Yifat Miller1, Buyong Ma, Ruth Nussinov. 1. Department of Chemistry and ‡Ilse Katz Institute for Nanoscale Science and Technology, Ben-Gurion University of the Negev , Beér-Sheva 84105, Israel.
Abstract
Hydrogels are proving to be an excellent class of materials for biomedical applications. The molecular self-assembly of designed MAX1 β-hairpin peptides into fibrillar networks has emerged as a novel route to form responsive hydrogels. Herein, computational modeling techniques are used to investigate the relative arrangements of individual hairpins within the fibrils that constitute the gel. The modeling provides insight into the morphology of the fibril network, which defines the gel's mechanical properties. Our study suggests polymorphic arrangements of the hairpins within the fibrils; however, the relative populations and the relative conformational energies of the polymorphic arrangements show a preference toward an arrangement of hairpins where their turn regions are not capable of forming intermolecular interaction. Repulsive intramolecular electrostatic interactions appear to dictate the formation of fibrils with shorter, rather than longer, persistent lengths. These repulsive intramolecular interactions also disfavor the formation of fibril entanglements. Taken together, the modeling predicts that MAX1 forms a network containing a large number of branch points, a network morphology supported by the formation of short fibril segments. We posit that, under static conditions, the preferred branched structures of the MAX1 peptide assembly result in a cross-linked hydrogel organization. At the same time, the shear stress leads to short fibrillar structures, thus fluidic hydrogel states.
Hydrogels are proving to be an excellent class of materials for biomedical applications. The molecular self-assembly of designed MAX1 β-hairpin peptides into fibrillar networks has emerged as a novel route to form responsive hydrogels. Herein, computational modeling techniques are used to investigate the relative arrangements of individual hairpins within the fibrils that constitute the gel. The modeling provides insight into the morphology of the fibril network, which defines the gel's mechanical properties. Our study suggests polymorphic arrangements of the hairpins within the fibrils; however, the relative populations and the relative conformational energies of the polymorphic arrangements show a preference toward an arrangement of hairpins where their turn regions are not capable of forming intermolecular interaction. Repulsive intramolecular electrostatic interactions appear to dictate the formation of fibrils with shorter, rather than longer, persistent lengths. These repulsive intramolecular interactions also disfavor the formation of fibril entanglements. Taken together, the modeling predicts that MAX1 forms a network containing a large number of branch points, a network morphology supported by the formation of short fibril segments. We posit that, under static conditions, the preferred branched structures of the MAX1 peptide assembly result in a cross-linked hydrogel organization. At the same time, the shear stress leads to short fibrillar structures, thus fluidic hydrogel states.
Hydrogel materials
are used in tissue engineering,[1−3] microfluidics,[4,5] and
drug delivery.[6−8] A promising approach for the design of hydrogels
is the use of self-assembling
peptides in which noncovalent interactions between molecules drive
the assembly and formation of supramolecular fibril networks that
define the material.[9,10] Using peptides as building blocks,
one can form self-assembled structures that result in a percolated
hydrogel network. Schneider and co-workers[11−18] have designed a class of peptides that undergo triggered folding
into facially amphiphilic β-hairpins that subsequently self-assemble
to form self-supporting, rigid hydrogels. Recently, the kinetic and
mechanical rigidity of amphiphilic β-hairpins were investigated
by Chen et al.[19] MAX1 is a 20-residue peptide
with the sequence VKVKVKVKVDPPTKVKVKVKV–NH2. It forms two β-strands consisting of alternating hydrophobic
valine and hydrophilic lysine residues connected by a tetrapeptide
sequence (−VDPPT−) designed to adopt a type
II′ turn structure. In its folded state, hairpin amphiphilicity
is manifested in the composition of its faces: one hydrophobic valines,
the other hydrophilic lysine residues (Figure 1A). Importantly, this amphiphilic folded state is highly prone to
self-assembly, forming a network of β-sheet-rich fibrils. It
is known that temperature, pH, and ionic strength trigger the self-assembly
of MAX1 peptides. Previously, it was shown that MAX1 self-assembles
under physiological conditions (pH 7.4 and a temperature of 37°).[20] Small angle neutron scattering (SANS) and transmission
electron microscopy (TEM) studies demonstrated that the hairpin self-assembles
laterally, forming a network of intermolecular hydrogen bonds that
define the long axis of a given fibril. All the β-strands of
the assembled hairpins are in register, affording fibrils with distinct
diameters of ∼3 nm.[11,20] MAX1 facial self-assembly
can also take place by burial of the valine-rich face to form a bilayer
that defines the thickness of a given fibril. Along the long axis
of a given fibril, bilayer formation occurs regularly with one hairpin
docked and in register with its partner, an arrangement that shields
the maximum surface area of the valine side chains from water (Figure 1B). It was suggested that imperfections in this
mechanism can occur where the face of one hairpin is rotated relative
to that of its bilayer partner, leading to nascent fibril growth in
three dimensions, forming an interfibril cross-link (branch point).
