Pillars of theoretical biology: "Biochemical systems analysis, I, II and III".

Michael Savageau's Biochemical Systems Analysis I, II, IIIpapers, published in volumes 25 and 26 of the journal,kickstarted a research programme that originated many of the core concepts and tools of Systems Biology. This article briefly summarizes these papers anddiscusses the most relevant developments in Biochemical Systems Theory since their publication.

Ligand's Partition to the Lipid Bilayer Should Be Accounted for When Estimating Their Affinity to Proteins.

Ligand-protein interactions are usually studied in complex media that also contain lipids. This is particularly relevant for membrane proteins that are always associated with lipid bilayers, but also for water-soluble proteins studied in in vivo conditions. This work addresses the following two questions: (i) How does the neglect of the lipid bilayer influence the apparent ligand-protein affinity? (ii) How can the intrinsic ligand-protein affinity be obtained? Here we present a framework to quantitatively characterize ligand-protein interactions in complex media for proteins with a single binding site. The apparent affinity obtained when following some often-used approximations is also explored, to establish these approximations' validity limits and to allow the estimation of the true affinities from data reported in literature. It is found that an increase in the ligand lipophilicity or in the volume of the lipid bilayer always leads to a decrease in the apparent ligand-protein affinity, both for water-soluble and for membrane proteins. The only exceptions are very polar ligands (excluded from the lipid bilayer) and ligands whose binding affinity to the protein increases supralinearly with ligand lipophilicity. Finally, this work discusses which are the most relevant parameters to consider when exploring the specificity of membrane proteins.

Modeling Gd3+ Complexes for Molecular Dynamics Simulations: Toward a Rational Optimization of MRI Contrast Agents.

The correct parametrization of lanthanide complexes is of the utmost importance for their characterization using computational tools such as molecular dynamics simulations. This allows the optimization of their properties for a wide range of applications, including medical imaging. Here we present a systematic study to establish the best strategies for the correct parametrization of lanthanide complexes using [Gd(DOTA)]- as a reference, which is used as a contrast agent in MRI. We chose the bonded model to parametrize the lanthanide complexes, which is especially important when considering the study of the complex as a whole (e.g., for the study of the dynamics of its interaction with proteins or membranes). We followed two strategies: a so-called heuristic approach employing strategies already published by other authors and another based on the more recent MCPB.py tool. Adjustment of the Lennard-Jones parameters of the metal was required. The final topologies obtained with both strategies were able to reproduce the experimental ion to oxygen distance, vibrational frequencies, and other structural properties. We report a new strategy to adjust the Lennard-Jones parameters of the metal ion in order to capture dynamic properties such as the residence time of the capping water (τm). For the first time, the correct assessment of the τm value for Gd-based complexes was possible by recording the dissociative events over up to 10 µs all-atom simulations. The MCPB.py tool allowed the accurate parametrization of [Gd(DOTA)]- in a simpler procedure, and in this case, the dynamics of the water molecules in the outer hydration sphere was also characterized. This sphere was divided into the first hydration layer, an intermediate region, and an outer hydration layer, with a residence time of 18, 10 and 19 ps, respectively, independent of the nonbonded parameters chosen for Gd3+. The Lennard-Jones parameters of Gd3+ obtained here for [Gd(DOTA)]- may be used with similarly structured gadolinium MRI contrast agents. This allows the use of molecular dynamics simulations to characterize and optimize the contrast agent properties. The characterization of their interaction with membranes and proteins will permit the design of new targeted contrast agents with improved pharmacokinetics.

Analysis of the Equilibrium Distribution of Ligands in Heterogeneous Media-Approaches and Pitfalls.

