Gain of Entrainment in Ribosome Flow Models with Nonlinear Steric Hindrance: Global Rigidity and Dimension-Induced Gai
Abstract
The ribosome flow model (RFM) is a nonlinear compartmental model for unidirectional transport along an mRNA chain. We study a generalized RFM in which the classical linear free-space factor is replaced by a monotone nonlinear steric-hindrance response. After recalling the global equilibrium and periodic entrainment properties needed for the analysis, we derive an exact weighted edge-dissipation identity for the gain of entrainment (GOE). This yields a global no-GOE criterion formulated through the curvature of the nonlinear hindrance law. In particular, the quadratic hindrance model admits no positive GOE in any dimension and for arbitrary periodic forcing amplitudes, with equality only when all rates share a common multiplicative modulation. In one dimension, we obtain a sharp convexity-based classification and construct positive-GOE examples when the relevant convexity fails. In higher dimensions, the second variation is governed by a symmetric Jacobi matrix whose diagonal terms encode local curvature and whose off-diagonal entries represent nearest-neighbor transport coupling. This leads to an exact Riccati criterion, a dimension-uniform condition for heterogeneous chains, and a closed-form critical dimension in the homogeneous case. We also exhibit a nonlinear hindrance for which low-dimensional chains have no positive second-order GOE, while a higher-dimensional chain admits a realizable positive GOE. These results reveal a dimension-induced gain mechanism that is absent from the classical RFM.
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BibTeX
@misc{zhou2026gain,
title = {{Gain of Entrainment in Ribosome Flow Models with Nonlinear Steric Hindrance: Global Rigidity and Dimension-Induced Gai}},
author = {Hui Zhou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10602},
eprint = {2610.10602},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10602},
}
RIS
TY - UNPB
TI - Gain of Entrainment in Ribosome Flow Models with Nonlinear Steric Hindrance: Global Rigidity and Dimension-Induced Gai
AU - Hui Zhou
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10602
UR - https://arxiv.org/abs/2610.10602
AB - The ribosome flow model (RFM) is a nonlinear compartmental model for unidirectional transport along an mRNA chain. We study a generalized RFM in which the classical linear free-space factor is replaced by a monotone nonlinear steric-hindrance response. After recalling the global equilibrium and periodic entrainment properties needed for the analysis, we derive an exact weighted edge-dissipation identity for the gain of entrainment (GOE). This yields a global no-GOE criterion formulated through the curvature of the nonlinear hindrance law. In particular, the quadratic hindrance model admits no positive GOE in any dimension and for arbitrary periodic forcing amplitudes, with equality only when all rates share a common multiplicative modulation. In one dimension, we obtain a sharp convexity-based classification and construct positive-GOE examples when the relevant convexity fails. In higher dimensions, the second variation is governed by a symmetric Jacobi matrix whose diagonal terms encode local curvature and whose off-diagonal entries represent nearest-neighbor transport coupling. This leads to an exact Riccati criterion, a dimension-uniform condition for heterogeneous chains, and a closed-form critical dimension in the homogeneous case. We also exhibit a nonlinear hindrance for which low-dimensional chains have no positive second-order GOE, while a higher-dimensional chain admits a realizable positive GOE. These results reveal a dimension-induced gain mechanism that is absent from the classical RFM.
ER -