Pedro M. B. M. Coelho

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.

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.

Relating mutant genotype to phenotype via quantitative behavior of the NADPH redox cycle in human erythrocytes.

Background The NADPH redox cycle plays a key role in antioxidant protection of human erythrocytes. It consists of two enzymes: glucose-6-phosphate dehydrogenase (G6PD) and glutathione reductase. Over 160 G6PD variants have been characterized and associated with several distinct clinical manifestations. However, the mechanistic link between the genotype and the phenotype remains poorly understood. Methodology/Principal Findings We address this issue through a novel framework (design space) that integrates information at the genetic, biochemical and clinical levels. Our analysis predicts three qualitatively-distinct phenotypic regions that can be ranked according to fitness. When G6PD variants are analyzed in design space, a correlation is revealed between the phenotypic region and the clinical manifestation: the best region with normal physiology, the second best region with a pathology, and the worst region with a potential lethality. We also show that Plasmodium falciparum, by induction of its own G6PD gene in G6PD-deficient erythrocytes, moves the operation of the cycle to a region of the design space that yields robust performance. Conclusions/Significance In conclusion, the design space for the NADPH redox cycle, which includes relationships among genotype, phenotype and environment, illuminates the function, design and fitness of the cycle, and its phenotypic regions correlate with the organisms clinical status.

Changes in glucose uptake rate and in the energy status of PC-12 cells acutely exposed to hexavalent chromium, an established human carcinogen

In the 1920s, Otto Warburg reported a striking metabolic shift in solid tumors: contrary to their normal counter parts, which exhibited a nearly pure respiratory metabolism, where cancer cells relied strongly on lactic fermentation for energy production, even in the presence of ample oxygen. This metabolic shift, later named the Warburg effect, is now viewed as a nearly universal cancer phenotype. To investigate whether it is operating in hexavalent chromium (Cr(VI))-induced carcinogenesis, PC-12 cells were exposed to low Cr(VI) concentrations and effects determined on the rates of glucose uptake, lactate production and oxygen consumption, critical indicators of the type of energy metabolism adopted by the cells. Further, the influence on the cells’ energy charge, an important parameter in the evaluation of the cellular physiological state was assessed. In the presence of ample oxygen, concentration-dependent, statistically significant decreases in the energy charge were detected, which were accompanied by an increased glucose uptake rate. This enhanced uptake may constitute the first step in a compensatory mechanism aimed at counteracting the decrease in energy charge. Although these changes may be too small to exert an impact in the cellular functions, they may provide insight into the initial steps of Cr(VI)-induced carcinogenesis.

Mapping the phenotypic repertoire of the cytoplasmic 2-Cys peroxiredoxin – Thioredoxin system. 1. Understanding commonalities and differences among cell types

The system (PTTRS) formed by typical 2-Cys peroxiredoxins (Prx), thioredoxin (Trx), Trx reductase (TrxR), and sulfiredoxin (Srx) is central in antioxidant protection and redox signaling in the cytoplasm of eukaryotic cells. Understanding how the PTTRS integrates these functions requires tracing phenotypes to molecular properties, which is non-trivial. Here we analyze this problem based on a model that captures the PTTRS’ conserved features. We have mapped the conditions that generate each distinct response to H2O2 supply rates (vsup), and estimated the parameters for thirteen human cell types and for Saccharomyces cerevisiae. The resulting composition-to-phenotype map yielded the following experimentally testable predictions. The PTTRS permits many distinct responses including ultra-sensitivity and hysteresis. However, nearly all tumor cell lines showed a similar response characterized by limited Trx-S- depletion and a substantial but self-limited gradual accumulation of hyperoxidized Prx at high vsup. This similarity ensues from strong correlations between the TrxR, Srx and Prx activities over cell lines, which contribute to maintain the Prx-SS reduction capacity in slight excess over the maximal steady state Prx-SS production. In turn, in erythrocytes, hepatocytes and HepG2 cells high vsup depletes Trx-S- and oxidizes Prx mainly to Prx-SS. In all nucleated human cells the Prx-SS reduction capacity defined a threshold separating two different regimes. At sub-threshold vsup the cytoplasmic H2O2 concentration is determined by Prx, nM-range and spatially localized, whereas at supra-threshold vsup it is determined by much less active alternative sinks and μM-range throughout the cytoplasm. The yeast shows a distinct response where the Prx Tsa1 accumulates in sulfenate form at high vsup. This is mainly due to an exceptional stability of Tsa1s sulfenate. The implications of these findings for thiol redox regulation and cell physiology are discussed. All estimates were thoroughly documented and provided, together with analytical approximations for system properties, as a resource for quantitative redox biology.

