Leading coordinate analysis of reaction pathways in proton chain transfer: Application to a two-proton transfer model for the green fluorescent protein

The ‘leading coordinate’ approach to computing an approximate reaction pathway, with subsequent determination of the true minimum energy profile, is applied to a two-proton chain transfer model based on the chromophore and its surrounding moieties within the green fluorescent protein (GFP). Using an ab initio quantum chemical method, a number of different relaxed energy profiles are found for several plausible guesses at leading coordinates. The results obtained for different trial leading coordinates are rationalized through the calculation of a two-dimensional relaxed potential energy surface (PES) for the system. Analysis of the 2-D relaxed PES reveals that two of the trial pathways are entirely spurious, while two others contain useful information and can be used to furnish starting points for successful saddle-point searches. Implications for selection of trial leading coordinates in this class of proton chain transfer reactions are discussed, and a simple diagnostic function is proposed for revealing whether or not a relaxed pathway based on a trial leading coordinate is likely to furnish useful information.

The octahedral manipulator: Geometry and mobility

In most Of the practical six-actuator in-parallel manipulators, the octahedral form is either taken as it stands or is approximated. Yet considerable theoretical attention is paid in the literature to more general forms. Here we touch on the general form, and describe some aspects of its behavior that vitiate strongly against its adoption as a pattern for a realistic manipulate,: We reach the conclusion that the structure for in-parallel manipulators must be triangulated as fully as possible, so leading to the octahedral form. In describing some of the geometrical properties of the general octahedron, we show how they apply to manipulators. We examine in detail the special configurations at which the 6 x 6 matrix of leg lines is singular presenting results from the point of view of geometry in preference to analysis. In extending and enlarging on some known properties, a few behavioral surprises materialize. In studying special configurations, we start with the most general situation, and every other case derives from this. Our coverage is more comprehensive than any that we have found. We bring to light material that is, we think, of significant use to a designer.

Column connection detail, Kangaroo Point House

Hand-made spotted gum column on edge of outdoor room.

West elevation, Cleveland Point House, Cleveland

Hand-drawn elevation.

Cottage, Cleveland Point House, Cleveland

Beach elevation of renovated existing cottage.

Lattice to boat house, Cleveland Point House, Cleveland

Lattice behind pull-down blind to boat house.

Beachfront elevation, Cleveland Point House, Cleveland

Timber framing to new bath house (centre), with existing buildings to either side.

Bath house, Cleveland Point House, Cleveland

New bath house under construction (centre), with existing buildings to either side.

Bath house, Cleveland Point House, Cleveland

Bath house under construction, as seen looking towards water from deck area.

Bath house, Cleveland Point House, Cleveland

As seen looking towards water from deck area.

Beachfront elevation, Cleveland Point House, Cleveland

New bath house (centre), with existing buildings to either side.

Boat house, Cleveland Point House, Cleveland

Existing boat house undergoing renovations.

Bath house hip rafters, Cleveland Point House, Cleveland

Timber framing to new bath house.

Beachfront elevation, Cleveland Point House, Cleveland

Timber framing to new bath house (centre), with existing buildings to either side.

Bath house section, Cleveland Point House, Cleveland

Section taken through new bath house.