An exactly solvable Ogston model of gel electrophoresis: X. Application to high-field separation techniques

Recently, we generalized our lattice model of gel electrophoresis to study the net velocity of particles being pulled by a high-intensity electric field through an arbitrary distribution of immobile obstacles (Gauthier, M. G., Slater, G. W., J. Chem. Phys. 2002, 117, 6745-6756). In this article, we show how the high-field version of our model can be used to compare the velocity of particles with different electric charges and/or physical sizes. We then investigate specific two-dimensional distributions of obstacles that can be used to separate particles, e.g., in a microfluidic device. More precisely, we compare the velocity of differently charged or sized analytes in sieving, trapping and deflecting systems to model various electrophoretic separation techniques. In particular, we study the nonlinear effects present in ratchet systems and how they can be combined with time-asymmetric pulsed fields to provide new modes of separation.     

An exactly solvable Ogston model of gel electrophoresis. V. Attractive gel-analyte interactions and their effects on the Ferguson plot

We examine the effect of attractive analyte-gel interactions within the framework of our recently developed lattice model of gel electrophoresis. We show that it is possible to take into account such interactions and still calculate exact mobilities for various analytes and gel structures. Our study then focuses on two main issues: (i) the effect of these interactions on the separation efficiency of the Ogston regime; and (ii) the presence of inflection points (changes of curvature) in Ferguson plots. We establish some general principles, and we describe the results for selected two- and three-dimensional model systems. Numerous practical problems, such as chiral separations and affinity electrophoresis, can be treated using this approach.     

An exactly solvable Ogston model of gel electrophoresis: VIII. Nonconducting gel fibers, curved field lines, and the Nernst-Einstein relation.

In this article, we examine the low-field electrophoretic migration of infinitely small analytes in dilute sieving media made of nonconducting gel fibers. Using an Ogston obstruction model, we show that the electrophoretic mobility is not affected by the presence of curved field lines. In other words, the Nernst-Einstein relation between the mobility and the diffusion coefficient is valid regardless of the electrical properties of the gel fibers. Although this finding may greatly simplify the development of obstruction models of electrophoretic sieving, it also represents a critical test for any analytical or computational approach.     

An exactly solvable model for the Fermi contact interaction

A model for the Fermi contact interaction is proposed in which the nuclear moment is represented as a magnetized spherical shell of radius r ₀. For a hydrogen-like system thus perturbed, the Schrödinger equation is solvable without perturbation theory by use of the Coulomb Green's function. Approximation formulas are derived in terms of a quantum defect in the Coulombic energy formula. It is shown that the usual Fermi potential cannot be applied beyond first-order perturbation theory.     

Condensed-phase relaxation of multilevel quantum systems. I. An exactly solvable model

An analytically solvable model of multilevel condensed-phase quantum dynamics relevant to vibrational relaxation and electron transfer is presented. Exact solutions are derived for the reduced system density matrix dynamics of a degenerate N-level quantum system characterized by nearest-neighbor hopping and off-diagonal coupling (which is linear in the bath coordinates) to a harmonic oscillator bath. We demonstrate that for N> 2 the long-time steady-state system site occupation probabilities are not the same for all sites; that is, they are distributed in a non-Boltzmann manner, which depends on the initial conditions and the number of levels in the system. Although the system-bath Hamiltonian considered here is restricted in form, the availability of an exact solution enables us to study the model in all regions of an extensive parameter space.     

An exactly solvable model for a ternary solution with three-body interactions and orientationally dependent bonding

A model is considered in which the bonds of a honeycomb lattice are covered by rodlike molecules of types AA, BB, and AB. Neighboring molecular ends have three-body and orientation-dependent interactions. The model is shown to be equivalent to a spin-1/2 Ising model on the same lattice with a field, but with only pairwise interactions. Symmetric and asymmetric coexistence surfaces for the separation into an AA-rich and a BB-rich phase are calculated exactly.     

