METATOOL: for studying metabolic networks.
MOTIVATION: To reconstruct metabolic pathways from biochemical and/or genome sequence data, the stoichiometric and thermodynamic feasibility of the pathways has to be tested. This is achieved by characterizing the admissible region of flux distributions in steady state. This region is spanned by what can be called a convex basis. The concept of 'elementary flux modes' provides a mathematical tool to define all metabolic routes that are feasible in a given metabolic network. In addition, we define 'enzyme subsets' to be groups of enzymes that operate together in fixed flux proportions in all steady states of the system. RESULTS: Algorithms for computing the convex basis and elementary modes developed earlier are briefly reviewed. A newly developed algorithm for detecting all enzyme subsets in a given network is presented. All of these algorithms have been implemented in a novel computer program named METATOOL, whose features are outlined here. The algorithms are illustrated by an example taken from sugar metabolism. AVAILABILITY: METATOOL is available from ftp://bmsdarwin.brookes.ac. uk/pub/software/ibmpc/metatool. SUPPLEMENTARY INFORMATION: http://www. biologie.hu-berlin.de/biophysics/Theory/tpfeiffer/metatoo l.html (+info)
The fourth dimension of life: fractal geometry and allometric scaling of organisms.
Fractal-like networks effectively endow life with an additional fourth spatial dimension. This is the origin of quarter-power scaling that is so pervasive in biology. Organisms have evolved hierarchical branching networks that terminate in size-invariant units, such as capillaries, leaves, mitochondria, and oxidase molecules. Natural selection has tended to maximize both metabolic capacity, by maximizing the scaling of exchange surface areas, and internal efficiency, by minimizing the scaling of transport distances and times. These design principles are independent of detailed dynamics and explicit models and should apply to virtually all organisms. (+info)
Generalization of the theory of transition times in metabolic pathways: a geometrical approach.
Cell metabolism is able to respond to changes in both internal parameters and boundary constraints. The time any system variable takes to make this response has relevant implications for understanding the evolutionary optimization of metabolism as well as for biotechnological applications. This work is focused on estimating the magnitude of the average time taken by any observable of the system to reach a new state when either a perturbation or a persistent variation occurs. With this aim, a new variable, called characteristic time, based on geometric considerations, is introduced. It is stressed that this new definition is completely general, being useful for evaluating the response time, even in complex transitions involving periodic behavior. It is shown that, in some particular situations, this magnitude coincides with previously defined transition times but differs drastically in others. Finally, to illustrate the applicability of this approach, a model of a reaction mediated by an allosteric enzyme is analyzed. (+info)
Metabolic and performance responses to constant-load vs. variable-intensity exercise in trained cyclists.
We studied glucose oxidation (Glu(ox)) and glycogen degradation during 140 min of constant-load [steady-state (SS)] and variable-intensity (VI) cycling of the same average power output, immediately followed by a 20-km performance ride [time trial (TT)]. Six trained cyclists each performed four trials: two experimental bouts (SS and VI) in which muscle biopsies were taken before and after 140 min of exercise for determination of glycogen and periodic acid-Schiff's staining; and two similar trials without biopsies but incorporating the TT. During two of the experimental rides, subjects ingested a 5 g/100 ml [U-(14)C]glucose solution to determine rates of Glu(ox). Values were similar between SS and VI trials: O(2) consumption (3.08 +/- 0.02 vs. 3.15 +/- 0.03 l/min), energy expenditure (901 +/- 40 vs. 904 +/- 58 J x kg(-1) x min(-1)), heart rate (156 +/- 1 vs. 160 +/- 1 beats/min), and rating of perceived exertion (12.6 +/- 0.6 vs. 12.7 +/- 0.7). However, the area under the curve for plasma lactate concentration vs. time was significantly greater during VI than SS (29.1 +/- 3.9 vs. 24.6 +/- 3. 7 mM/140 min; P = 0.03). VI resulted in a 49% reduction in total muscle glycogen utilization vs. 65% for SS, while total Glu(ox) was higher (99.2 +/- 5.3 vs. 83.9 +/- 5.2 g/140 min; P < 0.05). The number of glycogen-depleted type I muscle fibers at the end of 140 min was 98% after SS but only 59% after VI. Conversely, the number of type II fibers that showed reduced periodic acid-Schiff's staining was 1% after SS vs. 10% after VI. Despite these metabolic differences, subsequent TT performance was similar (29.14 +/- 0.9 vs. 30.5 +/- 0.9 min for SS vs. VI). These results indicate that whole body metabolic and cardiovascular responses to 140 min of either SS or VI exercise at the same average intensity are similar, despite differences in skeletal muscle carbohydrate metabolism and recruitment. (+info)
Acute plasma volume expansion: effect on metabolism during submaximal exercise.
