Variational Percolation Bounds for Cellular Membrane Occlusion
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arXiv
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| Format: | Preprint |
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2025
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| author | Mello, Cesar da Cunha, Fernando Medina |
| author_facet | Mello, Cesar da Cunha, Fernando Medina |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_00304 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Variational Percolation Bounds for Cellular Membrane Occlusion Mello, Cesar da Cunha, Fernando Medina Medical Physics 35P20, 58J50, 55N31, 82B43, 82C31 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. |
| title | Variational Percolation Bounds for Cellular Membrane Occlusion |
| topic | Medical Physics 35P20, 58J50, 55N31, 82B43, 82C31 |
| url | https://arxiv.org/abs/2511.00304 |