Luis Acerenza

Product dependence and bifunctionality compromise the ultrasensitivity of signal transduction cascades

Covalent modification cycles are ubiquitous. Theoretical studies have suggested that they serve to increase sensitivity. However, this suggestion has not been corroborated experimentally in vivo. Here, we demonstrate that the assumptions of the theoretical studies, i.e., irreversibility and absence of product inhibition, were not trivial: when the conversion reactions are close to equilibrium or saturated by their product, “zero-order” ultrasensitivity disappears. For high sensitivities to arise, not only substrate saturation (zero-order) but also high equilibrium constants and low product saturation are required. Many covalent modification cycles are catalyzed by one bifunctional ‘ambiguous’ enzyme rather than by two independent proteins. This makes high substrate concentration and low product concentration for both reactions of the cycle inconsistent; such modification cycles cannot have high responses. Defining signal strength as ratios of modified (e.g., phosphorylated) over unmodified protein, signal-to-signal response sensitivity equals 1: signal strength should remain constant along a cascade of ambiguous modification cycles. We also show that the total concentration of a signalling effector protein cannot affect the signal emanating from a modification cycle catalyzed by an ambiguous enzyme if the ratio of the two forms of the effector protein is not altered. This finding may explain the experimental result that the pivotal signal transduction protein PII plus its paralogue GlnK do not control steady-state N-signal transduction in Escherichia coli. It also rationalizes the absence of strong phenotypes for many signal-transduction proteins. Emphasis on extent of modification of these proteins is perhaps more urgent than transcriptome analysis.

In silico strategy to rationally engineer metabolite production: A case study for threonine in Escherichia coli

Genetic engineering of metabolic pathways is a standard strategy to increase the production of metabolites of economic interest. However, such flux increases could very likely lead to undesirable changes in metabolite concentrations, producing deleterious perturbations on other cellular processes. These negative effects could be avoided by implementing a balanced increase of enzyme concentrations according to the Universal Method [Kacser and Acerenza (1993) Eur J Biochem 216:361–367]. Exact application of the method usually requires modification of many reactions, which is difficult to achieve in practice. Here, improvement of threonine production via pyruvate kinase deletion in Escherichia coli is used as a case study to demonstrate a partial application of the Universal Method, which includes performing sensitivity analysis. Our analysis predicts that manipulating a few reactions is sufficient to obtain an important increase in threonine production without major perturbations of metabolite concentrations. Biotechnol. Bioeng. 2009;103: 609–620.

Modular metabolic control analysis of large responses

Deciphering the laws that govern metabolic responses of complex systems is essential to understand physiological functioning, pathological conditions and the outcome of experimental manipulations of intact cells. To this aim, a theoretical and experimental sensitivity analysis, called modular metabolic control analysis (MMCA), was proposed. This field was previously developed under the assumptions of infinitesimal changes and/or proportionality between parameters and rates, which are usually not fulfilled in vivo. Here we develop a general MMCA for two modules, not relying on those assumptions. Control coefficients and elasticity coefficients for large changes are defined. These are subject to constraints: summation and response theorems, and relationships that allow calculating control from elasticity coefficients. We show how to determine the coefficients from top‐down experiments, measuring the rates of the isolated modules as a function of the linking intermediate (there is no need to change parameters inside the modules). The novel formalism is applied to data of two experimental studies from the literature. In one of these, 40% increase in the activity of the supply module results in less than 4% increase in flux, while infinitesimal MMCA predicts more than 30% increase in flux. In addition, it is not possible to increase the flux by manipulating the activity of demand. The impossibility of increasing the flux by changing the activity of a single module is due to an abrupt decrease of the control of the modules when their corresponding activities are increased. In these cases, the infinitesimal approach can give highly erroneous predictions.

On the Origins of a Crowded Cytoplasm

Contemporary cells show a highly crowded macromolecular content, the processes which originated this state being largely unknown. We propose that a driving force leading to the crowded cellular state could be the increase in growth rate produced by an enhanced cytoplasmic protein concentration. Briefly, in a diluted scenario, an increase in protein concentration has two opposing effects on growth rate. The favorable effect is the increase in the activity per unit volume of the component proteins and the disadvantageous effect is the concomitant increase in the protein mass per unit volume which has to be produced. In this work we show that the first effect is quantitatively more important, resulting in an overall increase in growth rate. This result was obtained with a model of E. coli and using nonmechanistic physiological arguments. The proposed driving force operates even at low protein concentrations, where the nonspecific interactions of macromolecular crowding are not significant, and could be as ancient as the first protocells. Experimental measurement of this cytoplasmic protein concentration effect in present organisms is hindered by the prevailing nonspecific interactions, product of long-term evolution. However, chemical/biochemical systems, built up to mimic properties of living cells, could be an adequate tool to test this effect.

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

BackgroundLaboratory 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.ResultsTo 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.ConclusionsThis 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.

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.

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.

Temporal Aspects of the Control of Metabolic Processes

A metabolic system can be defined as composed of metabolites that are interconverted by enzyme reactions. The change of each metabolite concentration with time (dS i /dt) depends on the balance between the rates v j of production and consumption of the metabolite:

Sensitivity Analysis of Metabolic Cascades Catalyzed by Bifunctional Enzymes

\frac{{d{S_i}}}{{dt}} = \sum\limits_j {{n_{ij}}{v_j}} ,i = 1, \ldots ,m