The photochemical reaction cycle of retinal reconstituted bacteriorhodopsin

The function of three types of bacteriorhodopsins was compared: the wild-type, the bleached and retinal reconstituted and retinal deficient bacteriorhodopsin after retinal addition. The apparent pK(a) of the proton acceptor group for the bleached BR and retinal deficient BR shifted toward higher pH values compared to the wild-type BR. Fitting the photocycle model to the absorption kinetic signals for all three proteins showed the existence of the same intermediates, but the time-dependent concentration of the intermediates was different. Although measurements were made at pH 7, the absorption kinetics and photoelectric signals in both retinal reconstituted samples acted as wild-type bacteriorhodopsin at significantly higher pH. Below pH 3 the retinal deficient and reconstituted sample bleached. These results suggested that the added retinal was not able to rebind in the same position in the protein as in native bacteriorhodopsin. This points out that care should be taken, when bleached bacteriorhodopsin is reconstituted with different retinal analogs.     

The influence of the halide ions on the photochemical reaction cycle of pharaonis halorhodopsin

Sodium salt of chloride, bromide and iodide were used to elucidate the effect of the size of the anion on the binding to pharaonis halorhodopsin and its transport during the photocycle of this retinal protein. Spectroscopic titration revealed an apparent strong binding constant of 2 mM for chloride, 0.23 mM for bromide and 5 mM for iodide. In the case of iodide a second, week binding constant of about 10 M could be estimated. This second binding constant was similar to that observed earlier for nitrate. By changing the halide ions, only the transitions in the second half of the photocycle were affected, which contained intermediates N, O, and HR'. The O to HR' transition becomes faster with increasing ion volume, meaning that the ion uptake is accelerated. This effect shows a direct correlation with the ion radius. With increasing ion concentration the N-O-HR' equilibrium changed in such a way that the accumulated O tended to decrease. This tendency was overruled in iodide, by the appearance of the second binding constant. The increasing iodide concentration, up to 100mM decreases the accumulation of the intermediate O, due to kinetic reasons, but at higher ion concentration the amount of O increases, although its decay becomes faster. This effect correlates with the appearance of the second iodide bound to the protein.     

Parametric solutions of the eigenvalue equation for a convectively cooled slab

The convective cooling of a slab by an ambient fluid under the most general linear and homogeneous boundary conditions is considered. For the roots of the corresponding transcendental eigenvalue equation an explicit formula is written down in a parametric form. The practical consequences of this representation, among them certain “singular solutions” which cannot be obtained by a direct numerical treatment of the original eigenvalue equation, are discussed in detail.     

Exact analytical solution for a thermal boundary layer in a saturated porous medium

The forced convection thermal boundary layer in a porous medium as an analytically tractable special case of a mixed convection problem is considered. It is shown that some general features of the mixed convection solutions reported recently by other authors [B. Brighi, J.-D. Hoernel, On the concave and convex solutions of mixed convection boundary layer approximation in a porous medium, Appl. Math. Lett. (published online, 2005); M. Guedda, Multiple solutions of mixed convection boundary layer approximations in a porous medium, Appl. Math. Lett. (published online, 2005)] can already be recovered from this exactly solvable case.     

Effect of Viscous Dissipation on a Quasi-Parallel Free Convection Boundary-Layer Flow over a Vertical Flat Plate in a Porous Medium

Transport in Porous Media -     

The inertia mode of uniformly driven kinks in damped multistable systems

Linear arrays of damped multistable systems in a constant driving fieldF are considered in the tight coupling limit. The existence of a localized relaxation mode (inertia mode) of the driven kinks is pointed out. This mode, whose frequency on the time scale of theL-system is a universal (model independent) quantity, describes the accomodation of the kink to a new shape and terminal velocity when the driving field is changed infinitestimally. In a chain without inertia the accommodation is instantaneous. Whence the name inertia mode (IM). The IM is generated by the translation invariance of the kink equation, in addition to the Goldstone mode (GM). In the absence of the driving force and dissipation, the IM becomes defectively degenerate with the GM and represents a pure algebraic mode of the free kink, describing another free kink moving with infinitesimally changed velocity.Work supported by the Swiss National Science Foundation.     

Stability of uniformly driven domain walls

An infinite ferromagnetic medium with orthorombic crystal field anisotropy and with a constantdc field applied along the easy axis is considered in the framework of micromagnetics. It is shown that in the presence of Gilbert damping the uniformly driven plane domain wall (Walker wall) with positive Döring mass is linearly stable for any strengthH of the applied field below a critical valueH ₀, where it connects to an unstable wall configuration with negative Döring mass. The critical fieldH ₀ is lower than the existence limitH _W (Walker limit) of the solitary travelling-wave type domain wall solutions, and represents the threshold of the field regionH _{0 W} where negative wall mobilities occur. The instability atH=H ₀ is associated with a nonuniform localized relaxation mode (corrugating mode) of the plane domain wall. If coupling to the external circuit is taken into account, negative-mobility walls also become unstable against uniform perturbations for sufficiently small circuit resistance.Work supported by the Swiss National Science Foundation     

Domain wall instability in biaxial ferromagnets

The energetic and dynamic stability of domain walls (DW's) in a 1D Heisenberg ferromagnet with orthorhombic anisotropy is examined in the framework of classical continuum theory. It is shown that in the undamped chain the critical slowing-down accompanying the energetic instability of the static DW's at a critical ratioa _c of the anisotropy fields is not marked (as one might expect) by a localized soft dynamic mode of the DW's, but it is realized by a mechanism which may be termed softening of the velocity change. The role of the soft eigenmode is taken over by the perturbation which carries the static DW into a moving one with infinitesimal velocity, and the role of the soft-mode frequency is taken over by the velocity change induced by the perturbation. When spin damping is included, one does find a soft relaxation mode: Attenuation of the velocity of moving DW's gives rise to a perturbation which may be described as a superposition of the Goldstone mode and a relaxation mode. This behaviour is not a special feature of the system under consideration, but a similar situation arises in general, when a static DW becomes unstable with respect to a perturbation connecting it with a family of other static DW's. For moving DW's the softening of the velocity change also occurs, but here no energetic stability criterion is available and inclusion of spin damping makes the DW motion nonstationary. Thus, in the case of moving DW's no possibility seems to exist to define stability and instability in the usual terms of linear analysis.Work supported by the Swiss National Science Foundation