Spectral Topology Meets Mathematical Chemistry From Invariants to Innovation in Prodrug Discovery

Abstract Malignant cells sustain growth and therapy resistance by overexpressing nutrient transporters (GLUT1/3, LAT1, ASCT2, MCT1/4) within aberrantly glycosylated membranes. These carriers assemble into a redundant influx–efflux lattice, such that inhibition of one pathway is rapidly bypassed, rendering conventional blockade ineffective. Here we adapt the principle of topological replica neutralization, originally formulated in condensed-matter physics, to metabolic oncology. In topological systems, inversion of polarization generates a replica with opposite Euler class; superposition cancels global invariants and destabilizes protected modes. Inspired by this mechanism, we design a biochemical inverse replica that neutralizes malignant redundancy at its structural root. The strategy employs a branched polyethylene glycol scaffold bearing sulfonates (Cap--PEG--SO₃⁻). Sulfonate termini provide electrostatic anchoring to Lys/Arg-rich membrane patches, while the PEG backbone enforces steric occlusion, coherently reducing conductance across transporter families. Scaffold sulfonation was validated by FTIR, NMR, and mass spectrometry, and PEGylation ensures solubility and compatibility. Modeling shows that this dual mechanism enforces global contraction Vmax,i↦(1-θᵢ)Vmax,i, driving Qₙₒᵣₘ:1\!→ 0—a biochemical realization of Euler-class cancellation. Within the spectral--topological model, redundancy appears as a meronic half-covering (Q=1/2) that resists local perturbations. Global capping trivializes e(E⁾=0, annihilating the invariant stabilizing robustness. The framework predicts a critical occlusion θc at which Q collapses discretely while flux decays smoothly, with elasticities Eθᵢ[Jₜₒₜ]≈ -wᵢ([S]). Thus, malignant resilience is reframed as a geometric obstruction rather than kinetic surplus. Linking characteristic-class mathematics with scaffold engineering, this work outlines a translational paradigm: inverse replicas for neutralizing pathological transport.