Is the Peroxiredoxin 2/Thioredoxin/Thioredoxin Reductase system in human erythrocytes designed for redox signaling?

In human erythrocytes H2O2 is mainly consumed by glutathione peroxidase, catalase and peroxiredoxin 2 (Prx2). Our previous analyses indicate that Prx2s peroxidase activity is subjected to a strong but quickly reversible inhibition (see companion abstract). If this activity is inhibited then the main role of Prx2 cannot be to eliminate H2O2. What functional advantages could then such an inhibition confer?We set up and validated a kinetic model of H2O2 metabolism human erythrocytes that shows quantitative agreement with extensive experimental observations. We then applied it to analyze the behavior of Prx2 and Trx under the H2O2 exposure dynamics that erythrocytes face in circulation. The significance of Prx2 inhibition was assessed by comparing the behavior of this model with that of an otherwise identical model lacking inhibition.Our analysis shows that Prx2 inhibition leads to 25-40% lower NADPH consumption under low to moderately high H2O2 supply (<0.8µM H2O2/s). Further, the inhibition extends the range where the concentrations of potential redox signaling readouts - H2O2, Prx2 sulfenic acid, Prx2 disulfide and Trx disulfide- show a proportional response to changes in H2O2 supply, covering practically the whole physiological range of the latter. This is desirable for analogic signal transduction and allows the Prx2/Trx/TrxR system to reliably transduce changes in H2O2 supply as changes in thiol oxidation. Finally, the inhibition allows other less abundant peroxiredoxins in the erythrocyte to be oxidized by H2O2 at physiological H2O2 supplies.Altogether, these results suggest that the postulated reversible inhibition of Prx2s peroxidase facilitates signal transduction by the peroxiredoxins and spares NADPH.We acknowledge: fellowship SFRH/BD/51199/2010, grants PEst-C/SAU/LA0001/2013-2014, PEst-OE/QUI/UI0612/2013, PEst-OE/QUI/UI0313/2014, and FCOMP-01-0124-FEDER-020978 co-financed by FEDER through the COMPETE program and by FCT (project PTDC/QUI-BIQ/119657/2010).

Is Peroxiredoxin II's peroxidase activity strongly inhibited in human erythrocytes?

H2O2 elimination in human erythrocytes is mainly carried out by catalase (Cat), glutathione peroxidase (GPx1) and the more recently discovered peroxiredoxin 2 (Prx2). However, the contribution of Prx2 to H2O2 consumption is still unclear. Prx2s high reactivity with H2O2 (kPrx2=10×10(7) M(-1)s(-1), kCat =7×10(7) M(-1)s(-1), kGPx1 =4×10(7) M(-1)s(-1)) and high abundance ([Prx2]= 570µM, [Cat]= 32µM, [GPx1]= 1µM) suggest that under low H2O2 supply rates it should consume >99% of the H2O2. However, extensive evidence indicates that in intact erythrocytes Prx2 contributes no more than Cat to H2O2 consumption. In order for this to be attained, Prx2s effective rate constant with H2O2would have to be just ~10(5) M(-1)s(-1), much lower than that determined in multiple experiments with the purified proteins. Nevertheless, nearly all Prx2 is oxidized within 1min of exposing erythrocytes to a H2O2 bolus, which is inconsistent with an irreversible inhibition. A mathematical model of the H2O2 metabolism in human erythrocytes [Benfeitas et al. (2014) Free Radic. Biol. Med.] where Prx2 either has a low kPrx2 or is subject to a strong (>99%) but readily reversible inhibition achieves quantitative agreement with detailed experimental observations of the responses of the redox status of Prx2 in human erythrocytes and suggests functional advantages of this design (see companion abstract). By contrast, a variant where Prx2 is fully active with kPrx2=10(8) M(-1)s(-1) shows important qualitative discrepancies. Altogether, these results suggest that Prx2s peroxidase activity is strongly inhibited in human erythrocytes. We acknowledge fellowship SFRH/BD/51199/2010, grants PEst-C/SAU/LA0001/2013-2014, PEst-OE/QUI/UI0612/2013, PEst-OE/QUI/UI0313/2014, and FCOMP-01-0124-FEDER-020978 (PTDC/QUI-BIQ/119657/2010) co-financed by FEDER through the COMPETE program and by FCT.