These branch points are noncovalent physical cross-links that define
the mechanical rigidity of the gel.[13] Although
light scattering and microscopy studies clarified the network and
the local fibril morphology, a detailed molecular-level model of how
the peptides arrange themselves within the fibrils remained elusive.
Herein, we constructed variant models of MAX1 peptide arrangements
and investigated the stability of each variant model. Three sets of
models were examined. The first models the β-hairpin arrangement
along the long axis of fibrils constituting the network. The second
models the β-hairpin arrangement within the branch point regions
of the network. The third arrangement is an amyloid-like cross-β
structure, i.e., a β-arch structure (Figure 1C and D).
Figure 1
Building blocks of the MAX1 hydrogel are composed of β-hairpin
structures, not by an amyloid-like cross-β arch. (A) A folded
β-hairpin structure monomer of MAX1 peptide which presents intramolecular
hydrogen bonds. (B) Two folded β-hairpin structures of MAX1
peptide forming bilayer with a hydrophobic surface of valine residues.
(C) A proposed model for a folded amyloid-like β-arch monomer
of MAX1 peptide which does not present intramolecular hydrogen bonds.
(D) Two folded β-arch structures of MAX1 peptide are assembled
into an amyloid-like cross-β structure with intermolecular hydrogen
bonds. (E) A simulated self-assembled amyloid-like β-arch structure
presents an unstable cross-β structure. (F and G) A simulated
self-assembled β-hairpin structure illustrates a structurally
stable fibrillar state. (F) A view along the fibril axis and (G) a
view from the side of the fibril. In parts A–C, valine and
lysine residues are colored as blue and red, respectively, and serine
residues are colored green.
Building blocks of the MAX1 hydrogel are composed of β-hairpin
structures, not by an amyloid-like cross-β arch. (A) A folded
β-hairpin structure monomer of MAX1 peptide which presents intramolecular
hydrogen bonds. (B) Two folded β-hairpin structures of MAX1
peptide forming bilayer with a hydrophobic surface of valine residues.
(C) A proposed model for a folded amyloid-like β-arch monomer
of MAX1 peptide which does not present intramolecular hydrogen bonds.
(D) Two folded β-arch structures of MAX1 peptide are assembled
into an amyloid-like cross-β structure with intermolecular hydrogen
bonds. (E) A simulated self-assembled amyloid-like β-arch structure
presents an unstable cross-β structure. (F and G) A simulated
self-assembled β-hairpin structure illustrates a structurally
stable fibrillar state. (F) A view along the fibril axis and (G) a
view from the side of the fibril. In parts A–C, valine and
lysine residues are colored as blue and red, respectively, and serine
residues are colored green.Through extensive simulations, we found that the β-hairpins
exhibit polymorphic packing along the fibril long axis and in the
branch points. Previously, it was hypothesized that the cross-linking
phenomenon in MAX1 hydrogel is due to fibril imperfections. Our simulations
show that β-hairpin arrangements of branching structures are
preferred over β-hairpin arrangements of long fibril structures.
