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Supplementary Information

A Self-Assembly Pathway to Aligned Monodomain Gels

Shuming Zhang,1^ Megan A. Greenfield,2^ Alvaro Mata,3,4 Liam C. Palmer,5 Ronit Bitton,3

Jason R. Mantei,1 Conrado Aparicio,3 Monica Olvera de la Cruz,1,2,3,5 Samuel I. Stupp1,3,5†

1Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois

60208, USA. 2Department of Chemical and Biological Engineering, Northwestern University,

Evanston, Illinois 60208, USA. 3Institute for BioNanotechnology in Medicine, Northwestern

University, Chicago, Illinois 60611, USA. 4Current address is Nanotechnology Platform, Parc

Cientific, Barcelona, Spain. 5Department of Chemistry, Northwestern University 60208,

Evanston, Illinois, USA.

* These authors contributed equally to this work. † E-mail: [email protected]

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Materials Preparation

The peptide amphiphiles with a C-terminal carboxylic acid were synthesized on a 0.25–1

mmol scale using a procedure similar to that reported previously1. Briefly, the peptide sequence,

such as VVVAAAEEE,2 was synthesized using an automated peptide synthesizer and Fmoc

chemistry starting from pre-functionalized Wang resin. Following Fmoc removal from the final

residue, hexadecanoic acid (Aldrich) was conjugated to the free N-terminus. The alkylation

reaction was accomplished by using eight equivalents of the fatty acid, eight equivalents O-

Benzotriazole-N,N,N’,N’-tetramethyluronium hexafluorophosphate (HBTU) and 12 equivalents

of N,N-diisopropylethylamine in 1:1 N,N-dimethylformamide and dichloromethane. The reaction

was allowed to proceed for at least 6 h until the ninhydrin test (Kaiser Assay) was negative.

Cleavage of peptide amphiphile from the resin and side-chain deprotection was carried out in

95% trifluoroacetic acid, 2.5% H2O, 2.5% triisopropylsilane at room temperature for 2 h. The

cleavage mixture and two subsequent dichloromethane washings were filtered into a round-

bottom flask. This solution was concentrated by rotary evaporation to a thick viscous solution.

The crude PA was isolated by precipitating with cold diethyl ether, filtrating, washing with

copious cold ether, and drying under vacuum.

To purify the synthesized peptide amphiphile the resulting material was dissolved in water

at a concentration of 10 mg/ml with the addition of NH4OH to adjust the pH of the solution to 9.

The solution was then filtered through a 0.2-µm nylon Acros filter and purified by preparative-

scale high-performance liquid chromatography (HPLC). Collected fractions were analyzed by

analytical HPLC and electrospray ionization mass spectrometry (ESI-MS) (Fig. S1) and

confirmed targets were combined and lyophilized. After lyophilization, the white powder was

combined and re-dissolved in PBS at a concentration of 10 mg/ml. The pH of this solution was

gradually adjusted to 7.00 by adding 0.5 M NaOH and monitoring with pH meter. Excess salt

was then removed by dialyzing this solution against pure water. This step ensured that the

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peptide amphiphile molecules were uniformly ionized and therefore minimized batch-to-batch

variation. After dialysis, the solution was re-lyophilized and stored in –20°C freezer before use.

Figure S1. Peptide amphiphile molecule used in this study and purity test a, Chemical structure of the C15H31CO-VVVAAAEEE(COOH) PA. This molecule contains three sections: hydrophobic alkyl tail, beta-sheet forming peptide segment, and charged peptide head group. b, Singly and doubly charged molecules were detected in ESI-MS. c, Analytical HPLC showed a single peak after purification.





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Table S1. PA molecules with different peptide sequences that have been tested after heating and cooling cycle.

