{"paper":{"title":"Target Search of a Protein on DNA in the Presence of Position-dependent Bias","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Jinqiao Duan, Xi Chen, Xiujun Cheng, Yanmei Kang","submitted_at":"2018-09-29T07:46:56Z","abstract_excerpt":"We study the target searching on the DNA for proteins in the presence of non-constant drift and non-Gaussian $\\alpha$-stable L\\'evy fluctuations. The target searching is realized by the facilitated diffusion process. The existing works are about this problem in the case of constant drift. Starting from a non-local Fokker-Planck equation with a \"sink\" term, we obtain the possibility density function for the protein occurring at position $x$ on time $t$. Based on this, we further compute the survival probability and the first arrival density in order to quantify the searching mechanisms. The num"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00166","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}