## Introduction

Self-assembling peptides, a prominent class of supramolecular polymers, can form well-ordered nanostructures via non-covalent interactions (i.e., van der Waal’s forces, electrostatic forces, hydrogen bonding) as the main modulators for material tailoring1. Due to the dynamic and reversible nature of their interactions, self-assembling peptides offer novel functional properties for practical exploitation, e.g., multicomponent modularity2,3,4, semiconductivity5,6, and evolution-like adaptivity7.

In search for the link between the peptide monomers and the final assembly states, a number of previous reports on self-assembling peptides have studied the effect of changing the molecular properties of peptide monomer (e.g., sequences’ residues or stereochemistry8,9) toward the final assembled products. Many studies have treated the peptide self-assembly as a spontaneous thermodynamic process8,9,10. Therefore, the linear correlation between the properties of peptide monomers and the final assembled structures are often described in these studies. However, increasing evidence shows that, to overcome the huge desolvation barrier, rather than a spontaneous thermodynamic process, supramolecular assembly of amphiphilic peptides proceed via a multistep11 pathway, along which metastable oligomeric states are first formed before conversion to supramolecular nanofibers (Fig. 1a)12,13,14,15,16,17,18. This implies that the state of the intermediates in the assembly pathway also exert critical influence over the outcome of the peptide self-assembly19,20. For example, the polymorphic form of the assembled peptide fibrils are influenced by the properties of the oligomeric intermediates21. However, despite progress in the mechanistic understanding, the inter-relationship between the molecular properties of the peptide monomers, the oligomeric intermediates and the overall yield of the supramolecular assembly process remains largely elusive22.

Here we used surfactant-like peptides (SLPs) to show that the yield of peptide fibrillization are controlled by the properties of the oligomeric intermediates, which can be moderated by subtle molecular variations in the peptide sequences. SLPs consist of two modular subunits (Fig. 1b): hydrophobic tails that interact via van der Waals’ forces (side chain) and hydrogen bonds (backbone), as well as hydrophilic headgroups that confer mutually repulsive electrostatic interactions and determine the overall charges of the peptides23. The modularity of SLPs allow us to single out one molecular property at a time and study the effect it exerts in the downstream self-assembly pathway. We composed a set of cognate SLPs with small molecular variations (Fig. 1b). Using combined experimental techniques and molecular dynamics (MD) simulations, we demonstrate that these two molecular parameters (i.e., β-sheet propensities and charged residues flanking the aggregation domains) can modulate both the nucleation propensity of the oligomeric intermediates and the thermodynamic stability of the fibril structures. We demonstrate that the amount of peptide nanofibers being formed are critically defined by the oligomeric nucleation propensities. Altogether, our results offer a general molecular approach to moderate the properties of peptide assemblies for a variety of biomedical applications.

## Results and discussion

### Molecular design of SLPs

First, we designed a set of four cognate SLPs with different conformational propensities and headgroup charges in order to probe the effect of these molecular differences on the assembly pathway. We chose branched-chain amino acids (valine, leucine, isoleucine) as the major building blocks for the hydrophobic tail subunit, which are residues that often confer structural stability in proteins24. To limit the amount of molecular variability, we used Leu/Ile residue isomerism as the strategy for specific β-sheet propensity variation25. Ile has a higher β-sheet propensity compared to Leu but substitution does not change the overall side-chain molecular volume and hydrophobicity. Since the sequence order can also influence the overall β-sheet propensity26, we employed the position scoring matrix WALTZ27 to guide sequence design. The length of the tail group was chosen as N-terminal acetylated 7-mer peptide. An extra amino acid and an N-terminal acetyl cap was added to the 6-mer peptide sequence to minimize the influence of flanking effects by the charged residues28. The WALTZ database suggests that position 5 is a highly selective position for isoleucine, but not leucine, to drive cross-β structure formation. We also placed threonine between two aliphatic amino acid trimers in order to create two β-sheet faces of different hydrophobicity. This allowed assignment of the anisotropic side-chain interface that fits with the statistical mechanical model of fibril assembly (Fig. S5)29,30. The statistical thermodynamics algorithm TANGO was used to determine the residual aggregation propensities along the whole sequence (Table S1)31. Moreover, the number of charges in SLP was adjusted by altering the number of glutamic acid residues in the headgroup (Fig. 1b).