PA molecules that forming monodomain gel

PA1 C15H31CO-VVVAAAEEE(COOH)

PA2 C15H31CO-VVVAAAKKK(COOH)

PA3 C15H31CO-VVVAAAEE(COOH)

PA4 C15H31CO-VVVAAAEE(CONH2)

PA5 C15H31CO-VVVAAAEEEGG(CONH2)

PA6 C15H31CO-VVAAEE(CONH2)

PA7 C15H31CO-VVVAAAEEEGS(P)G(COOH)

PA8 C15H31CO-VVVEEE(COOH)

PA9 C15H31CO-IIIEEE(COOH)

Based on our experience with these PA molecules, we found that pH value has a large

impact over the formation of monodomain gel. Normally, when the beta-sheet is disrupted by

strong electrostatic repulsion at non-neutral pH, the formation of a monodomain gel will be

prohibited. However, when the electrostatic charge carried by the molecule is significantly

reduced, such a gel can be produced at pH value that is far from neutral (Figure S2). Therefore

one requirement for the noodle formation process is the average charge carried by individual PA

molecules cannot be so strong that it overwhelms the cohesive forces. We also noticed that most

of the molecules listed above that form monodomain gels have a strong beta-sheet segment and

other design factors favouring beta-sheet assisted anisotropic growth of macromolecular

aggregates in solution.

PA molecular designs with the above considerations in mind can form the plaque

structure as discussed in our theoretical explanation below. This monodomain gel formation

process is not very sensitive to monovalent screening salt concentration. For example, we have





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used solutions with either 160 mM NaCl or with no salt at all to dissolve the PA molecule before

heat treatment. We believe a system that favours beta-sheet assisted anisotropic growth of

macromolecule aggregates has the potential to form monodomain gel with this heating and

cooling treatment if the cohesive and repulsive forces are carefully balanced.

SEM Fixation and Imaging

Critical-point drying was used to preserve the structure of PA gels for SEM analysis. After

the gels were made, the water was slowly exchanged with a gradient of water-ethanol mixtures

until the gel was in 100% ethanol. The samples were then critical-point dried in a Polaron E3000

Critical Point Drying Apparatus and sputter coated with 3nm of a gold palladium alloy in a

Cressington 208 HR Sputter Coater. Samples were then imaged on a Hitachi S-4800 II SEM

(Hitachi, Pleasanton, CA).

SEM Sample Preparation for Plaque Structure

C15H31CO-VVVAAAEEE(COOH) PA powder was dissolved in pure water at 1 wt% and

placed in a water bath at 80°C. Separately, a 50 mM CaCl2 solution was heated to 80°C in a hot

water bath. After both solutions were equilibrated at 80°C for 5 minutes, the heated CaCl2

solution was rapidly injected into the heated PA solution, resulting in the formation of a dense

gel. This gel was prepared for SEM by critical point drying and imaged as described above.

Sample composition was studied with energy dispersive X-ray spectroscopy (EDX) (Figure S2

and Table S2).





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Figure S2. EDX data shows that the composition of nanofibre bundles and plaque structures found in SEM samples have the same atomic compositions. a, b, SEM micrographs of dense fibres and plaque regions. c, d, EDX composition spectrum collected from boxed regions in a and b. Quantitative data is listed in Table S2.

Table S2. EDX composition analysis of nanofibre bundles and plaque structures formed by Ca2+

induced gelation at 80°C. Fibre Composition Plaque Composition

Element Weight% Atomic% Element Weight% Atomic% C K 42.56 79.84 C K 41.28 80.33 O K 7.99 11.25 O K 6.96 10.17 Ca K 2.87 1.61 Ca K 2.69 1.57 Pd L 20.28 4.29 Pd L 20.95 4.60 Au M 26.31 3.01 Au M 28.11 3.34 Totals 100.00 Totals 100.00

c

a b

d





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Quick-Freeze/Deep-Etch (QFDE) Sample Preparation for TEM

Our QFDE method was adapted from H.K. Lee et al3. Briefly, a 30-µL aliquot of sample

was placed on an aluminium tab and slam frozen (Gentleman Jim Slam Freezing Apparatus) onto

a copper block chilled to liquid nitrogen temperature (–195°C). After transfer into a freeze-

fracture apparatus (Model CFE-40; Cressington Scientific Instruments, Watford, UK), the frozen

sample was fractured, etched for 25 minutes at –95°C, rotary shadowed with a platinum–carbon

mixture at a 20° angle, and then strengthened with carbon evaporated from a 90° angle overhead.

