A note on the calculation of the effective range

The closed form of the first order non-linear differential equation that is satisfied by the effective range within the variable phase formulation of scattering theory is discussed. It is shown that the conventional method of determining the effective range, by fitting a numerical solution of the Schr\"odinger equation to known asymptotic boundary conditions, can be modified to include the first order contribution of a long range interaction.Comment: 4 page

The variable phase method used to calculate and correct scattering lengths

It is shown that the scattering length can be obtained by solving a Riccati equation derived from variable phase theory. Two methods of solving it are presented. The equation is used to predict how long-range interactions influence the scattering length, and upper and lower bounds on the scattering length are determined. The predictions are compared with others and it is shown how they may be obtained from secular perturbation theory.Comment: 7 pages including 3 figure

Brain energy rescue:an emerging therapeutic concept for neurodegenerative disorders of ageing

The brain requires a continuous supply of energy in the form of ATP, most of which is produced from glucose by oxidative phosphorylation in mitochondria, complemented by aerobic glycolysis in the cytoplasm. When glucose levels are limited, ketone bodies generated in the liver and lactate derived from exercising skeletal muscle can also become important energy substrates for the brain. In neurodegenerative disorders of ageing, brain glucose metabolism deteriorates in a progressive, region-specific and disease-specific manner — a problem that is best characterized in Alzheimer disease, where it begins presymptomatically. This Review discusses the status and prospects of therapeutic strategies for countering neurodegenerative disorders of ageing by improving, preserving or rescuing brain energetics. The approaches described include restoring oxidative phosphorylation and glycolysis, increasing insulin sensitivity, correcting mitochondrial dysfunction, ketone-based interventions, acting via hormones that modulate cerebral energetics, RNA therapeutics and complementary multimodal lifestyle changes

The advantage of channeling nucleotides for very processive functions

Nucleoside triphosphate (NTP)s, like ATP (adenosine 5’-triphosphate) and GTP (guanosine 5’-triphosphate), have long been considered sufficiently concentrated and diffusible to fuel all cellular ATPases (adenosine triphosphatases) and GTPases (guanosine triphosphatases) in an energetically healthy cell without becoming limiting for function. However, increasing evidence for the importance of local ATP and GTP pools, synthesised in close proximity to ATP- or GTP-consuming reactions, has fundamentally challenged our view of energy metabolism. It has become evident that cellular energy metabolism occurs in many specialised ‘microcompartments’, where energy in the form of NTPs is transferred preferentially from NTP-generating modules directly to NTP-consuming modules. Such energy channeling occurs when diffusion through the cytosol is limited, where these modules are physically close and, in particular, if the NTP-consuming reaction has a very high turnover, i.e. is very processive. Here, we summarise the evidence for these conclusions and describe new insights into the physiological importance and molecular mechanisms of energy channeling gained from recent studies. In particular, we describe the role of glycolytic enzymes for axonal vesicle transport and nucleoside diphosphate kinases for the functions of dynamins and dynamin-related GTPases