing outward (S-S all FA out). The energies for the P-P and P-W in-
teractions are normalized according to the number of monomers in the structure. MDENERGY from the program NAMD (http://www.ks.uiuc.edu/
Research/namd/) was used to calculate the energies in intervals of 50 ps.
Biophysical Journal 109(6) 1202–1213
Oligomerization of a GLP1 Analog 1209
emphasizes the stabilization effect of the FA chains. The
system seems to have a tight packing (Fig. S7); however,
this fact is more likely to be a result of the missing FA
chains in the structure, and hence, less surface area. The
S-S energies bear witness to a great lack in possible interac-
tions because these energies are significantly less negative
(~29 kcal/mol) than for those systems with FA chains pre-
sent (S-S FA average energy ~54 kcal/mol). This corre-
sponds well with the hydrophobic/hydrophilic areas of the
monomer shown in Fig. 10, where it is evident that there
is a difference in the hydrophobicity around the monomeric
structure. All in all, it shows that the FA chains are impor-
tant in stabilizing the liraglutide oligomer.
It thus appears that the heptamer is the most favorable
arrangement, which is further supported by the comparison
between the experimentally determined SAXS (SAXS
exp
)
curve and curves extracted from the simulations. The theo-
retical SAXS (SAXS
comp
) curves along with the experimen-
tally determined curve are shown in Fig. S10. SAXS
comp
curves were calculated from the last structure of the 11
simulations.
The discrepancies (c
2
values) for the 11 curves compared
to the experimentally obtained SAXS curve are, with the
radii of gyration, given in Table S1. Besides the radius of gy-
ration for the octamer, the radii of the systems lie very close
to those found from the experimental data seen in Table 2.
Also, the discrepancies given in Table S1 do not present
one specific candidate with the best fit, as several of the sys-
tems have low discrepancies between their end structures
and the experimentally obtained data.
To clarify the best fit further, we show the time evolution
of the discrepancies between SAXS
comp
and SAXS
exp
for
the 11 oligomers in Fig. 11.
The discrepancy of the heptamer is rather stable and low
throughout the simulation. So is c
2
of the hexamer,
AA8_4udp, AA8_4uds, and the AA7_glp1 systems. On
the contrary, the discrepancy of the octamer and AA6_3ud
is very high and increases with simulation time. That of
the AA6_FAout, AA7_FAout, AA8_FAout, and AA7_1ud
systems fluctuate significantly throughout the simulations.
The results show that the global structure and size seems
to be correct, especially for the heptamer and hexamer,
but none of our simulated structures captures the precise
shape of SAXS
exp
.
Summarizing and combining all the results (see Table 4
for a combined scoring chart), it appears that the most likely
solution structure of liraglutide is a heptamer where the
monomers are oriented in such a way that the attached FA
chains can interact in three pairs in the direction of the ellip-
tical arrangement, and with the remaining monomer ori-
ented so that the FA chain is pointing out.
The heptamer, with the above-mentioned conformation,
presents the best model with a total score of 1.9 being the
best scoring structure in four out of seven categories and
landing either a second, third, or fourth place in the remain-
ing categories. It presents the best energy interactions as
well as the least structural deviation of the monomers and
highest packing. The hexamer presents the second-best
solution, but does not score best in any category. The
FIGURE 10 A surface plot of the liraglutide monomer showing the seg-
seg orientations. (Green) Hydrophobic; (orange) hydrophilic; (gray)FA
chain. (a–c) Different hydrophobicities on either side of the monomer. To
see this figure in color, go online.
FIGURE 11 Discrepancies calculated between the SAXS
comp
curves and
the experimentally determined SAXS curve of liraglutide as a function of
simulation time, calculated every 5 ns. (Arrows)c
2
values continuously in-
crease with simulation time. To see this figure in color, go online.
Biophysical Journal 109(6) 1202–1213
1210 Frederiksen et al.
AA6_3ud structure presents the worst arrangement of the
monomers, with a total score of 10.
