Mechanical Systems with Symmetry, Variational Principles, and Integration Algorithms

This paper studies variational principles for mechanical systems with symmetry and their applications to integration algorithms. We recall some general features of how to reduce variational principles in the presence of a symmetry group along with general features of integration algorithms for mechanical systems. Then we describe some integration algorithms based directly on variational principles using a discretization technique of Veselov. The general idea for these variational integrators is to directly discretize Hamilton’s principle rather than the equations of motion in a way that preserves the original systems invariants, notably the symplectic form and, via a discrete version of Noether’s theorem, the momentum map. The resulting mechanical integrators are second-order accurate, implicit, symplectic-momentum algorithms. We apply these integrators to the rigid body and the double spherical pendulum to show that the techniques are competitive with existing integrators

Triangle network motifs predict complexes by complementing high-error interactomes with structural information

BackgroundA lot of high-throughput studies produce protein-protein interaction networks (PPINs) with many errors and missing information. Even for genome-wide approaches, there is often a low overlap between PPINs produced by different studies. Second-level neighbors separated by two protein-protein interactions (PPIs) were previously used for predicting protein function and finding complexes in high-error PPINs. We retrieve second level neighbors in PPINs, and complement these with structural domain-domain interactions (SDDIs) representing binding evidence on proteins, forming PPI-SDDI-PPI triangles.ResultsWe find low overlap between PPINs, SDDIs and known complexes, all well below 10%. We evaluate the overlap of PPI-SDDI-PPI triangles with known complexes from Munich Information center for Protein Sequences (MIPS). PPI-SDDI-PPI triangles have ~20 times higher overlap with MIPS complexes than using second-level neighbors in PPINs without SDDIs. The biological interpretation for triangles is that a SDDI causes two proteins to be observed with common interaction partners in high-throughput experiments. The relatively few SDDIs overlapping with PPINs are part of highly connected SDDI components, and are more likely to be detected in experimental studies. We demonstrate the utility of PPI-SDDI-PPI triangles by reconstructing myosin-actin processes in the nucleus, cytoplasm, and cytoskeleton, which were not obvious in the original PPIN. Using other complementary datatypes in place of SDDIs to form triangles, such as PubMed co-occurrences or threading information, results in a similar ability to find protein complexes.ConclusionGiven high-error PPINs with missing information, triangles of mixed datatypes are a promising direction for finding protein complexes. Integrating PPINs with SDDIs improves finding complexes. Structural SDDIs partially explain the high functional similarity of second-level neighbors in PPINs. We estimate that relatively little structural information would be sufficient for finding complexes involving most of the proteins and interactions in a typical PPIN

Self-association studies on the EphB2 receptor SAM domain using analytical ultracentrifugation

The self-association behavior of the Eph-kinases SAM domain has been studied in phosphate buffer, pH 7.4, containing 0.14 M NaCl using concentration-dependent sedimentation equilibrium experiments. Only weak interactions typical for a monomer-dimer equilibrium up to at least 12 mg/mL were observed. Such concentrated solutions require a consideration of the non-ideality expressed by virial coefficients. A special centrifuge equation was used for the global analysis to estimate equilibrium constants based on the thermodynamic activities of the reactants. When neglecting this, the parameters deviate by about 20%. Association constants for dimerization of the EphB2-SAM domain vary between 163 M-1 at 10 °C and 395 M-1 at 32 °C, indicating hydrophobic forces are involved in the dimerization process. In solutions of about 12 mg/mL, less than 50% dimers are in solution and higher oligomers can be excluded