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International audience; Delays appear in the dynamics of many systems due to non-vanishing reaction times of control systems. In biochemical systems, long sequences of repeated steps, especially in biopolymerization processes, can be modeled by delays. However, modelling systems with delays is often complicated by physical constraints, such as the requirement that solutions representing concentrations of chemical species remain positive. In this work, we consider a model for a detoxifying enzyme whose synthesis is controlled by its substrate. The model includes bindingsite clearance delays, caused by the time required for an RNA polymerase or ribosome to clear its binding site before another such machine can bind. The existence of a positive equilibrium and the positivity and boundedness of solutions of the corresponding delay-differential equations are proven. In addition, the stability of the model is studied using the "small-gain" theorem.

The expression of the TGF-β protein Nodal on the left side of vertebrate embryos is a determining event in the development of internal-organ asymmetry. We present a mathematical model for the control of the expression of Nodal and its antagonist Lefty consisting entirely of realistic elementary reactions. We analyze the model in the absence of Lefty and find a wide range of parameters over which bistability (two stable steady states) is observed, with one stable steady state a low-Nodal state corresponding to the right-hand developmental fate, and the other a high-Nodal state corresponding to the left. We find that bistability requires a transcription factor containing two molecules of phosphorylated Smad2. A numerical survey of the full model, including Lefty, shows the effects of Lefty on the potential for bistability, and on the conditions that lead to the system reaching one or the other steady state.

During the templated biopolymerization processes of transcription and translation, a macromolecular machine, either an RNA polymerase or a ribosome, binds to a specific site on the template. Due to the sizes of these enzymes, there is a waiting time before one clears the binding site and another can bind. These clearance delays are relatively short, and one might think that they could be neglected. However, in the case of transcription, these clearance delays are associated with conservation laws, resulting in surprisingly large effects on the bifurcation diagrams in models of gene expression networks. We study an example of this phenomenon in a model of a gene regulated by a non-coding RNA displaying bistability. Neglecting the binding-site clearance delays in this model can only be compensated for by making ad hoc, unphysical adjustments to the model's kinetic constants.

Volume 1, Issue 1 of Mathematical Biosciences was the venue for a now-classic paper on the application of singular perturbation theory in enzyme kinetics, "On the mathematical status of the pseudo-steady state hypothesis of biochemical kinetics" by F. G. Heineken, H. M. Tsuchiya and R. Aris. More than 50 years have passed, and yet this paper continues to be studied and mined for insights. This perspective discusses both the strengths and weaknesses of the work presented in this paper. For many, the justification of the pseudo-steady-state approximation using singular perturbation theory is the main achievement of this paper. However, there is so much more material here, which laid the foundation for a great deal of research in mathematical biochemistry in the intervening decades. The parameterization of the equations, construction of the first-order uniform singular-perturbation solution, and an attempt to apply similar principles to the pseudo-equilibrium approximation are discussed in particular detail.

Network conditions for Turing instability in biochemical systems with two biochemical species are well known and involve autocatalysis or self-activation. On the other hand general network conditions for potential Turing instabilities in large biochemical reaction networks are not well developed. A biochemical reaction network with any number of species where only one species moves is represented by a simple digraph and is modeled by a reaction–diffusion system with non-mass action kinetics. A graph-theoretic condition for potential Turing-Hopf instability that arises when a spatially homogeneous equilibrium loses its stability via a single pair of complex eigenvalues is obtained. This novel graph-theoretic condition is closely related to the negative cycle condition for oscillations in ordinary differential equation models and its generalizations, and requires the existence of a pair of subnetworks, each containing an even number of positive cycles. The technique is illustrated with a double-cycle Goodwin type model.

