Gaussian distribution, single molecule

Thus we have found the distribution of the fluctuations around the macroscopic value. They have been computed to order Q 1/2 relative to the macroscopic value n, which will be called the linear noise approximation. In this order of Q the noise is Gaussian even in time-dependent states far from equilibrium. Higher corrections are computed in X.6 and they modify the Gaussian character. However, they are of order 2 1 relative to n and therefore of the order of a single molecule. 

Moment analysis provides the means to determine a model independent characteristic of the absorption rate or dissolution rate (Riegelman and Collier 1980). A single value characterising the rate of the entire dissolution or absorption process is obtained, which is called the mean absorption or dissolution time (MAT and MDT, respectively). These parameters can be determined without any assumptions regarding absorption or disposition pharmacokinetics, apart from the general prerequisites of linear pharmacokinetics and absence of intraindividual variability described above. MAT/MDT can be interpreted as the most probable time for a molecule to become absorbed/dissolved, based on a normal Gaussian distribution. 

For diffusion analysis, collect X-Y coordinate data of individual single molecules in each frame by determining the center of the fluorescent spot (Fig. 3c). The center position can be determined by calculating the center of the fluorescence intensities. Higher spatial resolution can be achieved when the intensity profiles of the fluorescence spots are fitted to the point spread function that has a Gaussian distribution (Fig. 3d). 

Figure 6.3 Histogram of the fluorescence intensity of solubilized H/K-ATPase. Distributions of fluorescence intensities of FITC- H/K-ATPase solubilized with SDS ((a) n = 189), Ci2Eg ((b) n = 283) and nOG ((c) n = 206) are shown. The fluorescence intensities of one to four dye molecules were in the linear range of the camera.The solid line indicates the sum of one to four Gaussian components fitted to the data. Single, double and quadruple arrowheads indicate the peak positions of each Gaussian distribution that is responsible for one, two or four fluorescence molecules, respectively. Reprinted with permission from Abe etal., Correlation between the activities and the oligomeric forms of pig gastric H/K-ATPase. Biochemistry 42 (2003) 1 5132-1 5138. Copyright 2003American Chemical Society.

Cyclic and pulsed voltammetric studies of Mb-surfac-tant films have been used to obtain electrochemical parameters such as electron transfer rate constants and formal potentials E° ), i.e. apparent standard potentials under given experimental conditions. Recent work has shown that a Gaussian distribution model for protein molecules with slightly different ° -values fits voltammetric data in thin surfactant films [26, 33]. This model was used with nonlinear regression to extract average ° and values from square wave voltammograms (SWV). Simple models for voltammetry of single species confined to the electrode surface did not fit the data, but formal potentials could be estimated from the midpoints of CV cathodic and anodic peaks. 

To further illuminate this rather subtle but important point, for the sake of simplicity, we may envisage an ideal Langmuir adsorption system where the adsorbent is made up of single crystal faces (in all N o them) of the same kind, each with M adsorption sites exposed to an adsorbing gas. On the average, N adsorbate molecules will be adsorbed on every crystal face. Let us assume a Gaussian distribution about the maximum term of the grand partition function ... 

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