The resulting replica was then separated from the organic sample and mounted on a copper grid

for TEM observation. All samples were imaged with a JEOL 1230 Transmission Electron

Microscope at 80 or 100kV. Figure S3 shows the morphologies of aggregates in freshly

dissolved PA solution at 25°C.

Figure S3. QFDE-TEM micrograph of fibrous and other structures in a freshly dissolved PA solution at 25°C.





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Circular Dichroism

Circular dichroism (CD) was used to study how elevated temperature affects the secondary

structure of peptide amphiphiles. The CD (J-715 CD spectrometer, JASCO Inc., Easton, MD)

was measured for 1 wt % solution (1.0 wt %, 0.01 mm path length plates) before and after

heating to 80°C. Solutions were dissolved in de-ionized water and then adjusted to pH 7 using a

0.5 M NaOH. The spectra are an average of five accumulations acquired at 20°C with a scan rate

of 100 nm/min. The beta-sheet remains strong before and after heating (Figure S4).

Figure S4. Circular dichroism of 1.0 wt% PA (C15H31CO-VVVAAAEEE(COOH)) before and after heating to 80°C. Path length = 0.01 mm.

Due to significant solvent evaporation, we were not able to use the plates for a variable-

temperature CD experiment. Therefore, variable-temperature CD was recorded on 0.01 wt %





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solutions during heating from 25°C to 80°C and then during cooling from 80°C to 25°C (Figure

S5). The solution was prepared by freshly dissolving the PA in de-ionized water. Samples were

equilibrated for 5 min at each temperature before scanning at a rate of 100 nm/min. Each line is

the average of five spectra. A strong beta-sheet signature was seen over the entire temperature

range covered. The CD signal of freshly dissolved filler PA solution slightly decreased as

temperature increased from room temperature to 80°C but changed little during cooling from

80°C to 25°C, consistent with previous reports4.

Figure S5. Variable-temperature circular dichroism scans of 0.01 wt% PA (C15H31CO-VVVAAAEEE(COOH)) solution during heating up and cooling down cycle. a, Heating scan. b, Cooling scan. Path length = 1 mm. The solution was equilibrated at 5 minutes between scans.





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FT-IR Spectroscopy

Transmission FT-IR spectra were acquired on Nexus 870 with the Tabletop optics

module (Thermo Nicolet). Samples were prepared by casting a 1 wt % solution of the PA

molecule in D2O onto undoped Si. These solutions appeared as broad and featureless, so the

dried film was observed in transmission mode. Unheated and heated samples both showed strong

parallel beta-sheet signals at ~1625 cm–1 (Figure S6).2 The heated sample additionally shows a

small local maximum at about 1660 cm–1,5 which could be related to formation of anti-parallel

beta-sheets within the fused bundle. Such a signal should be much weaker than the

corresponding parallel beta-sheet.

Figure S6. FT-IR spectra before and after heating. (Left) full spectrum and (right) zoom in of peak indicating strong presence of parallel beta sheets before and after heating.

Small Angle X-Ray Scattering

SAXS measurements were performed using beam line 5ID-D, in the DuPont-Northwestern-

Dow Collaborative Access team (DND-CAT) Synchrotron Research Center at the Advanced

Photon Source, Argonne National Laboratory. An energy of 15 keV corresponding to a





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wavelength of 0.83 A-1 was selected using a double-crystal monochromator. The data were

collected using a CCD detector (MAR) positioned 245 cm behind the sample. The scattering

intensity was recorded in the interval 0.008 < q < 0.25 A-1. The wave vector defined as q = (4 π /

λ) sin(θ / 2), where θ is the scattering angle. Samples were placed in 1.5 mm quartz capillaries.

