Qualitative Analysis of an ODE Model of a Class of Enzymatic Reactions

The present paper analyzes an ODE model of a certain class of (open) enzymatic reactions. This type of model is used, for instance, to describe the interactions between messenger RNAs and microRNAs. It is shown that solutions defined by positive initial conditions are well defined and bounded on \([0, \infty )\) and that the positive octant of \({\mathbb {R}}^3\) is a positively invariant set. We prove further that in this positive octant there exists a unique equilibrium point, which is asymptotically stable and a global attractor for any initial state with positive components; a controllability property is emphasized. We also investigate the qualitative behavior of the QSSA system in the phase plane \({\mathbb {R}}^2\). For this planar system we obtain similar results regarding global stability by using Lyapunov theory, invariant regions and controllability.     

Purinergic signaling in the lumen of a normal nephron and in remodeled PKD encapsulated cysts

The nephron is the functional unit of the kidney. Blood and plasma are continually filtered within the glomeruli that begin each nephron. Adenosine 5' triphosphate (ATP) and its metabolites are freely filtered by each glomerulus and enter the lumen of each nephron beginning at the proximal convoluted tubule (PCT). Flow rate, osmolality, and other mechanical or chemical stimuli for ATP secretion are present in each nephron segment. These ATP-release stimuli are also different in each nephron segment due to water or salt permeability or impermeability along different luminal membranes of the cells that line each nephron segment. Each of the above stimuli can trigger additional ATP release into the lumen of a nephron segment. Each nephron-lining epithelial cell is a potential source of secreted ATP. Together with filtered ATP and its metabolites derived from the glomerulus, secreted ATP and adenosine derived from cells along the nephron are likely the principal two of several nucleotide and nucleoside candidates for renal autocrine and paracrine ligands within the tubular fluid of the nephron. This minireview discusses the first principles of purinergic signaling as they relate to the nephron and the urinary bladder. The review discusses how the lumen of a renal tubule presents an ideal purinergic signaling microenvironment. The review also illustrates how remodeled and encapsulated cysts in autosomal dominant polycystic kidney disease (ADPKD) and remodeled pseudocysts in autosomal recessive PKD (ARPKD) of the renal collecting duct likely create an even more ideal microenvironment for purinergic signaling. Once trapped in these closed microenvironments, purinergic signaling becomes chronic and likely plays a significant epigenetic and detrimental role in the secondary progression of PKD, once the remodeling of the renal tissue has begun. In PKD cystic microenvironments, we argue that normal purinergic signaling within the lumen of the nephron provides detrimental acceleration of ADPKD once remodeling is complete.     

Modeling Dynamics and Function of Bone Marrow Cells in Mouse Liver Regeneration

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Redundancy in the pathway for redox regulation of mammalian methionine synthase: reductive activation by the dual flavoprotein,novel reductase 1

Methionine synthase is an essential cobalamin-dependent enzyme in mammals that catalyzes the transfer of a methyl group from methyltetrahydrofolate to homocysteine to give tetrahydrofolate and methionine. It is oxidatively labile and requires for its sustained activity an auxiliary repair system that catalyzes a reductive methylation reaction. Genetic and biochemical studies have demonstrated that the soluble dual flavoprotein oxidoreductase, methionine synthase reductase, serves as a redox partner for methionine synthase in an NADPH-dependent reaction. However, three reports suggest the possibility of redundancy in this redox pathway. First, a hyperhomocysteinemic patient has been reported who has an isolated functional deficiency of methionine synthase but appears to be distinct from the cblE and cblG classes of patients with defects in methionine synthase reductase and methionine synthase, respectively. Second, another dual flavoprotein oxidoreductase with significant homology to methionine synthase reductase, NR1, has been described recently, but its function is unknown. Third, methionine synthase can be activated in vitro by a two-component redox system comprised of soluble cytochrome b5 and P450 reductase. In this study, we demonstrate a function for human NR1 in vitro. It is able to fully activate methionine synthase in the presence of soluble cytochrome b5 with a Vmax of 2.8 +/- 0.1 micromol min(-1) mg(-1) protein, which is comparable with that seen with methionine synthase reductase. The K(actNR1) is 1.27 +/- 0.16 microm, and a 20-fold higher stoichiometry of reductase to methionine synthase is required for NR1 versus methionine synthase reductase, suggesting that it may represent a minor pathway in the cell, assuming that the two proteins are present at similar levels.     

Human ATP:Cob(I)alamin adenosyltransferase and its interaction with methionine synthase reductase

The final step in the conversion of vitamin B(12) into coenzyme B(12) (adenosylcobalamin, AdoCbl) is catalyzed by ATP:cob(I)alamin adenosyltransferase (ATR). Prior studies identified the human ATR and showed that defects in its encoding gene underlie cblB methylmalonic aciduria. Here two common polymorphic variants of the ATR that are found in normal individuals are expressed in Escherichia coli, purified, and partially characterized. The specific activities of ATR variants 239K and 239M were 220 and 190 nmol min(-1) mg(-1), and their K(m) values were 6.3 and 6.9 mum for ATP and 1.2 and 1.6 mum for cob(I)alamin, respectively. These values are similar to those obtained for previously studied bacterial ATRs indicating that both human variants have sufficient activity to mediate AdoCbl synthesis in vivo. Investigations also showed that purified recombinant human methionine synthase reductase (MSR) in combination with purified ATR can convert cob(II)alamin to AdoCbl in vitro. In this system, MSR reduced cob(II)alamin to cob(I)alamin that was adenosylated to AdoCbl by ATR. The optimal stoichiometry for this reaction was approximately 4 MSR/ATR and results indicated that MSR and ATR physically interacted in such a way that the highly reactive reaction intermediate [cob(I)alamin] was sequestered. The finding that MSR reduced cob(II)alamin to cob(I)alamin for AdoCbl synthesis (in conjunction with the prior finding that MSR reduced cob(II)alamin for the activation of methionine synthase) indicates a dual physiological role for MSR.     

Extracellular zinc and ATP-gated P2X receptor calcium entry channels: New zinc receptors as physiological sensors and therapeutic targets

In this review, we focus on two attributes of P2X receptor channel function, one essential and one novel. First, we propose that P2X receptors are extracellular sensors as well as receptors and ion channels. In particular, the large extracellular domain (that comprises 70% of the molecular mass of the receptor channel protein) lends itself to be a cellular sensor. Moreover, its exquisite sensitivity to extracellular pH, ionic strength, and multiple ligands evokes the function of a sensor. Second, we propose that P2X receptors are extracellular zinc receptors as well as receptors for nucleotides. We provide novel data in multiple publications and illustrative data in this invited review to suggest that zinc triggers ATP-independent activation of P2X receptor channel function. In this light, P2X receptors are the cellular site of integration between autocrine and paracrine zinc signaling and autocrine and paracrine purinergic signaling. P2X receptors may sense changes in these ligands as well as in extracellular pH and ionic strength and transduce these sensations via calcium and/or sodium entry and changes in membrane potential.