2010/11/11 by Yunxin Zhang, Zhang, Yunxin, Hao Ge +3
Physics and Astronomy · Chemistry · #Advanced Thermodynamics and Statistical Mechanics #thermodynamics and calorimetric analyses #Spectroscopy and Quantum Chemical Studies
paper · pdf · doi:10.48550/arxiv.1011.2554
Multistability of mesoscopic, driven biochemical reaction systems has implications to a wide range of cellular processes. Using several simple models, we show that one class of bistable chemical systems has a deterministic counterpart in the nonlinear dynamics based on the Law of Mass Action, while another class, widely known as noise-induced stochastic bistability, does not. Observing the system's volume (V) playing a similar role as the inverse temperature (β) in classical rate theory, an van't Hoff-Arrhenius like analysis is introduced. In one-dimensional systems, a transition rate between two states, represented in terms of a barrier in the landscape for the dynamics Φ(x,V), k∝exp\-VΔΦ^‡(V)\, can be understood from a decomposition ΔΦ^‡(V) ≈Δϕ0^‡ Δϕ1^‡/V. Nonlinear bistability means Δϕ0^‡>0 while stochastic bistability has Δϕ0^‡<0 but Δϕ1^‡>0. Stochastic bistabilities can be viewed as remants (or "ghosts) of nonlinear bifurcations or extinction phenomenon, and Δϕ0^‡ and Δϕ1^‡ as "enthalpic" and "entropic" barriers to a transition.