Reaction Route Graphs. II. Examples of Enzyme- and Surface-Catalyzed Single Overall Reactions

Abstract

The utility of the new reaction route (RR) graph theory developed in the preceding paper (Part I) is illustrated here, with the help of two examples. In the first example, the kinetics of the conversion of 7,8-dihydrofolate and NADPH to 5,6,7,8-tetrahydrofolate and NADP, as catalyzed by dihydrofolate reductase (DHFR), is considered. This system is described by a linear kinetic mechanism that includes 13 elementary reaction steps. The second example is a microkinetic model of the water-gas shift reaction on a copper catalyst, which is highly nonlinear and includes 15 elementary surface reaction steps. For both mechanisms, the RR graphs have been constructed and used to determine the overall rates. The RR graphs and the overall rate equations are further simplified and reduced, using the RR network approach.

Ockham's razor for paring microkinetic mechanisms: Electrical analogy vs.Campbell's degree of rate control

“…36 This may be accomplished by appropriately combining the elementary steps into the so-called intermediate reactions (IR). [41][42][43] There are different ways in which the Campbell's DRC, once hence numerically computed for all the steps in a microkinetic model, may be utilized for identification of key steps and model reduction. 46 One such method is the so-called principal component analysis, 40,47,48 in which the eigenvalues and eigenvectors of the matrix X T X are computed.…”

“…53 In other words, one needs both thermodynamic (affinity, or reversibility) and kinetic (resistance) characteristics of a reaction step to judge its significance in the overall scheme of things. The electrical network analogy based on the RR graph approach [41][42][43] incorporates both of these aspects. It, thus, comprehensively incorporates and illuminates the network structural constraints embodied by the two Kirchhoff's laws (mass balance, and Hess's law) described below, which further ascribe to reaction networks a complete and quantitative correspondence to electrical networks.…”

“…3,7,39,40 However, it is a "black box" numerical approach. Here, we discuss an alternate approach based on electrical network analogy of a reaction mechanism within the reaction route (RR) graph analysis approach [41][42][43][44] developed by us, which involves an evaluation of the reaction step "affinity," or driving force, and "resistance" under a variety of conditions. It is just as rigorous and substantially more revealing than Campbell's DRC, allowing transparent pruning of complex catalytic reaction networks.…”

Duality in Geometric Graphs: Vector Graphs, Kirchhoff Graphs and Maxwell Reciprocal Figures

“…Kirchhoff graphs were so-named because they satisfy both the Kirchhoff potential law and the Kirchhoff current law. The use of Kirchhoff graphs as reaction network diagrams was discussed by Fehribach [1], as well as by Fishtik, Datta et al [3][4][5][6], who discuss a related graph, the "reaction route graph". A number of other graphs have been used in the study of reaction networks; a summary can be found in [7,8].…”

Complex Process Networks: Passivity and Optimality

“…This theory could be applied to various types of networked systems previously examined with other methods, such as plant-wide (integrated) process networks (Luyben et al, 1999), (Hangos et al, 1999), (Gilles, 1998), (Kumar & Daoutidis, 2002), chemical reaction networks (Fishtik et al, 2004), or biological networks (Majewski & Domach, 1989), (Hatzimanikatis et al, 1996).…”