A designed β-sheet former and a spontaneously aggregating sequence run the same chemistry. Both bury a nonpolar face, both hydrogen-bond strand to strand along a fibril axis, and both end up as long fibres that an electron micrograph will not easily separate. The difference is procedural rather than physical: in designed assembly you specify the trigger, the concentration window and the target morphology in advance, then check that the material in the tube is the one you specified. The checking is the hard part, and most of this article is about it.

Sequence patterning fixes the geometry first

The oldest of the design logics is the alternating polar/nonpolar β-strand. A 16-residue peptide, (Ala-Glu-Ala-Glu-Ala-Lys-Ala-Lys)2, shows a characteristic β-sheet circular dichroism spectrum in water and, on addition of salt, spontaneously assembles into a macroscopic membrane; scanning electron microscopy revealed a network of interwoven filaments approximately 10–20 nm in diameter, and an important component of the stability was attributed to complementary ionic bonds between glutamic acid and lysine side chains [1]. That membrane did not dissolve in heat, in acidic or alkaline solutions, or on addition of guanidine hydrochloride, SDS/urea, or a variety of proteolytic enzymes [1]. Two patterns operate in one sequence. Side chains alternate faces along an extended strand, so alternating hydrophobic and hydrophilic residues segregate a nonpolar face from a charged face — that is strand geometry, not a result — while the alternation of negative and positive charge along the hydrophilic face sets which strand pairings are electrostatically complementary.

What the sheet reads is the arrangement of those charges, not merely their presence. Two 16-residue peptides of identical composition, AEAEAKAKAEAEAKAK and AEAEAEAEAKAKAKAK, behave differently: near neutrality the second forms globular assemblies and has a lower surface tension at the air–water interface than the first, which forms fibrillar assemblies at the same pH [4]. Lowering the pH below 6.5 or raising it above 7.5 drives the second peptide from globular to fibrillar structures, while the first shows no structural transition across that range [4]. Permuting a charge block, at constant length and constant amino acid content, therefore changes both the morphology and the pH window over which morphology switches.

The α-helical route uses the heptad repeat instead. Two 28-residue peptides were designed so that complementary core interactions and flanking ion pairs would direct staggered heterodimers rather than aligned ones, leaving "sticky ends" that promote longitudinal growth into fibres; a permuted control that formed blunt-ended canonical heterodimers could not associate longitudinally [6]. Sequence-level control of the register between two helices is what converts a discrete dimer into a polymer. The same idea carries into gels: linear peptides with purely α-helical structure form spanning networks of α-helical fibrils that give self-supporting physical hydrogels of more than 99% water content, and the sequences can be engineered to alter the underlying mechanism of gelation and, with it, the hydrogel properties [7].

Peptide amphiphiles bolt a peptide onto an alkyl tail. Across twelve derivatives, varying amino acid selection and alkyl tail modification yielded nanofibres differing in morphology and surface chemistry [8]. A purely peptidic version of the same logic uses surfactant-like peptides of 7–8 residues with an aspartic acid head and a tail of alanine, valine or leucine, each monomer approximately 2 nm long, comparable to a biological phospholipid [9]. Aromatic stacking supplies a fourth handle: for hydrogelators carrying aromatic substituents, a nanocylindrical architecture has been proposed in which antiparallel β-sheets are interlocked by π-stacking interactions of fluorenyl groups and phenyl rings, a model presented as consistent with the structures seen by transmission electron microscopy and with a range of spectroscopic data [10].

The hierarchy, and why a fibril has a width at all

Assembly does not stop at one level. A statistical-mechanical treatment of chiral rod-like units describes self-assembly into helical tapes which, with increasing concentration, associate into twisted ribbons (double tapes), then fibrils (twisted stacks of ribbons), then fibres (entwined fibrils) [3]. The finite width and helicity of a fibril in that model arise from a competition between the free-energy gain from attraction between ribbons and the elastic penalty of distorting intrinsically twisted ribbons as they are incorporated into a growing fibril [3]. For two rationally designed 11-residue peptides the 8-nm-wide fibrils consist of eight tapes, are extremely robust with a scission energy of roughly 200 kBT, and are sufficiently rigid, with a persistence length of about 20–70 µm, to form nematic solutions [3]. A fibril width is therefore a physical prediction, not an incidental observation, and a measured width that does not match the design is telling you the level of the hierarchy has moved.

