We consider the stationary solution for the Ca2+ concentration near a point Ca2+ source describing a single-channel Ca2+ nanodomain, in the presence of a single mobile buffer with one-to-one Ca2+ ...binding stoichiometry. Previously, a number of Ca2+ nanodomains approximations have been developed, for instance the excess buffer approximation (EBA), the rapid buffering approximation (RBA), and the linear approximation (LIN), each valid for appropriate buffering conditions. Apart from providing a simple method of estimating Ca2+ and buffer concentrations without resorting to computationally expensive numerical solution of reaction-diffusion equations, such approximations proved useful in revealing the dependence of nanodomain Ca2+ distribution on crucial parameters such as buffer mobility and its Ca2+ binding properties. In this study, we present a different form of analytic approximation, which is based on matching the short-range Taylor series of the nanodomain concentration with the long-range asymptotic series expressed in inverse powers of distance from channel location. Namely, we use a “dual” Padé rational function approximation to simultaneously match terms in the short- and the long-range series, and we show that this provides an accurate approximation to the nanodomain Ca2+ and buffer concentrations. We compare this approximation with the previously obtained approximations and show that it yields a better estimate of the free buffer concentration for a wide range of buffering conditions. The drawback of our method is that it has a complex algebraic form for any order higher than the lowest bilinear order, and cannot be readily extended to multiple Ca2+ channels. However, it may be possible to extend the Padé method to estimate Ca2+ nanodomains in the presence of cooperative Ca2+ buffers with two Ca2+ binding sites, the case that existing methods do not address.
We consider the stationary solution for the Ca
concentration near a point Ca
source describing a single-channel Ca
nanodomain, in the presence of a single mobile buffer with one-to-one Ca
binding ...stoichiometry. Previously, a number of Ca
nanodomains approximations have been developed, for instance the excess buffer approximation (EBA), the rapid buffering approximation (RBA), and the linear approximation (LIN), each valid for appropriate buffering conditions. Apart from providing a simple method of estimating Ca
and buffer concentrations without resorting to computationally expensive numerical solution of reaction-diffusion equations, such approximations proved useful in revealing the dependence of nanodomain Ca
distribution on crucial parameters such as buffer mobility and its Ca
binding properties. In this study, we present a different form of analytic approximation, which is based on matching the short-range Taylor series of the nanodomain concentration with the long-range asymptotic series expressed in inverse powers of distance from channel location. Namely, we use a "dual" Padé rational function approximation to simultaneously match terms in the short- and the long-range series, and we show that this provides an accurate approximation to the nanodomain Ca
and buffer concentrations. We compare this approximation with the previously obtained approximations and show that it yields a better estimate of the free buffer concentration for a wide range of buffering conditions. The drawback of our method is that it has a complex algebraic form for any order higher than the lowest bilinear order, and cannot be readily extended to multiple Ca
channels. However, it may be possible to extend the Padé method to estimate Ca
nanodomains in the presence of cooperative Ca
buffers with two Ca
binding sites, the case that existing methods do not address.
The highlights of the 24th International Exposition
Glass World
held in Moscow are briefly cited. About 100 companies from 12 countries of the world participated. New manufacturing and ...quality-control technologies of glass products and the main structural components of glass furnaces and methods of their high-quality production are demonstrated at the exposition. Examples of the most successful enterprises in the glass industry are given.
X-ray diffraction analysis is one of the famous widely used methods to study the structure of matter. It is well known that the scattering of ultrashort X-ray pulses can be used in X-ray diffraction ...analysis. The scattering of such pulses by various multiatomic objects and nanosystems leads to diffraction patterns carrying information not only on the structure of an object but also on the dynamics of processes in this object. Currently, it is technically possible to fabricate intense sources of femto- and attosecond pulses. New theories including the specificity of the interaction of such pulses with matter are not necessarily applied in the X-ray diffraction analysis involving ultrashort pulses. The inclusion of this specificity should lead to a better use of capabilities of sources of ultrashort pulses and to new scientific results. Sources of X-ray ultrashort pulses, widely used methods and new theories of the X-ray diffraction analysis including the specificity of the interaction of such pulses with matter, and modern experiments involving ultrashort pulses are briefly reviewed here.
PDF
