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

Relating Mutant Genotype to Phenotype via Quantitative Behavior of the NADPH Redox Cycle in Human Erythrocytes

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.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.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

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.This work was funded by FEDER funds through the Operational Programme Competitiveness Factors - COMPETE and by national funds by FCT - Foundation for Science and Technology under the strategic projects UID/NEU/04539/2013 (AS) and UID/FIS/04564/ 2016 (RT,FSA), and under the grant FCOMP-01-0124-FEDER-020978 (Project PTDC/QUI-BIQ/119657/2010) (AS). RT also acknowledges FCT's support through the FCT Researcher Program

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

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.info:eu-repo/semantics/publishedVersio

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

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 nonexpert 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

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 = β × 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

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.This work was funded by fellowship SFRH/BD/51576/2011 and grants UID/NEU/04539 COMPETE (POCI-01-0145-FEDER-007440), PEst-OE/QUI/UI0612/2013, 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)