CONCLUSIONS
From a pharmaceutical perspective, it is important to know
the oligomerization state of liraglutide with respect to sta-
bility, because uncontrolled and extensive oligomerization
can drive fibrillation. Hence, an important criterion for a sta-
ble formulation and, in turn, long shelf-life in the liquid
form is the solution structure. To gain further insight in
the solution structure of liraglutide, we performed a series
of MD simulations accompanied by MALS and SAXS ex-
periments. MALS provides information about the mass,
and SAXS provides information on mass, radius of gyra-
tion, and shape. The SAXS curves indicate that liraglutide
undergoes concentration-independent oligomerization. De-
pending on the partial specific volume used for deducing
the molecular weight and in turn the number of monomers
in an oligomer, liraglutide may form hexa-, hepta-, or oc-
tamers in solution. In contrast, the MALS results suggest
that liraglutide forms hexamers in solution. The experi-
mental results are not conclusive with respect to the size
of the oligomers. No information can be deduced from these
measurements regarding the orientation and stabilizing role
of the acyl chains in the oligomers.
We, therefore, performed MD simulations on several
oligomeric sets consisting of hexa-, hepta-, and octamers.
Our simulation results indicate that interactions between
the FA chains contribute to the stabilization of the structure
and that the heptamer presents the best representation of
the investigated liraglutide oligomers. Furthermore, com-
paring the experimentally determined SAXS curve with
the SAXS curves determined from the structures extracted
from the simulations shows qualitative agreement for
the overall size and shape. This indicates that liraglutide
in solution is most likely to form heptamers in a hollow,
water-filled, elliptical cylindrical-shaped structure where
the monomers are oriented in such a way that the FA chains
can interact pairwise. From the simulations, as of this
writing, we are not able to identify the absolute position
of the FA chains in the heptamer, but it is clear that interac-
tions between them are significant.
SUPPORTING MATERIAL
Supporting Materials and Methods, eleven figures, and two tables are avail-
able at http://www.biophysj.org/biophysj/supplemental/S0006-3495(15)
00815-2.
AUTHOR CONTRIBUTIONS
T.M.F. wrote the article and performed and analyzed simulations; P.S.
conducted and analyzed SAXS experiments, and contributed in writing
the article; L.A.R. performed preliminary simulations and contributed
to the article; P.H. conducted SAXS experiments and contributed in writing
the article; J.T.B. conducted SAXS experiments and contributed in writing
the article; A.M.S.-P. conducted and analyzed AF4-MALS experiments,
and contributed in writing the article; M.N.E.-L. performed preliminary
simulations; and G.H.P. performed and analyzed simulations, and contrib-
uted in writing the article.
ACKNOWLEDGMENTS
Simulations were performed at the Danish Center for Scientific Computing
at the Technical University of Denmark. MAXIV Synchrotron is acknowl-
edged for providing beamtime and for support during the experiments.
VMD (45) was used for all graphical representations of liraglutide.
The research leading to these results has received funding from the Euro-
pean Community’s Seventh Framework Program (grant No. FP7/2007-
2013) BioStruct-X, under grant agreement No. 283570. DANSCATT (the
Danish Agency for Science, Technology and Innovation) is acknowledged
for financial support.
SUPPORTING CITATIONS
References (48–50) appear in the Supporting Material.
TABLE 4 Scoring chart of the 11 oligomeric systems
Structure SASA RMSD 2D Projection
Energy SAXS
Total ScoreP-P vdW P-W vdW c
2
Value c
2
Value Fluctuation
Hexamer 2 8 3 5 5 7 4 4.9
Heptamer 1 4 1 1 1 3 2 1.9
Octamer 7 10 6 6 3 11 10 7.6
AA6_3ud 10 11 11 8 9 10 11 10
AA7_1ud 4 5 10 2 2 6 7 5.1
AA8_4udp 6 3 5 3 8 5 6 5.1
AA8_4uds 5 2 8 4 7 4 3 4.7
AA6_FAout 11 9 2 10 11 2 8 7.6
AA7_FAout 8 7 9 7 4 9 9 7.6
AA8_FAout 9 1 4 9 10 1 5 5.6
AA7_glp1 3 6 7 11 6 8 1 6.0
Each system is evaluated and compared to each of the others in these categories: lowest and most stable SASA, lowest and most stable RMSD, most stable
two-dimensional (2D) projection and elliptical shape, lowest P-P vdW energy, highest P-W vdW energy, lowest discrepancy from measured SAXS curve
taken for the end structure, and lowest mean and standard deviation of the discrepancy throughout the simulation (data taken from Fig. 11). The SASA,
RMSD, and 2D projection plots are inspected visually; 1 is the best score and 11 is the worst. The total score is normalized.
Biophysical Journal 109(6) 1202–1213
Oligomerization of a GLP1 Analog 1211
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