A tale of two elements: P1ncP1 and RTO

The and RT0 finite element schemes are among the most promising low order elements for use in unstructured mesh marine and lake models. They are both free of spurious elevation modes, have good dispersive properties and have a relatively low computational cost. In this paper, we derive both finite element schemes in the same unified framework and discuss their respective qualities in terms of conservation, consistency, propagation factor and convergence rate. We also highlight the impact that the local variables placement can have on the model solution. The main conclusion that we can draw is that the choice between elements is highly application dependent. We suggest that the element is better suited to purely hydrodynamical applications while the RT0 element might perform better for hydrological applications that require scalar transport calculations.

Twists and turns: a tale of two shikimate-pathway enzymes

We are studying two enzymes from the shikimate pathway, dehydroquinate synthase (DHQS) and 5-enolpyruvylshikimate-3-phosphate synthase (EPSPS). Both enzymes have been the subject of numerous studies to elucidate their reaction mechanisms. Crystal structures of DHQS and EPSPS in the presence and absence of substrates, cofactors and/or inhibitors are now available. These structures reveal movements of domains, rearrangements of loops and changes in side-chain positions necessary for the formation of a catalytically competent active site. The potential for using complementary small-angle X-ray scattering (SAXS) studies to confirm the presence of these structural differences in solution has also been explored. Comparative analysis of crystal structures, in the presence and absence of ligands, has revealed structural features critical for substrate-binding and catalysis. We have also analysed these structures by generating GRID energy maps to detect favourable binding sites. The combination of X-ray crystallography, SAXS and computational techniques provides an enhanced analysis of structural features important for the function of these complex enzymes.

Quantifying chaos: a tale of two maps

In many applications, there is a desire to determine if the dynamics of interest are chaotic or not. Since positive Lyapunov exponents are a signature for chaos, they are often used to determine this. Reliable estimates of Lyapunov exponents should demonstrate evidence of convergence; but literature abounds in which this evidence lacks. This paper presents two maps through which it highlights the importance of providing evidence of convergence of Lyapunov exponent estimates. The results suggest cautious conclusions when confronted with real data. Moreover, the maps are interesting in their own right.