### Headgroup charges regulate the size distribution of the oligomeric particles

To study the effect of headgroup charges toward the size of the metastable oligomeric particles, we employed multiscale MD simulations to confirm the structural arrangement of the oligomeric particles (see “Methods”). The final trajectory of atomistic simulations suggested that the SLP oligomeric particles adopt a micellar arrangement with surface-exposed headgroups and buried tail groups (Figs. 2a and S1 and S2). Next, given that higher surface electrostatic repulsive forces can impose higher repulsive forces between the oligomeric particles, thereby lower their coalescence tendency32, we speculated that the size of the micellar oligomer with three glutamic acid residues in the headgroup (SLP3–4) should be smaller than that with two glutamic acids (SLP1–2). To validate this hypothesis, we performed fluorescence correlation spectroscopy (FCS) measurements to study the diffusion properties of SLPs in the early phase of self-assembly. FCS was chosen to inspect the early assembly phase, as it gives high-resolution measurement for the small-sized oligomeric particles in solution state33. By comparing the autocorrelation graphs of SLP1–4 (Fig. 2b), we could confirm that the size of oligomers decreases with the number of negative charges in the peptide headgroup, i.e., SLPs with two negative charges (SLP1–2) form larger oligomers than SLPs those with three negative charges (SLP3–4). To explore these size differences in more detail, we fitted the FCS data with a higher-order fitting model. Maximum entropy method (MEM) was chosen to account for the polydispersity of the oligomers. Each condensed fraction was treated as one quasi-continuous distribution, so as to provide the widest data-complying size distribution (least chance of overinterpretation)34. We succeeded to resolve the monomeric peptides and oligomers for SLP1–3 (Fig. 2c), whereas, due to their close size range, monomers and oligomers were represented as one continuous distribution for SLP4 (Fig. 2c). In the MEM analysis, the diffusion coefficients of the SLP1–2 oligomers were ~10-fold smaller than for SLP3–4, clearly showing a correlation between headgroup charge and the size of oligomers, i.e., oligomers with two glutamates in the headgroup are considerably larger than those with three glutamates. Recent studies show that nucleation events only happens in a minority of the oligomer populations13,35. Therefore, although this analysis does not allow us to distinguish between larger oligomers and the early nucleated structures (particularly the 0.1–1 µm2/s SLP1 population in Fig. 2c), as they fall in the same size range, we were able to validate our hypothesis that headgroup charges determine the size distribution of the oligomeric particles.

### Mesoscale structure of SLP assemblies characterized by microscopy

Next, we investigated the downstream effect of the differences in size of oligomeric particles and β-sheet propensities on the supramolecular self-assembly. One of the pivotal events in defining supramolecular self-assembly is whether nucleation has taken place or not. This can be identified by the mesoscale structures of the assemblies after certain time of incubation, e.g., the formation of one-dimensional (1D) nanostructures is indicative that nucleation has taken place. We used negative-staining transmission electron microscopy (TEM) and atomic force microscopy (AFM) to compare SLPs that were assembled under the same preparation protocol (4 mM, pH 7.4 in phosphate-buffered saline (PBS) for 3 days). We could indeed detect markedly different mesoscale structures in these SLP systems (Figs. 3a and S1). While SLP1–3 formed 1D nanofibers (~10 nm in diameter, >1000 nm long), we observed polydisperse zero-dimensional nanostructures for SLP4 (diameter of 10–60 nm). Based on these mesoscale evidences, we can deduce that nucleation occurred in SLP1–3, however, not in SLP4.

### Determination of population size of fibril and non-fibril assemblies by solid-state nuclear magnetic resonance (ssNMR) spectroscopy

