Quantum chemical modelling of sequence encoded energetics and electrostatic landscapes governing early peptide association in α- synuclein and amyloid β

Technical Summary: Quantum Chemical Modelling of Sequence Encoded Energetics and Electrostatic Landscapes in Early Peptide Association

Problem Statement
Protein misfolding and aggregation are central to neurodegenerative disorders such as Parkinson's disease (PD) and Alzheimer's disease (AD), driven by the early molecular association of peptides like $\alpha$-synuclein and amyloid $\beta$ (A$\beta$). While experimental studies have characterized the kinetics and structures of mature fibrils, the energetic contributions of individual molecular configurations during the transient, heterogeneous early stages of association remain poorly resolved. A critical gap exists in understanding how the specific linear order of residues (sequence), distinct from the overall amino acid composition, shapes the molecular properties governing these initial association events. This study aims to isolate the contribution of sequence arrangement by comparing aggregation-prone peptide segments with composition-matched scrambled controls, thereby determining how residue order influences energetics, structural organization, and electrostatic landscapes.

Methodology
The study employs a consistent computational workflow integrating semi-empirical quantum chemistry and density functional theory (DFT) to model monomer and homodimer states.

• Systems: Aggregation-prone segments ($\alpha$-synuclein: VTGVTAVAQK; A$\beta$: LVFFAEDVGS) were compared against composition-matched scrambled controls (AGATQTVVVK and EFLVGSDVAF, respectively).
• Geometry Optimization: Monomer and homodimer structures were optimized using the GFN2-xTB method (Geometry, Frequency, Noncovalent extended Tight Binding, second generation) implemented in xTB. Dimer structures were initially relaxed using the GFN force field before final optimization.
• Energetics: Association energies ($\Delta E_{assoc}$) were calculated as the difference between the converged GFN2-xTB electronic energy of the optimized dimer and twice the energy of the independently optimized monomer.
• Electronic Structure Analysis: DFT calculations were performed on optimized monomers using GPAW with the PBE exchange-correlation functional and Projector Augmented Wave (PAW) formalism on a real-space grid (0.20 Å spacing).
• Descriptors:
  • Electrostatics: Molecular Electrostatic Potential (ESP) was mapped onto electron density surfaces (0.001 e Bohr$^{-3}$) and analyzed via mean-centering to visualize relative landscapes.
  • Charge Distribution: Hirshfeld population analysis was used to quantify atom-resolved charge distributions, including statistical metrics (mean, median, standard deviation) and residue-resolved sums.
  • Structural/Sequence: Descriptors included sequence charge decoration (SCD), local hydropathy, hydrophobic run length, radius of gyration ($R_g$), end-to-end distance, and asphericity.
  • Interface: Intermolecular contacts were quantified by heavy atom distances ($\le$ 4.5 Å and 5.0 Å) and specific N/O/S contacts ($\le$ 3.5 Å).

Key Results
The study reveals that residue rearrangement produces distinct, peptide-specific responses in both energetic and structural domains, despite conserved amino acid composition.

1. Monomer Energetics: Residue order significantly altered the electronic energy of the isolated monomers. For A$\beta$, the scrambled control was lower in energy by ~45.33 kJ/mol compared to the aggregation-prone sequence. Conversely, for $\alpha$-synuclein, the aggregation-prone sequence was lower in energy by ~151.12 kJ/mol compared to its scrambled control.
2. Association Energetics vs. Interface Packing:
   • A$\beta$: Both the aggregation-prone sequence (115.617 kJ/mol) and the scrambled control (232.552 kJ/mol) exhibited positive association energies, indicating that the optimized dimers were higher in electronic energy than the independently optimized monomers. However, the aggregation-prone sequence showed a lower positive association energy (by 116.935 kJ/mol) than the scrambled control. Paradoxically, this sequence formed fewer heavy atom contacts (40 vs. 81) and had a lower contact density than the control.
   • $\alpha$-Synuclein: The scrambled control exhibited a more favorable (more negative) association energy (-494.371 kJ/mol) than the aggregation-prone sequence (-172.819 kJ/mol), with a difference of 321.552 kJ/mol. However, the aggregation-prone sequence formed a more extensive interface, with 166 heavy atom contacts (vs. 105) and a higher density of close N/O/S contacts (15 vs. 5).
   • Conclusion: Association energy and interface packing (contact number/density) do not vary linearly; they represent complementary, not equivalent, measures of association.
3. Electrostatic Landscapes (ESP): Residue rearrangement reorganized the spatial distribution of ESP. While A$\beta$ and $\alpha$-synuclein pairs shared similar global charge states, the specific spatial organization of positive and negative potential regions shifted significantly between aggregation-prone and scrambled sequences. This indicates that sequence order dictates the 3D presentation of electrostatic character.
4. Hirshfeld Charge Distributions: Atomic charge analysis showed that residue rearrangement primarily redistributed atomic charge populations rather than uniformly shifting global charge magnitudes. In $\alpha$-synuclein, the proportion of positive/negative atoms remained nearly constant, but the probability distributions of charge values shifted. In A$\beta$, a modest shift in the balance of positive/negative atoms was observed alongside redistribution.
5. Sequence and Structural Descriptors:
   • A$\beta$: Rearrangement altered sequence charge decoration (SCD), hydrophobic run length (5 residues vs. 3), and molecular compactness, with the aggregation-prone peptide exhibiting an $R_g$ of approximately 10.1 Å compared to approximately 11.0 Å for the scrambled control.
   • $\alpha$-Synuclein: Rearrangement primarily altered local hydropathy (maximum 3-residue mean hydropathy increased from ~2.6 to ~4.2 in the control), while SCD, $R_g$, and asphericity remained comparable.

Significance and Claims
The paper establishes that residue order is a fundamental determinant of early peptide association, independent of amino acid composition. The study demonstrates that identical compositions can generate distinct energetic, structural, and electrostatic characteristics solely through sequence-dependent molecular organization.

Key claims include:

• Sequence as a Determinant: The arrangement of residues, not just the composition, governs the balance of intermolecular interactions, influencing both the thermodynamics of association and the geometry of the resulting interface.
• Peptide-Specific Responses: The molecular consequences of residue rearrangement are not universal; $\alpha$-synuclein and A$\beta$ exhibit contrasting responses where changes in sequence order lead to different combinations of energetic favorability and interface packing.
• Complementary Descriptors: The study highlights that association energy and interface contact metrics capture different aspects of molecular association. A more populated interface does not necessarily correlate with a more favorable association energy, as seen in the divergent trends between the two peptide systems.
• Electrostatic Reorganization: Identical amino acid compositions can yield distinct electrostatic environments due to the reorganization of charge patterning and 3D structure, providing a molecular basis for sequence-specific association behaviors.

The work provides a quantitative framework for identifying sequence-encoded molecular determinants, suggesting that the "code" for early aggregation lies in the specific linear ordering of residues which dictates the resulting energetic and electrostatic landscapes.