Analyte distribution

The flow profiles of electrodriven and pressure driven separations are illustrated in Figure 9.2. Electroosmotic flow, since it originates near the capillary walls, is characterized by a flat flow profile. A laminar profile is observed in pressure-driven systems. In pressure-driven flow systems, the highest velocities are reached in the center of the flow channels, while the lowest velocities are attained near the column walls. Since a zone of analyte-distributing events across the flow conduit has different velocities across a laminar profile, band broadening results as the analyte zone is transferred through the conduit. The flat electroosmotic flow profile created in electrodriven separations is a principal advantage of capillary electrophoretic techniques and results in extremely efficient separations. 

Y. Dai, R. M. Whittal, and L. Li. Confocal Fluorecence Microscopic Imaging for Investigating the Analyte Distribution in MALDI Matrices. Anal. Chem., 68(1996) 2494-2500. 

Because MALDI is a desorption technique, it is particularly suited for the analysis of surfaces such as biological tissues [50]. In this application, the matrix is applied on the complete surface of the tissue. The laser resolution is about 100 pm and complete analyte distribution images (low molecular weight compounds, peptides, proteins) can be recorded [51, 52]. 

Due to the hydrophobicity of the silicon surface, samples are typically dissolved in water or mixtures of water and methanol. While samples dissolved in pure non-polar solvents tend to spread over the whole surface, aqueous/organic mixtures form droplets that stay localized to a small surface area. Additionally, mixtures also guarantee that the sample penetrates sufficiently deep into the silicon. Spotted volumes are typically in the low microliter to submicroliter range. Traditionally, sample spotting in DIOS-MS is carried out using pipettes, which mostly suffers from an inhomogeneous analyte distribution. This can be overcome by... 

Uniform analyte distribution is often a good assumption for liquid samples such as blood serum or even whole blood if stirring is continuous. For biological tissue, human skin in particular, heterogeneity is a major factor. Detailed morphological structures and molecular constituents of skin have been studied using confocal Raman spectroscopy.9... 

Analytes distribute themselves between aqueous and organic layers according to the Nernst distribution law, where the distribution coefficient, Kq. is equal to the analyte ratio in each phase at equilibrium. 

The analyte distributes itself between the two immiscible liquids according to the relative solubility in each solvent [1,38,44,45]. To determine the effect of the distribution coefficient on an extraction, consider the following example. 

Paper/Card and Compound Dependence of Analyte Distribution in Blood Spots... 

There are various factors that can influence the distribution of analytes in a dried blood spot. Water-soluble chemicals uniformly coated on DBS cards would redistribute when the blood was spotted. The redistribution of chemicals may depend on their properties, viscosity of blood, the volume spotted, and the technique used for spotting. Another factor is the viscosity of the blood. Viscosity is normally dependent on the blood composition (hematocrit, protein, lipid levels), and it can affect the physical spread of the blood spot in that the same volume of a less viscous blood will form a larger diameter spot than that of a more viscous blood sample. Viscosity, combined with the chemical redistribution on the sample cards, will increase the complexity of the analyte distribution. 

In order to study the radial distribution of the six analytes on dried blood spots, smaller DBS punches (1 mm. i.d.) were extracted and quantified against blood standards. Six DBS 1 mm punches were taken from the centers of six separate spots and combined into one well of a 96-well plate. The next DBS punch was taken adjacent to the center one and each subsequent punch was taken adjacent to the previous one radially moving outward towards the edge as shown in Fig. 4. Additional punch was taken from just outside of the visual edge of the blood spot as a control sample to verify that analytes are not moving outside of the visual spot. All results from the control samples confirmed the absence of the tested compounds outside of the visual border of spots. Three types of paper/card and six compounds were used to evaluate the paper impact on the analyte distribution, but only FTA Elute and VWR 237 cards are presented here. 

Accurate quantitation of analytes requires consistent measurements independent from matrix lot variation. Matrix lot to lot variation becomes critical for successfully implementing DBS. In addition to the analyte distribution across dried blood spots, matrix effect was also evaluated. In addition to the blood pool used for standards and... 

Dai Y, Whittal R, Li L (1996) Confocal fluorescence microscopic imaging for investigating the analyte distribution in MALDI matrices. Anal Chem 68 2494-2500... 

This is especially useful for systems that cannot be described by an analytical distribution function. 

