Predicting aqueous solubility (log S), co-crystallization, and solvation dynamics remains one of the formidable bottlenecks in drug discovery, formulation engineering, and physical chemistry. Conventional approaches rely either on computationally expensive quantum mechanical methods (DFT/MD) or black-box machine learning models (e.g., Graph Neural Networks / QSAR) that lack physical interpretability. Here, we present a novel, explainable Spectral Graph Theory framework that predicts multi-solvent solubility and solvation structures at O(N log N) computational complexity. By integrating 3D water lone-pair tetrahedral geometry (109.5°) into a normalized graph Laplacian L_norm, our model calculates the Fiedler value (λ2)—the second smallest eigenvalue measuring algebraic connectivity—to quantify hydration shell ordering and micro-solvation free energy. Furthermore, by coupling Fiedler phase complementarity (vi · vj < 0) with Kabsch Singular Value Decomposition (SVD), optimal dimer/solvent orientations are determined analytically without grid searching. We introduce the Fiedler Crystallization Anomaly Index (FCAI) to disentangle micro-hydration attraction from solid-state crystal lattice packing penalties. Finally, we formulate Inverse Spectral Tomography, demonstrating that an unknown solute’s functional groups and molecular architecture can be reconstructed within seconds from an 8-solvent solubility fingerprint vector (y_exp ∈ R^8). Validated across benchmark pharmaceuticals (Carbamazepine, Nicotinamide, D-Mannitol) and diverse organic solvents, this framework establishes a unified graph-spectral theory bridging molecular structure, solvent percolation, and thermodynamic solubility. Keywords: Molecular Solubility, Spectral Graph Theory, Fiedler Value, Water Lone-Pair Geometry, Kabsch SVD Alignment, Inverse Spectral Tomography, Drug Discovery.
Yoshihiro Honda· Zenodo (CERN European Organi...· 0 citations
Predicting aqueous solubility (log S), co-crystallization, and solvation dynamics remains one of the formidable bottlenecks in drug discovery, formulation engineering, and physical chemistry. Conventional approaches rely either on computationally expensive quantum mechanical methods (DFT/MD) or black-box machine learning models (e.g., Graph Neural Networks / QSAR) that lack physical interpretability. Here, we present a novel, explainable Spectral Graph Theory framework that predicts multi-solvent solubility and solvation structures at O(N log N) computational complexity. By integrating 3D water lone-pair tetrahedral geometry (109.5°) into a normalized graph Laplacian L_norm, our model calculates the Fiedler value (λ2)—the second smallest eigenvalue measuring algebraic connectivity—to quantify hydration shell ordering and micro-solvation free energy. Furthermore, by coupling Fiedler phase complementarity (vi · vj < 0) with Kabsch Singular Value Decomposition (SVD), optimal dimer/solvent orientations are determined analytically without grid searching. We introduce the Fiedler Crystallization Anomaly Index (FCAI) to disentangle micro-hydration attraction from solid-state crystal lattice packing penalties. Finally, we formulate Inverse Spectral Tomography, demonstrating that an unknown solute’s functional groups and molecular architecture can be reconstructed within seconds from an 8-solvent solubility fingerprint vector (y_exp ∈ R^8). Validated across benchmark pharmaceuticals (Carbamazepine, Nicotinamide, D-Mannitol) and diverse organic solvents, this framework establishes a unified graph-spectral theory bridging molecular structure, solvent percolation, and thermodynamic solubility. Keywords: Molecular Solubility, Spectral Graph Theory, Fiedler Value, Water Lone-Pair Geometry, Kabsch SVD Alignment, Inverse Spectral Tomography, Drug Discovery.
Yoshihiro Honda· Zenodo (CERN European Organi...· 0 citations
Protein folding is traditionally described as a trajectory over a complex energy landscape governed by empirical physical forcefields (electrostatics, van der Waals, torsional potentials, and implicit/explicit solvent interactions). However, evaluating all atomic force interactions demands massive computational power, and long-standing questions remain regarding how peptides efficiently navigate the vast conformational space (Levinthal’s paradox) to reach their native structures. Here, we present a forcefield-free, graph-spectral paradigm for peptide folding. By mapping a peptide and its hydration shell onto a weighted graph, we demonstrate that protein self-assembly can be driven solely by maximizing the Fiedler value (λ2)—the second smallest eigenvalue of the graph Laplacian matrix, which measures algebraic connectivity. Incorporating a Contact-Locking mechanism to model topological cooperativity, our algorithm successfully folds the benchmark 10-residue peptide Chignolin (PDB ID: 1UAO) into its native β-hairpin conformation with a radius of gyration (Rg ≈ 5.12–5.29 Å) closely matching experimental values (5.17 Å) without calculating any potential energy. Furthermore, by introducing a Polar-Priority Phase Model, we quantitatively reproduce the classical "Framework Model" of biophysics, wherein backbone hydrogen-bond scaffolds form prior to hydrophobic packing. We extend this model to the stabilized variant CLN025 and the 20-residue Trp-cage (PDB ID: 1L2Y), achieving less than 1.9% error in compaction. Finally, we establish a theoretical duality between solvent Fiedler maximization and Proton-Coupled Electron Transfer (PCET) pathways (Proton Wires). This graph-spectral framework provides a novel alternative to molecular dynamics (MD) simulations and establishes λ2 as a fundamental topological reaction coordinate in structural biology. Keywords: Protein Folding, Spectral Graph Theory, Fiedler Value, Algebraic Connectivity, Contact-Locking, Chignolin, Framework Model, Solvent Network.
Yoshihiro Honda· Zenodo (CERN European Organi...· 0 citations
Protein folding is traditionally described as a trajectory over a complex energy landscape governed by empirical physical forcefields (electrostatics, van der Waals, torsional potentials, and implicit/explicit solvent interactions). However, evaluating all atomic force interactions demands massive computational power, and long-standing questions remain regarding how peptides efficiently navigate the vast conformational space (Levinthal’s paradox) to reach their native structures. Here, we present a forcefield-free, graph-spectral paradigm for peptide folding. By mapping a peptide and its hydration shell onto a weighted graph, we demonstrate that protein self-assembly can be driven solely by maximizing the Fiedler value (λ2)—the second smallest eigenvalue of the graph Laplacian matrix, which measures algebraic connectivity. Incorporating a Contact-Locking mechanism to model topological cooperativity, our algorithm successfully folds the benchmark 10-residue peptide Chignolin (PDB ID: 1UAO) into its native β-hairpin conformation with a radius of gyration (Rg ≈ 5.12–5.29 Å) closely matching experimental values (5.17 Å) without calculating any potential energy. Furthermore, by introducing a Polar-Priority Phase Model, we quantitatively reproduce the classical "Framework Model" of biophysics, wherein backbone hydrogen-bond scaffolds form prior to hydrophobic packing. We extend this model to the stabilized variant CLN025 and the 20-residue Trp-cage (PDB ID: 1L2Y), achieving less than 1.9% error in compaction. Finally, we establish a theoretical duality between solvent Fiedler maximization and Proton-Coupled Electron Transfer (PCET) pathways (Proton Wires). This graph-spectral framework provides a novel alternative to molecular dynamics (MD) simulations and establishes λ2 as a fundamental topological reaction coordinate in structural biology. Keywords: Protein Folding, Spectral Graph Theory, Fiedler Value, Algebraic Connectivity, Contact-Locking, Chignolin, Framework Model, Solvent Network.
Yoshihiro Honda· Zenodo (CERN European Organi...· 0 citations
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