The equilibrium distribution of small molecules (ligands) between binding agents in heterogeneous media is an important property that determines their activity. Heterogeneous systems containing proteins and lipid membranes are particularly relevant due to their prevalence in biological systems, and their importance to ligand distribution, which, in turn, is crucial to ligand's availability and biological activity. In this work, we review several approaches and formalisms for the analysis of the equilibrium distribution of ligands in the presence of proteins, lipid membranes, or both. Special attention is given to common pitfalls in the analysis, with the establishment of the validity limits for the distinct approaches. Due to its widespread use, special attention is given to the characterization of ligand binding through the analysis of Stern-Volmer plots of protein fluorescence quenching. Systems of increasing complexity are considered, from proteins with single to multiple binding sites, from ligands interacting with proteins only to biomembranes containing lipid bilayers and membrane proteins. A new formalism is proposed, in which ligand binding is treated as a partition process, while considering the saturation of protein binding sites. This formalism is particularly useful for the characterization of interaction with membrane proteins.

Mass isotopomer analysis of nucleosides isolated from RNA and DNA using GC/MS.

Nucleosides are biosynthesized from metabolites that are at key nodes of intermediary metabolism. Therefore, (13)C labeling patterns in nucleosides from ribonucleic acid (RNA) and deoxyribonucleic acid (DNA) in suitably designed isotopic tracer studies provide information on metabolic flux distributions of proliferating cells. Here, we present a gas chromatography (GC)-mass spectrometry (MS)-based approach that permits one to exploit that potential. In order to elucidate positional isotopomers of nucleosides from RNA and DNA, we screened the fragmentation spectra of their trimethylsilyl derivatives. We identified the molecular ion moieties retained in the respective fragment ions, focusing particularly on the carbon backbone. Nucleosides fragmented at the N-glycosidic bond provide nucleobase and/or ribose or 2'-deoxyribose fragment ions and fragments thereof. Nucleoside fragments composed of the nucleobase plus some carbons of the ribose ring were also observed. In total, we unequivocally assigned 31 fragments. The mass-isotopic distribution of the assigned fragments provides valuable information for later (13)C metabolic flux analysis as indicated by a labeling experiment applying [1-(13)C]glucose in a yeast culture.

Homeostasis of free cholesterol in the blood: a preliminary evaluation and modeling of its passive transport.

The rate of noncatalyzed transfer of cholesterol (Chol) among lipoproteins and cells in the blood is of fundamental importance as a baseline to assess the role of active transport mechanisms, but remains unknown. Here we address this gap by characterizing the associa-tion of the Chol analog, ergosta-5,7,9(11),22-tetraen-3ß-ol (DHE), with the lipoproteins VLDL, LDL, HDL2, and HDL3 Combining these results with data for the association of DHE with liposomes, we elaborated a kinetic model for the noncatalyzed exchange of free Chol among blood compartments. The computational results are in good agreement with experimental values. The small deviations are explained by the nonequilibrium distribution of unesterified Chol in vivo, due to esterification and entry of new unesterified Chol, and eventual effects introduced by incubations at low temperatures. The kinetic profile of the homeostasis of unesterified Chol in the blood predicted by the model developed in this work is in good agreement with the observations in vivo, highlighting the importance of passive processes.

The architecture of redox microdomains: Cascading gradients and peroxiredoxins' redox-oligomeric coupling integrate redox signaling and antioxidant protection.