The exposure times were between 2 and 4 seconds.

For the temperature controlled measurements (Figure 3c in the main text) samples were

sealed within 1.5mm glass capillaries that were placed in a Linkum THMS thermo stage. The

samples were heated at a rate of 10 °C min–1 and held for 1 h at 80°C before cooling at a rate of

1 °C min–1. The 2D SAXS images were azimuthally averaged to produce one-dimensional

profiles of intensity, I vs. q, using the two-dimensional data reduction program FIT2D

(http://www.esrf.fr/computing/scientific/FIT2D/). The scattering spectra of the capillary and

solvent (water) were also collected and subtracted from the corresponding solution data. No

attempt was made to convert the data to an absolute scale.

Wide Angle X-ray Diffraction

As further evidence of the beta-sheets, X-ray diffraction measurements were performed

using BioCARS (14 BM-C) beam line at the Advanced Photon Source, Argonne National

Laboratory beam line operating in fibre diffraction mode. The XRD measurements verified the

β-sheet secondary structural content of both fresh and thermally treated 1% wt V3A3E3 PA

solutions (Figure S7). Diffraction peaks that yield d-spacing of 4.7 Å, corresponding to the inter-

strand hydrogen-bonding repeat,6 were observed in both cases. The diffuse peak ~ 9 Å

corresponds to the stacking periodicity of the β-sheets.7





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Figure S7. Wide angle X-ray scattering of heated and cooled (A) and freshly dissolved (B) 1 wt % PA solution.

Cell Studies

To assess the ability of the noodle construct to allow for electrical communication

between encapsulated cells, we seeded noodles with HL-1 cardiomyocytes, an immortalized

atrial cell line with spontaneous electrical and contractile activity. C16-V2A2E2-NH2 PA was

solubilized in sterile phosphate buffered saline (PBS) at 1.1 % by weight and heated to 80°C in

Eppendorf centrifuge tubes for 30 min followed by slow cooling to room temperature overnight.

HL-1 cells cultured in fibronectin/gelatin-coated tissue culture flasks were lifted off with 0.05%

Trypsin/EDTA (Invitrogen) treatment and centrifuged to form a pellet. The cells were then re-

suspended in supplemented Claycomb medium for counting. After cell counting, aliquots of the

cell suspension were placed in centrifuge tubes and once again centrifuged to form pellets. After

aspirating the small amount of media present, the PA solution was added to the cell pellets and





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gently mixed, evenly dispersing the cells throughout the PA. The seeding density was 20,000

cells mL–1 PA solution.

Within a few minutes of cell pellet formation, cell-seeded noodle constructs were formed

by pipetting and dragging the PA solution on a glass cover slip through gelling medium

containing 160 mM NaCl and 7.5 mM CaCl2 in water. This cover slip was then picked up with

sterile tweezers and placed into a 35 mm Petri dish to which 2 mL of supplemented Claycomb

medium (Claycomb medium with 2 mM L-glutamine, 0.1 mM norepinephrine, 100 μg mL–1

penicillin/streptomycin, and 10% fetal bovine serum; Sigma-Aldrich) was added. The medium

was exchanged every 2–3 days until the cells were imaged.

Calcium fluorescence imaging was performed at 6 and 10 days after noodle formation by

adding Calcium Green-AM (Invitrogen) stain at a final concentration of 2.7 μM. The noodle

constructs were incubated at 37°C and 5% CO2 (standard culture conditions) for 30–45 min with

the stain. The medium was then exchanged for medium containing no stain to minimize

background fluorescence.

Imaging was performed by exciting the fluorophores with 460–500 nm light and

recording the green fluorescence intensity at 5x magnification on an Olympus BX51WI

microscope with a Redshirt NeuroCCD-SMQ high-speed camera using a frame-capture rate of

125 Hz. Neuroplex software was used to create colour maps of the fluorescence intensity and

display traces of the fluorescence signal over time for analysis.





