Investigation of binding event perturbations caused by elevated QCM-D oscillation amplitude

We report measurements with the quartz crystal microbalance with dissipation monitoring (QCM-D) technique, with focus on how the shear oscillation amplitude of the sensor surface influences biorecognition binding events. Technically, this is made as reported recently (M. Edvardsson, M. Rodahl, B. Kasemo, F. H??k, Anal. Chem., 2005, 77(15), 4918-4926) by operating the QCM in dual frequency mode; one harmonic (n = n1) is utilized for continuous excitation of the QCM-D sensor at resonance at variable driving amplitudes (1-10 V), while the second harmonic (n not equaln(1)) is used for combined f and D measurements. By using one harmonic as a "probe" and the other one as an "actuator", elevated amplitudes can be used to perturb - or activate - binding reactions in a controlled way, while simultaneously maintaining the possibility of probing the adsorption and/or desorption events in a non-perturbative manner using combined f and D measurements. In this work we investigate the influence of oscillation amplitude variations on the binding of NeutrAvidin-modified polystyrene beads (slashed circle approximately 200 nm) to a planar biotin-modified lipid bilayer supported on an SiO2-modified QCM-D sensor. These results are further compared with data on an identical system, except that the NeutrAvidin-biotin recognition was replaced by fully complementary DNA hybridization. Supported by micrographs of the binding pattern, the results demonstrate that there exists, for both systems, a unique critical oscillation amplitude, A(c), below which binding is unaffected by the oscillation, and above which binding is efficiently prevented. Associated with A(c), there is a critical crystal radius, r(c), defining the central part of the crystal where binding is prevented. From QCM-D data, A(c) for the present system was estimated to be approximately 6.5 nm, yielding a value of r(c) of approximately 3 mm--the latter number was nicely confirmed by fluorescent- and dark-field micrographs of the crystal. Furthermore, the fact that A(c) is observed to be identical for the two types of biorecognition reactions suggests that it is neither the strength, nor the number of contact points, that determine the amplitude at which binding is prevented. Rather, particle size seems to be the determining parameter.     

Effective mode area and its optimization in silicon-nanocrystal waveguides

We revisit the problem of the optimization of a silicon-nanocrystal (Si-NC) waveguide, aiming to attain the maximum field confinement inside its nonlinear core and to ensure optimal waveguide performance for a given mode power. Using a Si-NC/SiO2 slot waveguide as an example, we show that the common definition of the effective mode area may lead to significant errors in estimation of optical intensity governing the nonlinear optical response and, as a result, to poor strength evaluation of the associated nonlinear effects. A simple and physically meaningful definition of the effective mode area is given to relate the total mode power to the average field intensity inside the nonlinear region and is employed to study the optimal parameters of Si-NC slot waveguides.     

Finite- and Infinite-Dimensional Representations of the Lorentz Group

Finite- and infinite-dimensional representations of the Lorentz group are discussed and various topics in which this group is currently in use are mentioned. The infinitesimal approach of finding representations is reviewed and all finite-dimensional spinor representations of the Lorentz group are obtained. Infinite-dimensional representations are then discussed, including the principal, complementary, and complete series of representations. A generalized Fourier transformation is introduced which enables one to use the global approach to representation theory so as to express infinite-dimensional representations in terms of matrices. This method is shown to lead to a generalization of the spinor form of finite-dimensional representation to the infinite-dimensional case. However, whereas the usual spinor representations are nonunitary, the obtained new form describes both unitary and non-unitary representations, depending on the choice of certain parameters appearing in the representation formula.