The influence of the flow of the reacting gas on the conditions for a thermal explosion

The classical problem of thermal explosion is modified so that the chemically active gas is not at rest but is flowing in a long cylindrical pipe. Up to a certain section the heat-conducting walls of the pipe are held at low temperature so that the reaction rate is small and there is no heat release; at that section the ambient temperature is increased and an exothermic reaction begins. The question is whether a slow reaction regime will be established or a thermal explosion will occur. The mathematical formulation of the problem is presented. It is shown that when the pipe radius is larger than a critical value, the solution of the new problem exists only up to a certain distance along the axis. The critical radius is determined by conditions in a problem with a uniform axial temperature. The loss of existence is interpreted as a thermal explosion; the critical distance is the safe reactor’s length. Both laminar and developed turbulent flow regimes are considered. In a computational experiment the loss of the existence appears as a divergence of a numerical procedure; numerical calculations reveal asymptotic scaling laws with simple powers for the critical distance.

Galantamine: Effect on nicotinic receptor binding, acetylcholinesterase inhibition, and learning

Classical eyeblink conditioning is a well-characterized model paradigm that engages the septohippocampal cholinergic system. This form of associative learning is impaired in normal aging and severely disrupted in Alzheimer's disease (AD). Some nicotinic cholinergic receptor subtypes are lost in AD, making the use of nicotinic allosterically potentiating ligands a promising therapeutic strategy. The allosterically potentiating ligand galantamine (Gal) modulates nicotinic cholinergic receptors to increase acetylcholine release as well as acting as an acetylcholinesterase (AChE) inhibitor. Gal was tested in two preclinical experiments. In Experiment 1 with 16 young and 16 older rabbits, Gal (3.0 mg/kg) was administered for 15 days during conditioning, and the drug significantly improved learning, reduced AChE levels, and increased nicotinic receptor binding. In Experiment 2, 53 retired breeder rabbits were tested over a 15-wk period in four conditions. Groups of rabbits received 0.0 (vehicle), 1.0, or 3.0 mg/kg Gal for the entire 15-wk period or 3.0 mg/kg Gal for 15 days and vehicle for the remainder of the experiment. Fifteen daily conditioning sessions and subsequent retention and relearning assessments were spaced at 1-month intervals. The dose of 3.0 mg/kg Gal ameliorated learning deficits significantly during acquisition and retention in the group receiving 3.0 mg/kg Gal continuously. Nicotinic receptor binding was significantly increased in rabbits treated for 15 days with 3.0 mg/kg Gal, and all Gal-treated rabbits had lower levels of brain AChE. The efficacy of Gal in a learning paradigm severely impaired in AD is consistent with outcomes in clinical studies.

Intrinsic noise in gene regulatory networks

Cells are intrinsically noisy biochemical reactors: low reactant numbers can lead to significant statistical fluctuations in molecule numbers and reaction rates. Here we use an analytic model to investigate the emergent noise properties of genetic systems. We find for a single gene that noise is essentially determined at the translational level, and that the mean and variance of protein concentration can be independently controlled. The noise strength immediately following single gene induction is almost twice the final steady-state value. We find that fluctuations in the concentrations of a regulatory protein can propagate through a genetic cascade; translational noise control could explain the inefficient translation rates observed for genes encoding such regulatory proteins. For an autoregulatory protein, we demonstrate that negative feedback efficiently decreases system noise. The model can be used to predict the noise characteristics of networks of arbitrary connectivity. The general procedure is further illustrated for an autocatalytic protein and a bistable genetic switch. The analysis of intrinsic noise reveals biological roles of gene network structures and can lead to a deeper understanding of their evolutionary origin.