2009/01/31 by Golan Bel, Ilya Nemenman · 1 citation
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Gene Regulatory Network Analysis #cond-mat.stat-mech #q-bio.MN #q-bio.QM #stochastic dynamics and bifurcation
paper · pdf · doi:10.1088/1367-2630/11/8/083009
published as New J. Phys. 11, 083009 (2009)
openalex publication_date 2009/08/12 · arxiv created 2009/08/13 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
Inspired by problems in biochemical kinetics, we study statistical properties of an overdamped Langevin process whose friction coefficient depends on the state of a similar, unobserved process. Integrating out the latter, we derive the long-time behavior of the mean square displacement. Anomalous diffusion is found. Since the diffusion exponent cannot be predicted using a simple scaling argument, anomalous scaling appears as well. We also find that the coupling can lead to ergodic or non-ergodic behavior of the studied process. We compare our theoretical predictions with numerical simulations and find an excellent agreement. The findings caution against treating biochemical systems coupled with unobserved dynamical degrees of freedom by means of standard, diffusive Langevin descriptions.