scholarly journals Calculation of control coefficients of metabolic pathways. A flux-oriented graph-theoretic approach

1991 ◽  
Vol 279 (1) ◽  
pp. 55-65 ◽  
Author(s):  
A K Sen
Keyword(s):  
Directed Graph ◽  
Metabolic Pathways ◽  
Oriented Graph ◽  
Theoretic Approach ◽  
Control Structures ◽  
Graph Theoretic ◽  
Functional Relationships ◽  
Graph Theoretic Approach ◽  
The Individual ◽  
Control Coefficients

Within the premises of the flux-oriented theory of Crabtree & Newsholme [(1987) Biochem. J. 247, 113-120], I have used a graph-theoretic approach for calculating the Control Coefficients of metabolic pathways. It is shown that a directed graph representing the control structure of a metabolic pathway can be constructed in a heuristic manner directly from the reaction diagram of the pathway, without the necessity of writing down the governing equations for the Control Coefficients. The Control Coefficients are derived from an analysis of the topology of the directed graph. The graph-theoretic approach also provides a visual framework for analysing the functional relationships of the individual enzymes. The control structures of the following pathways are examined here: (a) a simple unbranched pathway with four enzymes, (b) a simple branched pathway with three enzymes, and (c) a branched pathway with both carbon and energy (ATP) fluxes.

A Graph-Theoretic Approach to Comparing and Integrating Genetic, Physical and Sequence-Based Maps

Genetics ◽  
2003 ◽  
Vol 165 (4) ◽  
pp. 2235-2247
Author(s):  
Immanuel V Yap ◽  
David Schneider ◽  
Jon Kleinberg ◽  
David Matthews ◽  
Samuel Cartinhour ◽  
...  
Keyword(s):  
Directed Graph ◽  
Source Material ◽  
Complete Picture ◽  
Theoretic Approach ◽  
Research Groups ◽  
Genome Coverage ◽  
Graph Theoretic ◽  
Novel Approach ◽  
Graph Theoretic Approach ◽  
Locus Order

AbstractFor many species, multiple maps are available, often constructed independently by different research groups using different sets of markers and different source material. Integration of these maps provides a higher density of markers and greater genome coverage than is possible using a single study. In this article, we describe a novel approach to comparing and integrating maps by using abstract graphs. A map is modeled as a directed graph in which nodes represent mapped markers and edges define the order of adjacent markers. Independently constructed graphs representing corresponding maps from different studies are merged on the basis of their common loci. Absence of a path between two nodes indicates that their order is undetermined. A cycle indicates inconsistency among the mapping studies with regard to the order of the loci involved. The integrated graph thus produced represents a complete picture of all of the mapping studies that comprise it, including all of the ambiguities and inconsistencies among them. The objective of this representation is to guide additional research aimed at interpreting these ambiguities and inconsistencies in locus order rather than presenting a “consensus order” that ignores these problems.

A graph-theoretic approach to modeling metabolic pathways

1991 ◽  
Vol 5 (4) ◽  
pp. 303-322 ◽  
Author(s):  
Eric Gifford ◽  
Mark Johnson ◽  
Chun-che Tsai
Keyword(s):  
Metabolic Pathways ◽  
Theoretic Approach ◽  
Graph Theoretic ◽  
Graph Theoretic Approach

Graph‐theoretic approach for identifying catalytic or metabolic pathways

2005 ◽  
Vol 28 (7) ◽  
pp. 1021-1037 ◽  
Author(s):  
Liang‐Tseng Fan ◽  
Shahram Shafie ◽  
Botond Bertók ◽  
Ferenc Friedler ◽  
Dong‐Yup Lee ◽  
...  
Keyword(s):  
Metabolic Pathways ◽  
Theoretic Approach ◽  
Graph Theoretic ◽  
Graph Theoretic Approach

scholarly journals Quantitative analysis of metabolic regulation. A graph-theoretic approach using spanning trees

1991 ◽  
Vol 275 (1) ◽  
pp. 253-258 ◽  
Author(s):  
A K Sen
Keyword(s):  
Metabolic Regulation ◽  
Spanning Trees ◽  
Feedback Loops ◽  
Theoretic Approach ◽  
Flux Control ◽  
Graph Theoretic ◽  
Graph Theoretic Approach ◽  
Flux Control Coefficients ◽  
Theoretic Technique ◽  
Control Coefficients

A graph-theoretic technique using spanning trees is described for the evaluation of Flux Control Coefficients of metabolic pathways. The technique is illustrated by investigating a linear pathway (a) in the absence of feedback and feedforward regulation. (b) with its first enzyme inhibited by the end product and (c) with multiple feedback loops. It is shown that the Flux Control Coefficients of a linear pathway with one or more feedback loops can be derived in a systematic manner by superimposing the effect of the feedback loop(s) on the expressions pertaining to the Flux Control Coefficients of the unregulated pathway.

scholarly journals Fluxes and Metabolic Pools as Model Traits for Quantitative Genetics. I. The L-Shaped Distribution of Gene Effects

Genetics ◽  
1999 ◽  
Vol 153 (4) ◽  
pp. 2001-2012 ◽  
Author(s):  
Bruno Bost ◽  
Christine Dillmann ◽  
Dominique de Vienne
Keyword(s):  
Enzyme Activity ◽  
Metabolic Pathways ◽  
Quantitative Traits ◽  
Intrinsic Property ◽  
Gene Effects ◽  
Analytical Approximations ◽  
Mean And Variance ◽  
The Individual ◽  
Metabolic Control Theory ◽  
Control Coefficients

Abstract The fluxes through metabolic pathways can be considered as model quantitative traits, whose QTL are the polymorphic loci controlling the activity or quantity of the enzymes. Relying on metabolic control theory, we investigated the relationships between the variations of enzyme activity along metabolic pathways and the variations of the flux in a population with biallelic QTL. Two kinds of variations were taken into account, the variation of the average enzyme activity across the loci, and the variation of the activity of each enzyme of the pathway among the individuals of the population. We proposed analytical approximations for the flux mean and variance in the population as well as for the additive and dominance variances of the individual QTL. Monte Carlo simulations based on these approximations showed that an L-shaped distribution of the contributions of individual QTL to the flux variance (R2) is consistently expected in an F2 progeny. This result could partly account for the classically observed L-shaped distribution of QTL effects for quantitative traits. The high correlation we found between R2 value and flux control coefficients variance suggests that such a distribution is an intrinsic property of metabolic pathways due to the summation property of control coefficients.

scholarly journals Study of the Concrete Production Process -A graph theoretic approach

2020 ◽  
Vol 1706 ◽  
pp. 012115
Author(s):  
P Sangeetha ◽  
M Shanmugapriya ◽  
R Sundareswaran ◽  
K Sowmya ◽  
S Srinidhi
Keyword(s):  
Production Process ◽  
Theoretic Approach ◽  
Graph Theoretic ◽  
Graph Theoretic Approach ◽  
Concrete Production
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