Therefore, the hairpins are more favored to form branch points than
to pack along the long fibril axis. We thus conclude that short persistence
lengths of the self-assembled hairpins exist within the gel. In addition,
all possible arrangements illustrate that the type II′ turns
that directly define the secondary structure of the β-hairpins
do not form intermolecular interactions between the β-hairpins
in the bilayer fibrils and thus do not contribute to the network morphology.
Materials
and Methods
MD simulations of the solvated variant models
M1–M8 and
other tested models were performed in the NPT ensemble using the NAMD
program[21] with the CHARMM27 force field[22,23] for 60 ns. The models were explicitly solvated with TIP3P water
molecules.[24,25] The Langevin piston method[21,26,27] with a decay period of 100 fs
and a damping time of 50 fs was used to maintain a constant pressure
of 1 atm. The temperature (330 K) was controlled by a Langevin thermostat
with a damping coefficient of 10 ps–1.[21] The short-range van der Waals (VDW) interactions
were calculated using the switching function, with a twin range cutoff
of 10.0 and 12.0 Å. Long-range electrostatic interactions were
calculated using the particle mesh Ewald method with a cutoff of 12.0
Å for all simulations.[28,29] The equations of motion
were integrated using the leapfrog integrator with a step of 2 fs.
All initial variant models were energy minimized and then solvated
in a TIP3P water box with a minimum distance of 15 Å from any
edge of the box to any β-hairpin atom. Any water molecule within
2.5 Å of the β-hairpin was removed. Counterions were added
at random locations to neutralize the β-hairpins’ charge.The solvated systems were energy minimized for 2000 conjugated
gradient steps, where the distance between the β-sheets in the
β-hairpins is fixed in the range 2.2–2.5 Å. The
counterions and water molecules were allowed to move. The hydrogen
atoms were constrained to the equilibrium bond using the SHAKE algorithm.[30] The minimized solvated systems were heated to
200 K, where all atoms were allowed to move. Then, the systems were
heated from 200 to 250 K for 300 ps and equilibrated at 330 K for
300 ps. All simulations ran for 60 ns, and structures were saved every
10 ps for analysis. These conditions (330 K and 60 ns of time scales)
are applied to test the stabilities of all variant models. All simulations
were performed at physiological pH. We applied a higher temperature
than the physiological temperature (310 K), aiming to investigate
the stability of the variant models. The self-assembly of MAX1 peptides
is triggered by the higher temperature; therefore, the choice of 330
K for MD simulations is a reasonable choice.To obtain the relative
structural stability of the variant models,
the trajectories during the last 5 ns were first extracted from the
explicit MD simulation excluding water molecules. The solvation energies
of all systems were calculated using the generalized Born method with
molecular volume (GBMV).[31,32] In the GBMV calculations,
the dielectric constant of water was set to 80.0. The solvent-accessible
surface area (SASA) term factor was set to 0.00592 kcal/mol·Å2. Each variant is minimized 1000 cycles, and the conformation
energy is evaluated by grid-based GBMV. The minimization does not
change the conformations of each variant but only relaxes the local
geometries due to thermal fluctuation which occur during the MD simulations.
A total of 4000 conformations (500 conformations for each of the 8
examined conformers) were used to construct the free energy landscape
of the conformers and to evaluate the conformer probabilities by Monte
Carlo (MC) simulations.
Results and Discussion
Polymorphic Packing of
β-Hairpin Bilayer Fibril and Cross-Linking
Structures
We based our constructed models on the overall
structure that had been proposed previously by Schneider and co-workers:
the MAX1 peptide is composed of two β-strands of alternating
lysine and valine residues, connected by a four-residue type II′
β-turn.[11,12,20] The model of MAX1 peptide based on the β-arch structure of
Aβ[33] was examined (Figure 1C and D) by applying MD simulations to the self-assembled
peptides. As one can see from Figure 1E, after
simulations of 26 ns, the self-assembled β-arch structure MAX1
is unstable due to the loss of hydrogen bond interactions along the
fibril axis (Figure 1E). We therefore conclude
that the folded state of MAX1 peptide is not a β-arch structure.Previously, it was suggested that the MAX1 peptide self-assembles
to form fibrils that cross-link through branch points.[34] Each fibril is composed of a bilayer of hairpins
that hydrogen-bond along the long axis of a given fibril (Figure 1B). We investigated four possible arrangements of
the β-hairpins constituting the fibril: variants M1–M4
(Figure 2A). They differ in the arrangement
and orientation of the turn regions. In models M1 and M2, the turn
regions in each layer are organized in the same direction. In the
bilayer of M1, the turn regions are organized in the same direction,
while in M2 they are organized in opposite directions along the fibril
axis. In models M3 and M4, the turn regions are organized in opposite
directions in each layer. In the bilayer of M3, the turn regions are
organized in the same direction, and in M4, the turn regions are organized
in opposite directions along the fibril axis. We further examined
two possible arrangements in the branching point region: variants
M5 and M7 and variants M6 and M8 (Figure 2B).
