title: Multiple coupled landscapes and non-adiabatic dynamics with applications to self-activating genes.
abstract: Many physical, chemical and biochemical systems (e.g. electronic dynamics and gene regulatory networks) are governed by continuous stochastic processes (e.g. electron dynamics on a particular electronic energy surface and protein (gene product) synthesis) coupled with discrete processes (e.g. hopping among different electronic energy surfaces and on and off switching of genes). One can also think of the underlying dynamics as the continuous motion on a particular landscape and discrete hoppings among different landscapes. The main difference of such systems from the intra-landscape dynamics alone is the emergence of the timescale involved in transitions among different landscapes in addition to the timescale involved in a particular landscape. The adiabatic limit when inter-landscape hoppings are fast compared to continuous intra-landscape dynamics has been studied both analytically and numerically, but the analytical treatment of the non-adiabatic regime where the inter-landscape hoppings are slow or comparable to continuous intra-landscape dynamics remains challenging. In this study, we show that there exists mathematical mapping of the dynamics on 2(N) discretely coupled N continuous dimensional landscapes onto one single landscape in 2N dimensional extended continuous space. On this 2N dimensional landscape, eddy current emerges as a sign of non-equilibrium non-adiabatic dynamics and plays an important role in system evolution. Many interesting physical effects such as the enhancement of fluctuations, irreversibility, dissipation and optimal kinetics emerge due to non-adiabaticity manifested by the eddy current illustrated for an N = 1 self-activator. We further generalize our theory to the N-gene network with multiple binding sites and multiple synthesis rates for discretely coupled non-equilibrium stochastic physical and biological systems.
authors.affiliation: Physics Department, Stony Brook University, NY 11794, USA. jin.wang.1@stonybrook.edu.
authors.forename: Cong
authors.initials: C
authors.lastname: Chen
authors.affiliation: State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, Jilin 130022, China.
authors.forename: Kun
authors.initials: K
authors.lastname: Zhang
authors.affiliation: Chemistry Department, Stony Brook University, NY 11794, USA.
authors.forename: Haidong
authors.initials: H
authors.lastname: Feng
authors.affiliation: Department of Computational Science and Engineering, Nagoya University, Nagoya 464-8603, Japan. sasai@cse.nagoya-u.ac.jp.
authors.forename: Masaki
authors.initials: M
authors.lastname: Sasai
authors.affiliation: Physics Department, Stony Brook University, NY 11794, USA. jin.wang.1@stonybrook.edu and Chemistry Department, Stony Brook University, NY 11794, USA.
authors.forename: Jin
authors.initials: J
authors.lastname: Wang
mesh_terms: D001665:Binding Sites; D053263:Gene Regulatory Networks; D008962:Models, Theoretical; D011506:Proteins / Q000235:genetics* / Q000378:metabolism; D013816:Thermodynamics
chemical_list: D011506:Proteins