Self-Assembly of Insulin-Derived Chimeric Peptides into Two-Component Amyloid Fibrils: The Role of Coulombic Interactions

Canonical amyloid fibrils are composed of covalently identical polypeptide chains. Here, we employ kinetic assays, atomic force microscopy, infrared spectroscopy, circular dichroism, and molecular dynamics simulations to study fibrillization patterns of two chimeric peptides, ACC1–13E8 and ACC1–13K8, in which a potent amyloidogenic stretch derived from the N-terminal segment of the insulin A-chain (ACC1–13) is coupled to octaglutamate or octalysine segments, respectively. While large electric charges prevent aggregation of either peptide at neutral pH, stoichiometric mixing of ACC1–13E8 and ACC1–13K8 triggers rapid self-assembly of two-component fibrils driven by favorable Coulombic interactions. The low-symmetry nonpolar ACC1–13 pilot sequence is crucial in enforcing the fibrillar structure consisting of parallel β-sheets as the self-assembly of free poly-E and poly-K chains under similar conditions results in amorphous antiparallel β-sheets. Interestingly, ACC1–13E8 forms highly ordered fibrils also when paired with nonpolypeptide polycationic amines such as branched polyethylenimine, instead of ACC1–13K8. Such synthetic polycations are more effective in triggering the fibrillization of ACC1–13E8 than poly-K (or poly-E in the case of ACC1–13K8). The high conformational flexibility of these polyamines makes up for the apparent mismatch in periodicity of charged groups. The results are discussed in the context of mechanisms of heterogeneous disease-related amyloidogenesis.


Estimation of the persistence length of fibrils
We estimated the persistence length, p, using formula where E is an end-to-end distance on a two-dimensional surface (2D) of the fibril and c denotes its contour length [1]. E and c were traced measured using SNT module in Fiji software [2,3]. The input data were taken from AFM images collected in this work.
These estimations of the persistence length must be approached cautiously. The fibrillar species probed by AFM in this study tend to be agglomerated, hence they, as individual specimens, may often not reach the state of mechanical relaxation. The calculated values appear to suggest that the ACC 1-13 E 8 -ACC 1-13 K 8 fibrils are distinct in terms of structural stiffness among all three coaggregates.

MMPBSA (Molecular Mechanics -Poisson-Boltzmann Surface Area) calculations
We have employed MMPBSA (Molecular Mechanics Poissson Boltzmann Surface Area) method to estimate the binding energy of the alternate ACC 1-13 E 8 -ACC 1-13 K 8 assembly. The binding free energy, ΔG, between a single layer of ACC 1-13 E 8 (E) and a consecutive layer of ACC 1-13 K 8 (K) is calculated as: i.e., as the difference between the respective free energies of the complex, G EK , and its components, G E , G K . The MMPBSA approximates these terms with molecular mechanics (force field) energy, E MM, and implicit solvation effects, G sol : where T denotes temperature and S MM is an estimation of the entropy.
To this end, we have employed MMPBSA.py script from AmberTools22 [4][5] with the default parameters. We have carried out calculations for a pair of adjacent layers, e.g. layer no. 3 and 4, serving as the 'complex', layer no. 3 served as a 'receptor' and layer no. 4 served as a 'ligand'. In the following step, the two subsequent pairs were considered and an average value is computed. As the symmetry of the fibril imposes periodic effects, we also employ similar scheme for 4 layers, 6, etc. until 16. The two outermost layers in the 20 layer assembly (no. 1, 2, 19, 20) were discarded from computations because of plausible boundary effects. 1500 evenly spaced snapshots were extracted from the second half (3 x 250 -500 ns) of the MD simulations (see the main article) and they were further used to conduct computations.
Entropy calculations carried out with normal mode approximation converge slowly and are very demanding in terms of computational time [6][7]. Therefore, we report here entropies computed using the quasi-harmonic estimation [8]. For the two layers of ACC 1-13 E 8 -ACC 1-13 K 8 , the estimated entropy of binding is such that TΔS 2 = -96.90 ± 8.76 kcal/mol. We assume that entropy loss associated with binding of four or more alternate layers can be approximated by multiplying the ΔS 2 by the appropriate number of pairs, n: The free energy of binding, ΔG = ΔH -TΔS, can be normalized per the number of pairs: where ΔH is the enthalpy calculated for 2 or more pairs. We note that according to these calculations the net thermodynamic stability of ACC 1-13 E 8 -ACC 1-13 K 8 aggregate is reached for at least three ACC 1-13 E 8 -ACC 1-13 K 8 co-assembling pairs.