Necessary conditions for multistationarity in discrete dynamical systems

R. Thomas conjectured, 20 years ago, that the presence of a positive circuit in the interaction graph of a dynamical system is a necessary condition for the presence of several stable states. Recently, E. Remy et al. stated and proved the conjecture for Boolean dynamical systems. Using a similar approach, we generalize the result to discrete dynamical systems, and by focusing on the asynchronous dynamics that R. Thomas used in the course of his analysis of genetic networks, we obtain a more general variant of R. Thomas’ conjecture. In this way, we get a necessary condition for genetic networks to lead to differentiation.     

Continuous fermentation of d-xylose by immobilizedpichia stipitis comparison between cstr and cpfr

Applied Biochemistry and Biotechnology - The main purpose of this work was to compare the performance of two different kinds of reactors (CSTR and CPFR) in order to enhance the ethanol productivity...     

Unprecedented hour-long residence time of a cation in a left-handed G-quadruplex

Cations are critical for the folding and assembly of nucleic acids. In G-quadruplex structures, cations can bind between stacked G-tetrads and coordinate with negatively charged guanine carbonyl oxygens. They usually exchange between binding sites and with the bulk in solution with time constants ranging from sub-millisecond to seconds. Here we report the first observation of extremely long-lived K⁺ and NH₄⁺ ions, with an exchange time constant on the order of an hour, when coordinated at the center of a left-handed G-quadruplex DNA. A single-base mutation, that switched one half of the structure from left- to right-handed conformation resulting in a right–left hybrid G-quadruplex, was shown to remove this long-lived behaviour of the central cation.

An extremely long-lived cation has been detected in left-handed G-quadruplexes.     

Solid-phase synthesis using a new polyacrylic resin : Synthesis of the fragment 14–21 of the amino acid sequence of histone H4

The solid-phase synthesis of the octapeptide 1 AcGly-Ala-Lys-Arg-His-Arg-Lys-ValOMe, which represents the fragment 14-21 of the amino acid sequence of the chromosomal histone H4, as well as of the structurally related nonapeptide 2 AcGly-Ala-Lys-Leu-Arg-His-Arg-Lys-ValOMe, is described using a new polyacrylic resin containing a glycolamide ester linkage(resin-NHCO-CH₂-OCO-peptide) acting as a labile anchoring moiety between the resin and the peptide.After elongation of the polypeptide chain using classical protecting groups, i.e. t-butyloxycarbonyl for the α-NH₂ function, benzyloxycarbonyl, nitro and 2,4-dinitrophenyl groups for the side-chains of Lys, Arg and His respectively, both peptides 1 and 2 were obtained in good yields and with a high purity as shown by high-pressure liquid chromatography, by amino-acid analysis and by high-field proton NMR spectroscopy.This work demonstrates the ability of the newly introduced polyacrylic resin to act as a convenient support for solid-phase peptide synthesis.     

Coordination solids via assembly of adaptable components: systematic structural variation in alkaline earth organosulfonate networks

A family of alkaline earth organosulfonate coordination solids is reported. In contrast to more typical crystal engineering approaches, these solids are sustained by the assembly of building blocks that are coordinatively adaptable rather than rigid in their bonding preferences. The ligand, 4,5-dihydroxybenzene-1,3-disulfonate, L, progressively evolves from a 0D, 1D, 2D, to a 3D microporous network with the Group II cations Mg(2+), Ca(2+), Sr(2+), and Ba(2+), (compounds 1-4), respectively. This trend in dimensionality can be explained by considering factors such as hard-soft acid-base principles and cation radii, a rationalization which follows salient crystal engineering principles. The selective gas sorption properties of the microporous 3D network [Ba(L)(H(2)O)].H(2)O, 4, with different gaseous guests are also presented.     

Following the aggregation of amyloid-forming peptides by computer simulations

There is experimental evidence suggesting that the toxicity of neurodegenerative diseases such as Alzheimer's disease may result from the soluble intermediate oligomers. It is therefore important to characterize extensively the early steps of oligomer formation at atomic level. As these structures are metastable and short lived, experimental data are difficult to obtain and they must be complemented with numerical simulations. In this work, we use the activation-relaxation technique coupled with a coarse-grained energy model to study in detail the mechanisms of aggregation of four lys-phe-phe-glu (KFFE) peptides. This is the shortest peptide known to form amyloid fibrils in vitro. Our simulations indicate that four KFFE peptides adopt a variety of oligomeric states (tetramers, trimers, and dimers) with various orientations of the chains in rapid equilibrium. This conformational distribution is consistent with all-atom molecular-dynamics simulations in explicit solvent and is sequence dependent; as seen experimentally, the lys-pro-gly-glu (KPGE) peptides adopt disordered structures in solution. Our unbiased simulations also indicate that the assembly process is much more complex than previously thought and point to intermediate structures which likely are kinetic traps for longer chains.     