As a next step, we hypothesized that higher-resolution methods might disclose further differences in the properties of the SLP assemblies. To examine our hypothesis, we profiled the SLP1–4 assemblies using ssNMR spectroscopy. Using the same conditions (4 mM, pH 7.4 in PBS for 3 days), we acquired the so-called dipolar cross-polarization (CP) ssNMR spectra and so-called scalar INEPT ssNMR spectra on isotopically (13C, 15N) labeled SLP assemblies (see “Methods”), which enables to quantify rigid and mobile populations of peptide assemblies in the systems36 (Fig. 3b). While dipolar signals report on immobilized peptides in 1D assemblies, scalar spectra report on peptides with fast pico-to-nanosecond dynamics, which can either be monomeric peptides or micellar oligomers16,32. We specifically labeled residues in the hydrophobic tail (Val1–2 and Leu6–7) that are responsible for the self-assembly. In line with the mesoscale differences observed by microscopy (Fig. 3a), ssNMR showed stark differences in the population profiles of SLP1–3 and SLP4 (Fig. 3b). SLP1–3 showed sizeable dipolar signals, indicating that a considerable number of peptides formed immobile assemblies, whereas dipolar signals were absent for SLP4, in line with the absence of 1D nanofibers for SLP4. A closer inspection into the population profiles of SLP1–3 revealed noticeable difference in the dipolar and scalar signals between SLP1–3. The intensity of the dipolar spectra correlates with the amount of rigid cross-β structure present in the system. We observe that the intensities of dipolar signal of SLP1 is larger than SLP2 (normalization scaling factor of 10, Fig. 3b) and SLP3 (normalization scaling factor of 25, Fig. 3b), which indicate the relative fibrillization yield of SLP1 > SLP2 > SLP3. Besides, the scalar signals were higher for SLP2–3 than for SLP1, which means that SLP2–3 have a higher number of mobile peptides than SLP1.

Furthermore, ssNMR signals are sensitive reporters of the peptide conformation in the assemblies28,36. We assigned 15N and 13C signals and amino protons in the assembled SLP1 system using two-dimensional (2D) 13C–13C PARIS37, 2D CαN, and 1H-detected 2D Cα(N)H experiments in combination with peptides in which only residues Val2 and Leu6 were isotope labeled. These assignments unambiguously show that assembled peptides adopt β-strand configuration, while the mobile population in the system is unstructured (Fig. 4c).

### Reconstruction of fibril models

Next, we sought to elucidate how these molecular variations can affect the thermodynamic properties of the fibril assemblies. Inspired by a previous computational approach38, we built models of the SLP fibrils and validated them with the help of X-ray diffraction (XRD) and ssNMR spectroscopy. SLP1–3 fibers exhibit typical cross-β XRD pattern, showing reflections at ~4.7 and 9–11 Å (Fig. 5c). Since XRD (sharp reflection at 4.7 Å in XRD) and ssNMR show that SLP1–3 share the same interstrand features (Fig. 3b), we used SLP1 as representative to elucidate the inter-β-strand configuration. We acquired a 2D 13C–13C PARIS ssNMR spectrum with a long magnetization transfer time of 700 ms that probes distances between 13C nuclei with a threshold of ~8 Å. Given that the Cαi–Cαi+5 distance within the same β-strand is 15–18 Å and hence markedly beyond the ssNMR distance threshold, our labeling scheme can conclusively distinguish parallel or antiparallel alignment of β-strands (Fig. 4b). However, measuring intermolecular contacts between the peptides in our dilute experimental concentration (4 mM) is a serious sensitivity challenge, and increasing the sample concentration was not possible because it could alter the kinetic pathway of fibril assembly. To this end, we used a CPMAS CryoProbe prototype (BioSolids CryoProbeTM, Bruker Biospin)39 that markedly enhanced spectral NMR sensitivity. With this advanced experimental set-up, we were able to observe a large number (>50) of intermolecular peptide–peptide contacts and could unambiguously establish an antiparallel alignment of β-strand in the fibers (Fig. 4a, b). Interestingly, while Leu6 showed intermolecular NMR correlations with all aliphatic carbons of Val1 and Val2, some intermolecular correlations were absent for Leu7. This suggests that the β-strand tails form interdigitated antiparallel arrangements from which the charged headgroups stick out in order to minimize electrostatic repulsion.28 The antiparallel, interdigitated dimer configuration was confirmed by NMR structure determination (Fig. 4d) for which we used NMR distance restraints and dihedral restraints40. The antiparallel alignment was also in line with 15N R1rho measurements that probe the slow microsecond dynamics of the assembly (Fig. S4). While the β-strand residues Val1–Leu7 are generally highly rigid, residue Leu7 showed modestly enhanced dynamics, in line with charge-flanking residue effect observed in antiparallel β-sheet arrangement previously28.

