Armindo Salvador

Tools for kinetic modeling of biochemical networks

The number of software packages for kinetic modeling of biochemical networks continues to grow. Although most packages share a common core of functionality, the specific capabilities and user interfaces of different packages mean that choosing the best package for a given task is not trivial. We compare 12 software packages with respect to their functionality, reliability, efficiency, user-friendliness and compatibility. Although most programs performed reliably in all numerical tasks tested, SBML compatibility and the set-up of multicompartmentalization are problematic in many packages. For simple models, GEPASI seems the best choice for non-expert users. For large-scale models, environments such as Jarnac/JDesigner are preferable, because they allow modular implementation of models. Virtual Cell is the most versatile program and provides the simplest and clearest functionality for setting up multicompartmentalization.

Lipid peroxidation in mitochondrial inner membranes. I. An integrative kinetic model.

An integrative mathematical model was developed to obtain an overall picture of lipid hydroperoxide metabolism in the mitochondrial inner membrane and surrounding matrix environment. The model explicitly considers an aqueous and a membrane phase, integrates a wide set of experimental data, and unsupported assumptions were minimized. The following biochemical processes were considered: the classic reactional scheme of lipid peroxidation; antioxidant and pro-oxidant effects of vitamin E; pro-oxidant effects of iron; action of phospholipase A2, glutathione-dependent peroxidases, glutathione reductase and superoxide dismutase; production of superoxide radicals by the mitochondrial respiratory chain; oxidative damage to proteins and DNA. Steady-state fluxes and concentrations as well as half-lives and mean displacements for the main metabolites were calculated. A picture of lipid hydroperoxide physiological metabolism in mitochondria in vivo showing the main pathways is presented. The main results are: (a) perhydroxyl radical is the main initiation agent of lipid peroxidation (with a flux of 10(-7)MS-1); (b) vitamin E efficiently inhibits lipid peroxidation keeping the amplification (kinetic chain length) of lipid peroxidation at low values (approximately equal to 10); (c) only a very minor fraction of lipid hydroperoxides escapes reduction via glutathione-dependent peroxidases; (d) oxidized glutathione is produced mainly from the reduction of hydrogen peroxide and not from the reduction of lipid hydroperoxides.

Phenotypes and tolerances in the design space of biochemical systems

One of the major unsolved problems of modern biology is deep understanding of the complex relationship between the information encoded in the genome of an organism and the phenotypic properties manifested by that organism. Fundamental advances must be made before we can begin to approach the goal of predicting the phenotypic consequences of a given mutation or an organisms response to a novel environmental challenge. Although this problem is often portrayed as if the task were to find a more or less direct link between genotypic and phenotypic levels, on closer examination the relationship is far more layered and complex. Although there are some intuitive notions of what is meant by phenotype at the level of the organism, it is far from clear what this term means at the biochemical level. We have described design principles that are readily revealed by representation of molecular systems in an appropriate design space. Here, we first describe a generic approach to the construction of such a design space in which qualitatively distinct phenotypes can be identified and counted. Second, we show how the boundaries between these phenotypic regions provide a method of characterizing a systems tolerance to large changes in the values of its parameters. Third, we illustrate the approach for one of the most basic modules of biochemical networks and describe an associated design principle. Finally, we discuss the scaling of this approach to large systems.

Why does SOD overexpression sometimes enhance, sometimes decrease, hydrogen peroxide production? a minimalist explanation

Toxic effects of superoxide dismutase (SOD) overexpression are commonly attributed to increased hydrogen peroxide (H(2)O(2)) production. Still, published experiments yield contradictory evidence on whether SOD overexpression increases or decreases H(2)O(2) production. We analyzed this issue using a minimal mathematical model. The most relevant mechanisms of superoxide consumption are treated as pseudo first-order processes, and both superoxide production and the activity of enzymes other than SOD were considered constant. Even within this simple framework, SOD overexpression may increase, hold constant, or decrease H(2)O(2) production. At normal SOD levels, the outcome depends on the ratio between the rate of processes that consume superoxide without forming H(2)O(2) and the rate of processes that consume superoxide with high (>/= 1) H(2)O(2) yield. In cells or cellular compartments where this ratio is exceptionally low (< 1), a modest decrease in H(2)O(2) production upon SOD overexpression is expected. Where the ratio is higher than unity, H(2)O(2) production should increase, but at most linearly, with SOD activity. The results are consistent with the available experimental observations. According to the minimal model, only where most superoxide is eliminated through H(2)O(2)-free processes does SOD activity have the moderately large influence on H(2)O(2) production observed in some experiments.