In the cytosol of human cells under low oxidative loads, hydrogen peroxide is confined to microdomains around its supply sites, due to its fast consumption by peroxiredoxins. So are the sulfenic and disulfide forms of the 2-Cys peroxiredoxins, according to a previous theoretical analysis [Travasso et al., Redox Biology 15 (2017) 297]. Here, an extended reaction-diffusion model that for the first time considers the differential properties of human peroxiredoxins 1 and 2 and the thioredoxin redox cycle predicts important new aspects of the dynamics of redox microdomains. The peroxiredoxin 1 sulfenates and disulfides are more localized than the corresponding peroxiredoxin 2 forms, due to the former peroxiredoxin's faster resolution step. The thioredoxin disulfides are also localized. As the H2O2 supply rate (vsup) approaches and then surpasses the maximal rate of the thioredoxin/thioredoxin reductase system (V), these concentration gradients become shallower, and then vanish. At low vsup the peroxiredoxin concentration determines the H2O2 concentrations and gradient length scale, but as vsup approaches V, the thioredoxin reductase activity gains influence. A differential mobility of peroxiredoxin disulfide dimers vs. reduced decamers enhances the redox polarity of the cytosol: as vsup approaches V, reduced decamers are preferentially retained far from H2O2 sources, attenuating the local H2O2 buildup. Substantial total protein concentration gradients of both peroxiredoxins emerge under these conditions, and the concentration of reduced peroxiredoxin 1 far from the H2O2 sources even increases with vsup. Altogether, the properties of 2-Cys peroxiredoxins and thioredoxin are such that localized H2O2 supply induces a redox and functional polarization between source-proximal regions (redox microdomains) that facilitate peroxiredoxin-mediated signaling and distal regions that maximize antioxidant protection.

The mammalian peroxisomal membrane is permeable to both GSH and GSSG - Implications for intraperoxisomal redox homeostasis.

Despite the large amounts of H2O2 generated in mammalian peroxisomes, cysteine residues of intraperoxisomal proteins are maintained in a reduced state. The biochemistry behind this phenomenon remains unexplored, and simple questions such as "is the peroxisomal membrane permeable to glutathione?" or "is there a thiol-disulfide oxidoreductase in the organelle matrix?" still have no answer. We used a cell-free in vitro system to equip rat liver peroxisomes with a glutathione redox sensor. The organelles were then incubated with glutathione solutions of different redox potentials and the oxidation/reduction kinetics of the redox sensor was monitored. The data suggest that the mammalian peroxisomal membrane is promptly permeable to both reduced and oxidized glutathione. No evidence for the presence of a robust thiol-disulfide oxidoreductase in the peroxisomal matrix could be found. Also, prolonged incubation of organelle suspensions with glutaredoxin 1 did not result in the internalization of the enzyme. To explore a potential role of glutathione in intraperoxisomal redox homeostasis we performed kinetic simulations. The results suggest that even in the absence of a glutaredoxin, glutathione is more important in protecting cysteine residues of matrix proteins from oxidation by H2O2 than peroxisomal catalase itself.

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.

Calculation of Permeability Coefficients from Solute Equilibration Dynamics: An Assessment of Various Methods.

Predicting the rate at which substances permeate membrane barriers in vivo is crucial for drug development. Permeability coefficients obtained from in vitro studies are valuable for this goal. These are normally determined by following the dynamics of solute equilibration between two membrane-separated compartments. However, the correct calculation of permeability coefficients from such data is not always straightforward. To address these problems, here we develop a kinetic model for solute permeation through lipid membrane barriers that includes the two membrane leaflets as compartments in a four-compartment model. Accounting for solute association with the membrane allows assessing various methods in a wide variety of conditions. The results showed that the often-used expression Papp = ß × r/3 is inapplicable to very large or very small vesicles, to moderately or highly lipophilic solutes, or when the development of a significant pH gradient opposes the solute's flux. We establish useful relationships that overcome these limitations and allow predicting permeability in compartmentalised in vitro or in vivo systems with specific properties. Finally, from the parameters for the interaction of the solute with the membrane barrier, we defined an intrinsic permeability coefficient that facilitates quantitative comparisons between solutes.

How abundant are superoxide and hydrogen peroxide in the vasculature lumen, how far can they reach?

