We report the addition of two visualisation algorithms, termed PaperChain and Twister, to the freely available Visual Molecular Dynamics (VMD) package. These algorithms produce visualisations of complex cyclic molecules and multi-branched polysaccharides and are a generalization and optimization of those we previously developed in a standalone package for carbohydrates. PaperChain highlights each ring in a molecular structure with a polygon, which is coloured according to the ring pucker. Twister traces glycosidic bonds with a ribbon that twists according to the relative orientation of successive sugar residues. Combination of these novel algorithms and new ring selection statements with the large set of visualisations already available in VMD allows for unprecedented flexibility in the level of detail displayed for glycoconjugate, glycoprotein and carbohydrate-binding protein structures, as well as other cyclic structures. We highlight the efficacy of these algorithms with selected illustrative examples, clearly demonstrating the value of the new visualisations, not only for structure validation, but for facilitating insights into molecular structure and mechanism.
It is well known that pulse-like solutions of the cubic complex Ginzburg-Landau equation are unstable but can be stabilised by the addition of quintic terms. In this paper we explore an alternative mechanism where the role of the stabilising agent is played by the parametric driver. Our analysis is based on the numerical continuation of solutions in one of the parameters of the Ginzburg-Landau equation (the diffusion coefficient c), starting from the nonlinear Schrödinger limit (for which c = 0). The continuation generates, recursively, a sequence of coexisting stable solutions with increasing number of humps. The sequence "converges" to a long pulse which can be interpreted as a bound state of two fronts with opposite polarities.
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