On the applicability of the Born-Oppenheimer approximation in a theory of nonadiabatic charge transfer reactions: An exactly solvable model

The question concerning the applicability of the Born-Oppenheimer approximation (BOA) for the calculation of the transition probability for a nonadiabatic process of charge transfer in a polar environment with allowance made for temperature effects is investigated theoretically. Considered is the transfer of a quantum particle (proton) that interacts with a local vibration mode in a model of bound harmonic oscillators. The model admits an exact solution for wavefunctions of the initial and final states. A calculation shows that BOA is applicable even for very large distances of the proton transfer. At the same time, the exact result and the BOA result severely differ from a probability calculated in a crude Condon approximation. It is demonstrated that the non-Condon effects are in a general case temperature-dependent and may substantially influence the calculated values of the transition probability.     

An apparatus for continuous separation of macromolecules by combined electrophoresis and gel filtration

Summary An apparatus for continuous separation of soluble and particulate macromolecules, and of other electrically charged particles by combined electrophoresis and gel filtration, is described. The two principles, electrophoresis and gel filtration, which operate simultaneously at right angles, enable separation between the various macromelecules, depending upon differences in electric charge and molecular wight. The sample to be fractionated is fed continuously into the apparatus while the separated macromolecules reaching the distal end of the instrument are collected at the outlet ports. Data for a continuous fractionation of human plasma proteins using the instrument are given.     

Does really Born–Oppenheimer approximation break down in charge transfer processes? An exactly solvable model

Effects of deviation from the Born–Oppenheimer approximation (BOA) on the non-adiabatic transition probability for the transfer of a quantum particle in condensed media are studied within an exactly solvable model. The particle and the medium are modeled by a set of harmonic oscillators. The dynamic interaction of the particle with a single local mode is treated explicitly without the use of BOA. Two particular situations (symmetric and non-symmetric systems) are considered. It is shown that the difference between the exact solution and the true BOA is negligibly small at realistic parameters of the model. However, the exact results differ considerably from those of the crude Condon approximation (CCA) which is usually considered in the literature as a reference point for BOA (Marcus–Hush–Dogonadze formula). It is shown that the exact rate constant can be smaller (symmetric system) or larger (non-symmetric one) than that obtained in CCA. The non-Condon effects are also studied.     

Length dependence of the optical transition energies of the exactly solvable Hubbard model for linear polyenes

Some accurate results on the length dependence of the excitation energies from the ground state to ionic excited states in the Hubbard model of linear polyenes are obtained based on the method of Lieb and Wu. To this end, it is first shown that singly ionic excited states with “plus” alternancy symmetry in the Hubbard model are described by the wave functions in which the two electron operator [∑(?)ⁿCC] is acted on (N ? 2)-electron covalent eigenstates. Then by solving the Lieb-Wu equations the exact excitation energies of the lowest ionic state, which corresponds to the E state in this model, are calculated for systems with up to 50 electrons. The result, together with a correction for the end effect, indicates that the excitation energies do not decrease as 1/N but converge to the limiting value more rapidly when the number of electrons N becomes large.     

Nuclear magnetic resonance restricted diffusion between parallel planes in a cosine magnetic field: an exactly solvable model

We propose a theoretical and numerical analysis of restricted diffusion between parallel planes in a cosine magnetic field. The specific choice of this spatial profile as proportional to an eigenfunction of the Laplace operator in this confining geometry considerably simplifies the underlying mathematics. In particular, exact and explicit relations for several moments of the total phase accumulated by diffusing spins are derived. These relations are shown to provide good approximations for the typical case of a linear magnetic field gradient, for which the theoretical analysis was in general limited to the second moment. We study the structure and the properties of the higher order moments which are responsible for the breakdown of the "Gaussian phase approximation" (GPA) at intense magnetic fields. The limits of applicability of the GPA for nonlinear magnetic fields and the transition to the localization regime are discussed. In particular, a diagram of different restricted diffusion regimes is presented.     