Paracrine superoxide (O2•-) and hydrogen peroxide (H2O2) signaling critically depends on these substances' concentrations, half-lives and transport ranges in extracellular media. Here we estimated these parameters for the lumen of human capillaries, arterioles and arteries using reaction-diffusion-advection models. These models considered O2•- and H2O2 production by endothelial cells and uptake by erythrocytes and endothelial cells, O2•- dismutation, O2•- and H2O2 diffusion and advection by the blood flow. Results show that in this environment O2•- and H2O2 have half-lives <60. ms and <40. ms, respectively, the former determined by the plasma SOD3 activity, the latter by clearance by endothelial cells and erythrocytes. H2O2 concentrations do not exceed the 10 nM scale. Maximal O2•- concentrations near vessel walls exceed H2O2's several-fold when the latter results solely from O2•- dismutation. Cytosolic dismutation of inflowing O2•- may thus significantly contribute to H2O2 delivery to cells. O2•- concentrations near vessel walls decay to 50% of maximum 12 µm downstream from O2•- production sites. H2O2 concentrations in capillaries decay to 50% of maximum 22 µm (6.0 µm) downstream from O2•- (H2O2) production sites. Near arterioles' (arteries') walls, they decay by 50% within 6.0 µm (4. µm) of H2O2 production sites. However, they reach maximal values 50 µm (24 µm) downstream from O2•- production sites and decrease by 50% over 650 µm (500 µm). Arterial/olar endothelial cells might thus signal over a mm downstream through O2•--derived H2O2, though this requires nM-sensitive H2O2 transduction mechanisms.

Glucose-6-Phosphate Dehydrogenase Deficiency and Neonatal Hyperbilirubinemia: Insights on Pathophysiology, Diagnosis, and Gene Variants in Disease Heterogeneity.

Glucose-6-phosphate dehydrogenase (G6PD) deficiency is a prevalent condition worldwide and is caused by loss-of-function mutations in the G6PD gene. Individuals with deficiency are more susceptible to oxidative stress which leads to the classical, acute hemolytic anemia (favism). However, G6PD deficiency in newborn infants presents with an increased risk of hyperbilirubinemia, that may rapidly escalate to result in bilirubin induced neurologic dysfunction (BIND). Often with no overt signs of hemolysis, G6PD deficiency in the neonatal period appears to be different in the pathophysiology from favism. This review discusses and compares the mechanistic pathways involved in these two clinical presentations of this enzyme disorder. In contrast to the membrane disruption of red blood cells and Heinz bodies formation in favism, G6PD deficiency causing jaundice is perhaps attributed to the disruption of oxidant-antioxidant balance, impaired recycling of peroxiredoxin 2, thus affecting bilirubin clearance. Screening for G6PD deficiency and close monitoring of affected infants are important aspects in neonatal care to prevent kernicterus, a permanent and devastating neurological damage. WHO recommends screening for G6PD activity of all infants in countries with high prevalence of this deficiency. The traditional fluorescent spot test as a screening tool, although low in cost, misses a significant proportion of cases with moderate deficiency or the partially deficient, heterozygote females. Some newer and emerging laboratory tests and diagnostic methods will be discussed while developments in genomics and proteomics contribute to increasing studies that spatially profile genetic mutations within the protein structure that could predict their functional and structural effects. In this review, several known variants of G6PD are highlighted based on the location of the mutation and amino acid replacement. These could provide insights on why some variants may cause a higher degree of phenotypic severity compared to others. Further studies are needed to elucidate the predisposition of some variants toward certain clinical manifestations, particularly neonatal hyperbilirubinemia, and how some variants increase in severity when co-inherited with other blood- or bilirubin-related genetic disorders.

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.

Intra-dimer cooperativity between the active site cysteines during the oxidation of peroxiredoxin 2.

