Order from Disorder with Intrinsically Disordered Peptide Amphiphiles

Amphiphilic molecules and their self-assembled structures have long been the target of extensive research due to their potential applications in fields ranging from materials design to biomedical and cosmetic applications. Increasing demands for functional complexity have been met with challenges in biochemical engineering, driving researchers to innovate in the design of new amphiphiles. An emerging class of molecules, namely, peptide amphiphiles, combines key advantages and circumvents some of the disadvantages of conventional phospholipids and block copolymers. Herein, we present new peptide amphiphiles composed of an intrinsically disordered peptide conjugated to two variants of hydrophobic dendritic domains. These molecules, termed intrinsically disordered peptide amphiphiles (IDPA), exhibit a sharp pH-induced micellar phase-transition from low-dispersity spheres to extremely elongated worm-like micelles. We present an experimental characterization of the transition and propose a theoretical model to describe the pH-response. We also present the potential of the shape transition to serve as a mechanism for the design of a cargo hold-and-release application. Such amphiphilic systems demonstrate the power of tailoring the interactions between disordered peptides for various stimuli-responsive biomedical applications.

. CMC measurements of (a) 2x12 and (b) 4x7 IDPAs. The CMC is taken to be the concentration at the intersection of the linear fits to the fluorescence intensity in both regimes. The concentrations are approximately 5 and 11 M, respectively. Figure S2. CD measurements a) of the IDPAs and the unconjugated peptide (IDP 1) in phosphate buffer (the buffer was changed due to strong absorption of the normal buffers used for sample preparation). b)-d) of the unconjugated peptide. Peptide was measured in the presence of 10mM sodium acetate, and sodium phosphate buffer for pH 3.5-5.5, pH 6-7.5, respectively. CD signal present random coil spectrum for all IDPs and IDPAs which indicates unstructured peptides/ peptide amphiphiles (disordered) 1 and no secondary structure for the relevant pHs.    Figure S6. The radius of gyration extracted from the Guinier analysis at low q for the unconjugated IDP, as a function of pH. The observed slight increase in size is due to a decrease in repulsive interactions between the peptides closer to the pI, and an increase of forward scattering I0.

Free-energy
We treat the transition between the two types of the self-assembled structures in terms of the free energy related to one molecule of the amphiphile, . We assume the free-energy to be described by two competing contributions, the electrostatic free-energy, ! ( ), associated with the charge density of the peptides in headgroup region, and the bending energy, " , related to the deviations of the amphiphile monolayers constituting the micelles from their intrinsic curvature. The electrostatic energy depends on the peptide's charge, , which in turn depends on pH. The bending energy is charge independent and is set by the micellar shape only.
The transition between the spherical and cylindrical micelles is determined by the accompanied change of the system free energy, Δ ( ), which can be presented as: where Δ ! ( ) and Δ " are the corresponding variations of the electrostatic and bending energy, respectively. To compute the free-energy contributions, we follow the procedure described in Ref. 2 and adapted to the system under consideration. Figure S7 shows a schematic representation of the cross-section of the spherical and cylindrical micelles assembled by the IDPAs. The figure also details the parameters used in the model, namely, the radius of hydrophobic core , the width of the peptide shell , the charging length (used for integration), the charge density , Debye screening length in the shell and outside denoted by # and $ respectively, the dielectric constants in the core, the shell, and the outside medium, denoted by % , # and $ respectively, and the electric potential , which has to be computed. To calculate the electrostatic free-energy of the micellar shell, we perform a procedure of a step-by-step charging of the space occupied by the shell. This procedure consists of sequential charging the concentric layers of infinitesimal thickness lying one on top of the other. One step involves charging of a layer with radius, , and area, ( ) , up to a charge ( ) ( ) , within the electric field produced by the previously charged layers characterized by the electric potential, ( ). The electrostatic free-energy related to one amphiphilic molecule is given by: Here, ' is the reference plane area chosen within the amphiphilic monolayer forming the micelle and representing the micellar surface, & # is the projection area of one amphiphile molecule on the reference plane. We take the reference surface to lie on the interface between the hydrophobic core and the hydrophilic shell of a micelle.
The electrostatic potential, ( ), is found by solving the Poisson-Boltzmann equations in the three regions: the core, the shell, and outside the shell: under the following boundary conditions: To perform the calculation, the values of , and the aggregation number must be known. We extract these values from the SAXS form factor fitting, as detailed in the main text. To the first approximation, the charge density can be calculated by equally distributing the total charge of the hydrophilic domain, , over the entire volume of the micellar shell. By computing the charge, , we consider its dependence on the pH of the surrounding solution, which is different for every specific IDPA.
We describe the bending energy per amphiphile molecule, " , by the relationship 3 : where is the bending modulus of the amphiphile monolayer, is the mean curvature of the reference plane and + is the monolayer intrinsic curvature.

