Local polarization fields

The recent development of high-resolution experimental techniques allows for the structural analysis of protein channels with unprecedented detail. However, the fundamental problem of relating the structure of ion channels to their function is a formidable task. This chapter describes some of the most popular simulation approaches used to model channel systems. Particle-based approaches such as Brownian and molecular dynamics will continue to play a major role in the study of protein channels and in validating the results obtained with the extremely fast continuum models. Research in the area of atomistic simulations will focus mainly on the force-field schemes used in the ionic dynamics simulation engines. In particular, polar interactions between the various components of the system need to be computed with algorithms that are more accurate than those currently used. The effects of the local polarization fields need to be accounted for explicitly and, at the same time, efficiently. Continuum models will remain attractive for their efficiency in depicting the electrostatic landscape of protein channels. Both Poisson-Boltzmann and Poisson-Nemst-Plank solvers will continue to be used to... 

After the discovery of the chevron structures, a number of complexities in observed optical and electrooptical phenomena could be interpreted in these new terms. For a more thorough discussion in this matter, we refer to references [166-168]. Our emphasis will be on the important consequences for the physics due to the presence of chevrons, but even this requires dealing with at least some structural details. First of all, the chevron fold forces the director n to be in the interface, i.e., to be parallel to the plane of the sample in this region, regardless of how n (r) may vary through the rest of the sample and independent of the surface conditions. Although the director n is continuous at the chevron interface, the local polarization field P cannot be, as shown in Fig. 96. It makes a jump in direction at the interface, nevertheless, in such a way that... 

A connnon teclmique used to enliance the signal-to-noise ratio for weak modes is to inject a local oscillator field polarized parallel to the RIKE field at the detector. This local oscillator field is derived from the probe laser and will add coherently to the RIKE field [96]. The relative phase of the local oscillator and the RIKE field is an important parameter in describing the optical heterodyne detected (OHD)-RIKES spectrum. If the local oscillator at the detector is in phase with the probe wave, the heterodyne mtensity is proportional to... 

The higher-order bulk contribution to the nonlmear response arises, as just mentioned, from a spatially nonlocal response in which the induced nonlinear polarization does not depend solely on the value of the fiindamental electric field at the same point. To leading order, we may represent these non-local tenns as bemg proportional to a nonlinear response incorporating a first spatial derivative of the fiindamental electric field. Such tenns conespond in the microscopic theory to the inclusion of electric-quadnipole and magnetic-dipole contributions. The fonn of these bulk contributions may be derived on the basis of synnnetry considerations. As an example of a frequently encountered situation, we indicate here the non-local polarization for SFIG in a cubic material excited by a plane wave (co) ... 

The PCM algorithm is as follows. First, the cavity siuface is determined from the van der Waals radii of the atoms. That fraction of each atom s van der Waals sphere which contributes to the cavity is then divided into a nmnber of small surface elements of calculable surface area. The simplest way to to this is to define a local polar coordinate frame at tlie centre of each atom s van der Waals sphere and to use fixed increments of AO and A(p to give rectangular surface elements (Figure 11.22). The surface can also be divided using tessellation methods [Paschual-Ahuir d al. 1987]. An initial value of the point charge for each surface element is then calculated from the electric field gradient due to the solute alone ... 

A further objective is the evaluation in group (c) of the local polarization state by taking account of IR errors due to direct currents. Here Eq. (3-28) and the further explanations in the second half of Section 3.3.1 are relevant. In practical application, the error effect of A /<,ff must be estimated [2]. When foreign fields are present, it is necessary to substitute for the At/ value the average of the measurements made on both sides of the pipeline [2,52]. Figure 3-30 gives an example of... 

The continuum electrostatic approximation is based on the assumption that the solvent polarization density of the solvent at a position r in space is linearly related to the total local electric field at that position. The Poisson equation for macroscopic continuum media... 

The influence of structured electrodes or multipoint electrodes, which enhance the local electric field [20,21], as well as the effect of discharge polarity [20-22] and gap length [21,23,24], was investigated. 