Quantitative evolutionary design of glucose 6-phosphate dehydrogenase expression in human erythrocytes

Why do the activities of some enzymes greatly exceed the flux capacity of the embedding pathways? This is a puzzling open problem in quantitative evolutionary design. In this work we investigate reasons for high expression of a thoroughly characterized enzyme: glucose 6-phosphate dehydrogenase (G6PD) in human erythrocytes. G6PD catalyses the first step of the pathway that supplies NADPH for antioxidant defense mechanisms. Normal G6PD activity far exceeds the capacity of human erythrocytes for a steady NADPH supply, which is limited upstream of G6PD. However, the distribution of erythrocyte G6PD activity in human populations reveals a selective pressure for maintaining high activity. To clarify the nature of this selective pressure, we studied how G6PD activity and other parameters in a model of the NADPH redox cycle affect metabolic performance. Our analysis indicates that normal G6PD activity is sufficient but not superfluous to avoid NADPH depletion and ensure timely adaptation of the NADPH supply during pulses of oxidative load such as those that occur during adherence of erythrocytes to phagocytes. These results suggest that large excess capacities found in some biochemical and physiological systems, rather than representing large safety factors, may reflect a close match of system design to unscrutinized performance requirements. Understanding quantitative evolutionary design thus calls for careful consideration of the various performance specifications that biological components/processes must meet in order for the organism to be fit. The biochemical systems framework used in this paper is generally applicable for such a detailed examination of the quantitative evolutionary design of gene expression levels in other systems.

Hydroperoxyl, superoxide and pH gradients in the mitochondrial matrix: a theoretical assessment.

The negative surface charge of many cellular membranes concentrates protons and rarefies superoxide in their vicinity. It was speculated that the low pH near membranes should facilitate superoxide protonation, thereby concentrating hydroperoxyl radical in this region. This process would exacerbate both lipid peroxidation and the transfer of oxidative damage between cellular compartments, as hydroperoxyl is a good initiator of lipid peroxidation and permeates lipid bilayers. Surface-charge-enhancement of hydroperoxyl production in mitochondria--which are main intracellular sources of superoxide--should be particularly relevant. Using a simple model of superoxide metabolism in the mitochondrial matrix, we calculated the gradients of pH, superoxide, and hydroperoxyl, and assessed the previous hypothesis in the light of available experimental data. The following predictions ensued: (i) Near the mitochondrial inner membrane, gradients of superoxide concentration with amplitude up to 36% of the maximal concentration, and pH gradients of up to 0.19 units between membrane and bulk. (ii) These electrostatically induced gradients die out within approximately 4 nm of the membrane. (iii) At high (hundreds of nanometres) inter-cristae separations, owing to enzyme-catalyzed dismutation of superoxide, both superoxide and hydroperoxyl become rarefied towards the midpoint between cristae. (iv) Surface charge should neither enhance superoxide protonation nor concentrate hydroperoxyl near biological membranes.

Quantifying Global Tolerance of Biochemical Systems: Design Implications for Moiety-Transfer Cycles

Robustness of organisms is widely observed although difficult to precisely characterize. Performance can remain nearly constant within some neighborhood of the normal operating regime, leading to homeostasis, but then abruptly break down with pathological consequences beyond this neighborhood. Currently, there is no generic approach to identifying boundaries where local performance deteriorates abruptly, and this has hampered understanding of the molecular basis of biological robustness. Here we introduce a generic approach for characterizing boundaries between operational regimes based on the piecewise power-law representation of the systems components. This conceptual framework allows us to define “global tolerance” as the ratio between the normal value of a parameter and the value at such a boundary. We illustrate the utility of this concept for a class of moiety-transfer cycles, which is a widespread module in biology. Our results show a region of “best” local performance surrounded by “poor” regions; also, selection for improved local performance often pushes the operating values away from regime boundaries, thus increasing global tolerance. These predictions agree with experimental data from the reduced nicotinamide adenine dinucleotide phosphate (NADPH) redox cycle of human erythrocytes.

