Citation Context

...42 doi:10.1049/ip-syb:20050042 Paper first received 1st July and in revised form 7th October 2005 R. Tanaka is with RIKEN, Bio-Mimetic Control Research Center, Nagoya 463-0003, Japan M. Csete is with Emory University, Atlanta, GA 30322, USA J. Doyle is with California Institute of Technology, Pasadena, CA 91125, USA E-mail: reiko@bmc.riken.jpIEE Proc.-Syst. Biol., Vol. 152, No. 4, December 2005explore both important ‘design’ (with no implication of a ‘designer’) features of metabolism and the sense in which stoichiometry itself has highly organised and optimised tolerances and tradeoffs (HOT) [3] for functional requirements such as flexibility, efficiency, robustness and evolvability, constrained by conservation of energy, redox and small moieties. This paper illustrates these features using the wellunderstood stoichiometry of metabolic networks in bacteria and reviews, compares and extends the results in [4, 5]. We then propose a simple HOT model of an abstract metabolism to clarify the essential elements of its architecture. These features are not apparent from analyses that ignore organisation and constraints but rather use ‘generic’ ensemble properties, such as the popular ‘scale-...

Citation Context

...network has been recently described in detail in terms of its stoichiometry (mass and energy balance). A higher level, mathematically defined description of the global organisation of complex metabolic networks is critical for a deep understanding of metabolism, from the interpretation of huge amounts of biologic data (sequences, various -omics) to design of therapies for disease processes. The stakes are high for obtaining the big picture right: biologic data plugged into a distorted model or interpreted in the context of a flawed universal law propagates misinterpretations. In flux analyses [1], stoichiometry is considered as a constraint, and fluxes are optimised to satisfy a global objective, typically growth. Previous studies, however, have not directly addressed whether the stoichiometry itself is highly optimal or organised in any sense and contributes to the origins and purpose of complexity in biological networks. Yet biochemistry textbooks describe metabolism as having evolved to be ‘highly integrated’ with the appearance of a ‘coherent design’ [2]. Here we # IEE, 2005 IEE Proceedings online no. 20050042 doi:10.1049/ip-syb:20050042 Paper first received 1st July and in revise...

Citation Context

...ion of its architecture, which we define as a collection of protocols and their organisation. When topology is viewed in isolation, however, it can create misleading views of the system architecture. An example arises when considering certain network representations of stoichiometry where the distribution of metabolite ‘node’ degrees (number of reactions in which a metabolite is involved) satisfies a power law, and then this is taken as evidence that ‘SF’ networks underlie structure in biology [6]. In this regard, however, our analysis revealing SR organisation is supported by recent analysis [8] of protein–protein interaction networks that do not exhibit power law node degree distribution, and thus are not SF networks. Although most of the graph-theoretical treatments of metabolic networks focus largely on the metabolite node degrees, it is important to note that degrees for both types of nodes, reaction and metabolite nodes, are biologically important (and equivalent to degrees of columns and rows, i.e. the number of non-zero elements in a column and in a row, of the s-matrix). In order to highlight the features of bacterial metabolism, the metabolite and reaction node degrees (the ...

Citation Context

...the coefficient of variation (CV s/m, where s and m are sample standard deviation and mean). Exponential distributions have low variability and CV 1, and power law distributions have divergent CV for large data sets (number of data!1), thus high variability. For low variability processes, Gaussians arise naturally because of the well-known central limit theorem (CLT), and thus require no additional ‘special’ explanations. Even more important is that relaxing finite variance condition in the CLT yields power laws, which are further invariant under marginalisation, mixtures and maximisation [9]. Given the abundance of high variability phenomena and these strong invariants, power laws are an obvious null hypothesis and should properly be viewed as ‘more normal than normal’ [10]. Thus mechanisms responsible for high variability in Fig. 4 Node degrees for carrier (W), precursor (S), other (), and all (1) metabolites in H.Pylori metabolism181 total metabolite degrees are more fundamental in capturing the nature of biologic organisation than are power laws. We will argue here that high variability in metabolite degree and low variability in reaction degree are a necessary feature for an...

Citation Context

...-mail: reiko@bmc.riken.jpIEE Proc.-Syst. Biol., Vol. 152, No. 4, December 2005explore both important ‘design’ (with no implication of a ‘designer’) features of metabolism and the sense in which stoichiometry itself has highly organised and optimised tolerances and tradeoffs (HOT) [3] for functional requirements such as flexibility, efficiency, robustness and evolvability, constrained by conservation of energy, redox and small moieties. This paper illustrates these features using the wellunderstood stoichiometry of metabolic networks in bacteria and reviews, compares and extends the results in [4, 5]. We then propose a simple HOT model of an abstract metabolism to clarify the essential elements of its architecture. These features are not apparent from analyses that ignore organisation and constraints but rather use ‘generic’ ensemble properties, such as the popular ‘scale-free’ (SF) approaches [6]. Here we show that domain-specific constraints and tradeoffs imposed by the environment are important factors in stoichiometry. One consequence of this HOT architecture is a highly structured modularity that is self-dissimilar and scale-rich (SR). 2 Basic features of metabolic networks Metabolis...

Citation Context

...e divergent CV for large data sets (number of data!1), thus high variability. For low variability processes, Gaussians arise naturally because of the well-known central limit theorem (CLT), and thus require no additional ‘special’ explanations. Even more important is that relaxing finite variance condition in the CLT yields power laws, which are further invariant under marginalisation, mixtures and maximisation [9]. Given the abundance of high variability phenomena and these strong invariants, power laws are an obvious null hypothesis and should properly be viewed as ‘more normal than normal’ [10]. Thus mechanisms responsible for high variability in Fig. 4 Node degrees for carrier (W), precursor (S), other (), and all (1) metabolites in H.Pylori metabolism181 total metabolite degrees are more fundamental in capturing the nature of biologic organisation than are power laws. We will argue here that high variability in metabolite degree and low variability in reaction degree are a necessary feature for any metabolic network to be efficient and robust to uncertain environments and cellular demands, although constrained by the physical limitations imposed on their chemical components. Ta b...

Citation Context

...l yields a fully connected network with long pathways between the remaining metabolites. In contrast, deleting precursor metabolites of only medium degree does (lethally) break up the pathways. Thus the true fragility of the network is obfuscated by focussing only on graph-theoretical properties of the network. It is possible to partially ‘fix’ this problem by a priori eliminating the carriers from graphs, but then the resulting graphs have low variability in metabolite node degree sequence and thus no longer have power laws, the defining feature of SF networks. Recent experimental results in [11] further shows that the degree of the metabolite nodes is not necessarily correlated with its lethality. As shown above, the high variability comes from the bowtie structure of metabolism with a small knot of high degree common currencies (carriers and precursors). Its robustness facilitates control, accommodating perturbations and fluctuations on many time and spatial scales. That is, the s-matrix by itself does not explicitly represent the regulatory mechanisms which directly affect the fluxes, but the structure and organisation of the s-matrix is such that it greatly facilitates that regula...