In models M5 and M7, the turn regions are organized in the same direction
in each layer. In models M6 and M8, the turn regions are organized
in opposite directions in each layer. While in M5 and M6 each of the
opposing monolayers illustrate that the hydrophobic residues are exposed
to the solvent, in M7 and M8, the opposing monolayers demonstrate
that the hydrophobic residues are not exposed to the solvent. Each
model of the fibril long axis comprises 16 β-hairpins. The number
of possible organizations at the branching points is large, because
the range of angles (0–90°) at which two layers in the
self-assembled peptide can be oriented toward each other is large.
We considered a single angle, 90°, between the two layers.
Figure 2
Illustration
of the variant models of the arrangements of the MAX1
hairpins in the gel network morphology. The secondary structure of
the hairpins is based on the experimentally designed peptide.[11,12,20] The variant models M1–M4
illustrate arrangement along the peptide fibril growth and in variant
models M5–M8 show arrangement in the cross-link branch point
regions.
Illustration
of the variant models of the arrangements of the MAX1
hairpins in the gel network morphology. The secondary structure of
the hairpins is based on the experimentally designed peptide.[11,12,20] The variant models M1–M4
illustrate arrangement along the peptide fibril growth and in variant
models M5–M8 show arrangement in the cross-link branch point
regions.After 60 ns simulations, all eight
self-assembled hairpin models
illustrated structurally stable fibrillar cross-β structures.
Interestingly, all M1–M4 fibrillar structural models presented
small RMSDs (Figure 3). While the fibrillar
structural models M1, M3, and M4 are relatively rigid, the fibrillar
model M2 is slightly flexible. The branching models M5–M8 are
relatively less rigid than the fibrillate models M1–M4. Interestingly,
models M5 and M6, that illustrate that the hydrophobic residues are
exposed to the solvent, showed relatively large RMSD values (∼2
Å) compared with the RMSD values of models M7 and M8 (∼1.2
Å) where the hydrophobic residues are not exposed to the solvent.
The RMSD values of 2 Å are in the range observed in protein structures.
In summary, we propose that the arrangements in branching point regions
in which the hydrophobic residues are not exposed to the solvent are
relatively flexible compared to the fibrillar models and present higher
rigidity than the arrangements in the branching point region in which
the hydrophobic residues are exposed to the solvent.
Figure 3
RMSD values along the
MD simulations indicating that the fibrillar
models are relatively more rigid than the branching models.
RMSD values along the
MD simulations indicating that the fibrillar
models are relatively more rigid than the branching models.The high structural stabilities
of the fibrillar models M1–M4
are due to the well protected backbone hydrogen bond networks that
are shielded from the solvent. The lysine-rich surface in the fibrillar
models is highly charged, while the hydrocarbon side chain of the
lysine residues provides a hydrophobic environment for the backbone
hydrogen bond networks. To examine this claim, we computed the solvation
backbone values for all 20 residues within the β-hairpin for
each of the fibrillar models M1–M4 and the branching models
M5–M8 (Figure 4). The backbone solvation
values for each residue are similar for all eight models, with slight
deviations for models M6 and M7, which illustrate hydrophobic residues
that are exposed to the solvent. As one can see from Figure 4, as expected among all 20 residues in the β-hairpin,
the residues in the C- and N-termini Val1 and Val20 and the residues
in the turn regions Pro11 illustrate relatively high solvation values.