Rubisco, the most abundant protein serving as the primary engine generating organic biomass on Earth, is characterized by a low catalytic constant (in higher plants approx. 3 s −1 ) and low specificity for CO 2 leading to photorespiration. We analyze here why this enzyme evolved as the main carbon fixation engine. The high concentration of Rubisco exceeding the concentration of its substrate CO 2 by 2–3 orders of magnitude makes application of Michaelis–Menten kinetics invalid and requires alternative kinetic approaches to describe photosynthetic CO 2 assimilation. Efficient operation of Rubisco is supported by a strong flux of CO 2 to the chloroplast stroma provided by fast equilibration of bicarbonate and CO 2 and forwarding the latter to Rubisco reaction centers. The main part of this feedforward mechanism is a thylakoidal carbonic anhydrase associated with photosystem II and pumping CO 2 from the thylakoid lumen in coordination with the rate of electron transport, water splitting and proton gradient across the thylakoid membrane. This steady flux of CO 2 limits photosynthesis at saturating CO 2 concentrations. At low ambient CO 2 and correspondingly limited capacity of the bicarbonate pool in the stroma, its depletion at the sites of Rubisco is relieved by utilizing O 2 instead of CO 2 , i.e. by photorespiration, a process which supplies CO 2 back to Rubisco and buffers the redox state and energy level in the chloroplast. Thus, the regulation of Rubisco function aims to keep steady non-equilibrium levels of CO 2 , NADPH/NADP and ATP/ADP in the chloroplast stroma and to optimize the condition of homeostatic photosynthetic flux of matter and energy.

Objectifs Analyse post-hoc de l’etude de securite cardiovasculaire SUSTAIN 6 evaluant l’effet du semaglutide sur la frequence cardiaque (FC) au repos, l’impact des beta-bloquants (BB) sur la FC et les consequences d’une augmentation de la FC sous semaglutide sur la survenue d’effets indesirables (EI) cardiaques. Patients et methodes Les patients ont ete stratifies selon l’utilisation des BB a l’inclusion et a la fin de l’etude. Resultats A S104, une augmentation de la FC est constatee sous semaglutide (2,8 et 3,2 bpm pour 0,5 et 1,0 mg) versus placebo (0,1 et 0,0 bpm) ; DET [IC95 %] : 2,75 bpm [1,75 ;3,75] pour semaglutide 0,5 mg versus placebo 0,5 mg ; 3,20 bpm [2,20 ;4,21] pour semaglutide 1,0 mg versus placebo 1,0 mg (tous p Discussion Augmentation de la FC sous semaglutide, sans majoration des EI cardiaques avec un impact de l’initiation ou de l’arret des BB en cours d’etude.

Objectifs L’etude SUSTAIN 6 qui a evalue la securite cardiovasculaire (CV) du semaglutide (0,5 mg et 1,0 mg) vs. le placebo, a montre a 2 ans une reduction significative de 26 % des evenements CV majeurs. Materiel et methodes Cette analyse post-hoc a evalue l’effet du semaglutide sur la fonction renale en fonction du DFGe initial calcule par la formule MDRD : normale, ≥ 90 ; legere, Resultats Le DFGe moyen a diminue entre l’inclusion et S104 dans tous les groupes et sous-groupes de traitement, les diminutions les plus importantes etant observees chez les patients avec une fonction renale normale (de −6,5 a −9,6 mL/min/1,73 m2) ou legerement diminuee (de −3,2 a −5,6 mL/min/1,73 m2). Le rapport UACR a diminue parallelement a la diminution de la fonction renale dans le bras semaglutide 1,0 mg (de −0,8 a −56 mg/mmol) mais pas dans les autres groupes de traitement. Les effets indesirables en rapport avec une insuffisance renale aigue etaient generalement proportionnel a l’atteinte renale, excepte pour le bras semaglutide 1,0 mg versus placebo (respectivement 2 a 12 % versus 2,8 a 21,2 %). L’incidence des nephropathies de novo ou d’aggravation d’une nephropathie preexistante etait plus faible avec les deux doses de semaglutide versus placebo (respectivement 4,4 et 2,8 % versus 6,6 et 5,5 %). Discussion Aucun nouveau signal de tolerance renale n’a ete observe avec le semaglutide quelle que soit la fonction renale initiale.