Other morphologies come from other packing. The surfactant-like peptides assemble into nanotubes and nanovesicles of average diameter 30–50 nm with a helical twist; quick-freeze/deep-etch transmission electron microscopy revealed a network of open-ended nanotubes plus vesicles that appear to fuse with and bud out of them, together with many three-way junctions [9]. Lateral association is the recurring surprise. The designed coiled-coil fibres were at least several hundred micrometres long and about 20 times thicker than expected for the dimeric design, and the authors proposed that complementary features in repeating structures promote lateral assembly [6]. Where lateral packing can be designed rather than merely tolerated it becomes a lever: in β-hairpin systems, varying strand asymmetry changes the peptide registry in the assembled state, and that registry can be used as a design element to generate fibrils that twist, do not twist, or laminate [14].

Critical assembly concentration, and what a CAC number licenses

Below some concentration you have monomer, above it you have assemblies, and the crossover is measurable. For AEAEAKAKAEAEAKAK the critical aggregation concentration was found to be approximately 0.1 mg/mL by surface tension measurement, and light scattering showed two different rates of aggregation depending on whether the peptide concentration sat above or below that value: at high concentration the scattered intensity rose strongly at early times, at low concentration only slightly [5]. The mechanism proposed there has the peptide forming protofibrils through seeding and/or nucleation, with protofibrils then associating into fibrils [5].

Read that number narrowly. It is the concentration at which one observable changed behaviour, for one peptide, under one set of solution conditions, by a method that reports on the air–water interface. It is not a gelation threshold. In the 11-residue system, fibrils formed nematic solutions at a peptide concentration of about 0.9 mM, corresponding to a volume fraction near 0.0009 vol/vol, and converted to self-supporting nematic gels only above about 4 mM — a separation of more than fourfold between assembled and load-bearing in the same system [3]. Concentration is also a trigger in its own right: for peptide amphiphiles, three distinct modes of self-assembly into nanofibres have been described, namely pH control, divalent ion induction, and concentration [8]. If you determine a CAC by one probe, state the probe; if you need a gel, determine the gel point separately by rheology.

Triggers, and why direction is not universal

Ionic strength screens the charges that keep monomers apart. Salt addition alone converts a β-sheet peptide solution into an assembled membrane [1], and a 20-residue β-hairpin peptide has been designed to fold and self-assemble in response to a defined cell culture medium, giving mechanically rigid hydrogels [12] — that source reports the medium itself as the trigger and does not isolate ionic strength as the operative variable. pH acts by protonating or deprotonating the side chains that carry those charges: the viscoelastic properties of β-sheet tape gels can be controlled by chemical (pH) or physical (shear) influences [2], morphology can switch across a narrow pH interval [4], and pH control is one of the three amphiphile assembly modes [8]. Divalent cation induction is a second [8].

Temperature is the trigger most often described loosely, and it should not be. Among α-helical hydrogels, those whose networks are held together by hydrogen bonding between fibrils melt on heating, whereas those formed through hydrophobic fibril–fibril interactions strengthen when warmed [7]. The sign of the thermal response is set by which interaction dominates the network junctions, so "thermoresponsive" on its own carries no information about which way a given gel will move. Enzymatic triggering makes the trigger a covalent event rather than an environmental one: proteases can be used to selectively trigger the self-assembly of peptide hydrogels via reversed hydrolysis [11]. A further form of control is compositional — dual-peptide systems can be designed to gel only on mixing [7].

Because these networks are held together by non-covalent forces, the order in which you apply triggers can matter as much as which ones you apply. In supramolecular systems including peptide amphiphiles engaged in hydrogen-bonded β-sheets, the minima of the energy landscape are defined by electrostatic repulsion and by the ability of the dominant attractive forces to trap molecules in thermodynamically unfavourable configurations; these competing interactions can be selectively switched on and off, and the order of switching determines where the final product sits in the landscape [15]. Within a single landscape the peptide amphiphile system gave a thermodynamically favoured product of long bundled fibres and a metastable product of short monodisperse fibres [15]. Two samples of the same peptide at the same final concentration, salt and pH are therefore not necessarily the same material, and the order and timing of additions belong in the method.

Rheology: what G′ and G″ buy you

Gelation in these systems is physical entanglement plus fibril–fibril junctions rather than covalent crosslinking: semi-flexible β-sheet tapes become entangled even at low volume fractions to form gels [2]. The operational criterion is the familiar one, a storage modulus exceeding the loss modulus across the measured frequency range, and it is interpretable only when reported with the frequency, the strain amplitude, and evidence that the strain sits inside the linear viscoelastic region — measurement convention rather than a result.

Absolute stiffness is dominated by sequence. Across four 11-residue β-sheet self-assembling peptides examined at various peptide concentrations and buffer compositions, the resulting hydrogels spanned stiffness values from 0.6 to 205 kPa, and stiffness was mostly affected by peptide sequence, followed by peptide concentration and then buffer composition [16]. That ranking was established within that set of four peptides, so treat it as a caution rather than a law: a modulus quoted for "a self-assembling peptide hydrogel" without the sequence, the concentration and the buffer is close to uninterpretable.