Next, we built structural models of the SLP fibrils. Therefore, based on the established interstrand configuration, we arranged side-chain faces of different hydrophobicity following the blueprint outlined from previous statistical mechanical model29,30 (Fig. S5) and built MD fibril models composed of 36 peptides for each of SLP1–3 (Figs. 5a and S6). Each fibril model was simulated for 100 ns. Fibrils remained stably associated over the entire trajectory. In agreement with previous reports, a left-handed twist was observed for all three fibril models due to the chirality of the constituting L-amino acids (Figs. 5b and S6)29,30. Radial distribution function (RDF) of the inter-backbone distances were calculated from the fibril model and cross-validated with XRD results. The RDF and XRD results are in mutual agreement, showing signal peak at ~4.7 and 9–11 Å (Fig. 5c, d). The good match between several experimental results and our MD model strongly corroborates the validity of our fibril models.

### Thermodynamic stability assessment by steered MD (SMD) simulations

As a next step, we evaluated the thermodynamic stability of the fibril models using SMD simulations. Analogously, we also determined the thermodynamic stability of the oligomer structures. In these pulling simulations, an external mechanical force is applied to one SLP, which is then dragged from an aggregate core. With this approach, we derived a potential of mean force (PMF) profile, which is a good representation of the dissociation energy (fibril: ∆Gd, oligomer: ∆Gd’)41,42. Since the choice of the pull-out SLP within the molecular model determines the resultant PMF profiles, we chose one random coil-forming SLP and one β-sheet SLP (Figs. 6a and S7). Each pull-out SLP was dragged along the x-direction (the reaction coordinate r) for 90 Å, while the other 35 SLPs were constrained by the application of a harmonic force. These results show that it takes ~3-fold more energy to pull one SLP out from the fibril structure than from the oligomer structure (Figs. 6a and S8). This means that fibril structures are much more stable configurations than the oligomer. For the fibril models, the increased headgroup charge in SLP3 caused reduction in ∆Gd and less fibril stability compared to SLP1–2. For the oligomer models, however, the charge differences in the peptide headgroups did not cause large differences in the ∆Gd’. Since the magnitude of the dissociation energy is an indicator for the thermodynamic stability of the supramolecular assemblies, these results suggested that an increasing number of charges in the headgroup caused more perturbations to the more ordered fibril structures than to the less ordered oligomer. We suspected that these differences are due to the structural elasticity. The structural strain caused by increased electrostatic repulsion forces would be more detrimental for brittle rigid structures (fibrils) than for flexible structures (oligomers). Such differences in structural elasticity are well supported by the strongly deviating sizes of the rigid and mobile equilibrium populations that we observed for SLP1–3 and SLP4 with the ssNMR experiments described above.

### The yield of nanofibers is moderated by the nucleation propensity in the oligomeric intermediates

After characterizing the properties of SLP at the oligomer and fibril states, we sought to search for the underpinning reason behind the differences in yield of peptide nanofibers between SLP1–4. It was suggested that the final yield of the peptide nanofibers is determined by its structural stability10. However, with the high thermodynamic stability of the peptide nanofibers, the amount of monomeric peptide dissociation from fibrils are typically negligible43. Indeed, we have observed that SLP1 and SLP2, although their fibril exhibits similar thermodynamic stability, they show markedly different amounts of fibril and non-fibril assemblies. We therefore rationalize the difference in yields of nanofibers between SLP1–4 is instead influenced by the properties of the oligomer intermediates. Due to the heterogenic nature of the oligomeric species, it was reported that nucleation only happens in a minority of the oligomers13. Furthermore, the nucleation probability is correlated with the size of the oligomers, in which the chance of nucleation increases with the oligomer size16,35. Indeed, we observed that SLP1–2, which form larger-sized oligomers than SLP3–4, also gives higher nanofiber yields (Fig. 3b). Besides, the nucleation probability is also influenced by the conformation propensity of the SLPs, in which more β-sheet-prone SLPs have a higher chance of forming cross-β nucleates. Therefore, for the SLPs that bear the same headgroup charges, we consistently observed higher yield of nanofibers for those with more β-sheet-prone tail groups, i.e., SLP1 > 2 and SLP3 > 4 (Fig. 3b).