The inflammatory cytokine, TNF-alpha, induces IL-8 gene transcription via a mechanism involving proteasome-mediated IkappaBalpha degradation and NF-kappaB activation. Here, we investigated whether arsenic, which has been shown to inhibit the ubiquitin-proteasome pathway, could inhibit TNF-alpha-mediated increases in IL-8 expression. Using RT-PCR, we show that the addition of TNF-alpha to human bronchial epithelial (BEAS 2B) or embryonic kidney (HEK293) cells resulted in increased steady-state levels of IL-8 mRNA. This was preceded by a rapid decrease in cellular IkappaBalpha levels, as demonstrated by Western analysis, and an increase in nuclear levels of NF-kappaB, as demonstrated by gel shift analysis. Further demonstrating the activation of NF-kappaB, TNF-alpha induced the transcription of a NF-kappaB-dependent reporter gene. Exposing the cells to 500 microM arsenite, prior to adding TNF-alpha, completely inhibited IkappaBalpha degradation, NF-kappaB translocation, NF-kappaB-dependent gene transcription, and transcription of the endogenous gene for IL-8. In comparison with the proteasome inhibitor MG-132, which does not affect the phosphorylation and ubiquitination of IkappaBalpha, arsenite inhibited the phosphorylation of IkappaBalpha. Furthermore, arsenite directly blocked the activity of IKK, the kinase responsible for IkappaBalpha phosphorylation. These studies demonstrate that high levels of arsenic may inhibit NF-kappaB-mediated gene transcription by specifically blocking IKK activity, thereby limiting the phosphorylation and subsequent degradation of the NF-kappaB inhibitor, IkappaBalpha.

A recently developed vibrating tube densimeter has been used to measure relative densities of aqueous sodium bromide from 373 to 523 K over a pressure range of 10–30 MPa. The instrument produces time period data consisting of both baseline and sample plateau regions. The number of samples injected into the instrument is known. The time period data have been analysed using a visual user defined baseline method and a computer program which performs an automated analysis of the data. The analysis program locates the transition from reference fluid baseline to sample solution plateau and back by testing the local slope against the null hypothesis. An adaptive algorithm is used to adjust the confidence level of the test to ensure that the correct number of samples are identified. A polynomial in temperature is fit to the baseline region surrounding each sample plateau datum to estimate the baseline at the time of measurement. Apparent molar volumes of aqueous sodium bromide have been calculated using both methods and compared to theoretical results obtained from Archer’s semi-empirical Pitzer Ion Interaction program. The statistical analysis program performs as well as the visual extrapolation method, completed by three different experimentalists, and outperforms individual experimentalists. Automated analysis allows the calculation of density errors which are shown to be better estimated than errors obtained from visual analysis. Furthermore, because the automated method can estimate errors from a single peak and the visual method requires two peaks for each sample, the need for replicate measurements is reduced.

Single-enzyme systems can undergo weakly damped concentration oscillations if the enzyme can be converted to an inactive form which only slowly reverts to the active form. Inactivation can take many forms, including a simple (hysteretic) conformational change of the enzyme. This observation may provide an explanation for the damped oscillations seen in photosynthetic activity following a sudden disturbance since rubisco, the enzyme responsible for fixing carbon, is a hysteretic enzyme with appropriate kinetic constants for oscillation. Copyright 1998 Academic Press