Hydrogen peroxide metabolism and sensing in human erythrocytes: A validated kinetic model and reappraisal of the role of peroxiredoxin II

Hydrogen peroxide (H2O2) metabolism in human erythrocytes has been thoroughly investigated, but unclear points persist. By integrating the available data into a mathematical model that accurately represents the current understanding and comparing computational predictions to observations we sought to (a) identify inconsistencies in present knowledge, (b) propose resolutions, and (c) examine their functional implications. The systematic confrontation of computational predictions with experimental observations of the responses of intact erythrocytes highlighted the following important discrepancy. The high rate constant (10(7)-10(8) M(-1) s(-1)) for H2O2 reduction determined for purified peroxiredoxin II (Prx2) and the high abundance of this protein indicate that under physiological conditions it consumes practically all the H2O2. However, this is inconsistent with extensive evidence that Prx2s contribution to H2O2 elimination is comparable to that of catalase. Models modified such that Prx2s effective peroxidase activity is just 10(5) M(-1) s(-1) agree near quantitatively with extensive experimental observations. This low effective activity is probably due to a strong but readily reversible inhibition of Prx2s peroxidatic activity in intact cells, implying that the main role of Prx2 in human erythrocytes is not to eliminate peroxide substrates. Simulations of the responses to physiological H2O2 stimuli highlight that a design combining abundant Prx2 with a low effective peroxidase activity spares NADPH while improving potential signaling properties of the Prx2/thioredoxin/thioredoxin reductase system.

Synergism analysis of biochemical systems. I. Conceptual framework

The detection of synergisms--deviations from additive or linear behaviour--is often an important step in uncovering mechanisms of biochemical processes. Yet, a theoretical background for systemic analysis of synergisms in metabolic networks is lacking. Based on suitable mathematical models, such a theoretical approach should allow predicting synergisms and analysing what mechanistic features contribute to specific synergisms. This work presents a conceptual framework and formalism that fulfil these purposes. The synergism between perturbations of a pair of parameters is quantified as the difference between the response to the simultaneous perturbation of both parameters and the sum of the individual responses to the perturbations of each parameter. A generalisation measures deviations from multiplicative or power-law behaviour. These deviations were called log-synergisms, as in logarithmic coordinates they are quantified in the same way as the synergisms are in Cartesian coordinates. For small perturbations, synergisms and log-synergisms are approximately proportional to the second derivatives (in Cartesian and logarithmic coordinates, respectively) of the observable to the perturbed parameter(s). These derivatives, here called synergism or log-synergism coefficients, measure how steeply the responses diverge from linearity/additivity or power-law/multiplicativity. The formalism now presented allows evaluating (log-)synergism coefficients for systemic steady-state responses, and relates these coefficients to intrinsic kinetic properties of the underlying processes. A robust homeostasis of metabolite concentrations requires that these have moderate systemic log- and relative-synergism coefficients.

Localized redox relays as a privileged mode of cytoplasmic hydrogen peroxide signaling

Hydrogen peroxide (H2O2) is a key signaling agent. Its best characterized signaling actions in mammalian cells involve the early oxidation of thiols in cytoplasmic phosphatases, kinases and transcription factors. However, these redox targets are orders of magnitude less H2O2-reactive and abundant than cytoplasmic peroxiredoxins. How can they be oxidized in a signaling time frame? Here we investigate this question using computational reaction-diffusion models of H2O2 signaling. The results show that at H2O2 supply rates commensurate with mitogenic signaling a H2O2 concentration gradient with a length scale of a few tenths of μm is established. Even near the supply sites H2O2 concentrations are far too low to oxidize typical targets in an early mitogenic signaling time frame. Furthermore, any inhibition of the peroxiredoxin or increase in H2O2 supply able to drastically increase the local H2O2 concentration would collapse the concentration gradient and/or cause an extensive oxidation of the peroxiredoxins I and II, inconsistent with experimental observations. In turn, the local concentrations of peroxiredoxin sulfenate and disulfide forms exceed those of H2O2 by several orders of magnitude. Redox targets reacting with these forms at rate constants much lower than that for, say, thioredoxin could be oxidized within seconds. Moreover, the spatial distribution of the concentrations of these peroxiredoxin forms allows them to reach targets within 1 μm from the H2O2 sites while maintaining signaling localized. The recruitment of peroxiredoxins to specific sites such as caveolae can dramatically increase the local concentrations of the sulfenic and disulfide forms, thus further helping these species to outcompete H2O2 for the oxidation of redox targets. Altogether, these results suggest that H2O2 signaling is mediated by localized redox relays whereby peroxiredoxins are oxidized to sulfenate and disulfide forms at H2O2 supply sites and these forms in turn oxidize the redox targets near these sites.