Band 4, Heft 1

Novel approaches for generating and comparing flexible (non-rigid) molecular surface meshes are developed. The mesh-generating method is fast and memory-efficient. The resulting meshes are smooth and accurate, and possess high mesh quality. An isometric-invariant shape descriptor based on the Laplace- Beltrami operator is then explored for mesh comparing. The new shape descriptor is more powerful in discriminating different surface shapes but rely only on a small set of signature values. The shape descriptor is applied to shape comparison between molecules with deformed structures. The proposed methods are implemented into a program that can be used as a stand-alone software tool or as a plug-in to other existing molecular modeling tools. Particularly, the code is encapsulated into a software toolkit with a user-friendly graphical interface developed by the authors.

Topological data analysis has been recently used to extract meaningful information frombiomolecules. Here we introduce the application of persistent homology, a topological data analysis tool, for computing persistent features (loops) of the RNA folding space. The scaffold of the RNA folding space is a complex graph from which the global features are extracted by completing the graph to a simplicial complex via the notion of clique and Vietoris-Rips complexes. The resulting simplicial complexes are characterised in terms of topological invariants, such as the number of holes in any dimension, i.e. Betti numbers. Our approach discovers persistent structural features, which are the set of smallest components to which the RNA folding space can be reduced. Thanks to this discovery, which in terms of data mining can be considered as a space dimension reduction, it is possible to extract a new insight that is crucial for understanding the mechanism of the RNA folding towards the optimal secondary structure. This structure is composed by the components discovered during the reduction step of the RNA folding space and is characterized by minimum free energy.

A continuum mechanical model based on the Helfrich Hamiltonian is devised to investigate the coupling between lipid composition and membrane curvature. Each monolayer in the bilayer is modeled as a freely deformable surface with a director field for lipid orientation. A scalar field for the mole fraction of two lipid types accounts for local changes in composition. It allows lipids to access monolayer regions favorable to their intrinsic curvature at the expense of increasing entropic free energy. Hemifusion is one of the key fusion intermediates with regions of both positive and negative membrane curvature and where proteins must supply energy in order to bring about large elastic distortions. Using a numerical gradient descent scheme, minimal energy axisymmetric shapes of hemifusion diaphragms are calculated for varying radii. Previous studies assumed a fixed, weighted average for spontaneous curvature. Allowing for local changes in spontaneous curvature yields energies and forces of expansion significantly lower than those obtained from a fixed composition.

Proteins interact to perform biological functions through specific interface residues. Correctly understanding the mechanisms of interface recognition and prediction are important for many aspects of life science studies. Here, we report a novel architecture to study protein interface residues. In our method, multiple dimensional space was built on some meaningful features. Then we divided the space and put all the surface residues into the regions according to their features’ values. Interestingly, interface residues were found to prefer some grids clustered together. We obtained excellent result on a public and verified data benchmark. Our approach not only opens up a new train of thought for interface residue prediction, but also will help to understand proteins interaction more deeply.

In this work, the existence of a global minimizer for the previous Lagrangian formulation of nonpolar solvation model proposed in [1] has been proved. One of the proofs involves a construction of a phase field model that converges to the Lagrangian formulation. Moreover, an Eulerian formulation of nonpolar solvation model is proposed and implemented under a similar parameterization scheme to that in [1]. By doing so, the connection, similarity and difference between the Eulerian formulation and its Lagrangian counterpart can be analyzed. It turns out that both of them have a great potential in solvation prediction for nonpolar molecules, while their decompositions of attractive and repulsive parts are different. That indicates a distinction between phase field models of solvation and our Eulerian formulation.