Improved DNA equilibrium binding affinity determinations of platinum(II) complexes using synchrotron radiation circular dichroism.

The binding affinity of a series of square planar platinum(II) compounds of the type [Pt(A(L))(I(L))](2+), where A(L) is 1,2-diaminoethane and I(L) are 1,10-phenanthroline (phen), 4-methyl-1,10-phenanthroline (4Mephen), 5-methyl-1,10-phenanthroline (5Mephen), 4,7-dimethyl-1,10-phenanthroline (47Me2phen), 5,6-dimethyl-1,10-phenanthroline (56Me2phen) or 3,4,7,8-tetramethyl-1,10-phenanthroline (3478Me4phen) has been reinvestigated using Synchrotron Radiation Circular Dichroism (SRCD) spectroscopy. The additional peaks exhibited considerably greater intensity than those observed between 200 and 400 nm affording additional binding affinity determinations. In addition, the authors have reviewed the various mathematical approaches used to estimate equilibrium binding constants and thereby demonstrate that their mathematical approach, implemented with Wolfram Mathematica, has merit over other methods.

A magnetic gradient induced force in NMR restricted diffusion experiments.

We predict that the phase cancellation of a precessing magnetisation field carried by a diffusing species in a bounded geometry under certain nuclear magnetic resonance pulsed magnetic field gradient sequences results in a small force over typically micrometre length scales. Our calculations reveal that the total magnetisation energy in a pore under the influence of a pulsed gradient will be distance-dependent thus resulting in a force acting on the boundary. It is shown that this effect of the magnetisation of diffusing particles will appear as either an attractive or repulsive force depending on the geometry of the pore and magnetic properties of the material. A detailed analysis is performed for the case of a pulsed gradient spin-echo experiment on parallel planes. It is shown that the force decays exponentially in terms of the spin-spin relaxation. The proof is based on classical electrodynamics. An application of this effect to soft matter is suggested.

Restricted diffusion in annular geometrical pores.

Nuclear magnetic resonance (NMR) diffusion (including diffusion MRI) experiments are only as powerful as the models used to analyse the NMR diffusion data. A major problem, especially with measurements on biological systems, is that the existing models are only very poor approximations of cellular shape. Here, diffusion propagators and pulsed gradient spin-echo attenuation equations are derived in the short gradient pulse limit for diffusion within the annular region of a concentric cylinder of finite length and, similarly, within the annular region of a concentric sphere. The models include the possibility of relaxation at the boundaries and, in the case of the concentric cylinder, having the cylinder arbitrarily oriented with respect to the direction of the applied field gradient. The two models are also of interest due to their direct analogy to optical double slit diffraction. Also expressions for the mean square displacements, which are very useful information for determining the diffusion coefficient within these complex geometries, are obtained as well as for the limiting cases of diffusion on cylindrical and spherical shells and in a ring.

Modeling diffusion in restricted systems using the heat kernel expansion.

The averaged return-to-origin probability of finding a diffusing particle within a volume or in the neighborhood of the surface of a bounded region can be separated into a volume and a surface integral of the corresponding probability densities. However with the usual treatments (e.g., the commonly encountered diffusion propagator approach) there is no clear method to separate the integration of the diffusion propagators in each domain. Here we propose a general procedure based on applying the heat kernel expansion in restricted diffusion problems for the Green's function of the diffusion equation on an arbitrary region with an arbitrary boundary condition. We apply this method to the treatment of surface reaction rate in a sphere subject to the reflecting boundary condition. We determine that the rate of diffusion of a particle from the interior to the surface of the sphere changes by the square root of time plus some extra correction terms. Further, we are able to relate the diffusion propagator to the invariant properties of the region. Also in this approach we investigate how the heat kernel expansion can be applied to the problem of determining the return-to-origin probability, where we obtain a more precise result for the expansion of this probability in the case of a sphere. The advantage of this method lies in its generality and applicability to any geometrical boundary configuration and any kind of boundary condition.

Numerical analysis of NMR diffusion measurements in the short gradient pulse limit.

Pulsed gradient spin-echo (PGSE) NMR diffusion measurements provide a powerful technique for probing porous media. The derivation of analytical mathematical models for analysing such experiments is only straightforward for ideal restricting geometries and rapidly becomes intractable as the geometrical complexity increases. Consequently, in general, numerical methods must be employed. Here, a highly flexible method for calculating the results of PGSE NMR experiments in porous systems in the short gradient pulse limit based on the finite element method is presented. The efficiency and accuracy of the method is verified by comparison with the known solutions to simple pore geometries (parallel planes, a cylindrical pore, and a spherical pore) and also to Monte Carlo simulations. The approach is then applied to modelling the more complicated cases of parallel semipermeable planes and a pore hopping model. Finally, the results of a PGSE measurement on a toroidal pore, a geometry for which there is presently no current analytical solution, are presented. This study shows that this approach has great potential for modelling the results of PGSE experiments on real (3D) porous systems. Importantly, the FEM approach provides far greater accuracy in simulating PGSE diffraction data.