In earlier studies, treatment with sodium arsenite was shown to decrease total hepatic CYP in rats. A concomitant increase in heme oxygenase, the rate-limiting step in heme degradation to biliverdin, was considered responsible for the decrease in CYP. Here we investigated the effect of sodium arsenite on induction of CYP2H, CYP1A, and heme oxygenase in primary cultures of chicken embryo hepatocytes. When added simultaneously with inducer, arsenite inhibited phenobarbital-mediated increases in CYP2H and 3-methylcholanthrene-mediated increases in CYP1A, as measured enzymatically and immunochemically. Near maximal decreases were observed in these forms of CYP at a concentration of 2.5 microM sodium arsenite. The concentration-dependent decreases in CYP2H and CYP1A by sodium arsenite were concomitant with increases in heme oxygenase. Sodium arsenite was not toxic at concentrations as high as 10 microM, as indicated by protein synthesis and the reduction of MTT by intact cells. Sodium arsenite had no effect on induction of CYP2H1 mRNA, suggesting that the decreases in this form of CYP occurred post-transcriptionally. Treatment of cells with tin mesoporphyrin (SnMeso), an inhibitor of heme oxygenase, resulted in inhibition of arsenite-induced heme oxygenase. However, SnMeso did not alter the effect of arsenite to prevent phenobarbital-mediated increases in CYP2H protein. SnMeso alone inhibited phenobarbital-mediated increases in CYP2H. Inclusion of 2 or 5 microM exogenous heme with arsenite did not prevent the arsenite-mediated decrease in CYP2H. Combined treatment with heme and phenobarbital induced heme oxygenase to the same extent as treatment with heme, arsenite, and phenobarbital. However, CYP2H activity was decreased only when the treatment included arsenite. These results suggest that elevated levels of heme oxygenase alone are not responsible for arsenite-mediated decreases in CYP2H.

Introduction Une caracteristique commune des diabetes de type 1 et 2 (DT1 et DT2) est le developpement de complications microvasculaires. Cependant, le risque renal de des sujets proteinuriques en fonction du type de diabete reste mal etudie. Methodes Nous avons compare les caracteristiques des patients DT1 (n = 277) et DT2 (n = 942). Tous les sujets presentaient une proteinurie, sans insuffisance renale terminale (IRT) a l’inclusion et ont ete suivis prospectivement pour evaluer l’incidence de deces, d’IRT et de baisse du debit de filtration glomerulaire estime (eGFR). Resultats Le deces a ete constate chez 285 sujets DT2 et 73 sujets DT1 : incidence de 6,7 (IC 95 % : 5,9–7,5) vs 2,5 (IC 95 % : 1,9–3,0) % patients.annees, respectivement. Le risque non ajuste de deces est plus eleve chez les sujets DT2 (HR : 3,423 ; IC 95 % : 2,501–4,683 ; p Conclusion Dans la nephropathie diabetique, le risque de deces, d’IRT et de declin de la fonction renale n’est pas different entre DT1 et DT2 apres l’ajustement sur les principaux facteurs de risque.

Introduction Le diabete de type 2 (DT2) est un facteur de risque important de fibrillation auriculaire (FA) et de maladies cardiovasculaires. Si la nephropathie diabetique (ND) est un facteur de risque bien etabli d’evenements cardiovasculaires, son association avec la FA est moins clairement definie. L’objectif de notre etude etait de caracteriser les relations entre ND et vulnerabilite atriale electrique (FA permanente et duree de l’onde P). Patients et methodes Les donnees clinico-biologiques et ECG de 2671 patients, DT2 et issus des etudes DIAB2NEPHROGENE & SURDIAGENE, ont ete examinees pour la presence d’une FA ou d’une anomalie de l’onde P. Resultats La FA a ete observee chez 95 sujets. La concentration d’albumine urinaire (Ualb) etait significativement plus elevee chez les sujets en FA par rapport a ceux en rythme sinusal (56.0 [15–202] vs 23.0 [8–112] mg/L, P 30 mg/L et l’augmentation de la duree de l’onde P > 100 ms persistait en analyse multivariee (OR[IC95] = 1.43 [1.09–2.60], P = 0,023) mais pas avec le DFGe. Ces associations etaient independantes de la pression arterielle. Conclusion Les lesions renales s’associent avec la presence d’une FA permanente ou d’une augmentation de la duree de l’onde P, suggerant un lien entre les maladies renales et la dysfonction atriale dans le DT2. La valeur predictive des anomalies renales dans l’apparition de la FA et du risque d’accident vasculaire cerebral reste a etablir.