Our findings advance our fundamental understanding of the molecular design principles of SLPs (and self-assembling peptides in general) to tailor their properties for various applications (Fig. S9). For applications that require that SLPs stay in dynamic form, e.g., the solubilization of membrane proteins44, one should increase the charges and lower the β-sheet propensities of SLPs in order to prevent fibrillization, as we here demonstrate it for SLP4. In contrast, for applications that require the fibril infrastructure, e.g., for therapeutic scaffolds2,3,4, one should engineer the SLP with higher β-sheet propensities and lower number of charges to maximize the yield of fibril structures (like SLP1). In addition, for applications that use 1D nanofibers as reservoir for hydrophobic drug release45, the amount of micellar oligomer co-present in the system can affect the overall drug release profile. At last, with respect to protein aggregation, a previous genome-wide sequence analysis revealed that, in close proximity to the aggregation-prone β-strand regions in proteins, charged ‘’gatekeeper” residues often prevent the β-strand sequences from aggregating46. Our current study implies that, on top of preventing aggregation, the charged protein gatekeeper sequences can also lower the chance of amyloid nucleation through lowering the size of the oligomers.

## Conclusion

The data presented here demonstrated, for the first time, the molecular strategy to modulate the yield of the supramolecular polymerization process. The effect of the molecular changes toward the size distribution of the oligomeric particles and the thermodynamic stability of the fibrils are also evaluated, which helps defining the mechanism leading to the differential polymerization yield. Thereby, our study enhances our understanding of the important role of oligomeric intermediates in defining the outcome of self-assembly systems and advances the rational design principles of self-assembling peptides that give different supramolecular properties for a wide latitude of applications2,3,4,44,45. Moreover, our findings suggest that charged protein gatekeeper sequences46 can prevent amyloidosis by lowering the size of the oligomeric particles. This knowledge will be instrumental for the design of strategies to prevent amyloidosis.

## Methods

### Materials

Preloaded Fmoc-Glu(Otbu)-Wang resin was purchased from Novabiochem GmbH (Hohenbrunn, Germany), 2-(1H-Benzotriazol-1-yl)-1,1,3,3-tetramethyluronium hexafluorophosphate (HBTU), 9-fluorenylmethyloxycarbonyl (Fmoc)-protected amino acids, and trifluoroacetic acid (TFA) were purchased from Iris Biotech (Marktredwitz, Germany). Peptide-grade N-methyl-2-pyrrolidone (NMP), dichloromethane, piperidine, N,N-diisopropylethylamine (DIPEA), and high-performance liquid chromatography (HPLC)-grade acetonitrile (ACN) were purchased from Biosolve BV (Valkenswaard, Netherlands). 1-Hydroxy-benzotriazole hydrate (HOBt), triisopropylsilane (TIPS), and BioUltra-grade ammonium bicarbonate and sodium bicarbonate were purchased from Sigma-Aldrich Chemie BV (Zwijndrecht, Netherlands). 13C,15N-labeled Fmoc-amino acids were purchased from Cortec-net (Les Ulis, France).

### Bioinformatic analysis

To predict the aggregation and fibrillization propensity of the designer SLPs, statistical thermodynamics algorithm, TANGO31, and position scoring matrices WALTZ27 were used to calculate the respective scores (available at http://tango.crg.es/tango.jsp and http://waltz.switchlab.org/).

### Solid-phase peptide synthesis and characterization

The SLP were synthesized by standard Fmoc solid-phase peptide synthesis using Symphony peptide synthesizer (Protein Technologies, US). NMP was used as the coupling and washing solvent for the whole synthesis process. For each coupling step, Fmoc-amino acids were activated by 4 eq HBTU/HOBt and 8 eq DIPEA to react with the free N-terminal amino acids in the resin for 1 h. After each coupling step, Fmoc group was removed by fourfold treatment of 20% piperidine for 10 min. TFA/water/TIPS (95/2.5/2.5) was used to simultaneously cleave the peptide off from the resin and remove the side-chain protecting groups. Peptides were purified by Prep-HPLC using Reprosil-Pur C18 column (10 μm, 250 × 22 mm) eluted with water–ACN gradient 5–80% ACN (10 mM ammonium bicarbonate) in 40 min at flow rate of 15.0 ml/min with ultraviolet (UV) detection at 220 nm. Purity was confirmed to be >90% by analytical RP-HPLC using Waters XBridge C18 column (5 µm, 4.6 × 150 mm) eluted with water–ACN gradient 10–80% ACN (10 mM ammonium bicarbonate) in 20 min at flow rate 1.0 ml/min and UV detection at 220 nm. Mass spectrometry (MS) analysis was performed using electrospray ionization (ESI)-LC/MS instrument (Supplementary Notes 18).