The link between nanostructure and modulus can be made explicit. Combining small-angle neutron scattering with in situ cryogenic transmission electron microscopy at identical concentrations and conditions, network mass density was shown to vary significantly with local fibrillar morphology and with peptide concentration, and bulk rheology tracked it: stiffer, laminated fibrils formed networks with higher G′ than networks of flexible, singular fibrils [14]. Fibril cross-section is thus a design target, not merely a characterisation output.

Shear-thinning and recovery are the properties most often quoted and least often qualified. For a β-hairpin peptide hydrogel, applying an appropriate shear stress causes the gel to shear-thin into a low-viscosity gel, and once the shear stops the gel quickly resets and recovers its initial mechanical rigidity in a near-quantitative fashion [12]. The mechanism is fracture rather than dissolution: structural analysis during flow indicated that the network fractures into large hydrogel domains greater than 200 nm, and after flow ceases those domains immediately percolate, which immediately reforms the solid gel [13]. Critically, the same work found that the duration of shear and the strain rate affected both the stiffness recovered immediately after flow and the ultimate stiffness reached after complete rehealing [13]. A recovery percentage is therefore a function of the shear history you imposed rather than a constant of the material, and it must be reported with the strain rate and the duration that produced it.

Characterisation: what each method can and cannot conclude

Circular dichroism reports population-averaged secondary structure and nothing about morphology. It establishes that a peptide is in a β-sheet conformation in water [1], and for coiled-coil systems the concentration-dependent rise in the 222 nm signal on mixing two peptides is consistent with the intended α-helical structure [6]. Since tapes, ribbons, fibrils and fibres in the hierarchical model are all built from the same β-sheet [3], a β-sheet CD spectrum cannot by itself tell you which level of that hierarchy you are looking at.

Microscopy supplies the morphology that CD cannot. Atomic force microscopy has been used to image and quantify the dimensions of globular and fibrillar aggregates [5] and to establish the sequence- and pH-dependence of nanostructure [4]. Transmission electron microscopy of quick-freeze/deep-etch preparations revealed the open-ended nanotubes, vesicles and three-way junctions of the surfactant-like peptide system [9]. Because a deposited or dried specimen has passed through a concentration and solvent history the bulk sample never saw, corroborate it: the cryogenic transmission electron microscopy in the β-hairpin work was performed in situ, at concentrations and conditions identical to the scattering measurement it was substantiating [14].

Scattering gives you the ensemble at solution concentration without drying — small-angle neutron scattering quantified network mass density and tied it to fibril morphology in those gels [14]. Orientation methods add a further axis: linear dichroism during flow orientation indicated the presence of long fibrous structures, and X-ray fibre diffraction of partially aligned samples gave patterns indicative of coiled-coil structure [6]. Dynamic light scattering is worth running as a kinetic measurement rather than a single reading: for the peptide nanotubes it showed structures of very discrete sizes whose distribution broadened over time, indicating a highly dynamic process of assembly and disassembly [9]. A size distribution taken at one time point is a snapshot of an ensemble that may still be moving.

Designed and undirected assembly are the same physics

The models developed for designed systems were not built in isolation from fibrillation. The statistical-mechanical treatment that accounts for designed tapes, ribbons, fibrils and fibres was offered by its authors as insight into the factors governing the structures and stability of amyloid fibrils [3], and the designed coiled-coil work proposed that the lateral-association mechanism it uncovered may underlie fibrillogenesis in certain natural systems [6]. What separates a designed nanofibre from an unwanted one is not a distinct mechanism. It is that the designed case arrives with a stated trigger, a stated concentration window, a stated target morphology, and measurements chosen to discriminate that morphology from its neighbours in the hierarchy.

Minimum record for a self-assembly experiment

  • Peptide sequence, terminal capping, concentration in both mass and molar units, and buffer composition including counter-ion identity — sequence dominated stiffness in the four-peptide comparison that ranked these variables against each other [16].
  • The trigger, and the order and timing of additions, given that switching order can determine which minimum the system lands in [15].
  • The CAC together with the probe used to measure it, kept separate from the concentration at which the sample becomes load-bearing [3, 5].
  • G′ and G″ with frequency, strain amplitude and linear-viscoelastic-region evidence; for recovery data, the strain rate and shear duration, because both change the recovered stiffness [13].
  • At least one solution-state measurement, scattering or cryogenic microscopy, taken at the same concentration as any dried image used to claim a morphology [14].
  • A time course rather than a single time point for any size or kinetic readout, since these ensembles assemble and disassemble continuously [9].