Photocycles of Channelrhodopsin-2

Recent developments have used light-activated channels or transporters to modulate neuronal activity. One such genetically-encoded modulator of activity, channelrhodopsin-2 (ChR2), depolarizes neurons in response to blue light. In this work, we first conducted electrophysiological studies of the photokinetics of hippocampal cells expressing ChR2, for various light stimulations. These and other experimental results were then used for systematic investigation of the previously proposed three-state and four-state models of the ChR2 photocycle. We show the limitations of the previously suggested three-state models and identify a four-state model that accurately follows the ChR2 photocurrents. We find that ChR2 currents decay biexponentially, a fact that can be explained by the four-state model. The model is composed of two closed (C1 and C2) and two open (O1 and O2) states, and our simulation results suggest that they might represent the dark-adapted (C1-O1) and light-adapted (C2-O2) branches. The crucial insight provided by the analysis of the new model is that it reveals an adaptation mechanism of the ChR2 molecule. Hence very simple organisms expressing ChR2 can use this form of light adaptation.     

Analysis of small-angle X-ray scattering from fibers: Structural changes in nylon 6 upon drawing and annealing

The changes in the fibrillar and the lamellar structure in nylon 6 fibers resulting from drawing and annealing were studied by a detailed analysis of their two-dimensional small-angle scattering patterns. The scattering object that gives to rise the diffuse equatorial scattering in the angular range of Q = 0.02 to 0.3 Å⁻¹ is assumed to be a fibril. There are two distinct regimes in the equatorial diffuse scattering. The scattering at Q < 0.1 Å⁻¹ is dominated by scattering due to the longitudinal dimension of the fibril, and that at Q > 0.1 Å⁻¹ to the lateral dimensions/organization of the fibril. The interfibrillar regions, unlike the interlamellar regions that are essentially made of amorphous chain segments, may have microvoids in addition to amorphous chain segments. The intensity distribution within the lamellar reflections was used to obtain the lamellar spacings and the dimension of the lamellar stacks. The length of the fibrils is between 1000 and 3000 Å, the higher values being more prevalent at lower draw ratios. The fibril length is larger than the length of the lamellar stack, and approaches the latter at higher draw ratios. Annealing does not change the lengths of the fibrils, but the length of the lamellar stack increases. The fibrils form crystalline aggregates with a coherence length of ∼200 Å at higher draw ratios. The diameter of the fibrils (50–100 Å) determined from the lamellar reflection using both the Scherrer equation and the Guinier law are consistent with the lateral size of the crystallites derived from wide-angle x-ray diffraction. The longitudinal correlation of the lamellae between the neighboring fibrils improves upon drawing and decreases upon annealing. The degree of fibrillar and lamellar orientation is about the same as the crystalline orientation. Lamellar spacing increases upon drawing (from ∼60 to 95 Å) and annealing (from ∼85 to 100 Å). This is accompanied by an increase in the width of the amorphous domains from 30 to 50 Å in drawn fibers, and from 45 to 55 Å in annealed fibers. The diameter of the fibrils decreases slightly upon drawing and increases considerably upon annealing. © 1996 John Wiley & Sons, Inc.     

Tilted lamellae in an affinely deformed 3D macrolattice and elliptical features in small‐angle scattering

Lamellar reflections in small‐angle X‐ray and neutron scattering patterns of uniaxially drawn semicrystalline polymers appear to fall on elliptical or hyperbolic arcs. We attribute this to a 3D lattice of tilted lamellae, a macrolattice. Affine deformation of this lattice, such as during uniaxial draw, moves and spreads the reflections along elliptical arcs, and nonaffine deformation, such as during rolling, moves and spreads the reflections along an arc that deviates from an ellipse. Discrete reflections are the product of two functions: the elliptical trace that is the Fourier transform of the affinely deformed lattice and the radial streak that is the Fourier transform of the individual lamella in the reciprocal space. Four‐point patterns are obtained if the lamellar‐surface normal is tilted away from the fiber‐axis, and two‐point patterns if it is not. This model is used to discuss the transformation between four‐ and two‐point patterns and other changes in lamellar morphology that occur during drawing and annealing of oriented semicrystalline polymers. The deformation of the macrolattice of crystalline lamellae, need not be correlated to the tilt of the lamellae. The tilt of the lamellae is shown to be important. It reflects the cross‐sectional area mismatch at the lamellar surface between crystalline stems and amorphous chains segments, and this indicates the internal strain in the interfibrillar amorphous regions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1277–1286, 2006     

Irreducible partitions and the construction of quasi-measures

A quasi-measure is a non-subadditive measure defined on only open or closed subsets of a compact Hausdorf space. We investigate the nature of irreducible partitions as defined by Aarnes and use the results to construct quasi-measures when . The cohomology ring is an important tool for this investigation.

     

Nonhomogeneous Dirichlet Navier—Stokes Problems in Low Regularity Lp Sobolev Spaces

The time-dependent Navier--Stokes problem on an interior or exterior smooth domain, with nonhomogeneous Dirichlet boundary condition, is treated in anisotropic L_p Sobolev spaces (1 < p < ￥ \infty ) of Bessel-potential type H^s+2,s/2+1_p H^{s+2,s/2+1}_p or Besov type B^s+2,s/2+1_p B^{s+2,s/2+1}_p by use of a reformulation of the linearized problem to a parabolic pseudodifferential boundary value problem. Earlier studies required s > \frac 1p - 1 s > {\frac 1p} - 1 ; the present work extends the solvability to spaces with s > \frac 1p - 2 s > {\frac 1p} - 2 for zero initial data (s > - 2 s > - 2 if f = 0), s > \frac 2p - 2 s > {\frac 2p} - 2 for nonzero initial data, with s,p subject to other conditions stemming from the nonlinearity.