Variational Percolation Bounds for Cellular Membrane Occlusion

TL;DR

The paper develops a membrane-centered, three-layer framework linking interfacial chemistry to multichannel nutrient transport and energetic redox balance in malignant membranes. It combines a screened Poisson–Nernst–Planck electrodiffusion model, an interfacial potential of mean force, and a reduced ATP/NADPH network to derive a capacitary–spectral bound: $J_{\rm tot} \le C\,e^{-\beta\chi_{\rm eff}}\,P(\theta)$, with two orthogonal design levers $\theta$ (geometric coverage) and $\chi_{\rm eff}$ (interfacial field) and a percolation knee at $\theta=\eta_c$. The authors prove existence, regularity, and spectral monotonicity for the self-adjoint PNP operator, and map molecular design parameters (branching, sulfonation) to macroscopic flux and metabolic outcomes, enabling a predictive safety window. They further integrate a two-stage CAP–prodrug strategy to couple transport suppression to energetic collapse and irreversible commitment, offering a falsifiable, chemistry-driven route to selectively target malignant membranes while preserving normal tissue function. The framework provides a rigorous link between molecular interfacial design and macroscopic phenotypes (flux, ATP/NADPH, ROS) with potential implications for therapeutic strategies exploiting multichannel occlusion and interfacial field tuning.

Abstract

Malignant membranes cluster nutrient transporters within glycan-rich domains, sustaining metabolism through redundant intake routes. A theoretical framework links interfacial chemistry to transport suppression and energetic or redox collapse. The model unites a screened Poisson-Nernst-Planck electrodiffusion problem, an interfacial potential of mean force, and a reduced energetic-redox module connecting flux to ATP/NADPH balance. From this structure, capacitary-spectral bounds relate total flux to the inverse principal eigenvalue (J_tot <= C*exp(-beta*chi_eff)*P(theta)). Two near-orthogonal levers, geometry and field strength, govern a linear suppression regime below a percolation-type knee, beyond which conductance collapses. A composite intake index Xi = w_G*J_GLUT + w_A*J_LAT/ASCT + w_L*J_MCT dictates energetic trajectories: once below a maintenance threshold, ATP and NADPH fall jointly and redox imbalance drives irreversible commitment. Normal membranes, with fewer transport mouths and weaker fields, remain above this threshold, defining a natural selectivity window. The framework demonstrates existence, regularity, and spectral monotonicity for the self-adjoint PNP operator, establishing a geometric-spectral transition that links molecular parameters such as branching and sulfonation to measurable macroscopic outcomes with predictive precision.

Figures (5)

• Figure 1: Screened electro-diffusion near occluded pores. A membrane band with alternating absorbing mouths and CAP-occluded mouths ($c_k{=}0$, $\phi{=}\psi_s$). The interfacial field decays over $\lambda_D$.
• Figure 2: Interfacial interaction manifold at a glycan–transporter cluster. A branched PEG–SO$_3^-$ cap generates a composite potential-of-mean-force, stabilizing residence and narrowing access.
• Figure 3: Modeled viability and apoptotic trajectory under CAP blockade. Malignant profiles (red) display irreversible decline; non-malignant controls (grey) show partial recovery. Vertical markers denote energetic/redox and mitochondrial transitions.
• Figure 4: Flux-suppression landscape. Left: exponential decline of normalized flux with increasing $\chi_{\mathrm{eff}}$. Right: time-to-50% ATP drop versus $\theta$, with a percolation-type knee at $\eta_c$.
• Figure 5: Linear coupling between transport suppression and energetic/redox state. Left: ATP and NADPH versus $\Xi$. Right: time-to-50% ATP drop versus $\theta$, showing near-linear slopes in the controllable region.