Additionally, one can see an alternative pattern of backbone solvation
along the two β-strands of the hairpin in line with the alternating
sequence of valine and lysine residues. Valine residues illustrate
relatively small backbone solvation values compared to the lysine
residues. At the same time, the backbone solvation values for both
valines and lysines are relatively small, indicating the well protected
backbone hydrogen bond networks that are shielded from the solvation
for all models.
Figure 4
Average water molecules around each side chain Cβ
carbon
and backbone atoms (within 4 Å) for models M1–M8.
Average water molecules around each side chain Cβ
carbon
and backbone atoms (within 4 Å) for models M1–M8.Table 1 summarizes the conformational energies
of the eight variants of the self-assembled β-hairpins computed
by the generalized Born method with the molecular volume (GBMV) method
and the populations using Monte Carlo (MC) simulations. Among the
four possible arrangements of the β-hairpins constituting the
fibril, variants M1–M4, M2 and M4 have the highest and similar
energies and the highest population and M2 is slightly more stable
energetically than M4 and dramatically more stable than the other
models M1 and M3. Among the possible M5–M8 arrangements in
the branching point region, variants M6 and M8 are dramatically more
favored energetically than M5 and M7.
Table 1
Conformational
Energies and the Populations
of the Simulated Variant Models of the Hairpin MAX1a
variant
energy (kcal/mol)
energy
differenceb (kcal/mol)
populations
(%)
M1
–5799.3 (±221.2)
139.3 (±13.1)
10.2
M2
–5876.2 (±239.6)
62.4 (±13.8)
13.6
M3
–5793.1 (±237.4)
145.3 (±13.7)
10.1
M4
–5829.0 (±216.8)
109.6 (±13.0)
11.2
M5
–5845.1 (±237.9)
93.5 (±13.7)
12.0
M6
–5938.6 (±193.7)
0.0
15.7
M7
–5836.0 (±252.0)
102.6 (±14.2)
12.1
M8
–5911.4 (±227.6)
27.2 (±13.4)
15.1
Conformational energies were computed
using the GBMV calculations (refs (31 and 32)). Standard deviation values are presented in parentheses.
The standard deviation of the energy
difference is calculated by σ = sqrt[σ12/n1 + σ22/n2], where x1 and x2 are the means of
two samplings and n1 and n2 are the sizes of the sampling (500).
Conformational energies were computed
using the GBMV calculations (refs (31 and 32)). Standard deviation values are presented in parentheses.The standard deviation of the energy
difference is calculated by σ = sqrt[σ12/n1 + σ22/n2], where x1 and x2 are the means of
two samplings and n1 and n2 are the sizes of the sampling (500).We therefore suggest that these
constructed variant models may
provide insight into the mechanisms of the self-assembly of the β-hairpins
within the hydrogel network’s morphology. β-hairpins
self-assemble to form polymorphic arrangements with a preference toward
arrangement along the fibril axis and a preference toward arrangement
within the branching point regions. While along the fibril axis the
preferred self-assembling occurs when the turn regions oriented in
the same directions in each layer and in opposite directions in the
bilayer (e.g., model M2), within the branching point regions, preferred
self-assembling occurs when the turn regions are organized in opposite
directions in each layer (e.g., models M6 and M8).
Short Persistence
Lengths of Hairpins Are Favored along the
Bilayer Fibril Axis
The persistence lengths of the self-assembled
fibril of MAX1 hydrogels were previously estimated from rheological
experiments to be 55 nm.[13] The interactions
that control the self-assembly along the fibril bilayer include electrostatic
and hydrophobic interactions, and hydrogen bonding between individual
β-hairpins. Electrostatic interactions have also been found
to influence the persistence length.Electrostatic frustration
may affect the organization and persistence length of the assembly
of the peptide. To test the effect of electrostatic frustration on
the persistence length along the fibril growth of the 16 β-hairpins,
pairs of β-hairpins were removed from the most stable model
M2, that is, 14 β-hairpins and a dimer of β-hairpins.
