A transformed time-dependent Michaelis–Menten enzymatic reaction model and its asymptotic stability

The dynamic form of the Michaelis–Menten enzymatic reaction equations provide a time-dependent model in which a substrate $S$ reacts with an enzyme $E$ to form a complex $C$ which in turn is converted into a product $P$ and the enzyme $E$ . In the present paper, we show that this system of four nonlinear equations can be reduced to a single nonlinear differential equation, which is simpler to solve numerically than the system of four equations. Applying the Lyapunov stability theory, we prove that the non-zero equilibrium for this equation is globally asymptotically stable, and hence that the non-zero steady-state solution for the full Michaelis–Menten enzymatic reaction model is globally asymptotically stable for all values of the model parameters. As such, the steady-state solutions considered in the literature are stable. We finally discuss properties of the numerical solutions to the dynamic Michaelis–Menten enzymatic reaction model, and show that at small and large time scales the solutions may be approximated analytically.     

Synthesis of 5,6-dimethoxyquinazolin-2(1H)-ones

Synthesis of 5,6-dimethoxyquinazolin-2(1H)-one derivatives was the subject of investigations leading to the preparation of title compounds 11, 13, 14 and 26 . Target quinazolines 1 were synthesized in three ways; the route starting from o-vanillin via the intermediacy of 6-amino-2,3-dimethoxyacetophenone ( 19 ) was used for most of the preparative work. The unexpected formation of an acid-labile dimer of 13 was discovered and solid state ¹³C nmr was used for structural assignment. The 5-methoxy substituent in these systems shows anomalous spectral characteristics and, in one case, was cleaved in acid media to 22 .     

An asymmetric synthesis of indole alkaloids

Chiral formamidines derived from β-carbolines are metallated and alkylated stereoselectively opening a route to indole alkaloids and analogous compounds.     

Photodegradation of polyethylene film

A structure occurs in radical-polymerized polyethylene which leads to formation of a triene on ultraviolet radiation. An inhibition of oxidative processes is observed while the triene or its precursor are being consumed. Subsequent formation of oxygenated products—hydroxyl, carbonyl, and carboxyl—is well behaved and arises from short wavelenght light. A crosslinking reaction is initiated by light of ～4000 Å wavelength.     

Fused s-triazino heterocycles. XVI. 13H-1,3,7,8,12a, 13c-hexaazabenzo[de]naphthacene and 1,3,7,8,11b, 12,14,14d-octaazadibenzo[de,hi]naphthacene,two new ring systems

The reaction of 7,9-dibromo-5-tribromomethyl-2-t-butyl-4-cyano-1,3,6,9b-tetraazaphenalene ( 1a ) with 2-amino-5-picoline is shown to give 4,6-dibromo-2-t-butyl-13-imino-11-methyl-13H-1,3,7,8,12a,13c-hexaazabenzo[de]naphthacene ( 3 ) and the isomeric 7,9-dibromo-2-t-butyl-4-cyano-5N-(5-methyl-2-pyridyl)amino-1,3,-6,9b-tetraazaphenalene ( 2a ). A related annulation reaction of 7,9-dibromo-2-t-butyl-5-chloro-4-cyano-1,3,6,9b-tetraazaphenalene ( 1g ) with 2-amino-6-trimethylacetamidopyridine leads in two steps to 4,6-dibromo-2,13-di-t-butyl-1,3,7,8,11b,12,14,14d-octaazadibenzo[de,hi]naphthacene ( 4a ). The preparation of 1g , 5-azido-7,9-dibromo-2-t-butyl-4-cyano-1,3,6,9b-tetraazaphenalene ( 1c ) and the reaction of the latter with pyrrolidine leading to 7,9-dibromo-2-t-butyl-4-cyano-5-(1-pyrrolidino)-1,3,6,9b-tetraazaphenalene ( 1e ) are also reported. Attempted displacement of the azido-group on 1c by 2,6-diaminopyridine affords surprisingly 5-amino-7,9-dibromo-2-t-butyl-4-cyano-1,3,6,9b-tetraazaphenalene ( 1d ).     

Asymmetrical hippocampal connectivity in mesial temporal lobe epilepsy: evidence from resting state fMRI

Background

Recent studies have shown that the human right-hemispheric auditory cortex is particularly sensitive to reduction in sound quality, with an increase in distortion resulting in an amplification of the auditory N1m response measured in the magnetoencephalography (MEG). Here, we examined whether this sensitivity is specific to the processing of acoustic properties of speech or whether it can be observed also in the processing of sounds with a simple spectral structure. We degraded speech stimuli (vowel /a/), complex non-speech stimuli (a composite of five sinusoidals), and sinusoidal tones by decreasing the amplitude resolution of the signal waveform. The amplitude resolution was impoverished by reducing the number of bits to represent the signal samples. Auditory evoked magnetic fields (AEFs) were measured in the left and right hemisphere of sixteen healthy subjects.

Results

We found that the AEF amplitudes increased significantly with stimulus distortion for all stimulus types, which indicates that the right-hemispheric N1m sensitivity is not related exclusively to degradation of acoustic properties of speech. In addition, the P1m and P2m responses were amplified with increasing distortion similarly in both hemispheres. The AEF latencies were not systematically affected by the distortion.

Conclusions

We propose that the increased activity of AEFs reflects cortical processing of acoustic properties common to both speech and non-speech stimuli. More specifically, the enhancement is most likely caused by spectral changes brought about by the decrease of amplitude resolution, in particular the introduction of periodic, signal-dependent distortion to the original sound. Converging evidence suggests that the observed AEF amplification could reflect cortical sensitivity to periodic sounds.     

A mechanistic model for asymmetric alkylation of chiral dipole stabilized anions

Stereoselective deprotonation, deuteriation, and alkylation of chiral formamidines are described.