QM/MM simulation of liquid water with an adaptive quantum region.

The simulation of complex chemical systems often requires a multi-level description, in which a region of special interest is treated using a computationally expensive quantum mechanical (QM) model while its environment is described by a faster, simpler molecular mechanical (MM) model. Furthermore, studying dynamic effects in solvated systems or bio-molecules requires a variable definition of the two regions, so that atoms or molecules can be dynamically re-assigned between the QM and MM descriptions during the course of the simulation. Such reassignments pose a problem for traditional QM/MM schemes by exacerbating the errors that stem from switching the model at the boundary. Here we show that stable, long adaptive simulations can be carried out using density functional theory with the BLYP exchange-correlation functional for the QM model and a flexible TIP3P force field for the MM model without requiring adjustments of either. Using a primary benchmark system of pure water, we investigate the convergence of the liquid structure with the size of the QM region, and demonstrate that by using a sufficiently large QM region (with radius 6 Å) it is possible to obtain radial and angular distributions that, in the QM region, match the results of fully quantum mechanical calculations with periodic boundary conditions, and, after a smooth transition, also agree with fully MM calculations in the MM region. The key ingredient is the accurate evaluation of forces in the QM subsystem which we achieve by including an extended buffer region in the QM calculations. We also show that our buffered-force QM/MM scheme is transferable by simulating the solvated Cl(-) ion.

Quantitative convergence analysis of multi-agent systems

We introduce a characterization of contraction for bounded convex sets. For discrete-time multi-agent systems we provide an explicit upperbound on the rate of convergence to a consensus under the assumptions of contractiveness and (weak) connectedness (across an interval.) Convergence is shown to be exponential when either the system or the function characterizing the contraction is linear. Copyright © 2007 IFAC.

Zebrafish eaf1 and eaf2/u19 Mediate Effective Convergence and Extension Movements through the Maintenance of wnt11 and wnt5 Expression

Studies have attributed several functions to the Eaf family, including tumor suppression and eye development. Given the potential association between cancer and development, we set forth to explore Eaf1 and Eaf2/U19 activity in vertebrate embryogenesis, using zebrafish. In situ hybridization revealed similar eaf1 and eaf2/u19 expression patterns. Morpholino-mediated knockdown of either eaf1 or eaf2/u19 expression produced similar morphological changes that could be reversed by ectopic expression of target or reciprocal-target mRNA. However, combination of Eaf1 and Eaf2/U19 (Eafs)-morpholinos increased the severity of defects, suggesting that Eaf1 and Eaf2/U19 only share some functional redundancy. The Eafs knockdown phenotype resembled that of embryos with defects in convergence and extension movements. Indeed, knockdown caused expression pattern changes for convergence and extension movement markers, whereas cell tracing experiments using kaeda mRNA showed a correlation between Eafs knockdown and cell migration defects. Cardiac and pancreatic differentiation markers revealed that Eafs knockdown also disrupted midline convergence of heart and pancreatic organ precursors. Noncanonical Wnt signaling plays a key role in both convergence and extension movements and midline convergence of organ precursors. We found that Eaf1 and Eaf2/U19 maintained expression levels of wnt11 and wnt5. Moreover, wnt11 or wnt5 mRNA partially rescued the convergence and extension movement defects occurring in eafs morphants. Wnt11 and Wnt5 converge on rhoA, so not surprisingly, rhoA mRNA more effectively rescued defects than either wnt11 or wnt5 mRNA alone. However, the ectopic expression of wnt11 and wnt5 did not affect eaf1 and eaf2/u19 expression. These data indicate that eaf1 and eaf2/u19 act upstream of noncanonical Wnt signaling to mediate convergence and extension movements.