Validity of rate equation results for reaction rates in reaction networks with fluctuations

2008 ◽  
Vol 78 (4) ◽  
Author(s):  
Adina Lederhendler ◽  
Ofer Biham
Keyword(s):  
Rate Equation ◽  
Reaction Rates ◽  
Reaction Networks

Experimental evidence for the need of thermodynamic considerations in modelling of anaerobic environmental bioprocesses

1997 ◽  
Vol 36 (10) ◽  
pp. 109-115 ◽  
Author(s):  
Choon-Yee Hoh ◽  
Ralf Cord-Ruwisch
Keyword(s):  
Free Energy ◽  
Experimental Evidence ◽  
Positive Reaction ◽  
Rate Equation ◽  
Dynamic Equilibrium ◽  
Reaction Rates ◽  
Product Inhibition ◽  
Experimental Results ◽  
Biological Processes ◽  
Laws Of Thermodynamics

For modeling of biological processes that operate close to the dynamic equilibrium (eg. anaerobic processes), it is critical to prevent the prediction of positive reaction rates when the reaction has already reached dynamic equilibrium. Traditional Michaelis-Menten based models were found to violate the laws of thermodynamics as they predicted positive reaction rates for reactions that were endergonic due to high endproduct concentrations. The inclusion of empirical “product inhibition factors” as suggested by previous work could not prevent this problem. This paper compares the predictions of the Michaelis-Menten Model (with and without product inhibition factors) and the Equilibrium Based Model (which has a thermodynamic term introduced into its rate equation) with experimental results of reactions in anaerobic bacterial environments. In contrast to the Michaelis-Menten based models that used traditional inhibition factors, the Equilibrium Based Model correctly predicted the nature and the degree of inhibition due to endproduct accumulation. Moreover, this model also correctly predicted when reaction rates must be zero due to the free energy change of the conversion reaction being zero. With these added advantages, the Equilibrium Based Model thus seemed to provide a scientifically correct and more realistic basis for a variety of models that describe anaerobic biosystems.

An algorithm for evaluating reaction rates of catalytic reaction networks with strong diffusion limitations

2001 ◽  
Vol 25 (9-10) ◽  
pp. 1185-1198 ◽  
Author(s):  
Sergio P. Bressa ◽  
Néstor J. Mariani ◽  
Néstor O. Ardiaca ◽  
Germán D. Mazza ◽  
Osvaldo M. Martı́nez ◽  
...  
Keyword(s):  
Catalytic Reaction ◽  
Reaction Rates ◽  
Reaction Networks ◽  
Diffusion Limitations ◽  
Strong Diffusion

scholarly journals In silico modeling of biochemical pathways

2021 ◽  
Vol 4 (s1) ◽  
Author(s):  
Paolo Milazzo ◽  
Roberta Gori ◽  
Alessio Micheli ◽  
Lucia Nasti ◽  
Marco Podda
Keyword(s):  
Kinetic Parameters ◽  
In Silico ◽  
In Silico Analysis ◽  
Reaction Rates ◽  
Reaction Networks ◽  
Interaction Patterns ◽  
Biochemical Pathways ◽  
Stochastic Simulation Algorithms ◽  
Dynamical Properties ◽  
In Silico Models

We present in silico modeling methods for the investigation of dynamical properties of biochemical pathways, that are chemical reaction networks underlying cell functioning. Since pathways are (complex) dynamical systems, in-silico models are often studied by applying numerical integration techniques for Ordinary Differential Equations (ODEs), or stochastic simulation algorithms. However, these techniques require a rather accurate knowledge of the kinetic parameters of the modeled chemical reactions. Moreover, in the case of very complex reaction networks, in silico analysis can become unfeasible from the computational viewpoint. Consequently, in the last few years several approaches have been proposed that focus on estimating or predicting dynamical properties from the analysis of the structure of the biochemical pathway. This means that the analysis focuses more on the interaction patterns than on the kinetic parameters, and this usually makes it possible to deduce the role of each molecule and how each molecule qualitatively influences each other, by abstracting away from quantitative details about concentrations and reaction rates.

scholarly journals Linear conjugacy in biochemical reaction networks with rational reaction rates

2016 ◽  
Vol 54 (8) ◽  
pp. 1658-1676 ◽  
Author(s):  
Attila Gábor ◽  
Katalin M. Hangos ◽  
Gábor Szederkényi
Keyword(s):  
Reaction Rates ◽  
Biochemical Reaction ◽  
Reaction Networks ◽  
Biochemical Reaction Networks

scholarly journals Energy-based analysis of biomolecular pathways

2017 ◽  
Vol 473 (2202) ◽  
pp. 20160825 ◽  
Author(s):  
Peter J. Gawthrop ◽  
Edmund J. Crampin
Keyword(s):  
Reaction Rates ◽  
Reaction Networks ◽  
Cycle Model ◽  
Stoichiometric Matrix ◽  
Transporter Protein ◽  
Biomolecular Networks ◽  
Energy Flows ◽  
Powerful Approach ◽  
Mass Flows ◽  
Glucose Transport Protein