Peptides for Cy5 modification were synthesized as described above with addition of one lysine to the C-terminus. Peptides were then dissolved in 0.1 M sodium bicarbonate solution (pH 8.3) and Cy5 NHS ester (10 eq in 1/10 volume of dimethylformamide) was added and incubated overnight. Cy5-conjugated peptides were purified by Prep-HPLC. MS analysis was performed using ESI-MS instrument (Supplementary Notes 912).

### Sample preparation

Peptide assemblies were prepared by dissolving peptide powders in nine volumes of 10 mM sodium hydroxide in 1.5 ml Eppendorf tube. One volume of PBS (10×) was added to make sample of pH 7.4 ± 0.2 and a final concentration of 4 mM. Solution was vortexed for 5 s and incubated statically for 3 days at room temperature before proceeding for measurements.

### X-ray diffraction

XRD measurements were carried out on a Bruker-AXS D8 Advance powder X-ray diffractometer in Bragg–Brentano mode equipped with automatic divergence slit (0.6 mm 0.3°) and a PSD Våntec-1 detector. The radiation used was Co-Kα1,2, λ = 1.79026 Å, operated at 30 kV, 45 mA.

### Negative-staining TEM

Samples prepared at 4 mM were diluted tenfold with 1× PBS. Formvar/carbon-coated 400 mesh copper grid (Polysciences Inc.) was placed on top of a droplet of 20 μl of diluted samples. After 2-min incubation, the grid was washed three times with 0.2 μM filtered mili-Q water and blotted dry with filter paper. Negative staining was performed for 1 min with 2% w/v uranyl acetate in water. Staining solution was blotted off with filter paper. Samples were imaged on a Tecnai 20 transmission electron microscope (FEI, Eindhoven, the Netherlands) equipped with 4 K square pixel Eagle CCD camera (FEI, Eindhoven, the Netherlands) and operated at 200 kV accelerating voltage.

### AFM imaging

AFM micrographs were recorded using a Bruker MultiMode 8 (ScanAsyst Air silicon nitride probes, spring constant 0.4 N/m, nominal tip radius 2 nm) and post-processed by a plane subtraction and line alignment. Three different spots (one in main text, two in Fig. S3) were measured on the sample to confirm uniformity and get a comprehensive view of the sample’s features.

### Fluorescence correlation spectroscopy

Fluorescence time traces were obtained by focusing a 640-nm laser line through a water immersion objective lens (×60 Plan Apo VC, N.A. 1.2, Nikon, Japan) at ~50 µm above the bottom of the glass-bottom 96-well plate (Grainer Bio-one, Frickenhausen, Germany). The measurement concentration was 1 µM Cy5-SLP in 4 mM of unlabeled SLPs and PBS (pH 7.4). After 5 min of preparatory work, 50 µl of sample was measured with confocal microscope (Nikon C1). Photon counting instrument (PicoHarp 300, PicoQuant) was used to record time trace by binning the photon counts in intervals of 600 s. Autocorrelation curves were fitted by using QuickFit 3.047 using three-dimensional diffusion with triplet as described below:

$$G\left( \tau \right) = \mathop {\sum}\limits_{i = 1}^N {\alpha _i\left( {1 + \frac{\tau }{{\tau _{D_i}}}} \right)^{ - 1}\left( {1 + \frac{\tau }{{\gamma ^2\tau _{D_i}}}} \right)^{ - \frac{1}{2}}},$$

where τ represents lag time, $$\tau _{D_i}$$ is the diffusion time of the sample component, and γ is the aspect ratio of the focal volume (~6 for common confocal microscope), N is the number of discretization steps to sample the maximum entropy distribution (MEM), and αi is the relative amplitude of the component. The MEM methodology works toward maximization of Shannon–Jaynes entropy (S), which is defined as

$$S = - \mathop {\sum}\limits_{j = 1}^N {\rho _j\ln \rho _j},$$

where ρj represents the probability of detecting a component in the confocal volume.

$$\rho _j = \frac{{\alpha _j\tau _{D_j}}}{{\mathop {\sum}\nolimits_{i = 1}^N {\alpha _i\tau _{D_i}} }}.$$

The diffusion coefficient D is derived from:

$$D = \frac{{w_{xy}^2}}{{4\tau _D}},$$

where wxy is the lateral radius of the focal volume. wxy was calibrated with a solution of Alexa-647 (D = 330 μm2/s at 25 °C), giving wxy ~ 300 nm.