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Theoretical Explanation for Observed Fibre Bundles

The cohesive energy difference per amphiphile in plaque and fibre states

It is difficult to determine the relative stability of sheet-like versus cylindrical aggregates

of molecules because the different contributions to the free energy per molecule in these states is

close in value and atomistic calculations do not help to describe these complex systems.

Moreover, the observed structures are most probably not true equilibrium structures due to

kinetic effects. That is, the width of the lamellar phase cannot be determined by a statistical

mechanics and/or thermodynamic approach. Nevertheless, one can understand the possibility of

a transition by estimating the main contributions to the difference in free energy per thermal

energy kBT, of the fibre Ff and the lamella F

l per amphiphile,

Ff – F

l = (F

fe - F

le )-(F

fc - F

lc ) (1),

where Ffe and F

le are the electrostatic free energies of the fibre and lamella, respectively, and F

fc

and Flc are the cohesive free energies of molecules in these two different structures assuming a

single fibre state and a single bilayer lamellar state. The electrostatic interactions do not play a

dominant role in the observed transition as demonstrated by our calculations detailed below,

which indicate that the effective charge per molecule in both lamellae and fibres is nearly zero.

Therefore, the transition should be dominated by the difference in cohesive energies of lamellae

and fibres, ΔF c = F

fc - F

lc , which is given by

ΔF c =

ΔHPA kBT - [ΔSPA + ΔSwater] (2),





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where ΔHPA is the enthalpy difference per PA molecule in lamellar or fibre aggregates, and ΔSPA

and ΔSwater are the entropy differences of the PA and water molecules, respectively. Since the β-

sheet signature in the CD spectrum of our system does not change significantly during cooling,

we assumed that the internal energy of the β-sheet is similar in the lamellae and the fibres.

Therefore, the enthalpy difference between lamellae and fibres must originate from the coupling

of interactions among peptide segments and hydrophobic tails. This coupling is supported by our

previous spectroscopic experiments that showed order can exist in the hydrophobic core of PA

nanofibres and is enhanced by β-sheet orientation8. The fibre architecture could also optimize

interactions among peptide segments and alkyl segments and polar head group and water

molecules. We estimate ΔHPA to be on the order of van der Waals forces, which are on the order

of the thermal energy. However, the increase in entropy of water molecules in the plaque state

can offset the enthalpy difference at elevated temperature. Specifically, the higher entropy in the

plaque structure could originate from an increase in the number of translation of water molecules

per amphiphile (ΔSwater) that is less restricted in the flat membranes than in the fibre, since the

plaque have less water interface per PA than the fibre structure, and therefore less number of

restricted water molecules per amphiphile n. The entropy difference between the fibre and

lamella, ΔS =ln(Ωfibre /Ωlamella), where Ω is the number of possible configurations, can then be

estimated by assuming a constant number of water molecules per PA head group, n. In the

plaque the water molecules explore a two dimensional (x,y) surface, which leads to twice as

many possible configurations than in the 1D fibre just from decreasing the degrees of freedom,

as shown in Figure S8. Therefore, the total change in entropy per amphiphile ΔSwater = - n ln 2

(where n can also be seen as the number of restricted molecules per PA in the fibre). We note

that for n=2 we recover the range found by calculations for the free energy differences in





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cylindrical and bilayer aggregates of simple amphiphiles9. The entropy of the counterions is

negligible in both the plaque and fibres since they are tightly bound to the charged groups at such

high charge densities, as explain below. Therefore, the total entropy change ΔS is at most of the

order of -(n)ln 2.

Figure S8. Water molecules per sectional area in the fibre (left) and lamellar (right) states. The number of released water molecules per amphiphile in the lamellar state are shown.