The total energies of M2 and its small β-hairpin pair “fragments”
were computed with the GBMV method. Figure 5 demonstrates the total energies of M2 and its “fragment”
pairs. Energetically, short pairs of the self-assembled hairpins are
more favored than the longest self-assembled hairpin, indicating that
electrostatic repulsion might overcome hydrogen bonding and hydrophobic
interactions permitting further fibril elongation. The energy gap
between the 16 β-hairpins M2 and its pairs of “fragments”
reveals that the preferred size is between 6 and 10 hairpins (Figure 5C). Figure 5B illustrates
a similar scenario; the sum of the conformational energies of three
pairs of M2 “fragments” is less than the conformational
energy of the 16. Therefore, the electrostatic frustration disfavors
long-axis fibril growth and it is more likely that short persistence
lengths are formed, suggesting that the large numbers of cross-links
in the network morphology is due to the preference of short persistence
lengths. Therefore, the shorter persistence lengths may contribute
to a stiffer gel material, since the fibrillar structural models are
relatively more rigid (Figure 3).
Figure 5
Sum of energies
of self-assembled short persistence lengths and
the energy of model M2 that consists of 16 monomers. Parts A and B
demonstrate that short persistence lengths along the fibril’s
growth are energetically more favored than the longer fibril (consisting
of 16 monomers). As seen in part B, the most favored short persistence
lengths for model M2 are octamers and two tetramers. (C) The energy
gap between the self-assembled model M2 and the self-assembled short
persistence length. The energy gap increases with the formation of
shorter fragments.
Sum of energies
of self-assembled short persistence lengths and
the energy of model M2 that consists of 16 monomers. Parts A and B
demonstrate that short persistence lengths along the fibril’s
growth are energetically more favored than the longer fibril (consisting
of 16 monomers). As seen in part B, the most favored short persistence
lengths for model M2 are octamers and two tetramers. (C) The energy
gap between the self-assembled model M2 and the self-assembled short
persistence length. The energy gap increases with the formation of
shorter fragments.
Electrostatic Repulsion
of Bilayer Fibrils in the Network Morphology
Disfavors the Formation of Entanglements
In addition to the
bilayer and the interfibril cross-linking, i.e., the branch points
within the network, it has also been suggested that, at a sufficiently
high hairpin concentration, entanglements of the fibrils may also
contribute to the mechanical rigidity of the gel.[11,13,20,35,36] Our simulations demonstrate that the short persistence
length of the fibrils and interfibril cross-linking strongly contribute
to the mechanical rigidity of the fibril. To test the hypothesis that
the entanglements of the fibrils also contribute to the mechanical
rigidity of the gel, we simulated two self-assembled fibrils that
are in close and far proximity from each other (Figure 6A). To this end, we applied the most stable variant, M2. The
simulations illustrate that electrostatic repulsions of the lysines
between the two fibrils prevent the formation of fibril entanglements.
The strong electrostatic repulsions lead to the “breaking”
of one fibril, reflecting that fibril entanglements cannot be achieved
when two lysine-rich surfaces are in contact (Figure 6B). Since it has been proposed that the formation of the entanglements
of the fibrils may occur at high concentrations of salt ions, we increased
the concentrations of the counterions in the simulations while keeping
the system neutralized. Interestingly, the simulations at high counterion
concentrations illustrated a similar scenario of electrostatic repulsions
of the lysines that prevent the formation of the fibril entanglements.
We conclude that the electrostatic repulsions of the lysines within
the fibrils disfavor the formation of entanglements and therefore
help to define the percolated nature of the network. In the network
morphology, while the interfibril cross-linking contributes to the
material’s mechanical rigidity, it is unlikely that the fibrils
form entanglements. This conclusion and our results that (1) MAX1
prefers to have short fibrils and (2) branched models are more stable
than a long MAX1 fibril point to a cross-linking mechanism for MAX1
hydrogel (Figure 6C). We suggest that the MAX1
hydrogel cross-linking is not caused by “imperfection”
or entanglements of MAX1 fibril; rather, the cross-linking state is
one of the low energy and stable polymorphic states of MAX1 peptide
ensembles. Our mechanism is consistent with several experimental observations.[17,19] MAX1 hydrogel can become fluidic under shear stress and immediately
resume its gel state when the shear stress is relieved. In our mechanism,
shear stress provides the energy to reach the available short fibrillar
structures and thus yield a fluidic hydrogel. When the shear energy
disappears, the cross-linking state again becomes more populated.