To examine the effect of acute plasma volume expansion (PVE) on substrate selection during exercise, seven untrained men cycled for 40 min at 72 +/- 2% peak oxygen uptake (VO(2 peak)) on two occasions. On one occasion, subjects had their plasma volume expanded by 12 +/- 2% via an intravenous infusion of the plasma substitute Haemaccel, whereas on the other occasion no such infusion took place. Muscle samples were obtained before and immediately after exercise. In addition, heart rate and pulmonary gas and venous blood samples were obtained throughout exercise. No differences in oxygen uptake or heart rate during exercise were observed between trials, whereas respiratory exchange ratio, blood glucose, and lactate were unaffected by PVE. Muscle glycogen and lactate concentrations were not different either before or after exercise. In addition, there was no difference in total carbohydrate oxidation between trials (control: 108 +/- 2 g; PVE group: 105 +/- 2 g). Plasma catecholamine levels were not affected by PVE. These data indicate that substrate metabolism during submaximal exercise in untrained men is unaltered by acute hypervolemia. (+info)
Advantages and disadvantages of aggregating fluxes into synthetic and degradative fluxes when modelling metabolic pathways.
It is now widely accepted that mathematical models are needed to predict the behaviour of complex metabolic networks in the cell, in order to have a rational basis for planning metabolic engineering with biotechnological or therapeutical purposes. The great complexity of metabolic networks makes it crucial to simplify them for analysis, but without violating key principles of stoichiometry or thermodynamics. We show here, however, that models for branched complex systems are sometimes obtained that violate the stoichiometry of fluxes at branch points and as a result give unrealistic metabolite concentrations at the steady state. This problem is especially important when models are constructed with the S-system form of biochemical systems theory. However, the same violation of stoichiometry can occur in metabolic control analysis if control coefficients are assumed to be constant when trying to predict the effects of large changes. We derive the appropriate matrix equations to analyse this type of problem systematically and to assess its extent in any given model. (+info)
Cytochrome b evolution in birds and mammals: an evaluation of the avian constraint hypothesis.
Patterns of molecular evolution in birds have long been considered anomalous. Compared with other vertebrates, birds have reduced levels of genetic divergence between groups of similar taxonomic ranks for a variety of nuclear and mitochondrial markers. This observation led to the avian constraint hypothesis, which identifies increased functional constraint on avian proteins as the cause for the reduction in genetic divergence. Subsequent investigations provided additional support for the avian constraint hypothesis when rates of molecular evolution were found to be slower in birds than in mammals in a variety of independent calibrations. It is possible to test the avian constraint hypothesis as an explanation for this avian slowdown by comparing DNA sequence data from protein-coding regions in birds and homologous regions in mammals. The increased selective constraints should lead to a reduction in the proportion of amino acid replacement substitutions. To test for such a decrease, we calculated the numbers of amino acid replacement substitutions per replacement site (dN) and silent substitutions per silent site (dS) for the complete mitochondrial cytochrome b gene using 38 avian and 43 mammalian comparisons that were phylogenetically independent. We find that dN/dS is significantly smaller in birds than in mammals. This difference cannot be explained by differences in codon bias affecting dS values. We suggest that the avian slowdown can be explained, at least in part, by a decreased tolerance for amino acid substitutions in avian species relative to mammalian species. (+info)
Fluxes and metabolic pools as model traits for quantitative genetics. I. The L-shaped distribution of gene effects.
The fluxes through metabolic pathways can be considered as model quantitative traits, whose QTL are the polymorphic loci controlling the activity or quantity of the enzymes. Relying on metabolic control theory, we investigated the relationships between the variations of enzyme activity along metabolic pathways and the variations of the flux in a population with biallelic QTL. Two kinds of variations were taken into account, the variation of the average enzyme activity across the loci, and the variation of the activity of each enzyme of the pathway among the individuals of the population. We proposed analytical approximations for the flux mean and variance in the population as well as for the additive and dominance variances of the individual QTL. Monte Carlo simulations based on these approximations showed that an L-shaped distribution of the contributions of individual QTL to the flux variance (R(2)) is consistently expected in an F(2) progeny. This result could partly account for the classically observed L-shaped distribution of QTL effects for quantitative traits. The high correlation we found between R(2) value and flux control coefficients variance suggests that such a distribution is an intrinsic property of metabolic pathways due to the summation property of control coefficients. (+info)