General Rate Equations and Their Applications for Cyclic Reaction Networks:  Single-Cycle Systems

2000 ◽  
Vol 39 (11) ◽  
pp. 4100-4105 ◽  
Author(s):  
Jia-Ming Chern
Keyword(s):  
Rate Equations ◽  
Reaction Networks ◽  
Single Cycle ◽  
Cycle Systems ◽  
Cyclic Reaction

scholarly journals A numerical approach for detecting switch-like bistability in mass action chemical reaction networks with conservation laws

2022 ◽  
Vol 23 (1) ◽  
Author(s):  
Brandon C Reyes ◽  
Irene Otero-Muras ◽  
Vladislav A Petyuk
Keyword(s):  
Conservation Laws ◽  
Signaling Pathways ◽  
Chemical Reaction ◽  
Reaction Network ◽  
Chemical Reaction Networks ◽  
Mass Action ◽  
Numerical Continuation ◽  
Rate Equations ◽  
Reaction Networks ◽  
Bistable Switch

Abstract Background Theoretical analysis of signaling pathways can provide a substantial amount of insight into their function. One particular area of research considers signaling pathways capable of assuming two or more stable states given the same amount of signaling ligand. This phenomenon of bistability can give rise to switch-like behavior, a mechanism that governs cellular decision making. Investigation of whether or not a signaling pathway can confer bistability and switch-like behavior, without knowledge of specific kinetic rate constant values, is a mathematically challenging problem. Recently a technique based on optimization has been introduced, which is capable of finding example parameter values that confer switch-like behavior for a given pathway. Although this approach has made it possible to analyze moderately sized pathways, it is limited to reaction networks that presume a uniterminal structure. It is this limited structure we address by developing a general technique that applies to any mass action reaction network with conservation laws. Results In this paper we developed a generalized method for detecting switch-like bistable behavior in any mass action reaction network with conservation laws. The method involves (1) construction of a constrained optimization problem using the determinant of the Jacobian of the underlying rate equations, (2) minimization of the objective function to search for conditions resulting in a zero eigenvalue, (3) computation of a confidence level that describes if the global minimum has been found and (4) evaluation of optimization values, using either numerical continuation or directly simulating the ODE system, to verify that a bistability region exists. The generalized method has been tested on three motifs known to be capable of bistability. Conclusions We have developed a variation of an optimization-based method for the discovery of bistability, which is not limited to uniterminal chemical reaction networks. Successful completion of the method provides an S-shaped bifurcation diagram, which indicates that the network acts as a bistable switch for the given optimization parameters.

scholarly journals Kinetic modelling of compartmentalised reaction networks

2020 ◽  
Author(s):  
Jan-Hendrik Servaas Hofmeyr
Keyword(s):  
Kinetic Modelling ◽  
Time Derivative ◽  
Rate Equations ◽  
Reaction Networks ◽  
Comprehensive Treatment ◽  
3 Dimensional ◽  
Rate Laws ◽  
Modelling Framework ◽  
Compartment Boundary ◽  
Definition Of

This paper presents a comprehensive treatment of kinetic modelling of compartmentalised reaction networks in the context of systems biology. There is still a lot of confusion about how to go about constructing compartment models, and many published models are flawed with respect to how they handle compartmentation. The modelling framework described here answers two key questions: Which rate laws should be used to describe the rates of reactions in compartmentalised systems? How should these rate laws be incorporated in the ordinary differential equations (ODEs) that describe the dynamics of the compartmentalised system? The framework rests on the fundamental definition of reaction rate as the number of reaction events per time, which is related to the time derivative of mole amount of reactant or product, an extensive property that is directly proportional to the size of the compartment in which the reaction events occur. This means that the rates of reactions that occur in a 3-dimensional compartment are proportional to the volume of the compartment, while the rates of transfers over a 2-dimensional compartment boundary or interface between compartments are proportional to the area of the boundary. Transfer rates are often incorrectly scaled with a volume instead of an area, and the reasons why this is wrong are extensively discussed. I also show how `textbook' rate equations, which I term canonical rate equations, should be modified for compartmental modelling and how they should be incorporated into either amount-change or concentration-change ODEs.

Sizing, Part-Load Operation, and System Performance of Combined Heat and Power

2007 ◽  
Author(s):  
Asfaw Beyene ◽  
Benjamin Erpelding
Keyword(s):  
Peak Load ◽  
Single Cycle ◽  
Significant Cost ◽  
Load Variations ◽  
Load Factors ◽  
Cycle Systems ◽  
Tax Benefits ◽  
And Performance ◽  
Address System ◽  
Combined Cooling

Because of its superior efficiency and peak load mitigation capabilities, considerable attention has been given recently to combined Cooling, Heating and Power (CCHP). They technology enjoys tax benefits, incentives, accelerated permit processes, etc both at the local, state, and federal levels. One serious challenge to the implementation of CCHP systems is matching and sizing of the system to strongly and frequently varying load conditions. This paper presents matching and sizing related challenges of CCHP systems with emphasis on operation-related and weather-driven load factors. Regional data from the California Public Utilities Commission (CPUC) were used to evaluate the success of recent incentive-driven CHP implementations. It is concluded that while CCHPs have significant cost and performance advantages over traditional single-cycle systems, inadequate strategies — failure to address system flexibilities to accommodate load variations in particular, seem to have negatively impacted these promising technology.

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