Software autocorrelation

The traditional method of using DLS to determine the intensity autocorrelation function is to detect the scattered light at a fixed angle with a photomultiplier tube and then process this signal with a hard-wired electronic correlator." " Commercial instruments with hardware and software optimized for this purpose are available from manufacturers such as Brookhaven Instraments, Malvern Instruments, and others. Here we will utilize... 

A major disadvantage is the time required for the computation. The entire algorithm (generation of 3-D structure, conformation analyses, property calculation, property mapping on surface or field and autocorrelation transformation) needs between 100 and 100000 s for one molecule. With today s computer technology, using multi-processor compute servers and highly vectorized software, it is possible to calculate up to several thousand three-dimensional autocorrelation descriptors vtithin a day (Table 7). 

The correlation between observations made at different times (autocorrelation) is described mathematically by computing the autocorrelation function, the degree of correlation between observations made k time units apart k = 1,2, ). The correlation coefficient is a measure of the linear association between two variables. It does not describe a cause-and-effect relation. The autocorrelation depends on sampling interval. Most statistical and mathematical software packages include routines for computing correlation and autocorrelation. 

An important feature of GRIND is that, with the use of appropriate software, the original descriptors (molecular interaction fields) can be regenerated from the autocorrelation transform and, thus, the results of the analysis are represented graphically, together with the original molecular structures in three-dimensional plots. The use of the methodology was recently illustrated in examples from the... 

The autocorrelation function can be calculated in real time using a hardware correlator or in software after the collection of a photon count trace using a multichannel scalar card. Details of the instrumentation will be discussed in Chapter 3. Formally, the un-normalized autocorrelation of time series data is given as [6] ... 

The size distribution of the liposomes is determined by dynamic light scattering (DLS) with a Dynapro apparatus (http //www.wyatt.com). DLS is a hydrodynamic method by which one determines the rate of diffusion of particles through the solvent. The hydrodynamic radius is defined as the radius of a theoretical hard sphere that diffuses with the same speed as the particle under examination. The measurement is performed at 25° and requires about 2 /ul of the extruded liposome suspension diluted in 18 /ul of liposome buffer (final lipid concentration in the range of 0.1 roM). Ten autocorrelation functions are sequentially measured, from which the size distribution of the liposome is determined using the Dynamics v5 software from Dynapro. A complete measurement takes a few minutes. Figure lA shows typical size distributions of extruded liposomes as determined by DLS. Figure IB shows how the actual hydrodynamic radius of the liposomes varies with the pore size of the polycarbonate filter. 

The resolving ability of the software was investigated using the simulated autocorrelation functions of a 50/50 mixture, on intensity basis, of two monodisperse samples. The first species was characterised by a diameter of 50 nm, whereas the second contained particles of respectively 60, 75, 100, 150 and 200 nm, the standard... 

Deconvolution of the measured intensity autocorrelation was achieved by the DTS software. For a pure diffusive relaxation, F is related to the translational diffusion coefficient D tq 0 and c 0 according to Eq. (3) ... 

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