Fixed-points in random Boolean networks: The impact of parallelism in the Barabási-Albert scale-free topology case.

Fixed points are fundamental states in any dynamical system. In the case of gene regulatory networks (GRNs) they correspond to stable genes profiles associated to the various cell types. We use Kauffman's approach to model GRNs with random Boolean networks (RBNs). In this paper we explore how the topology affects the distribution of the number of fixed points in randomly generated networks. We also study the size of the basins of attraction of these fixed points if we assume the α-asynchronous dynamics (where every node is updated independently with probability 0≤α≤1). It is well-known that asynchrony avoids the cyclic attractors into which parallel dynamics tends to fall. We observe the remarkable property that, in all our simulations, if for a given RBN with Barabási-Albert topology and α-asynchronous dynamics an initial configuration reaches a fixed point, then every configuration also reaches a fixed point. By contrast, in the parallel regime, the percentage of initial configurations reaching a fixed point (for the same networks) is dramatically smaller. We contrast the results of the simulations on Barabási-Albert networks with the classical Erdös-Rényi model of random networks. Everything indicates that Barabási-Albert networks are extremely robust. Finally, we study the mean and maximum time/work needed to reach a fixed point when starting from randomly chosen initial configurations.

Continuous modeling of metabolic networks with gene regulation in yeast and in vivo determination of rate parameters.

A continuous model of a metabolic network including gene regulation to simulate metabolic fluxes during batch cultivation of yeast Saccharomyces cerevisiae was developed. The metabolic network includes reactions of glycolysis, gluconeogenesis, glycerol and ethanol synthesis and consumption, the tricarboxylic acid cycle, and protein synthesis. Carbon sources considered were glucose and then ethanol synthesized during growth on glucose. The metabolic network has 39 fluxes, which represent the action of 50 enzymes and 64 genes and it is coupled with a gene regulation network which defines enzyme synthesis (activities) and incorporates regulation by glucose (enzyme induction and repression), modeled using ordinary differential equations. The model includes enzyme kinetics, equations that follow both mass-action law and transport as well as inducible, repressible, and constitutive enzymes of metabolism. The model was able to simulate a fermentation of S. cerevisiae during the exponential growth phase on glucose and the exponential growth phase on ethanol using only one set of kinetic parameters. All fluxes in the continuous model followed the behavior shown by the metabolic flux analysis (MFA) obtained from experimental results. The differences obtained between the fluxes given by the model and the fluxes determined by the MFA do not exceed 25% in 75% of the cases during exponential growth on glucose, and 20% in 90% of the cases during exponential growth on ethanol. Furthermore, the adjustment of the fermentation profiles of biomass, glucose, and ethanol were 95%, 95%, and 79%, respectively. With these results the simulation was considered successful. A comparison between the simulation of the continuous model and the experimental data of the diauxic yeast fermentation for glucose, biomass, and ethanol, shows an extremely good match using the parameters found. The small discrepancies between the fluxes obtained through MFA and those predicted by the differential equations, as well as the good match between the profiles of glucose, biomass, and ethanol, and our simulation, show that this simple model, that does not rely on complex kinetic expressions, is able to capture the global behavior of the experimental data. Also, the determination of parameters using a straightforward minimization technique using data at only two points in time was sufficient to produce a relatively accurate model. Thus, even with a small amount of experimental data (rates and not concentrations) it was possible to estimate the parameters minimizing a simple objective function. The method proposed allows the obtention of reasonable parameters and concentrations in a system with a much larger number of unknowns than equations. Hence a contribution of this study is to present a convenient way to find in vivo rate parameters to model metabolic and genetic networks under different conditions.

A discrete mathematical model applied to genetic regulation and metabolic networks.

This paper describes the use of a discrete mathematical model to represent the basic mechanisms of regulation of the bacteria E. coli in batch fermentation. The specific phenomena studied were the changes in metabolism and genetic regulation when the bacteria use three different carbon substrates (glucose, glycerol, and acetate). The model correctly predicts the behavior of E. coli vis-à-vis substrate mixtures. In a mixture of glucose, glycerol, and acetate, it prefers glucose, then glycerol, and finally acetate. The model included 67 nodes; 28 were genes, 20 enzymes, and 19 regulators/biochemical compounds. The model represents both the genetic regulation and metabolic networks in an inrtegrated form, which is how they function biologically. This is one of the first attempts to include both of these networks in one model. Previously, discrete mathematical models were used only to describe genetic regulation networks. The study of the network dynamics generated 8 (2(3)) fixed points, one for each nutrient configuration (substrate mixture) in the medium. The fixed points of the discrete model reflect the phenotypes described. Gene expression and the patterns of the metabolic fluxes generated are described accurately. The activation of the gene regulation network depends basically on the presence of glucose and glycerol. The model predicts the behavior when mixed carbon sources are utilized as well as when there is no carbon source present. Fictitious jokers (Joker1, Joker2, and Repressor SdhC) had to be created to control 12 genes whose regulation mechanism is unknown, since glycerol and glucose do not act directly on the genes. The approach presented in this paper is particularly useful to investigate potential unknown gene regulation mechanisms; such a novel approach can also be used to describe other gene regulation situations such as the comparison between non-recombinant and recombinant yeast strain, producing recombinant proteins, presently under investigation in our group.

