Metrics for measuring distances in configuration spaces

In order to characterize molecular structures we introduce configurational fingerprint vectors which are counterparts of quantities used experimentally to identify structures. The Euclidean distance between the configurational fingerprint vectors satisfies the properties of a metric and can therefore safely be used to measure dissimilarities between configurations in the high dimensional configuration space. We show that these metrics correlate well with the RMSD between two configurations if this RMSD is obtained from a global minimization over all translations, rotations and permutations of atomic indices. We introduce a Monte Carlo approach to obtain this global minimum of the RMSD between configurations

Boundary Conditions on Internal Three-Body Wave Functions

For a three-body system, a quantum wave function $\Psi^\ell_m$ with definite $\ell$ and $m$ quantum numbers may be expressed in terms of an internal wave function $\chi^\ell_k$ which is a function of three internal coordinates. This article provides necessary and sufficient constraints on $\chi^\ell_k$ to ensure that the external wave function $\Psi^\ell_m$ is analytic. These constraints effectively amount to boundary conditions on $\chi^\ell_k$ and its derivatives at the boundary of the internal space. Such conditions find similarities in the (planar) two-body problem where the wave function (to lowest order) has the form $r^{|m|}$ at the origin. We expect the boundary conditions to prove useful for constructing singularity free three-body basis sets for the case of nonvanishing angular momentum.Comment: 41 pages, submitted to Phys. Rev.

Genetic associations with learning over 100 days of practice

Cognitive performance is both heritable and sensitive to environmental inputs and sustained practice over time. However, it is currently unclear how genetic effects on cognitive performance change over the course of learning. We examine how polygenic scores (PGS) created from genome-wide association studies of educational attainment and cognitive performance are related to improvements in performance across nine cognitive tests (measuring perceptual speed, working memory, and episodic memory) administered to 131 adults (N = 51, ages = 20–31, and N = 80, ages = 65–80 years) repeatedly across 100 days. We observe that PGS associations with performance on a given task can change over the course of learning, with the specific pattern of change in associations differing across tasks. PGS correlations with pre-test to post-test scores may mask variability in how soon learning occurs over the course of practice. The associations between PGS and learning do not appear to simply reconstitute patterns of association between baseline performance and subsequent learning. Associations involving PGSs, however, were small with large confidence intervals. Intensive longitudinal research such as that described here may be of substantial value for clarifying the genetics of learning when implemented as far larger scale

Confined Mobility of TonB and FepA in Escherichia coli Membranes

The important process of nutrient uptake in Escherichia coli, in many cases, involves transit of the nutrient through a class of beta-barrel proteins in the outer membrane known as TonB-dependent transporters (TBDTs) and requires interaction with the inner membrane protein TonB. Here we have imaged the mobility of the ferric enterobactin transporter FepA and TonB by tracking them in the membranes of live E. coli with single-molecule resolution at time-scales ranging from milliseconds to seconds. We employed simple simulations to model/analyze the lateral diffusion in the membranes of E.coli, to take into account both the highly curved geometry of the cell and artifactual effects expected due to finite exposure time imaging. We find that both molecules perform confined lateral diffusion in their respective membranes in the absence of ligand with FepA confined to a region 0.180−0.007+0.006 μm in radius in the outer membrane and TonB confined to a region 0.266−0.009+0.007 μm in radius in the inner membrane. The diffusion coefficient of these molecules on millisecond time-scales was estimated to be 21−5+9 μm2/s and 5.4−0.8+1.5 μm2/s for FepA and TonB, respectively, implying that each molecule is free to diffuse within its domain. Disruption of the inner membrane potential, deletion of ExbB/D from the inner membrane, presence of ligand or antibody to FepA and disruption of the MreB cytoskeleton was all found to further restrict the mobility of both molecules. Results are analyzed in terms of changes in confinement size and interactions between the two proteins.Yeshttp://www.plosone.org/static/editorial#pee

Initial Results of the S3-Humerus Plate

Fractures of the humeral head account for 5% of all fractures and incidence increases with age. Depending on fracture form and patients age a wide variety of therapeutical options exist. Stable fractures can be treated conservatively, while the majority of unstable and displaced fractures require surgical treatment. Many different surgical options are available; open reduction and internal fixation are widely preferred. The S3 Proximal Humerus Plate is a contoured plate to match the complex shape of the proximal humerus. It is designed to be positioned distal to the greater tuberosity preventing subacromial impingement