A model combining cell physiology and population genetics to explain Escherichia coli laboratory evolution

BACKGROUND: Laboratory experiments under controlled conditions during thousands of generations are useful tools to assess the processes underlying bacterial evolution. As a result of these experiments, the way in which the traits change in time is obtained. Under these conditions, the bacteria E. coli shows a parallel increase in cell volume and fitness. RESULTS: To explain this pattern it is required to consider organismic and population contributions. For this purpose we incorporate relevant information concerning bacterial structure, composition and transformations in a minimal modular model. In the short time scale, the model reproduces the physiological responses of the traits to changes in nutrient concentration. The decay of unused catabolic functions, found experimentally, is introduced in the model using simple population genetics. The resulting curves representing the evolution of volume and fitness in time are in good agreement with those obtained experimentally. CONCLUSIONS: This study draws attention on physiology when studying evolution. Moreover, minimal modular models appear to be an adequate strategy to unite these barely related disciplines of biology

Elasticity analysis and design for large metabolic responses produced by changes in enzyme activities.

Metabolic control analysis has been extensively used to describe how the sensitivity properties of the component enzymes in a metabolic pathway (represented by the elasticity coefficients) determine the way in which metabolic variables respond (described by the control coefficients). Similarly, metabolic control design addresses the inverse problem of obtaining the sensitivity properties of the component enzymes that are required for the system to show a pre-established pattern of responses. These formalisms, including what is called elasticity analysis and design, were developed for small, strictly speaking infinitesimal, changes. Here we extend them to large metabolic responses. The new approach can be applied to simple two-step pathways or to any arbitrary metabolic system divided into two groups linked by one intermediate. General expressions that relate control and elasticity coefficients for large changes are derived. Concentration and flux connectivity relationships are obtained. The relationships for large changes indicate that the pattern of responses is not necessarily the same as the one obtained with the traditional infinitesimal approach, in some cases the patterns being qualitatively different. The general analysis is used to study the control of ketogenesis in rat liver mitochondria, starting from data available in the literature. The control profile of the pathway subject to large changes shows both quantitative and qualitative differences from the one obtained from an analysis that is performed with infinitesimal coefficients. This exemplifies the type of errors that may be introduced when drawing conclusions about large metabolic responses from results obtained with an infinitesimal treatment

A Strategy to Calculate the Patterns of Nutrient Consumption by Microorganisms Applying a Two-Level Optimisation Principle to Reconstructed Metabolic Networks

Bacterial responses to environmental changes rely on a complex network of biochemical reactions. The properties of the metabolic network determining these responses can be divided into two groups: the stoichiometric properties, given by the stoichiometry matrix, and the kinetic/thermodynamic properties, given by the rate equations of the reaction steps. The stoichiometry matrix represents the maximal metabolic capabilities of the organism, and the regulatory mechanisms based on the rate laws could be considered as being responsible for the administration of these capabilities. Post-genomic reconstruction of metabolic networks provides us with the stoichiometry matrix of particular strains of microorganisms, but the kinetic aspects of in vivo rate laws are still largely unknown. Therefore, the validity of predictions of cellular responses requiring detailed knowledge of the rate equations is difficult to assert. In this paper, we show that by applying optimisation criteria to the core stoichiometric network of the metabolism of Escherichia coli, and including information about reversibility/irreversibility only of the reaction steps, it is possible to calculate bacterial responses to growth media with different amounts of glucose and galactose. The target was the minimisation of the number of active reactions (subject to attaining a growth rate higher than a lower limit) and subsequent maximisation of the growth rate (subject to the number of active reactions being equal to the minimum previously calculated). Using this two-level target, we were able to obtain by calculation four fundamental behaviours found experimentally: inhibition of respiration at high glucose concentrations in aerobic conditions, turning on of respiration when glucose decreases, induction of galactose utilisation when the system is depleted of glucose and simultaneous use of glucose and galactose as carbon sources when both sugars are present in low concentrations. Preliminary results of the coarse pattern of sugar utilisation were also obtained with a genome-scale E. coli reconstructed network, yielding similar qualitative results

A Hierarchical Approach to Cooperativity in Macromolecular and Self-Assembling Binding Systems

The study of complex macromolecular binding systems reveals that a high number of states and processes are involved in their mechanism of action, as has become more apparent with the sophistication of the experimental techniques used. The resulting information is often difficult to interpret because of the complexity of the scheme (large size and profuse interactions, including cooperative and self-assembling interactions) and the lack of transparency that this complexity introduces into the interpretation of the indexes traditionally used to describe the binding properties. In particular, cooperative behaviour can be attributed to very different causes, such as direct chemical modification of the binding sites, conformational changes in the whole structure of the macromolecule, aggregation processes between different subunits, etc. In this paper, we propose a novel approach for the analysis of the binding properties of complex macromolecular and self-assembling systems. To quantify the binding behaviour, we use the global association quotient defined as Kc = [occupied sites]/([free sites] L), L being the free ligand concentration. Kc can be easily related to other measures of cooperativity (such as the Hill number or the Scatchard plot) and to the free energies involved in the binding processes at each ligand concentration. In a previous work, it was shown that Kc could be decomposed as an average of equilibrium constants in two ways: intrinsic constants for Adair binding systems and elementary constants for the general case. In this study, we show that these two decompositions are particular cases of a more general expression, where the average is over partial association quotients, associated with subsystems from which the system is composed. We also show that if the system is split into different subsystems according to a binding hierarchy that starts from the lower, microscopic level and ends at the higher, aggregation level, the global association quotient can be decomposed following the hierarchical levels of macromolecular organisation. In this process, the partial association quotients of one level are expressed, in a recursive way, as a function of the partial quotients of the level that is immediately below, until the microscopic level is reached. As a result, the binding properties of very complex macromolecular systems can be analysed in detail, making the mechanistic explanation of their behaviour transparent. In addition, our approach provides a model-independent interpretation of the intrinsic equilibrium constants in terms of the elementary ones