Decomposition of biomolecular reaction networks into pathways is a powerful approach to the analysis of metabolic and signalling networks. Current approaches based on analysis of the stoichiometric matrix reveal information about steady-state mass flows (reaction rates) through the network. In this work, we show how pathway analysis of biomolecular networks can be extended using an energy-based approach to provide information about energy flows through the network. This energy-based approach is developed using the engineering-inspired bond graph methodology to represent biomolecular reaction networks. The approach is introduced using glycolysis as an exemplar; and is then applied to analyse the efficiency of free energy transduction in a biomolecular cycle model of a transporter protein [sodium-glucose transport protein 1 (SGLT1)]. The overall aim of our work is to present a framework for modelling and analysis of biomolecular reactions and processes which considers energy flows and losses as well as mass transport.

scholarly journals Quantum Techniques for Reaction Networks

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
John C. Baez
Keyword(s):  
Master Equation ◽  
Rate Equation ◽  
Quantum Physics ◽  
Time Derivative ◽  
Reaction Network ◽  
Reaction Networks ◽  
Expected Number ◽  
Second Quantization ◽  
Stochastic Time ◽  
Number Of Particles

Reaction networks are a general formalism for describing collections of classical entities interacting in a random way. While reaction networks are mainly studied by chemists, they are equivalent to Petri nets, which are used for similar purposes in computer science and biology. As noted by Doi and others, techniques from quantum physics, such as second quantization, can be adapted to apply to such systems. Here we use these techniques to study how the “master equation” describing stochastic time evolution for a reaction network is related to the “rate equation” describing the deterministic evolution of the expected number of particles of each species in the large-number limit. We show that the relation is especially strong when a solution of master equation is a “coherent state”, meaning that the numbers of entities of each kind are described by independent Poisson distributions. Remarkably, in this case the rate equation and master equation give the exact same formula for the time derivative of the expected number of particles of each species.

scholarly journals Kinetic Monte Carlo simulations of the grain-surface back-diffusion effect

2017 ◽  
Vol 13 (S332) ◽  
pp. 370-373
Author(s):  
Eric R. Willis ◽  
Robin T. Garrod
Keyword(s):  
Monte Carlo ◽  
Rate Equation ◽  
Binding Sites ◽  
Interstellar Dust ◽  
Kinetic Monte Carlo ◽  
Reaction Rates ◽  
Dust Particles ◽  
Back Diffusion ◽  
Diffusion Effect ◽  
Grain Surface

AbstractBack-diffusion is the phenomenon by which random walkers revisit binding sites on a lattice. This phenomenon must occur on interstellar dust particles, slowing down dust-grain reactions, but it is not accounted for by standard rate-equation models. Microscopic kinetic Monte Carlo models have been used to investigate the effect of back-diffusion on reaction rates on interstellar dust grains. Grain morphology, size, and grain-surface coverage were varied and the effects of these variations on the magnitude of the back-diffusion effect were studied for the simple H+H reaction system. This back-diffusion effect is seen to reduce reaction rates by a maximum factor of ∼5 for the canonical grain of 106 binding sites. The resulting data were fit to logarithmic functions that can be used to reproduce the effects of back-diffusion in rate-equation models.

scholarly journals Short relaxation times but long transient times in both simple and complex reaction networks

2016 ◽  
Vol 13 (120) ◽  
pp. 20160388 ◽  
Author(s):  
Adrien Henry ◽  
Olivier C. Martin
Keyword(s):  
Relaxation Time ◽  
Linear Chain ◽  
Relaxation Times ◽  
Relevant Information ◽  
Reaction Rates ◽  
Mass Action ◽  
Reaction Networks ◽  
Complex Reaction ◽  
Linear Chains ◽  
Simple Systems

When relaxation towards an equilibrium or steady state is exponential at large times, one usually considers that the associated relaxation time τ , i.e. the inverse of the decay rate, is the longest characteristic time in the system. However, that need not be true, other times such as the lifetime of an infinitesimal perturbation can be much longer. In the present work, we demonstrate that this paradoxical property can arise even in quite simple systems such as a linear chain of reactions obeying mass action (MA) kinetics. By mathematical analysis of simple reaction networks, we pin-point the reason why the standard relaxation time does not provide relevant information on the potentially long transient times of typical infinitesimal perturbations. Overall, we consider four characteristic times and study their behaviour in both simple linear chains and in more complex reaction networks taken from the publicly available database ‘Biomodels’. In all these systems, whether involving MA rates, Michaelis–Menten reversible kinetics, or phenomenological laws for reaction rates, we find that the characteristic times corresponding to lifetimes of tracers and of concentration perturbations can be significantly longer than τ .

Sign in / Sign up

Export Citation Format

Share Document