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 organism's 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 system's 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 system's 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.

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 Tsa1's 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.

Integration between anticipatory blocking and redox signaling by the peroxiredoxin/thioredoxin/thioredoxin-reductase system.

Cells are occasionally exposed to high H2O2 concentrations, often preceding exposure to other electrophylic compounds. Both H2O2 and these compounds can irreversibly modify protein thiols, with deleterious consequences. Induction of enzymatic defenses against those agents is too slow to avoid significant damage. Cells may solve this conundrum by reversibly "blocking" the thiols once H2O2 concentrations begin to increase. We term this mechanism "anticipatory blocking" because it acts in anticipation of irreversible damage upon detection of early signs of stress. Here we examine the design requirements for the Peroxiredoxin/Thioredoxin/Thioredoxin-Reductase/Protein-Dithiol System (PTTRDS) to effectively integrate H2O2 signaling and anticipatory blocking of protein dithiols as disulfides, and we compared them to the designs found in cells. To that effect, we developed a minimal model of the PTTRDS, and we defined a set of quantitative performance criteria that embody the requirements for (a) efficient scavenging capacity, (b) low NADPH consumption, (c) effective signal propagation, and (d) effective anticipatory blocking. We then sought the design principles (relationships among rate constants and species concentrations) that warrant fulfillment of all these criteria. Experimental data indicates that the design of the PTTRDS in human erythrocytes fulfills these principles and thus accomplishes effective integration between anticipatory blocking, antioxidant protection and redox signaling. A more general analysis suggests that the same principles hold in a wide variety of cell types and organisms. We acknowledge grants PEst-C/SAU/LA0001/2013-2014, PEst-OE/QUI/UI0612/2013, FCOMP-01-0124-FEDER-020978 (PTDC/QUI-BIQ/119657/2010) financed by FEDER through the "Programa Operacional Factores de Competitividade, COMPETE" and by national funds through "FCT, Fundação para a Ciência e a Tecnologia".

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 Prx2's contribution to H2O2 elimination is comparable to that of catalase. Models modified such that Prx2's 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 Prx2's 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 organism's clinical status.