Centre for Complex Systems in Transition

The principal aim of systems biology is to search for general principles that govern living systems. We develop an abstract dynamic model of a cell, rooted in Mesarovic´and Takahara's general systems theory. In this conceptual framework the function of the cell is delineated by the dynamic processes it can realize. We abstract basic cellular processes, i.e., metabolism, signalling, gene expression, into a mapping and consider cell functions, i.e., cell differentiation, proliferation, etc. as processes that determine the basic cellular processes that realize a particular cell function. We then postulate the existence of a 'coordination principle' that determines cell function. These ideas are condensed into a theorem: If basic cellular processes for the control and regulation of cell functions are present, then the coordination of cell functions is realized autonomously from within the system. Inspired by Robert Rosen's notion of closure to efficient causation, introduced as a necessary condition for a natural system to be an organism, we show that for a mathematical model of a self-organizing cell the associated category must be cartesian closed. Although the semantics of our cell model differ from Rosen's (M,R)-systems, the proof of our theorem supports (in parts) Rosen's argument that living cells have non-simulable properties. Whereas models that form cartesian closed categories can capture self-organization (which is a, if not the, fundamental property of living systems), conventional computer simulations of these models (such as virtual cells) cannot. Simulations can mimic living systems, but they are not like living systems. r

Systems biology approaches, such as kinetic modelling, could provide valuable insights into how thioredoxins, glutaredoxins and peroxiredoxins (here collectively called redoxins), and the systems that reduce these molecules are regulated. However, it is not clear whether redoxins should be described as redox couples (with redox potentials) or as enzymes (with Michaelis–Menten parameters) in such approaches. We show that in complete redoxin systems, redoxin substrate saturation and other purported enzymatic behaviours result from limitations in the redoxin redox cycles in these systems. Michaelis–Menten parameters are therefore inappropriate descriptors of redoxin activity; data from redoxin kinetic experiments should rather be interpreted in terms of the complete system of reactions under study. These findings were confirmed by fitting kinetic models of the thioredoxin and glutaredoxin systems to in vitro datasets. This systems approach clarifies the inconsistencies with the descrip...

Systems biology approaches, such as kinetic modelling, could provide valuable insights into how thioredoxins, glutaredoxins and peroxiredoxins (here collectively called redoxins), and the systems that reduce these molecules are regulated. However, it is not clear whether redoxins should be described as redox couples (with redox potentials) or as enzymes (with Michaelis–Menten parameters) in such approaches. We show that in complete redoxin systems, redoxin substrate saturation and other purported enzymatic behaviours result from limitations in the redoxin redox cycles in these systems. Michaelis–Menten parameters are therefore inappropriate descriptors of redoxin activity; data from redoxin kinetic experiments should rather be interpreted in terms of the complete system of reactions under study. These findings were confirmed by fitting kinetic models of the thioredoxin and glutaredoxin systems to in vitro datasets. This systems approach clarifies the inconsistencies with the descrip...

Aspects of metabolic regulation can be fruitfully studied with a combination of generic modelling, control analysis and graphical analysis using rate characteristics. This paper analyses a prototypical supply-demand system consisting of a biosynthetic subsystem subject to allosteric inhibition by its product and a demand process that consumes this product. The effect of changes in affinity of the committing supply enzyme for the pathway substrate on the regulatory properties of the supply subsystem is compared for the Monod-Wyman-Changeux and the reversible Hill allosteric enzyme models. We found that the Hill model has a distinct advantage in that the steady-state concentration at which it maintains the product is set by the half-saturating product concentration and is independent of changes in the degree of saturation for substrate. In contrast, with the Monod-Wyman-Changeux model this set point varies with affinity for substrate. Explicitly incorporating reversibility in all rate...

Stoicheiometric analysis of metabolic pathways provides a systematic way of determining which metabolite concentrations are subject to constraints, information that may otherwise be very difficult to recognize in a large branched pathway. The procedure involves representing the pathway structure in the form of a matrix and then carrying out row operations to convert the matrix into ‘row echelon form’: this is a form in which as many as possible of the elements on the main diagonal are non-zero, and all of the elements below the main diagonal are zero. If exactly the same operations are carried out on a unit matrix of order equal to the number of intermediate metabolites in the pathway, the resulting matrix allows the stoicheiometric constraints to be read off directly.

Metabolic control analysis is a powerful quantitative framework for understanding the relationship between the steady-state properties of a (bio)chemical reaction network as a whole and the properties of its component reactions. Although in essence it is a typical ...

MetaModel is a user-friendly program for calculating steadystate fluxes and metabolite concentrations of metabolic systems on the IBM PC and compatible computers. For any steady state that is obtained, one can then calculate a matrix of elasticity coefficients at that steady state, or a matrix of control and response coefficients. It thus offers a simple way to calculate the control structure of a pathway: it provides not only an educational tool that allows the student to verify empirically the classic summation relationships of metabolic control analysis but also a research tool for addressing 'what if?' questions about the behaviour of metabolic systems. Results can not only be printed or stored in a file, but can also be written to a special file that can be read by popular spreadsheet programs, thereby giving access to rapid, flexible and powerful methods for subsequent analysis and plotting of these results.

Metabolic control analysis can relate control properties of an intact system to kinetic properties (elasticity coeffkients) of the enzymes within that system. The method formulating the former as matrix inverse of the latter is elaborated here for the general case and founded in standard metabolic control theory. Then a method is developed that accomplishes the reverse: it is shown that a matrix containing all elasticity coefficients and information concerning the pathway structure equals the inverse of a matrix cantainiag flux and concentration control coefficients. As a consequence, by measuring the control properties of an intact system, one is able to deduce its in situ pathway structure and enzyme kinetic properties: This solves the ever-present question of whether the kinetic properties of enzymes in their isolated state differ from those under the conditions prevailing in the cell.

Inspired by the application of metabolic control analysis (MCA) to biochemical networks, we conduct a generalized sensitivity analysis of the equilibrium of a set of differential equations used to model trophic chains. We focus on changes in the equilibrium to perturbations of feeding (i.e. functional responses) and growth rate functions. So-called control coefficient connectivity relationships are derived for two broad classes of trophic chains: those governed by linear and those governed by nonlinear growth functions. These connectivity relationships link global sensitivity coefficients to local elasticities represented by the normalized partial derivatives of the rate functions. We derive results for specific classes of trophic chains, including hyperbolic growth functions used in metaphysiological models. Our results provide formulae for computing the degree to which control by the feeding and growth functions is top-down versus bottom-up at any level in any given trophic chain. Control analysis provides a framework for articulating the degree to which equilibrium-or, more usefully, long term average-population levels are influenced by the different rate functions in terms of local elasticity functions. Control Analysis also provides techniques for probing the trophic cascade hypothesis.