scholarly journals Lyapunov Functions, Stationary Distributions, and Non-equilibrium Potential for Reaction Networks

2015 ◽  
Vol 77 (9) ◽  
pp. 1744-1767 ◽  
Author(s):  
David F. Anderson ◽  
Gheorghe Craciun ◽  
Manoj Gopalkrishnan ◽  
Carsten Wiuf
Keyword(s):  
Lyapunov Functions ◽  
Equilibrium Potential ◽  
Reaction Networks ◽  
Stationary Distributions ◽  
Non Equilibrium

scholarly journals Parasitic Behavior in Competing Chemically Fueled Reaction Cycles

2021 ◽  
Author(s):  
Patrick S. Schwarz ◽  
Sudarshana Laha ◽  
Jacqueline Janssen ◽  
Tabea Huss ◽  
Job Boekhoven ◽  
...  
Keyword(s):  
Dynamic Behavior ◽  
Model Systems ◽  
Reaction Networks ◽  
Reaction Cycles ◽  
Non Equilibrium

Non-equilibrium, fuel-driven reaction cycles serve as model systems of the intricate reaction networks of life. Rich and dynamic behavior is observed when reaction cycles regulate assembly processes, such as phase...

scholarly journals Derivation of stationary distributions of biochemical reaction networks via structure transformation

2021 ◽  
Author(s):  
Hyukpyo Hong ◽  
Jinsu Kim ◽  
M Ali Al-Radhawi ◽  
Eduardo D. Sontag ◽  
Jae Kyoung Kim
Keyword(s):  
Stochastic Dynamics ◽  
Steady States ◽  
Biochemical Reaction ◽  
Reaction Networks ◽  
Toggle Switch ◽  
Biochemical Reaction Networks ◽  
Deterministic Models ◽  
Stationary Distributions ◽  
User Friendly

Long-term behaviors of biochemical reaction networks (BRNs) are described by steady states in deterministic models and stationary distributions in stochastic models. Unlike deterministic steady states, stationary distributions capturing inherent fluctuations of reactions are extremely difficult to derive analytically due to the curse of dimensionality. Here, we develop a method to derive analytic stationary distributions from deterministic steady states by transforming BRNs to have a special dynamic property, called complex balancing. Specifically, we merge nodes and edges of BRNs to match in- and out-flows of each node. This allows us to derive the stationary distributions of a large class of BRNs, including autophosphorylation networks of EGFR, PAK1, and Aurora B kinase and a genetic toggle switch. This reveals the unique properties of their stochastic dynamics such as robustness, sensitivity and multi-modality. Importantly, we provide a user-friendly computational package, CASTANET, that automatically derives sym- bolic expressions of the stationary distributions of BRNs to understand their long-term stochasticity.

scholarly journals Non-Boltzmann stationary distributions and non-equilibrium relations in active baths

2017 ◽  
Author(s):  
Aykut Argun ◽  
Ali-Reza Moradi ◽  
Erçağ Pinçe ◽  
Gokhan Baris Bagci ◽  
Alberto Imparato ◽  
...  
Keyword(s):  
Stationary Distributions ◽  
Non Equilibrium

scholarly journals Chemical Basis of Biological Homochirality during the Abiotic Evolution Stages on Earth

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 814 ◽  
Author(s):  
Josep M. Ribó ◽  
David Hochberg
Keyword(s):  
Symmetry Breaking ◽  
Chemical Evolution ◽  
Mirror Symmetry ◽  
Reaction Network ◽  
Reaction Networks ◽  
Stationary States ◽  
Cell Systems ◽  
Basic Model ◽  
Stochastic Distribution ◽  
Non Equilibrium

Spontaneous mirror symmetry breaking (SMSB), a phenomenon leading to non-equilibrium stationary states (NESS) that exhibits biases away from the racemic composition is discussed here in the framework of dissipative reaction networks. Such networks may lead to a metastable racemic non-equilibrium stationary state that transforms into one of two degenerate but stable enantiomeric NESSs. In such a bifurcation scenario, the type of the reaction network, as well the boundary conditions, are similar to those characterizing the currently accepted stages of emergence of replicators and autocatalytic systems. Simple asymmetric inductions by physical chiral forces during previous stages of chemical evolution, for example in astrophysical scenarios, must involve unavoidable racemization processes during the time scales associated with the different stages of chemical evolution. However, residual enantiomeric excesses of such asymmetric inductions suffice to drive the SMSB stochastic distribution of chiral signs into a deterministic distribution. According to these features, we propose that a basic model of the chiral machinery of proto-life would emerge during the formation of proto-cell systems by the convergence of the former enantioselective scenarios.

scholarly journals Reaction Networks as Systems for Resource Allocation: A Variational Principle for Their Non-Equilibrium Steady States

PLoS ONE ◽  
2012 ◽  
Vol 7 (7) ◽  
pp. e39849 ◽  
Author(s):  
Andrea De Martino ◽  
Daniele De Martino ◽  
Roberto Mulet ◽  
Guido Uguzzoni
Keyword(s):  
Resource Allocation ◽  
Variational Principle ◽  
Steady States ◽  
Reaction Networks ◽  
Non Equilibrium
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