Partial inhibition and bilevel optimization in flux balance analysis

Motivation: Within Flux Balance Analysis, the investigation of complex subtasks, such as finding the optimal perturbation of the network or finding an optimal combination of drugs, often requires to set up a bilevel optimization problem. In order to keep the linearity and convexity of these nested optimization problems, an ON/OFF description of the effect of the perturbation (i.e. Boolean variable) is normally used. This restriction may not be realistic when one wants, for instance, to describe the partial inhibition of a reaction induced by a drug.Results: In this paper we present a formulation of the bilevel optimization which overcomes the oversimplified ON/OFF modeling while preserving the linear nature of the problem. A case study is considered: the search of the best multi-drug treatment which modulates an objective reaction and has the minimal perturbation on the whole network. The drug inhibition is described and modulated through a convex combination of a fixed number of Boolean variables. The results obtained from the application of the algorithm to the core metabolism of E.coli highlight the possibility of finding a broader spectrum of drug combinations compared to a simple ON/OFF modeling.Conclusions: The method we have presented is capable of treating partial inhibition inside a bilevel optimization, without loosing the linearity property, and with reasonable computational performances also on large metabolic networks. The more fine-graded representation of the perturbation allows to enlarge the repertoire of synergistic combination of drugs for tasks such as selective perturbation of cellular metabolism. This may encourage the use of the approach also for other cases in which a more realistic modeling is required. \ua9 2013 Facchetti and Altafini; licensee BioMed Central Ltd

Curcuminoid Binding to Embryonal Carcinoma Cells: Reductive Metabolism, Induction of Apoptosis, Senescence, and Inhibition of Cell Proliferation

Curcumin preparations typically contain a mixture of polyphenols, collectively referred to as curcuminoids. In addition to the primary component curcumin, they also contain smaller amounts of the co-extracted derivatives demethoxycurcumin and bisdemethoxycurcumin. Curcuminoids can be differentially solubilized in serum, which allows for the systematic analysis of concentration-dependent cellular binding, biological effects, and metabolism. Technical grade curcumin was solubilized in fetal calf serum by two alternative methods yielding saturated preparations containing either predominantly curcumin (60%) or bisdemethoxycurcumin (55%). Continual exposure of NT2/D1 cells for 4–6 days to either preparation in cell culture media reduced cell division (1–5 µM), induced senescence (6–7 µM) or comprehensive cell death (8–10 µM) in a concentration-dependent manner. Some of these effects could also be elicited in cells transiently exposed to higher concentrations of curcuminoids (47 µM) for 0.5–4 h. Curcuminoids induced apoptosis by generalized activation of caspases but without nucleosomal fragmentation. The equilibrium binding of serum-solubilized curcuminoids to NT2/D1 cells incubated with increasing amounts of curcuminoid-saturated serum occurred with apparent overall dissociation constants in the 6–10 µM range. However, the presence of excess free serum decreased cellular binding in a hyperbolic manner. Cellular binding was overwhelmingly associated with membrane fractions and bound curcuminoids were metabolized in NT2/D1 cells via a previously unidentified reduction pathway. Both the binding affinities for curcuminoids and their reductive metabolic pathways varied in other cell lines. These results suggest that curcuminoids interact with cellular binding sites, thereby activating signal transduction pathways that initiate a variety of biological responses. The dose-dependent effects of these responses further imply that distinct cellular pathways are sequentially activated and that this activation is dependent on the affinity of curcuminoids for the respective binding sites. Defined serum-solubilized curcuminoids used in cell culture media are thus suitable for further investigating the differential activation of signal transduction pathways