Peroxiredoxin 2 (Prdx2) and other typical 2-Cys Prdxs function as homodimers in which hydrogen peroxide oxidizes each active site cysteine to a sulfenic acid which then condenses with the resolving cysteine on the alternate chain. Previous kinetic studies have considered both sites as equally reactive. Here we have studied Prdx2 using a combination of non-reducing SDS-PAGE to separate reduced monomers and dimers with one and two disulfide bonds, and stopped flow analysis of tryptophan fluorescence, to investigate whether there is cooperativity between the sites. We have observed positive cooperativity when H2O2 is added as a bolus and oxidation of the second site occurs while the first site is present as a sulfenic acid. Modelling of this reaction showed that the second site reacts 2.2 ± 0.1 times faster. In contrast, when H2O2 was generated slowly and the first active site condensed to a disulfide before the second site reacted, no cooperativity was evident. Conversion of the sulfenic acid to the disulfide showed negative cooperativity, with modelling of the exponential rise in tryptophan fluorescence yielding a rate constant of 0.75 ± 0.08 s-1 when the alternate active site was present as a sulfenic acid and 2.29 ± 0.08-fold lower when it was a disulfide. No difference in the rate of hyperoxidation at the two sites was detected. Our findings imply that oxidation of one active site affects the conformation of the second site and influences which intermediate forms of the protein are favored under different cellular conditions.

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.

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.

Quantitative Assessment of Methods Used To Obtain Rate Constants from Molecular Dynamics Simulations-Translocation of Cholesterol across Lipid Bilayers.

Accurately calculating rate constants of macroscopic chemical processes from molecular dynamics simulations is a long-sought but elusive goal. The problem is particularly relevant for processes occurring in biological systems, as is the case for ligand-protein and ligand-membrane interactions. Several formalisms to determine rate constants from easily accessible free-energy profiles [Δ Go( z)] of a molecule along a coordinate of interest have been proposed. However, their applicability for molecular interactions in condensed media has not been critically evaluated or validated. This work presents such evaluation and validation and introduces improved methodology. As a case study, we have characterized quantitatively the rate of translocation of cholesterol across 1-palmitoyl-2-oleoyl- sn-glycero-3-phosphocholine bilayers. Translocation across lipid bilayers is the rate-limiting step in the permeation of most drugs through biomembranes. We use coarse-grained molecular dynamics simulations and different kinetic formalisms to calculate this rate constant. A self-consistent test of the applicability of various available formalisms is provided by comparing their predictions with the translocation rates obtained from actual events observed in long unrestrained simulations. To this effect, a novel procedure was used to obtain the effective rate constant, based on an analysis of time intervals between transitions among different states along the reaction coordinate. While most tested formalisms lead to results in reasonable agreement (within a factor of 5) with this effective rate constant, the most adequate one is based on the explicit relaxation frequencies from the transition state in the forward and backward directions along the reaction coordinate.

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.

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.

Organizing principles underlying microorganism's growth-robustness trade-off.

Growth Robustness Reciprocity (GRR) is an intriguing microbial manifestation: the impairment of microorganism's growth enhances their ability to resist acute stresses, and vice-versa. This is caused by regulatory interactions that determine higher expression of protection mechanisms in response to low growth rates. But because such regulatory mechanisms are species-specific, GRR must result from convergent evolution. Why does natural selection favor such an outcome? We used mathematical models of optimal cellular resource allocation to identify the general principles underlying GRR. Non-linear optimization allowed to predict allocation patterns of biosynthetic resources (ribosomes devoted to the synthesis of each cell component) that maximize growth. These models predict the down-regulation of stress defenses under high substrate availabilities and low stress levels. Under these conditions, stress tolerance ensues from growth-related damage dilution: the higher the substrate availability, the fastest the dilution of damaged proteins by newly synthesized proteins, the lower the accumulation of damaged components into the cell. In turn, under low substrate availability growth is too slow for effective damage dilution, and the expression of the defenses up to some optimal level then increases growth. As a consequence, slow-growing cells are pre-adapted to withstand acute stresses. Therefore, the observed negative correlation between growth and stress tolerance can be explained as a consequence of optimal resource allocation for maximal growth. We acknowledge fellowship SFRH/BPD/90065/2012 and grants PEst-C/SAU/LA0001/2013-2014 and FCOMP-01-0124-FEDER-020978 financed by FEDER through the "Programa Operacional Factores de Competitividade, COMPETE" and by national funds through "FCT, Fundação para a Ciência e a Tecnologia" (project PTDC/QUI-BIQ/119657/2010).