The temperature of the plaque- to-fibre transition Tt can be estimated then from the main

contributions of the cohesive energy in Eq. (2) by assuming for example three water molecule

restricted per PA in the fibres (see Figure S8), n=3, and ΔHPA ≈ -2KBTroom. Then, Tt is given by -

2 kBTroom /kBTt – (-3ln 2) = 0, which suggests Tt ≈ 282 K. Though this transition temperature is

for a single bilayer, it is close to the observed transition (333 K) that involves a plaque with

various bilayers. This argument, nevertheless, helps to understand the possible competition

between the energies that drive the observed transformation from sheets to fibres. Note that

although the plaque is formed by multiple lamellae (see Figure S9) and the fibrous state after





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heating is also composed of fused bundles, the surface energy per amphiphile is nevertheless

larger in the monodisperse bundle of fibres state.

Figure S9. Three stacks of lamellae form fused bundles as the temperature is lowered after annealing.

Electrostatic energy difference per molecule between the plaque and the fibre

The fraction of ions condensed on the surface of PA fibres and plaques is usually estimated

by solving the Poisson-Boltzmann (PB) equation,





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where ε(r) is the dielectric constant, φ(r) is the electrostatic potential, Zi is the charge of ion

species i, ni0 is the bulk ion density of species i, ρext is the charge density of external fixed

charges, r is the distance vector, T is the absolute temperature, and kB is the Boltzmann constant.

Solutions of the PB equation describe the electrostatic potential and the density of ions in space.

We explore the salt-free limit by computing the electrostatic potential and the resulting ion

profiles for the charge densities of a lamella and a fibre.

The solution of the PB equation for a charged plate with charge density σ is the

electrostatic potential

( ) ( ) 02 ln ,

2B

B

k T er re l

φ λ φ λπ σ

= + + =

where λ is the Gouy–Chapman length (λ= e/2π|σ|lB), which defines a layer in which most of the

counterions are confined10, r is the distance from the lamella surface, σ is the surface charge

density, and lB is the Bjerrum length (lB= e2/4πεoεrkBT). The Bjerrum length is the distance at

which the electrostatic potential energy of two elementary charges e in a solvent with a relative

dielectric constant εr is comparable to the thermal energy kBT. The resulting counterion profile

near the lamella surface is

( )( )21 .

2 B

n rl rπ λ

=+

The solution to the PB equation for a charged cylinder of radius Ro is the electrostatic

potential





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( ) ( ) ( ) ( ) 0 0 02 ln / ln 1 1 ln / 1 ,B

m mk Tr r R r Rφ ξ φ ξε

⎡ ⎤= + + − + >⎣ ⎦

where r is the distance from the centre of the cylinder and ξm = lBρ, where ρ is the linear charge

density of the fibre11. Since PA molecules are highly charged ξm is always greater than unity in

PA assemblies. The corresponding counterion distribution for ξm >1 is

( ) ( )( ) ( )

2

220

11 .2 1 1 ln /

m

B m

n rl r r R

ξπ ξ

−=

+ −⎡ ⎤⎣ ⎦

Since it is physically unreasonable to compare the ion profiles and energies in different

dimensionalities using PB, we compare the normalized ion profiles from the surface of the

lamella and fibre (see Figure S10).





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Figure S10. Ion profile solution of the Poisson-Boltzmann equation near a fibre (red) or lamellar sheet (blue).

Both ion profiles decay exponentially to nearly zero within the Bjerrum length (~7 Å in water)

and have an overall similar shape. It is important to note, however, that at the high charge

density in PA assemblies the PB theory may not be valid because PB theory does not account for

short-range correlations. In the limit of high surface charge density, PB theory breaks down

because the counterions near the surface are strongly correlated or bounded to the charge groups

on the PA12. Therefore, the surface counterions are confined even closer to the surface than PB

theory predicts. (Note that here we are assuming one bilayer and one fibre so there are no

internal counterions; in any case, the counterions not exposed to water are totally bounded

forming ionic bonds due to the low internal dielectric constant of the medium so they do not

contribute to the analysis). That is, if the average distance between the ions confined within in

the Gouy–Chapman layer d is smaller than the Bjerrum length lB, then the energy U(d)=