It is necessary to note that fluorescence characteristics demonstrate remarkable sensitivity to variations of physicochemical parameters of the environment. Therefore, such parameters as polarity, viscosity, temperature, electric potential, local electric field, pressure, pH, etc., can be registered successfully using the modem sensitive apparatus for fluorescence detection [1, 4—12]. As a consequence, fluorescent molecules are used successfully as molecular probes to study the local characteristics of physicochemical, biochemical and biological systems. 

The muon spin relaxation technique uses the implantation and subsequent decay of muons, n+, in matter. The muon has a polarized spin of 1/2 [22]. When implanted, the muons interact with the local magnetic field and decay (lifetime = 2.2 ps) by emitting a positron preferentially in the direction of polarization. Adequately positioned detectors are then used to determine the asymmetry of this decay as a function of time, A t). This function is thus dependant on the distribution of internal magnetic fields within a... 

The Tokyo Tech group assigned a C2 structure for the layers in the B2 phase, and ferroelectric packing of such layers to form a locally polar C2v macroscopic structure, as indicated in Figure 8.20. Other early workers in the field also adopted this structural model for the B2 phase. Brand et al. had discussed a C2 smectic chevron structure in their 1992 theoretical study,29 and while they seem to be referring to an all-anticlinic bilayer smectic, their actual graphic is basically identical to that shown in Figure 8.20. Furthermore,... 

In the case of iron, magnetism is due to the unpaired electrons in the 3d-orbitals, which have all parallel spin. These electrons interact with all other electrons of the atom, also the s-electrons that have overlap with the nucleus. As the interaction between electrons with parallel spins is slightly less repulsive than between electrons with anti parallel spins, the s-electron cloud is polarized, which causes the large but also highly localized magnetic field at the nucleus. The field of any externally applied magnet adds vectorially to the internal magnetic field at the nucleus. 

As reviewed above, when a solute is placed in a dielectric medium, it electrically polarizes that medium. The polarized medium produces a local electrostatic field at the site of the solute, this field polarizes the solute, and the polarized solute interacts with the polarized medium. The interaction is typically too large to be treated by perturbation theory, and some sort of self-consistent treatment of polarized solute and polarized medium is more appropriate. At this point several options present themselves. It promotes orderly discussion to classify these... 

As discussed in Section 2, one key assumption of reaction field models is that the polarization field of the solvent is fully equilibrated with the solute. Such a situation is most likely to occur when the solute is a long-lived, stable molecular structure, e g., the electronic ground state for some local minimum on a Bom-Oppenheimer potential energy surface. As a result, continuum solvation models... 

Two principal ways exist to use a dye as a sensor of local polarity (or of microscopic electric fields) (1) monitoring the polarity-induced shift of the energy levels, e.g., the red shift of the fluorescence and (2) monitoring changes in fluorescence intensity induced by the polarity- or field-induced modulation of nonradiative rates. As these compete with the fluorescence emission, the fluorescence intensity (and lifetime) is correspondingly modulated. (3) In some cases, the radiative rates are also solvent sensitive this is usually connected with the formation of luminescent products. 

The interference process in this collinear approach is, however, different from the interference realized by mixing the local oscillator and the CARS field on a beam splitter. Interference takes place in the sample, which, in the presence of multiple frequencies, mediates the transfer of energy between the beams that participate in the nonlinear process. The local oscillator mixes with the anti-Stokes polarization in the focal volume, and is thus coherently coupled with the pump and Stokes beams in the sample through the third-order polarization of the material. In other words, the material s polarization, and its ability to radiate, is directly controlled in this collinear interferometric scheme. Under these conditions, energy from the local oscillator may flow to the pump and Stokes fields, and vice versa. For instance, when the local oscillator field is rout of phase with the pump/Stokes-induced anti-Stokes polarization in the focal interaction volume, complete depletion of the local oscillator may occur. The energy of the local oscillator field is not redistributed in terms... 

Orientation polarization can occur in materials composed of molecules that have permanent electric dipole moments. The permanent dipoles tend to become aligned with the apphed electric field, but entropy and thermal effects tend to counter this alignment. Thus, orientation polarization is highly temperature-dependent, unlike the forms of induced polarization which are nearly temperature-independent. In electric fields of moderate intensity, the orientation polarization is proportional to the local electric field, as for the other forms of polarization... 

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