Two Highly Populated Conformations at Room Temperature of Monterine and Granjine, Antitumor Bisbenzylisoquinoline Alkaloids: Origin and Tridimensional Structures

Monterine 1 as well as granjine 3, 1R,1'S configured biphenylic bisbenzylisoquinoline alkaloids, generate two highly populated conformers. The interconversion of two forms was detected by saturation tranfer in (1)H NMR NOEs experiments. Tridimensional structure of the conformers was determined on the basis of (1)H NMR analysis of anisotropic shielding protons, by NOEs measurements and vicinal proton coupling constants of CH1-CH(2)alpha and CH1'-CH(2)alpha'. The structures established from NMR data were further refined to observe the mobility of 3D conformations by molecular dynamics simulation in vacuo. The highly populated conformers, monterine 1a and 1b, as well as granjine 3a and 3b, are interconvertible by rotation about the C1'-Calpha', Calpha'-C9', and C11'-C11 bonds and inversion of the benzyl D ring by reference to CH(2)alpha'. The slow exchange system was investigated by dynamic NMR spectroscopy: DeltaG()(c) 77.9 KJ/mol and k(c) 200 s(-)(1) for monterine 1; DeltaG()(c) 77.7 KJ/mol and k(c) 211 s(-)(1) for granjine 3. Natural and synthetic biphenylic bisbenzylisoquinolines displayed, in vitro, cytotoxic activities against human prostate and breast cancer cell lines.     

Thermal and electrochemical C-X activation (X = Cl,Br, I) by the strong Lewis acid Pd3(dppm)3(CO)2+ cluster and its catalytic applications

The stoichiometric and catalytic activations of alkyl halides and acid chlorides by the unsatured Pd(3)(dppm)(3)(CO)(2+) cluster (Pd(3)(2+)) are investigated in detail. A series of alkyl halides (R-X; R = t-Bu, Et, Pr, Bu, allyl; X = Cl, Br, I) react slowly with Pd(3)(2+) to form the corresponding Pd(3)(X)(+) adduct and "R(+)". This activation can proceed much faster if it is electrochemically induced via the formation of the paramagnetic species Pd(3)(+). The latter is the first confidently identified paramagnetic Pd cluster. The kinetic constants extracted from the evolution of the UV-vis spectra for the thermal activation, as well as the amount of electricity to bring the activation to completion for the electrochemically induced reactions, correlate the relative C-X bond strength and the steric factors. The highly reactive "R(+)" species has been trapped using phenol to afford the corresponding ether. On the other hand, the acid chlorides react rapidly with Pd(3)(2+) where no induction is necessary. The analysis of the cyclic voltammograms (CV) establishes that a dissociative mechanism operates (RCOCl --> RCO(+) + Cl(-); R = t-Bu, Ph) prior to Cl(-) scavenging by the Pd(3)(2+) species. For the other acid chlorides (R = n-C(6)H(13), Me(2)CH, Et, Me, Pr), a second associative process (Pd(3)(2+) + RCOCl --> Pd(3)(2+.....)Cl(CO)(R)) is seen. Addition of Cu(NCMe)(4)(+) or Ag(+) leads to the abstraction of Cl(-) from Pd(3)(Cl)(+) to form Pd(3)(2+) and the insoluble MCl materials (M = Cu, Ag) allowing to regenerate the starting unsaturated cluster, where the precipitation of MX drives the reaction. By using a copper anode, the quasi-quantitative catalytic generation of the acylium ion ("RCO(+)") operates cleanly and rapidly. The trapping of "RCO(+)" with PF(6)(-) or BF(4)(-) leads to the corresponding acid fluorides and, with an alcohol (R'OH), to the corresponding ester catalytically, under mild conditions. Attempts were made to trap the key intermediates "Pd(3)(Cl)(+)...M(+)" (M(+) = Cu(+), Ag(+)), which was successfully performed for Pd(3)(ClAg)(2+), as characterized by (31)P NMR, IR, and FAB mass spectrometry. During the course of this investigation, the rare case of PF(6)(-) hydrolysis has been observed, where the product PF(2)O(2)(-) anion is observed in the complex Pd(3)(PF(2)O(2))(+), where the substrate is well-located inside the cavity formed by the dppm-Ph groups above the unsatured face of the Pd(3)(2+) center. This work shows that Pd(3)(2+) is a stronger Lewis acid in CH(2)Cl(2) and THF than AlCl(3), Ag(+), Cu(+), and Tl(+).     

Linear extension sums as valuations on cones

The geometric and algebraic theory of valuations on cones is applied to understand identities involving summing certain rational functions over the set of linear extensions of a poset.