It is clear that CD measurements can provide unique information which can be used to design and optimize the separation of structurally complex, biologically active materials. However, the fact that HPLC is a time dependent experiment, and the time dependence of the analyte distribution is not compatible with the scanning rate of conventional CD instruments currently limits the CD-HPLC measurement to a single wavelength. This problem will be solved if multichannel detection can be effectively coupled to the CD experiment. 

Take, for example, an LC peak whose 4ct width was measured to be 0.80 mm with a chart speed of 1.0 cm/min and a flow rate of 1.0 mL/min. By multiplying these values together, we find that this width corresponds to a volume of 80 jjlL. If the detector had a volume of 80 p.L or more, the entire analyte could be contained in it at one time and the peak would appear to be very broad due to dilution with mobile phase. A smaller detector volume—say 8 p,L—would have to be swept 10 times to accommodate all the analyte, and it would give a tall, sharp peak that more nearly represents the actual analyte distribution. As a general rule, the detector volume should be I or less of the volume of the smallest peak (usually the first peak unless there is a large solvent peak). 

As a very rough first approximation the chromatographic retention process could be described on the basis of simple single equilibria of the analyte distribution between the mobile and stationary phases. The equilibrium constant of this process is proportional to the analyte retention factor... 

Equation (2-31) represents the analyte amount accumulated in the zone dx during the time dt. This amount undergoes some distribution processes in the selected zone. These processes are the actual reason for the analyte accumulation. The analyte distribution function in the selected zone is the second half of the mass balance equation the amount of analyte accumulated in zone dx should be equal to the amount distributed inside this zone. In general form, it could be written as... 

The retention volume is essentially proportional to the derivative of the analyte distribution function definedi per unit of the column length. 

Further development of the mathematical description of the chromatographic process requires the definition of the analyte distribution function y/(c), or essentially the introduction of the retention model (or mechanism). 

As a first example of an applicable model traditional partitioning mechanism will be considered. In this mechanism the analyte is distributed between the mobile and stationary phases, and phenomenological description of this process is given in Section 2.1. The Vm and Vs are the volume of the mobile and the volume of the stationary phases in the column, respectively. Instant equilibrium of the analyte distribution between mobile and stationary phases is assumed. 

This equation has been derived for the model of the analyte distribution between mobile and stationary phases and is the same as expression (2-30) in Section 2.6. To be able to use this equation, we need to dehne (or independently determine) the volumes of these phases. The question of the determination or definition of the volume of stationary phase is the subject of significant controversy in scientihc literature, especially as it is related to the reversed-phase HPLC process [19]. 

Adsorbent nonpermeability is an important condition, since it essentially states that all processes occurs in the liquid phase. Since adsorption is related to the adsorbent surface, it is possible to consider the analyte distribution between the whole liquid phase and the surface. Using surface concentrations and the Gibbs concept of excess adsorption [20], it is possible to describe the adsorption from binary mixtures without the definition of adsorbed phase volume. 

In any instant in the cross-section zone dx (Figure 2-5) of the column, the analyte distribution function, yd c), could be expressed as... 

Expression (2-45) is essentially the analyte distribution function that could be used in the mass-balance equation (2-33). The process of mathematical solution of equation (2-33) with distribution function (2-45) is similar to the one shown above and the resulting expression is... 

The analyte distribution function in the column cross section dx could be written in the following form ... 

Because of the assumption made above, the solution is limited to the linear region of analyte partitioning and adsorption isotherms. The analyte distribution between two liquid phases (eluent and adsorbed phase) at equilibrium could be described as follows ... 

Applying this function into the mass-balance equation (2-33) and performing the same conversions [Eqs. (2-34)-(2-39)], the final equation for the analyte retention in binary eluent is obtained. In expression (2-67) the analyte distribution coefficient (Kp) is dependent on the eluent composition. The volume of the acetonitrile adsorbed phase is dependent on the acetonitrile adsorption isotherm, which could be measured separately. The actual volume of the acetonitrile adsorbed layer at any concentration of acetonitrile in the mobile phase could be calculated from equation (2-52) by multiplication of the total adsorbed amount of acetonitrile on its molar volume. Thus, the volume of the adsorbed acetonitrile phase (Vj) can be expressed as a function of the acetonitrile concentration in the mobile phase (V, (Cei)). Substituting these in equation (2-67) and using it as an analyte distribution function for the solution of mass balance equation, we obtain... 

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