### ssNMR spectroscopy

1D CP48 and scalar49 ssNMR experiments to probe rigid and mobile populations, respectively, were acquired at 11.7 T magnetic field (500 MHz (1H frequency) with 10 kHz magic angle spinning (MAS) and 280 K sample temperature. 2D 13C–13C and 2D CαN for peptide assignments were also performed at similar conditions37. 2D Ca(N)H experiments for 15NT1rho relaxation studies were performed at 950 MHz magnetic field strength with 60 kHz. 13C was detected in the indirect dimension because of spectral overlap in the 15N dimension. The 2D 13C–13C PARIS37 experiment with the CPMAS CryoProbe39 to measure intermolecular peptide contacts was performed at 600 MHz and 12 kHz MAS using 700 ms magnetization transfer and a 1H recoupling amplitude of 6 kHz.

### NMR structure determination

An NMR structure of the SLP1 dimer was obtained using HADDOCK version 2.450 using default parameters. In total, we used 6 NMR chemical shift-derived40 dihedral angle restraints and 60 intermolecular NMR distance restraints. The resulting dimer structure was very well defined and scored all within the same cluster.

### MD simulations

Coarse-grained (CG) MD simulations were performed with the Martini force field version 2.251 and GROMACS 5.0.452. Thirty-six SLPs were randomly immersed into a box with water beads to which 140 mM of NaCl was added (including neutralizing counterions). The systems were energy minimized and simulated for 3 µs (150,000,000 steps of 25 fs) using standard settings for nonbonded interactions in an NPT ensemble with period boundary conditions. Simulated systems were weakly coupled to a pressure bath at 1 bar (τp = 3 ps) and coupled to a heat bath of 300 K temperature (τT = 1.0 ps) using Berendsen algorithm53. Since Ile and Leu share the same CG beads in the Martini force field, SLP1–2 and SLP3–4 share the same CG models. Secondary structure of the SLPs were assigned as random coil with the martinize.py script. Random coil secondary structures were used in CG MD simulations to represent the initial steps of self-assembly. Polar P4 backbone beads were used to represent the N-terminal acetylate group. The final trajectories were transformed54 to the atomistic coordinates and subject to the atomistic simulation.

Atomistic MD simulation were performed with the g53a6 force field55 in GROMACS 5.0.452. The fibril and oligomer models were first immersed into a box of simple point charge (SPC) water56 to which 140 mM of NaCl was added (including neutralizing counterions). The systems were energy minimized, then equilibrated for 100 ps in NVT ensemble at 300 K using V-rescale thermostat57. After that, 100 ps of NPT equilibration were performed at 1.0 bar using Parrinello–Rahman barostat58. Finally, the systems were simulated for 100 ns without restraints. The trajectories are available as Supplementary Data 1.

### SMD simulation

SMD simulation were performed with the g53a6 force field55 in GROMACS 4.5.552. The equilibrated (100 ns) structures from the atomistic MD simulation were transferred to larger rectangular boxes of SPC water to which 140 mM of NaCl was added (including neutralizing counterions). The systems were energy minimized, then briefly equilibrated for 100 ps in NVT ensemble at 300 K, followed by 100 ps in an NPT ensemble at 1.0 bar. After that, 200 ps of NVE ensemble was performed with position-restrained peptides to optimize the charged side-chain orientations. Following the NVE equilibration, 1 SLP was pulled-out from the core of each structures along x-coordinate using a force constant of 1000 kJ/mol/nm2 and pull-rate of 0.01 nm/ps. The other 35 SLPs were constrained by applying a harmonic force along the x-direction. The measurements of force and displacement of individual trajectories were saved every 10 fs. From these recorded trajectories, we derived the PMF profiles using Jarzisky’s equality41,42. The trajectories are available in Supplementary Data 1.

### Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.