Algorithm engineering for optimal alignment of protein structure distance matrices

Protein structural alignment is an important problem in computational biology. In this paper, we present first successes on provably optimal pairwise alignment of protein inter-residue distance matrices, using the popular Dali scoring function. We introduce the structural alignment problem formally, which enables us to express a variety of scoring functions used in previous work as special cases in a unified framework. Further, we propose the first mathematical model for computing optimal structural alignments based on dense inter-residue distance matrices. We therefore reformulate the problem as a special graph problem and give a tight integer linear programming model. We then present algorithm engineering techniques to handle the huge integer linear programs of real-life distance matrix alignment problems. Applying these techniques, we can compute provably optimal Dali alignments for the very first time

A Mathematical Framework for Protein Structure Comparison

Comparison of protein structures is important for revealing the evolutionary relationship among proteins, predicting protein functions and predicting protein structures. Many methods have been developed in the past to align two or multiple protein structures. Despite the importance of this problem, rigorous mathematical or statistical frameworks have seldom been pursued for general protein structure comparison. One notable issue in this field is that with many different distances used to measure the similarity between protein structures, none of them are proper distances when protein structures of different sequences are compared. Statistical approaches based on those non-proper distances or similarity scores as random variables are thus not mathematically rigorous. In this work, we develop a mathematical framework for protein structure comparison by treating protein structures as three-dimensional curves. Using an elastic Riemannian metric on spaces of curves, geodesic distance, a proper distance on spaces of curves, can be computed for any two protein structures. In this framework, protein structures can be treated as random variables on the shape manifold, and means and covariance can be computed for populations of protein structures. Furthermore, these moments can be used to build Gaussian-type probability distributions of protein structures for use in hypothesis testing. The covariance of a population of protein structures can reveal the population-specific variations and be helpful in improving structure classification. With curves representing protein structures, the matching is performed using elastic shape analysis of curves, which can effectively model conformational changes and insertions/deletions. We show that our method performs comparably with commonly used methods in protein structure classification on a large manually annotated data set

What is problem actuation?

Problemaktualisierung ist ein Wirkfaktor in allen psychologischen Therapien. Durch die Aktualisierung der Probleme, die den Patienten in die Therapie führen, werden diese für die therapeutische Bearbeitung zugänglich gemacht. Bereiche mangelnder Befriedigung psychologischer Grundbedürfnisse (Inkongruenz) werden vom Patienten als Probleme wahrgenommen. Problemaktualisierung sollte auf der Basis einer guten therapeutischen Beziehung und bei gleichzeitiger Ressourcenaktivierung erfolgen. Problemaktualisierung kann im therapeutischen Prozess unbeabsichtigt geschehen oder gezielt vom Therapeuten hergestellt werden. Therapeuten haben vielfältige Möglichkeiten der gezielten Problemaktualisierung: Beispiele sind die Exposition mit angstauslösenden Situationen und Orten, die Einbeziehung von Partnern oder Familienmitgliedern in konflikthaften Beziehungen, die Aktualisierung problematischer Emotionen in Stuhlübungen, das Aufgreifen problematischer Verhaltensweisen gegenüber dem Therapeuten oder die Inszenierung problematischer Beziehungen im Tanz. Patienten können durch Beziehungsgestaltung sowie Aufbau und Aktivierung persönlicher Ressourcen auf die Problemaktualisierung vorbereitet werden.Problem actuation is a change factor in all forms of psychological therapy. By actuation of the problem that motivated a patient to undergo therapy, the problems are made accessible to therapeutic processing. Areas that do not satisfy the fundamental psychological needs (incongruence) are perceived by patients as problems. Problem actuation should be implemented on the foundation of a good therapeutic relationship and simultaneous resource activation. Problem actuation may happen unintentionally during the therapeutic process or may be initiated deliberately by the therapist. Therapists have a multitude of options for targeted problem actuation: examples are exposure to fear-provoking situations and places, the inclusion of partners or family members in conflictual relationships, the actuation of problematic emotions in chairwork, tackling problematic behavior patterns towards the therapist or staging problematic relationships in dancing. Patients can be prepared for problem actuation by tailoring the relationship offer as well as by building or activating personal resources

Radiative lifetime of the A 2Π1/2 state in RaF with relevance to laser cooling

International audienceThe radiative lifetime of the $A$$^2 \Pi_{1/2}$ (v=0) state in radium monofluoride (RaF) is measured to be 35(1) ns. The lifetime of this state is of relevance to the laser cooling of RaF via the optically closed $A$$^2 \Pi_{1/2} \leftarrow X$$^2\Sigma_{1/2}$ transition, which is an advantageous aspect of the molecule for its promise as a probe for new physics. The radiative decay rate $\Gamma = 2.9(2)\times 10^7$ s$^{-1}$ is extracted using the lifetime, which determines the natural linewidth of 4.6(3) MHz and the maximum photon scattering rate of $4.1(3)\times 10^6$ s$^{-1}$ of the laser-cooling transition. RaF is thus found to have a comparable photon-scattering rate with other laser-cooled molecules, while thanks to its highly diagonal Franck-Condon matrix it is expected to scatter an order of magnitude more photons when using 3 cooling lasers before it decays to a dark state. The lifetime measurement in RaF is benchmarked by measuring the lifetime of the $8P_{3/2}$ state in Fr to be 83(3) ns, in agreement with literature

Radiative lifetime of the A 2Π1/2 state in RaF with relevance to laser cooling

The radiative lifetime of the $A$$^2 \Pi_{1/2}$ (v=0) state in radium monofluoride (RaF) is measured to be 35(1) ns. The lifetime of this state and the related decay rate $\Gamma = 2.86(8) \times 10^7$$s^{-1}$ are of relevance to the laser cooling of RaF via the optically closed $A$$^2 \Pi_{1/2} \leftarrow X$$^2\Sigma_{1/2}$ transition, which makes the molecule a promising probe to search for new physics. RaF is found to have a comparable photon-scattering rate to homoelectronic laser-coolable molecules. Thanks to its highly diagonal Franck-Condon matrix, it is expected to scatter an order of magnitude more photons than other molecules when using just 3 cooling lasers, before it decays to a dark state. The lifetime measurement in RaF is benchmarked by measuring the lifetime of the $8P_{3/2}$ state in Fr to be 83(3) ns, in agreement with literature