Phenomenological definition of response times with application to metabolic reactions

The metabolic response time, i.e. the delay the system introduces in the response to an input flux, is considered. A novel phenomenological definition is presented, which is valid for any kind of behavior, including transitory or permanent oscillatory responses. In order to calculate the response time of single-input systems, output fluxes have to be deconvoluted with the input flux. The bases for this are established. The resulting function (unit impulse response in time-invariant linear systems) is transformed by subtracting its final state, taking the absolute value and normalizing by the resulting area, so that a norm can be applied that weights the response at every time. This response time can also be interpreted as an average. It coincides with the transition (characteristic) time of an output flux, provided that the input is performed instantaneously (step function). A strictly non-negative response function is needed for the response time to be interpreted as a mass balance. A simple example is used to study the deviation otherwise. The method is advantageous in that it provides clues on the phenomenological behavior of biochemical systems. For example, deconvolution reveals the intrinsic oscillation-generating mechanism of an allosteric enzyme, which becomes hidden when the input flux increases in a slow way. This is illustrated by means of a model.     

Equivalence of branched and unbranched Michaelian pathways concerning periodic signal transmission

Sinusoidal oscillation transmission through branched metabolic pathways is studied. Two systems are analyzed, which are composed of two convergent reaction branches and differ in the length of one of them. Linear kinetics is assumed first. Michaelis-Menten enzymes are then considered by using previous results that suggest their behavior with respect to propagation of oscillations is close to linearity around the mean input flux. As a result, there exist ways to modulate the activity of the enzymes so that propagation is equivalent for branched and specific unbranched pathways. Cells may have taken advantage of such a possibility in cases where oscillations have a biological role.     

Susceptibility of non-linear systems as an approach to metabolic responses

MOTIVATION: Recent developments of several analytical techniques and fast sampling procedures are making it possible to study non-linear dynamics on an automated basis. Approaches that suggest experimental setups and fully exploit the data are needed. To prevent unreliable fits of parameters to experimental data, model-independent methods would be advantageous. One such method consists in representing the response of a system by means of a transformation or functional, of an excitation, i.e. a flux of a metabolite. RESULTS: A functional of unknown form can be expanded in series if its functional derivatives are known. An algorithm for calculating such generalized derivatives from impulse-perturbation experiments was developed. The only assumption was that the implicit kinetics is time-independent, i.e. the system is time-invariant. The method is illustrated on a part of fructose catabolism. A reaction network that involves 14 metabolites and 11 enzymes and includes several branches and feedback loops is considered. It is shown that the method provides good approximations to the responses of this complex system. AVAILABILITY: FUNDER is available from http://bbm1.ucm.es/torralba/funder/down/ SUPPLEMENTARY INFORMATION: http://bbm1.ucm.es/torralba/funder/     

Influence of boron and calcium on the tolerance to salinity of nitrogen-fixing pea plants

The effects of different levels of B (from 9.3 to 93 M B) and Ca (from 0.68 to 5.44 mM Ca) on plant development, nitrogen fixation, and mineral composition of pea (Pisum sativum L. cv. Argona) grown in symbiosis with Rhizobium leguminosarum bv. viciae 3841 and under salt stress, were analysed. The addition of extra B and extra Ca to the nutrient solution prevented the reduction caused by 75 mM NaCl of plant growth and the inhibition of nodulation and nitrogen fixation. The number of nodules recovered by the increase of Ca concentration at any B level, but only nodules developed at high B and high Ca concentrations could fix nitrogen. Addition of extra B and Ca during plant growth restored nodule organogenesis and structure, which was absolutely damaged by high salt. The increase in salt tolerance of symbiotic plants mediated by B and Ca can be co-related with the recovery of the contents of some nutrients. Salinity produced a decrease of B and Ca contents both in shoots and in nodulated roots, being increased by the supplement of both elements in the nutrient solution. Salinity also reduced the content in plants of other nutrients important for plant development and particularly for symbiotic nitrogen fixation, as K and Fe. A balanced nutrition of B and Ca (55.8 M B, 2.72 mM Ca) was able to counter-act the deficiency of these nutrients in salt-stressed plants, leading to a huge increase in salinity tolerance of symbiotic pea plants. The necessity of nutritional studies to successfully cultivate legumes in saline soils is discussed and proposed.     

Phylogenetic and gene-centric metagenomics of the canine intestinal microbiome reveals similarities with humans and mice

This study is the first to use a metagenomics approach to characterize the phylogeny and functional capacity of the canine gastrointestinal microbiome. Six healthy adult dogs were used in a crossover design and fed a low-fiber control diet (K9C) or one containing 7.5% beet pulp (K9BP). Pooled fecal DNA samples from each treatment were subjected to 454 pyrosequencing, generating 503 280 (K9C) and 505 061 (K9BP) sequences. Dominant bacterial phyla included the Bacteroidetes/Chlorobi group and Firmicutes, both of which comprised ∼35% of all sequences, followed by Proteobacteria (13–15%) and Fusobacteria (7–8%). K9C had a greater percentage of Bacteroidetes, Fusobacteria and Proteobacteria, whereas K9BP had greater proportions of the Bacteroidetes/Chlorobi group and Firmicutes. Archaea were not altered by diet and represented ∼1% of all sequences. All archaea were members of Crenarchaeota and Euryarchaeota, with methanogens being the most abundant and diverse. Three fungi phylotypes were present in K9C, but none in K9BP. Less than 0.4% of sequences were of viral origin, with >99% of them associated with bacteriophages. Primary functional categories were not significantly affected by diet and were associated with carbohydrates; protein metabolism; DNA metabolism; cofactors, vitamins, prosthetic groups and pigments; amino acids and derivatives; cell wall and capsule; and virulence. Hierarchical clustering of several gastrointestinal metagenomes demonstrated phylogenetic and metabolic similarity between dogs, humans and mice. More research is required to provide deeper coverage of the canine microbiome, evaluate effects of age, genetics or environment on its composition and activity, and identify its role in gastrointestinal disease.     

Susceptibilities of an Irreversible Michaelis – Menten Enzyme

The nonlinear response of the simplest irreversible Michaelis – Menten enzyme is considered. In the context of metabolic networks, i.e. in vivo, the enzyme is subject to sustained, frequently time-dependent, input fluxes that keep the system out of equilibrium. The connection between the fluxes and the response is investigated by means of a new sensitivity analysis. The kinetics of the enzyme is simple enough to allow for the computations to be carried out analytically. In particular, a set of sensitivities of the response with respect to the substrate influx, the susceptibilities, is derived. The susceptibilities are multivariate functions and thus are suitable for predicting complete progress curves of several variables of biochemical interest, namely, rates and concentrations. This is shown by means of an example. The relationship between the susceptibilities and the stoichiometry of the reaction is also taken into account. Moreover, all the required information comes from decay experiments of initial concentrations, which are common in enzymological setups.