Haptic-assisted interactive docking tools immerse the user in an environment where intuition and knowledge can be used to help guide the docking process. Here we present such a tool where the user "holds" a rigid ligand via a haptic device through which they feel interaction forces with a flexible receptor biomolecule. To ensure forces transmitted through the haptic device are smooth and stable, they must be updated at a rate greater than 500 Hz. Due to this time constraint, the majority of haptic docking tools do not attempt to model the conformational changes that would occur when molecules interact during binding. Our haptic-assisted docking tool, "Haptimol FlexiDock", models a receptor's conformational response to forces of interaction with a ligand whilst maintaining the required haptic refresh rate. In order to model receptor flexibility we use the method of linear response for which we determine the variance-covariance matrix of atomic fluctuations from the trajectory of an explicit-solvent Molecular Dynamics simulation of the ligand-free receptor molecule. Key to satisfying the time constraint is an eigenvector decomposition of the variance-covariance matrix which enables a good approximation to the conformational response of the receptor to be calculated rapidly. This exploits a feature of protein dynamics whereby most fluctuation occurs within a relatively small subspace. The method is demonstrated on Glutamine Binding Protein in interaction with glutamine, and Maltose Binding Protein in interaction with maltose. For both proteins the movement that occurs when the ligand is docked near to its binding site matches the experimentally determined movement well. It is thought that this tool will be particularly useful for structure-based drug design.

Producing high quality depictions of molecular structures has been an area of academic interest for years, with visualisation tools such as UCSF Chimera, Yasara and PyMol providing a huge number of different rendering modes and lighting effects. However, no visualisation program supports per-pixel lighting effects with shadows whilst rendering a molecular trajectory in space filling mode. In this paper, a new approach to rendering high quality visualisations of molecular trajectories is presented. To enhance depth, ambient occlusion is included within the render. Shadows are also included to help the user perceive relative motions of parts of the protein as they move based on their trajectories. Our approach requires a regular grid to be constructed every time the molecular structure deforms allowing per-pixel lighting effects and ambient occlusion to be rendered every frame, at interactive refresh rates. Two different regular grids are investigated, a fixed grid and a memory efficient compact grid. The algorithms used allow trajectories of proteins comprising of up to 300,000 atoms in size to be rendered at ninety frames per second on a desktop computer using the GPU for general purpose computations. Regular grid construction was found to only take up a small proportion of the total time to render a frame. It was found that despite being slower to construct, the memory efficient compact grid outperformed the theoretically faster fixed grid when the protein being rendered is large, owing to its more efficient memory access patterns. The techniques described could be implemented in other molecular rendering software.

When considering user charges for the provision and maintenance of marine aids to navigation, it must be recognized that the basis on which they are calculated and levied is to a large extent due to historical accident. There is no internationally recognised system for levying these dues and every country has its own ideas as to how much money, if any, should be raised by this means.User charges paid by shipping for marine aids to navigation normally fall into two categories. First there are national charges which go towards the running of the national lighthouse authority, either in whole, or in part. Such charges are referred to in this paper as ‘light dues’.