The entanglement mechanism can explain the fast restoration of the
gel state immediately after the shear stress stops. Our mechanism
does not require converting all branching states to short fibrillar
structures; it suffices to provide enough energy to break a large
gel domain into a smaller one. Consistently, experimental works have
shown that random orientation of fibrillar structures does not change
under shear stress.[17] Our mechanism also
implies that stronger hydrophobic interactions can increase the hydrogel
mechanical stiffness, since the cross-linking is still provided by
hydrophobic surfaces rather than entanglement through lysine-rich
surface contact. In support of this, recent experiments have shown
that, after the valine residues of MAX1 were replaced by the more
hydrophobic isoleucines, the resulting gels displayed higher mechanical
stiffness.[19]
Figure 6
A proposed cross-link
mechanism of MAX1 peptide hydrogel. (A) Initial
structure of two MAX1 fibrils that are contacted with 90° between
them. (B) Simulated structure of the two contacted MAX1 fibrils demonstrating
that the strong electrostatic repulsion between the lysine-rich surfaces
does not allow two stable MAX1 fibrils to form an entangled complex.
(C) Shear forces provide energy to flow and therefore yield for structural
transitions. Under static conditions, the branching structures of
the MAX1 peptide assembly are more favored and thus provide cross-linking
of the hydrogel. However, the shear stress provides energy flow, leading
to short fibrillar structures and therefore yields to a fluidic hydrogel.
A proposed cross-link
mechanism of MAX1 peptide hydrogel. (A) Initial
structure of two MAX1 fibrils that are contacted with 90° between
them. (B) Simulated structure of the two contacted MAX1 fibrils demonstrating
that the strong electrostatic repulsion between the lysine-rich surfaces
does not allow two stable MAX1 fibrils to form an entangled complex.
(C) Shear forces provide energy to flow and therefore yield for structural
transitions. Under static conditions, the branching structures of
the MAX1 peptide assembly are more favored and thus provide cross-linking
of the hydrogel. However, the shear stress provides energy flow, leading
to short fibrillar structures and therefore yields to a fluidic hydrogel.
Conclusions
MAX1
undergoes triggered self-assembly at the nanoscale to form
a physically cross-linked network of fibrils with a defined cross
section.[11−13,20] The folded state of
MAX1 is characterized by a type II′ β-turn (−VDPPT−), which connects two amphiphilic β-strands
of alternating lysine and valine residues, resulting in a hairpin
with one hydrophilic, lysine-rich face and one hydrophobic, valine-rich
face.[11] This conformation rapidly self-assembles
following an external stimulus, yielding a mechanically rigid hydrogel.
How the hairpins self-assemble and how the branch points are formed
are elusive. To understand the structural features that contribute
to the network’s morphology and the material’s mechanical
rigidity of the gel, it is necessary to investigate the structure
of the network morphology at the molecular level. Recently, the morphologies
of the self-assembly of amphiphilic β-sheet peptides into various
organizations have been investigated at high resolution.[37]Herein, using all-atom molecular dynamics
(MD) simulations in explicit
solvent, we investigated the network morphology of the hairpins in
the fibril’s growth domains and at the branch points. The stable
variant models of the self-assembled β-hairpins were based on
the secondary structure which has been designed by Schneider and co-workers.[11−15] Overall, our study provides insight into the molecular network morphology
of the hairpins in the gel state. The preferred conformation of the
MAX1 peptide is the β-hairpin structure, rather than the amyloid-like
β-arch structure. It is interesting to note that there is similar
temperature sensitivity between MAX1 peptide gel formation and some
amyloid formations. Because hydrophobic interactions have higher contributions
at higher temperatures,[12] they can trigger
the formation of the MAX1 hydrogel. Similarly, tau protein amyloids
also form at high temperature which can be reversed to small oligomers
at low temperature.[38] However, there is
an important difference between the temperature sensitivities of the
monomer conformation of MAX1 peptide and tau protein. With increasing
temperature, the MAX1 peptide monomer changes from a random conformation
into a β-hairpin. On the other hand, tau peptides K19 and K18
present metastable secondary structure states[39] (both β-strand and α-helix) at room temperature, and
the β-strand percentage decreases with increasing temperature.