Computing the free-energy
Electrostatic free-energy Using the computed potential and charge density, we calculate the electrostatic free-energy using Eq. (2) for a specified salt concentration in solution.

Elastic free-energy
Computing the contribution to the total free-energy of bending (Eq. 5) is straightforward for a given intrinsic curvature, + , and bending modulus, , of the amphiphile monolayer. However, since we have no experimentally determined values of these parameters for our system, we will treat the difference in elastic free-energy between the spherical and cylindrical micelles

Non-specific peptide-peptide interactions
From the data presented in the main text, it is apparent that alternative sequences self-assembled differently, even when the net charge is kept constant. The model described in the previous section does not take into account a possible interaction between the amphiphile molecules related to the sequence specificity. Therefore, we expand the model by explicitly including the energy of this interaction into the energy balance of the micellar transition, where Δ 66 stands for the sequence-specific interaction between neighboring polyampholytes due to the distribution of charges on the peptide. Relative conformations of neighboring peptides can result in an attractive interaction, as was previously demonstrated for other intrinsically disordered proteins [4][5][6][7][8] We qualitatively model this using the "Handshake analysis", previously described in Refs. 4,5 . This analysis generates a heat-map of electrostatic interaction between different segments of interacting peptides, revealing "attractive conformations". The calculation of electrostatically interacting segments is performed by setting the peptide persistence length (PL), which determines the segment size ( amino acids are in contact in each segment), and the number of nearest neighbors (NN) that interact within that segment (each amino acid interacts with 2 + 1 amino acids from the opposite segment) The outcome of the analysis is a prediction regarding the possibility of a preferred conformation of attractively interacting peptides, as well as an approximation of the strength of the interaction. Figure    The diagonal lines that increase in strength from pH 10 to 5.5 (dark color diagonal line) are a specific shifted conformation of adjacent peptides that is favorable. In this case, a shift of about five amino acids produces attractive interaction between parallel peptides, and the strength of the interaction is approximated by the strongest contact point (darkest square on the diagonal). Using these values, we can approximate the dependence of the handshake interaction on pH (bottom right panel of Figure S8-S9). Mapping this dependence is useful for assessing the contribution of the conformation-specific interaction to the overall interaction leading to the phase-transition, at least semi-quantitatively.

Sequence variants
When considering the sensitivity of the phase to pH, and more specifically, the phase-transition being located somewhere between pH 4 and 6, a possible explanation can be the histidine residue's charging state.
Histidine is the only amino acid with a side chain group that gets protonated in this pH range.
We used the handshake analysis tool to design slightly modified headgroup sequences and predict their behavior of interaction. Two variants of the original sequence were produced: IDPA2 -swapping the it will no longer have an additional positive charge below pH 6. IDPA2, on the other hand, retains the same total (and net) charge, but has a different distribution of charges along the sequence.
The handshake analysis also predicts a weaker interaction for the same conformation chosen for the original sequence ( Figure ). The IDPA2 variation was predicted by the analysis to abolish the favorable interaction of the conformation seen in the original (Figure ). Figure S16 The handshake analysis, with PL = 2 and NN = 1, for the IDPA3 sequence. The interaction energy is weaker than for the original sequence, and there is no longer a minimum around pH 5.5. The color bar indicates the interaction strength in kBT300K. The bottom right graph shows our approximation of the strength of interaction at each pH, chosen to be the strongest point of attractive interaction (marked in red on the heat-maps). Figure S17. The handshake analysis, with PL = 2 and NN = 1, for the IDPA2 sequence. The switching has abolished the attractive conformation from the original sequence. The color bar indicates the interaction strength in kBT300K. The bottom right graph shows our approximation of the strength of interaction at each pH, chosen to be the strongest point of attractive interaction (marked in red on the heat-maps).
Both of these variants are still considered highly disordered and are assigned the random coil conformation by the bioinformatic predictors ( figure S4).