Gröbnersche Basen in speziellen Ringen (Aus der Geschichte der Gröbnerschen Basen)

The basic concepts of Gröbner basis of an ideal in the polynomial ring is described. Particularly the computation of the standard basis in a local ring is explained. A short history of the development of the theory of Gröbner bases is sketched

Simulated holographic three-dimensional intensity shaping of evanescent-wave fields

The size of bright structures in traveling-wave light fields is limited by diffraction. This in turn limits a number of technologies, for example, optical trapping. One way to beat the diffraction limit is to use evanescent waves instead of traveling waves. Here we apply a holographic algorithm, direct search, to the shaping of complex evanescent-wave fields. We simulate three-dimensional intensity shaping of evanescent-wave fields using this approach, and we investigate some of its limitations. (c) 2008 Optical Society of America.</p

Controlling waves in space and time for imaging and focusing in complex media

In complex media such as white paint and biological tissue, light encounters nanoscale refractive-index inhomogeneities that cause multiple scattering. Such scattering is usually seen as an impediment to focusing and imaging. However, scientists have recently used strongly scattering materials to focus, shape and compress waves by controlling the many degrees of freedom in the incident waves. This was first demonstrated in the acoustic and microwave domains using time reversal, and is now being performed in the optical realm using spatial light modulators to address the many thousands of spatial degrees of freedom of light. This approach is being used to investigate phenomena such as optical super-resolution and the time reversal of light, thus opening many new avenues for imaging and focusing in turbid medi

Femtosecond optoinjection of intact tobacco BY-2 cells using a reconfigurable photoporation platform

A tightly-focused ultrashort pulsed laser beam incident upon a cell membrane has previously been shown to transiently increase cell membrane permeability while maintaining the viability of the cell, a technique known as photoporation. This permeability can be used to aid the passage of membrane-impermeable biologically-relevant substances such as dyes, proteins and nucleic acids into the cell. Ultrashort-pulsed lasers have proven to be indispensable for photoporating mammalian cells but they have rarely been applied to plant cells due to their larger sizes and rigid and thick cell walls, which significantly hinders the intracellular delivery of exogenous substances. Here we demonstrate and quantify femtosecond optical injection of membrane impermeable dyes into intact BY-2 tobacco plant cells growing in culture, investigating both optical and biological parameters. Specifically, we show that the long axial extent of a propagation invariant (“diffraction-free”) Bessel beam, which relaxes the requirements for tight focusing on the cell membrane, outperforms a standard Gaussian photoporation beam, achieving up to 70% optoinjection efficiency. Studies on the osmotic effects of culture media show that a hypertonic extracellular medium was found to be necessary to reduce turgor pressure and facilitate molecular entry into the cells.Publisher PDFPeer reviewe

Optoinjection efficiency (O) and viability (V) of the BY-2 plant cells at different laser powers.

<p>After irradiation by (A) three shots or (B) a single shot with the Gaussian beam or (C) a single shot with the Bessel beam. For both beam geometries the optoinjection efficiency (represented by open squares) increases with power at the focal plane while viability (solid squares) usually decreases. C shows N (the proportion of cells being both viable and optoinjected) for varying central spot intensities. N increases as the intensity increases. The Bessel beam (black) shows a higher value for N than the Gaussian beam (red) when considering a single shot. When comparing with three axially separated shots of the Gaussian beam (blue), N is comparable to the Bessel beam. Each data point represents the mean for n = 5 with 20 cells per experiment. Error bars represent the standard error of the mean (S.E.M.).</p

Optical injection of PI into a BY-2 cell.

<p>Shown in bright field (A–C) and fluorescence (D–F). A) Before shooting, B) transient bubble created on cell membrane during laser dose, C) no visible laser damage left post-irradiation. D) Pre-irradiation showing faint PI staining of the cell wall. E) Laser induced transient auto-fluorescence at the point of irradiation. F) Permanent increase in cytosolic fluorescence as PI enters the cell. Arrows indicate site of laser irradiation. Scale bar denotes 10 µm.</p

Optoinjection efficiency differs depending upon the osmolarity of the surrounding medium.

<p>From looking at A, as we increase the osmolarity, the efficiency of optoinjection (black squares) increases from zero up to 50% as the surrounding medium changes from hypertonic to hypotonic. Conversely, the optoejection efficiency (red circles) falls from around 10% to 0% above 320±2 mOsm/L. As the molarity of the solution increases, the likelihood of cell death (represented by blue triangles) is increased. At 320±2 mOsm/L the optoinjection and ejection efficiency are approximately equal. Each data point was performed in triplicate with 20 cells; error bars represent S.E.M. B and C show brightfield and fluorescence overlays of a cell prior to (B) and 2 minutes after (C) laser irradiation in standard culture medium in the presence of PI. Photoporation induces a flux of cytosol from the cell into the extracellular medium. The cytosol ejected from the cell becomes stained with PI and a bright fluorescence is seen exterior to the cell. Large changes in cell morphology occur and cell death is induced. D shows the osmotic effect on plasmolysis of BY-2 cells. Both the void space (blue) and fraction of plasmolyzed cells (red) increases with the osmolarity of the surrounding medium but the red line shows a much steeper incline around the point of incipient plasmolysis (50%). Error bars denote the S.E.M. for n = 3 experiments with 20 cells counted in each. E-G show example cells in standard culure medium (171±2 mOsm/L), very weakly hypotonic (320±2 mOsm/L) and strongly hypotonic (699±4 mOsm/L) solutions respectively, with the resulting plasmolysis occurring slightly in F but seen very strongly in G as the membrane pulls away from the cell wall in the highly osmotic solution. Scale bars denote 10 µm.</p

Effect of molecule size on cellular uptake.

<p>From looking at A, it can be seen that as the Stokes radius increases, the amount of dextran taken up by the cell decreases. The protoplasts take up less dextrans than the intact cells for Stokes radii smaller than 5 = 30 cells with error bars representing the S.E.M. B shows representative images (those depicting uptake most comparable to the average uptake) of intact cells and protoplasts before (1) and 3 mins after (2) photoporation in the presence of small and large dextrans. The larger dextrans show less (though still visible) entry into the cell than the smaller dextrans.</p