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e2/d4πεoε among the charges in the Gouy–Chapman layer is larger than their thermal energy

(since by definition U(d=lB) =1 then U(d < lB) / kBT > 1), and a strong cohesive energy among

the confined ions (neglected by PB) develops13. These correlations result in stronger

confinement (or condensation) of the ions near the surface. Since the charges of the PA

molecules should be screened by the condensation of counterions, the net surface charge should

be nearly zero for both the lamella and fibre. For this reason we assume that the difference in

electrostatic energies between the fibre and lamellae is negligible. Indeed, the fraction of

condensed counterions on the PA fibre in salt-free conditions can be easily estimated by using

Manning’s theory of counterion condensation14. In the fibre state, the effective charge is

renormalized by a fraction of condensed ions fc to decrease the electrostatic potential of the fibre,

which for infinite fibres at infinite dilution, is fc = 1– b/(lB|zizp|), where b is the distance between

two neighboring charge groups along the rod, zi is the valence of the counterions and zp is the

valence of the charge groups per length b of the fibre, and lB is the Bjerrum length. When the PA

fibre is projected onto a line to calculate the charge per distance between β-strands, b = 4.7 Å,

one obtains zp = (–4 charges/molecule)*(30 PA molecules/fibre cross-section) = –120 (this is an

estimated charge per cross-section of PA fibre, assuming all carboxylic acids are fully charged).

Since zi=+1 (monovalent salt), we obtain fc = 0.996 and it increases slightly with temperature

when we include the temperature dependence on ε. However, as PB, Manning model only gives

a lower bound for fc since it neglects all short-range correlations including the excluded volume

of the counterions15.





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The rupture of the anisotropic plaque into mono-disperse bundles of fibres

As the QFDE-TEM micrographs in Figure S11 show, some regions of the plaque

structure retain a texture with a length scale equivalent to the diameter of a canonical nanofibre

(twice the length of a PA molecule) but in other regions the plaque appears smooth. Our

hypothesis is that the 2D plaque structure fluctuates between states with and without a 1D

fibrous texture. The organization and dynamics of molecules in this emergent plaque structure is

therefore crucial for its ability to form at lower temperatures arrays of highly aligned nanofibres.

Figure S11. QFDE-TEM images of PA solutions at 80 °C, which are composed of large plaque-like structures. Some of these plaques had a periodic surface texture with a characteristic spacing of about 7.5 nm, which corresponds to the expected diameter of a single canonical nanofibre. 1,16

If composition fluctuations develop due to an underlying preference for the cylindrical

fibre morphology, membrane rupture by one-dimensional undulations may be possible17. In the

case of beta-sheet formation there is a tethering along one dimension and waves appear as





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surface ripples when the beta-sheets align in one dimension. It has been argued that long-range

forces are responsible for the rupture of membranes18. Fluctuations are stable in flat surfaces

since that is the lowest interfacial energy state. The film can be unstable, however, if the van der

Waals forces are such that a thinner film has lower energy than a thicker film19. This scenario is

possible in the presence of amphiphile surface concentration fluctuations since the surface

tension changes as the surfactant concentration varies. As shown below, the curvatures of a

cooperative amphiphile undulations in the multilayer plaque that lead to rupture are of the order

of the diameter D of the plaque. Therefore, a bundle of monodisperse interpenetrating fibres

roughly of the width of the lamellae may result (see cartoon, Figure S12).

Figure S12. Cartoon of plaque structure illustrating the alignment of beta-sheets to form surface

texture. Cooling results in breaking into bundles of adjacent fibres.