A multivariate spot filtering model for two-dimensional gel electrophoresis

Image segmentation plays an important role in the automatic analysis of protein spots in 2-DE. Using image segments representing protein spots, the amount of protein in each segment can be quantified, and corresponding segments can be matched and compared for multiple gels. However, the common presence of image segments caused by noise and unwanted artefacts highly disturb the analysis and comparison of the gels. Common sources of such artefacts are cracks in the gel surface, fingerprints, dust and other pollutions. It would be advantageous to remove these unwanted artefacts during or after the segmentation procedure. To achieve this task a multivariate spot filtering model is developed using image segments from a gel segmentation. Parameters in the model are based on texture, shape and intensity measurements of the image segments. The model successfully managed to separate segments caused by noise, artefacts and cracks from image segments representing true protein spots. The classification method used is discriminant partial least squares regression.     

Effective mass schrödinger equation for exactly solvable class of one-dimensional potentials

We deal with the exact solutions of Schr?dinger equation characterized by position-dependent effective mass via point canonical transformations. The Morse, P?schl-Teller, and Hulthén type potentials are considered, respectively. With the choice of position-dependent mass forms, exactly solvable target potentials are constructed. Their energy of the bound states and corresponding wavefunctions are determined exactly.      

Development of a novel two-dimensional gel electrophoresis protocol with agarose native gel electrophoresis

A new protocol for conducting two-dimensional (2D) electrophoresis was developed by combining the recently developed agarose native gel electrophoresis with either vertical sodium dodecyl sulfate (SDS) polyacrylamide gel electrophoresis (PAGE) or flat SDS agarose gel electrophoresis. Our innovative technique utilizes His/MES buffer (pH 6.1) during the first-dimensional (1D) agarose native gel electrophoresis, which allows for the simultaneous and clear visualization of basic and acidic proteins in their native states or complex structures. Our agarose gel electrophoresis is a true native electrophoresis, unlike blue native–PAGE, which relies on the intrinsic charged states of the proteins and their complexes without the need for dye binding. In the 2D, the gel strip from the 1D agarose gel electrophoresis is soaked in SDS and placed on top of the vertical SDS–PAGE gels or the edge of the flat SDS–MetaPhor high-resolution agarose gels. This allows for customized operation using a single electrophoresis device at a low cost. This technique has been successfully applied to analyze various proteins, including five model proteins (BSA, factor Xa, ovotransferrin, IgG, and lysozyme), monoclonal antibodies with slightly different isoelectric points, polyclonal antibodies, and antigen–antibody complexes, as well as complex proteins such as IgM pentamer and β-galactosidase tetramer. Our protocol can be completed within a day, taking approximately 5–6 h, and can be expanded further into Western blot analysis, mass spectrometry analysis, and other analytical methods.     

Modified apparatus for voltage gradient gel electrophoresis.

We built a modified version of voltage gradient gel electrophoresis system to correct distortions in nucleic acids electrophoretic migration patterns occurring at the edges of the gel when the original voltage gradient apparatus is used. The new device allows correct fractionation of nucleic acids also when electrophoresis is performed at high voltages.     

Pulsed-field gel electrophoresis analysis of a Pseudomonas aeruginosa pathovar.

This paper presents the genome organization and mobility of Pseudomonas aeruginosa strains that had been isolated in half-year intervals from 30 patients with cystic fibrosis since the onset of colonization over a 2- to 8-year period. The chromosomes were digested with DraI or SpeI, separated by pulsed-field gel electrophoresis, blotted and hybridized with probes encoding housekeeping or virulence genes. Strains were differentiated by relatedness of macrorestriction fingerprints. After some turnover of strains during the first two years of colonization, each patient had acquired a set of strains that diversified during the course of the disease. In the majority of patients, two clonal lineages were found to account for colonization in the air passages but each lung habitat was characterized by some specific signature of bands in the macrorestriction fragment pattern.     

An improved voltage measurement device for gel electrophoresis in tube apparatus

A device for the measurement of voltage across tube gels was designed and constructed which allows one to measure voltage during electrophoresis without any manipulation of the gel electrophoresis apparatus or gel tube and with the elimination of a source of inaccuracy in previous such devices.