New approaches for predicting protein retention time in hydrophobic interaction chromatography.

Hydrophobic interaction chromatography (HIC) is an important technique for the purification of proteins. In this paper, we review three different approaches for predicting protein retention time in HIC, based either on a protein's structure or on its amino-acidic composition, and we have extended one of these approaches. The first approach correlates the protein retention time in HIC with the protein average surface hydrophobicity. This methodology is based on the protein three-dimensional structure data and considers the hydrophobic contribution of the exposed amino acid residues as a weighted average. The second approach, which we have extended, is based on the high correlation level between the average surface hydrophobicity of a protein's hydrophobic interacting zone and its retention time in HIC. Finally, a third approach carries out a prediction of the average surface hydrophobicity of a protein, using only its amino-acidic composition, without knowing its three-dimensional structure. These models would make it possible to test different operating conditions for the purification of a target protein by computer simulations, and thus make it easier to select the optimal conditions, contributing to the rational design and optimization of the process.

Diclofenac/N-(2-hydroxyethyl)pyrrolidine: a new salt for an old drug.

Twenty-four diclofenac salts were prepared using inorganic and organic, linear and cyclic, hydrophilic and hydrophobic bases and their behaviour in polar and poorly polar solvents was examined. Most salts were found more soluble in 1-octanol than in water, suggesting a fair hydrophobicity of these compounds and their existence as ion pairs in non-polar solvents. The salt diclofenac/N-(2-hydroxyethyl)pyrrolidine (DHEP) is the most soluble of this group in 1-octanol (8.39% w/w) and in water (1.89% w/w), where it displays a surfactant behaviour above 1.44% w/w, which can be considered as a critical micellar concentration. It was possible to study the surface activity of diclofenac only using DHEP, since all other salts of this group are not soluble enough to overcome the critical concentration. The mild detergent properties of DHEP were confirmed by the solubilization of lecithin and the formation of mixed micelles with bile salts: these properties appear very interesting in developing new pharmaceutical forms containing DHEP, as a chemical form for the delivery of the active principle diclofenac.

Chemical properties-dissolution relationship. IV. Behaviour in solution of the diclofenac/N-(2-hydroxyethyl) pyrrolidine salt (DHEP).

The behaviour in solution of the salt formed between diclofenac and N-(2-hydroxyethyl) pyrrolidine (DHEP) was examined. This salt is more soluble and dissolves more rapidly than sodium diclofenac and tends to give rise to supersaturated solutions, that only slowly evolve to equilibrium. Above 35 mM of DHEP, the solutions show unexpected solubilization ability towards sparingly soluble materials. The faster plasma level found, when DHEP is administered per os, can be associated to this weak detergency. These properties make DHEP a suitable pharmaceutical form to prepare extemporary solutions for short term analgesic therapy.

Intraocular ossification.

Intraocular ossification was investigated in a series of 20 eyes. Only 12 eyes were phthisical. The etiological factors were trauma, inflammation, glaucoma and massive intraocular gliosis. Bone tissue was of the compact and spongy type. A correlation was found between the intraocular ossification and retinal detachment, intraocular hemorrhage, intraocular neovascularization and uveitis.

Operant conditioning of skin resistance tonic levels.

The purpose of the current investigation was to determine whether increases and decreases in skin resistance tonic level could be controlled by individuals given discrete visual feedback of such activity. Thirty-six male undergraduate students served as subjects. They were assigned randomly in equal numbers to four groups; two of the groups received accurate feedback of skin resistance level changes and two received inaccurate feedback. The two accurate-feedback groups differed with respect to the order in which increases and decreases in skin resistance level were reinforced. Each noncontingent group was matched with one of the contingent groups in terms of reinforcement density. The results indicated that accurate feedback produced skin resistance level changes consistent with the type of reinforcement employed. However, operant control was not clearly sustained subsequent to a reversal in the type of tonic level change reinforced. Some problems related to the clinical application of skin resistance level training are discussed.