Model dynamic exchange

A somewhat different model was proposed more recently by Nandi and Bagchi [4]. This model was initially proposed to explain the anomalous DR of aqueous protein solutions, but since then has been used to explain protein and DNA SD. This is termed the dynamic exchange model as it envisaged the exchange of water between the surface and the bulk water as a distinct dynamic process, as shown in Figure 6.2. 

The dynamic exchange model (illustrated in Figure 6.2) is based on the assumption that the water molecules at the surface of proteins can be categorized into distinct species as bound and free depending on the nature of their hydrogenbonding to the biomolecular surface (Figure 6.2). This equilibrium can be symbolically written as [4]... 

The above dynamic exchange model applies mainly to the rotational relaxation of interfaeial water molecules. It has also been extended by Bhattaeharyya et al. [6] to treat wave-number-dependent relaxation, whieh includes translational diffusion more realistically. As stated, the model is simple and phenomenological but captures several essential aspects of water dynamics at the biological interface, in addition to being analytically tractable. 

Clearly, the dynamic exchange model is phenomenological and does not address in detail the microscopic dynamics in the hydration layer. However, it is simple and largely analytical, and provides an appealingly simple picture of the altered dynamics at protein and DNA surfaces. In the appendix, a more detailed discussion of the model is presented. 

The dynamic exchange model (DEM) of dynamics in protein and the DNA hydration layer was originally proposed in 1997 and was subsequently further developed in several other studies [4]. It is a simple phenomenological model, based on arguments common in chemical kinetics, but serves as a starting point to address the influence of protein or DNA (or lipid, micelles) on the surrounding water molecules. 

The dynamic exchange model employs a hydrodynamic approach wherein the dynamics of the three species in the surface layer is described by a reaction-diffusion equation and the bulk water dynamics is described by a simple diffusion equation. Therefore, in this approach, the interactions are not considered explicitly... 

Figure 8.3. The real part of the complex frequency-dependent dielectric function [e (co)] of aqueous myoglobin solution for different concentrations. Concentrations are (from top to bottom) 161, 99, and 77 mg/mL at 293.15 K. The symbols denote experimental results while the solid line is a fit to the theory of dynamics exchange model developed by Nandi and Bagchi. Adapted with permission from J. Phys. Chem. A, 102 (1998), 8217-8221. Copyright (1998) American Chemical Society.

There have been two different interpretations of the slow dynamics observed in the SD of the lysozyme hydration layer. The first attributes the intermediate time-scales (30 0 ps) to slow water. Bagchi and co-workers employed the dynamic exchange model to relate the observed slow dynamics to the timescale of the fluctuation of water in the hydration layer [11]. In an alternative interpretation. Song et al. used the formulation developed by Song and Marcus that relates the solvation time correlation function to the DR of the medium. They attributed the... 

The solvation dynamics results of Zewail and co-workers are shown in Figure 8.5 for the protein Subtilisin Carlsberg (SC). The inset in the same figure shows faster solvation when the probe was dansyl-bonded and placed at a distance of 6-7 A from the protein surface. The 20-40 ps component was interpreted in terms of the bound free dynamic equilibrium proposed in a dynamic exchange model of the hydration layer. 

Dynamic simulation models include fluid inertia and compressibility and exchanger shell expansion to determine the pressure spikes associated with... 

Okada et al. have presented a dynamic dissociation model, which is schematically shown in one dimension in Fig. 4. They assumed that the separating motion of a cation (or anion) of interest from the reference anion (cation), which is called the self-exchange velocity,is the electrically conducting process, which will be considered in Section III.7( ) in more detail. The Chemla effect can also be reproduced by the SEV. 

Several theoretical models, such as the ion-pair model [342,360,361,363,380], the dyneuaic ion-exchange model [342,362,363,375] and the electrostatic model [342,369,381-386] have been proposed to describe retention in reversed-phase IPC. The electrostatic model is the most versatile and enjoys the most support but is mathematically complex euid not very intuitive. The ion-pair model emd dynamic ion-exchange model are easier to manipulate and more instructive but are restricted to a narrow range of experimental conditions for trtilch they might reasonably be applied. The ion-pair model assumes that an ion pair is formed in the mobile phase prior to the sorption of the ion-pair complex into the stationary phase. The solute capacity factor is governed by the equilibrium constants for ion-pair formation in the mobile phase, extraction of the ion-pair complex into the stationary phase, and the dissociation of th p ion-pair complex in the... 

We will then compare the dynamics of the radial diffusion model with a first-order exchange model which gives the same half-life as the radial model (Eq. 18-37). A preview of this comparison is given in Fig. 18.7b, which shows that the linear model underpredicts the exchange at short times and overpredicts it at long times. 

Figure 19.12 (a) Experimental setup to determine the exchange dynamics of a combined NAPL-water system using the slow stirring method (SSM). (6) - (d) Measured and calculated aqueous concentrations of benzene m/p-xylene and naphthalene. The solid lines give the result of the linear bottleneck exchange model with an aqueous boundary layer thickness of 8bl = 2.4 x 1CT2 cm = 240 pm (adapted from Schluep et al., 2000). 

Contents 1. Introduction 176 2. Static NMR Spectra and the Description of Dynamic Exchange Processes 178 2.1. Simulation of static NMR spectra 178 2.2. Simulation of DNMR spectra with average density matrix method 180 3. Calculation of DNMR Spectra with the Kinetic Monte Carlo Method 182 3.1. Kinetic description of the exchange processes 183 3.2. Kinetic Monte Carlo simulation of DNMR spectra for uncoupled spin systems 188 3.3. Kinetic Monte Carlo simulation of coupled spin systems 196 3.4. The individual density matrix 198 3.5. Calculating the FID of a coupled spin system 200 3.6. Vector model and density matrix in case of dynamic processes 205 4. Summary 211 Acknowledgements 212 References 212... 

There are three popular hypotheses. Two models propose extreme situations and each encompasses a substantial amount of chromatographic data. These two proposals are the ion-pair model and the dynamic ion-exchange model. The third view, which is broader in scope than the previous two concepts, accommodates both the extreme views without combining the two models. This proposal is the ion-interaction model. 

Model makers named the technique solvent generated ion exchange [7] and hydrophobic chromatography with dynamically coated stationary phase [8], thereby emphasizing a dynamic ion exchange model. 

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