For amyloids, the rate limiting step of self-assembly depends on the
nucleus size.[40] Thus, the preferred hydrophobic
interactions at higher temperatures accelerate the nucleus formation
of tau oligomer. While it is possible that formation of the MAX1 hydrogel
is also limited by the nucleus size, the monomeric folding into the
β-hairpin conformation could be a prerequisite for the formation
of the MAX1 hydrogel nucleus.Several important observations
emerged from our study. First, simulations
of the hairpins exhibit polymorphic packing of hairpins along the
long fibrillar axis and within the branch point regions of the network.
Our computations suggest a slight preference for turn regions of neighboring
hairpins in the bilayer to be organized in opposing directions, as
demonstrated by the variant model M2. Second, short persistence lengths
along the fibril growth indicate that packing of hairpins within the
branch points is preferred over packing along the fibril long axis.
Electrostatic frustration disfavors long-axis fibril growth; in the
network morphology, it is thus more likely that short persistence
lengths are formed. These observations indicate that both the short
persistence and the large number of cross-linked branch points may
be largely responsible for contributing to the material’s mechanical
rigidity.[13,41] A network morphology that is comprised of
a large number of branch points and fibrils of shorter persistence
lengths leads to a stiffer material. Our results indicate that small
sizes of self-assembled peptides, i.e., short persistence lengths
along the fibril growth, are energetically preferred over longer fibril
sizes. This indicates that the rate limiting step for formation of
the hydrogel depends on the nucleus size. Finally, electrostatic repulsions
between fibrils due to the hydrophilic lysine-rich face disfavor the
formation of fibril entanglements and consequently assist in defining
the percolated nature of the network morphology.In summary,
we confirmed that the building block of MAX1 hydrogel
is a β-hairpin structure, not an amyloid-like β-arch structure.
The self-assembled β-hairpin structure of MAX1 illustrates a
well-packed cross-β structure. Recent MD simulations have demonstrated
cross-β structures in a small collection of peptide molecules.[42,43] Our MD simulations and energy estimation presented a polymorphic
energy landscape of the MAX1 peptide assembly, clarifying the mechanism
of structural transition in the hydrogel (Figure 6C). It was hypothesized that the MAX1 hydrogel cross-linking
is due to imperfections of fibrils. Herein, we examined this hypothesis
and found that branching structures are more stable than long fibrillar
structures. Finally, under static conditions, the preferred branching
structures of the MAX1 peptide assembly provide the cross-linking
of the hydrogel. However, shear stress provides the energy to convert
some branching states into short fibrillar structures, thereby breaking
large gel domains into smaller ones and yielding a fluidic hydrogel.
Authors: Kshitij Gupta; Hyunbum Jang; Kevin Harlen; Anu Puri; Ruth Nussinov; Joel P Schneider; Robert Blumenthal Journal: Biophys J Date: 2013-11-05 Impact factor: 4.033
Authors: Sameer Sathaye; Huixi Zhang; Cem Sonmez; Joel P Schneider; Christopher M MacDermaid; Christopher D Von Bargen; Jeffery G Saven; Darrin J Pochan Journal: Biomacromolecules Date: 2014-10-17 Impact factor: 6.988
Authors: Pim W J M Frederix; Julien Idé; Yigit Altay; Gaël Schaeffer; Mathieu Surin; David Beljonne; Anna S Bondarenko; Thomas L C Jansen; Sijbren Otto; Siewert J Marrink Journal: ACS Nano Date: 2017-07-21 Impact factor: 15.881