The rupture of the plaque is assumed here to be due to a decrease in the overall surface

tension γ, which is the change of free energy (F) as the interface area (A) increase, ∂F/∂A. The

lamellar or plaque surface tension γl if higher than the fibre surface tension γf, due to the increase

of hydration and of PA order in the fibre (that is, ∆γ = γf - γl < 0), since, as explained above in





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Eq. (2), ΔFc ≤ 0 under cooling, and the change in surface tension is related to these difference.

Unfortunately, the standard linear theory that assumes γ is constant under a deformation of the

interface is not appropriate to describe the breaking of lamellae19. We consider here fluctuations

that induce changes in the surface tension. A fluctuation perpendicular to the lamellar surface, on

the surface plane ρ=(x,y), can be described by a sum of waves of different wave vectors, q,

h(x,y) ~ (1/√A) Σ h(q) exp (iqρ),

where h(q) is the amplitude of the wave of wavevector q and wavelength λ=2π/⎢q⎢, and A is the

area of the membrane. These fluctuations induce a decrease in γl to γflu that may result in the

rupture of the plaque if the resulting free energy change, ∆F =Ff – F, is negative, or ∆F ≤ 0,

where Ff is the free energy of the fluctuating plaque, given by

Ff = (1/2) ∫ dxdy γflu (1 + hx2 + hy

2)1/2

with hx = ∂h/∂x and hy = ∂h/∂y, and F is the flat plaque free energy, F=(γl /2) ∫ dxdy. Notice that

we are extending the analysis to a non-equilibrium situation. Let us assume a one-dimensional

fluctuation along x of maximum amplitude h0, which is half the plaque diameter h0 = D/2 as

shown in Figure S8, and of wavelength λ,

h(x,y) = h(x) = h0 exp (i2πx/λ).

Since we are considering the case when the amplitude h0 has its maximum value (h0=D/2) we

can assume that γflu(h) is equal to the value in the fibre, γf. Neglecting higher order terms (hx2)n

with n>1 and curvature effects in γflu(h), we approximate γflu(h) (1 + hx2 + hy

2)1/2 to γf (1 +

hx2/2), given that hy=0, in the integrant of Ff. Therefore, carrying out the integration and

collecting terms we find





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∆F/A ≈ ∆γ/2 + γf (2π h0/λ)2 /4.

Since breaking occurs if ∆F/A≤0, where A is the total area of the plaque of volume V=AD, then

the condition for rupture reads

∆γ/2 + γf (2π h0/λ)2 /4 ≤ 0,

where ∆γ = γf - γl. This inequality gives a bound for the characteristic sizes of fluctuation that

lead to rupture

(2πh0/λ)2 ≤ –2∆γ /γf

Given that when the amplitude is largest one can expect rupture, ho = D/2, and that ∆γ = γf - γl <

0, the critical size of the fluctuation λc above which all other fluctuation sizes grow, λ≥ λc, is

given by

(πD/λc) 2 = 2(γl/γf - 1).

According to our estimates of the free energy differences between lamellar and the fibre

described above, γl/γf is of the order of 2, which gives a characteristic size of the fluctuation for

breaking λc or the order of the thickness of the plate D, λc= π D/√2 in agreement with the

expected size of the breaking of a cylinder by Rayleigh instability. Therefore, the one-

dimensional texture in the plaque can account for unusual breaking of this nearly solid materials

by two-dimensional Rayleigh instabilities that describe the breaking of fluids in certain

conditions17 though in flat isotropic membranes Rayleigh instabilities are not expected to lead to

rupture19,20.





S26

References

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amphiphile nanofibers. Science 294 (5547), 1684-1688 (2001). 2 Behanna, H.A., Donners, J.J.J.M., Gordon, A.C., & Stupp, S.I., Coassembly of

amphiphiles with opposite peptide polarities into nanofibers. J Am Chem Soc 127 (4), 1193-1200 (2005).

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4 Meijer, J.T. et al., Stabilization of peptide fibrils by hydrophobic interaction. Langmuir 23 (4), 2058-2063 (2007).

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