Ein Toolkit zur Quantifizierung der Stichprobenqualität von Molekül-Dynamik Trajektorien: eine Studie über hochflexible Biomoleküle

In this computational work, we investigate the sampling of molecular dynamics (MD) simulations of the two highly flexible biomolecules: Methionine-enkephalin (Met-Enkephalin) and the third variable loop (V3) of the glycoprotein 120 (gp120) from the human immunodeficiency virus type-1 (HIV-1). The conformational dynamics of the three-dimensional (3D) protein structures are of central importance for the biomolecular function. A common possibility to obtain these dynamics at atomic resolution are MD simulations. But reaching a converged MD sampling in adequate time is limited by the huge conformational space of flexible systems. Moreover, an automatic sampling validation is still not established as settled protocol in today's MD studies. Furthermore, existing tools aim primarily to investigate single trajectory convergence which is not always practical for flexible molecules. But in fact, a universal assessment is necessary to classify, whether the sampling is sufficient or not. Otherwise the extracted thermodynamic results are completely meaningless. The aim of this work is to develop a toolkit to quantitatively assess the MD sampling quality for flexible systems. This toolkit is freely available at https://github.com/MikeN12/PySamplingQuality. We use diverse sets of trajectories with different initial conformations along with enhanced sampling techniques such as accelerated MD (aMD) and scaled MD (sMD). These distort the energy landscape to ease conformational transitions. The sampling is assessed by two new quantities, the conformational Oconf and density overlap Odens, including also the cluster number Nc and cluster distribution entropy Sc. These new overlap quantities measure the self-consistency of sampling as a necessary condition for complete sampling. We use Met-Enkephalin as benchmarking system because of its small size but non-trivial dynamics. Our tool reveals that the MD sampling of already such a small molecule converges in a microsecond regime. Furthermore, we can show that aMD is the most efficient algorithm to assess the convergence and also to detect wrong sampling. However, Odens analysis comparing MD with aMD/sMD reveals that we have not completely corrected the bias from enhanced sampling. Therefore, Odens can also be used to compare different methods. On the other hand, V3 demonstrates that much more resources must be spent to achieve convergence compared to those generally invested today. The results highlight the necessity of a multi-trajectory approach to detect incomplete sampling. Altogether, we are able to generate a universally and easily applicable toolkit to assess the MD sampling quality of any kinds of multi-trajectory experiments using certain error estimates and decide, whether the extracted thermodynamic properties are correct or not.In dieser Arbeit wird das Sampling von Molekulardynamik (MD) Simulationen von zwei flexiblen Biomolekülen untersucht: Methionin-Enkephalin (Met-Enkephalin) und dem dritten variablen Loop (V3) des Glykoproteins 120 (gp120) des Humanen Immundefizienz-Virus Typ-1 (HIV-1). Die Dynamik von drei-dimensionalen (3D) Protein-Strukturen ist von zentraler Bedeutung für die Beschreibung der biomolekularen Funktion. Die Dynamik wird mittels MD Simulationen auf atomarem Level untersucht. Das Erreichen eines konvergierten MD Samplings in adäquater Zeit ist jedoch durch den riesigen Konformationsraum von flexiblen Molekülen begrenzt. Des Weiteren ist eine automatische Validierung des Samplings bisher nicht etabliert in heutigen MD Studien, und existierende Verfahren konzentrieren sich vorwiegend auf die Konvergenzanalyse einzelner Trajektorien. Dies ist für flexible Moleküle problematisch. Dabei ist es notwendig ein ausreichendes Sampling zu quantifizieren, ansonsten sind berechnete thermodynamische Größen bedeutungslos. Das Ziel dieser Arbeit ist die Entwicklung eines Toolkits, welches die Samplingqualität von MD Simulationen von flexiblen Systemen quantifiziert. Dieses ist frei verfügbar unter https://github.com/MikeN12/PySamplingQuality. Hierzu werden verschiedene Sätze von Trajektorien aus verschiedenen Startkonformationen und sogenannte Enhanced Sampling Algorithmen wie accelerated MD (aMD) und scaled MD (sMD) kombiniert. Diese modifizieren die Energielandschaften um Übergänge zu vereinfachen. Die Samplingqualität wird durch zwei neue Messungen quantifiziert, dem Konformations- Oconf und Dichteüberlapp Odens, unter Hinzunahme der Clusteranzahl Nc und der Entropie der Clusterverteilung Sc. Diese neuen Überlappgrößen klassifizieren die Selbstkonsistenz. Met-Enkephalin wird als Testsystem verwendet, aufgrund dessen geringer Peptidlänge aber dennoch hochflexiblen Verhaltens. Unser Tool zeigt, dass bereits ein so kleines Molekül Simulationen von Mikrosekunden zur Konvergenz des Samplings benötigt. Weiterhin gilt, dass aMD sowohl Konvergenz als auch ungenügendes Sampling am schnellsten erkennt. Dennoch hat der Vergleich von Odens zwischen MD und aMD/sMD gezeigt, dass die Modifikation des Enhanced Samplings nicht vollständig wiederhergestellt werden konnte. Dies kann jedoch mittels Odens untersucht werden. V3 hingegen beweist, dass viel mehr Ressourcen als gewöhnlich notwendig sind, um Konvergenz zu erhalten. Die Ergebnisse unterstreichen die Notwendigkeit eines Multitrajektorien Ansatzes, um ungenügendes Sampling eindeutig zu erkennen. Zusammenfassend ist es mit dem Toolkit möglich, das Sampling von Multitrajektorie-Experimenten zu validieren, unter der Angabe von Fehlerabschätzungen, und zu entscheiden, ob die berechneten thermodynamischen Größen korrekt beschrieben werden

The Periodic Spectroscopic Variability of FU Orionis

FU Orionis systems are young stars undergoing outbursts of disc accretion and where the optical spectrum contains lines associated with both the disc photosphere and a wind component. Previous observations of the prototype FU Orionis have suggested that the wind lines and the photospheric lines are modulated with periods of 14.54 and 3.54 days respectively (Herbig et al. 2003). We have re-observed the system at higher spectral resolution, by monitoring variations of optical line profiles over 21 nights in 2007 and have found periods of 13.48 and 3.6 days in the wind and disc components consistent with the above: this implies variability mechanisms that are stable over at least a decade. In addition we have found: i) that the variations in the photospheric absorption lines are confined to the blue wing of the line (around -9km/s): we tentatively ascribe this to an orbiting hotspot in the disc which is obscured by a disc warp during its receding phase. ii) The wind period is manifested not only in blue-shifted Halpha absorption, but also in red-shifted emission of Halpha and Hbeta, as well as in blue-shifted absorption of Na I D, Li I and Fe II. iii) We find that the periodic modulation of blue-shifted Halpha absorption at around -100km/s, is phase lagged with respect to variations in the other lines by ~1.8days. This is consistent with a picture in which variations at the wind base first affect chromospheric emission and then low velocity blue-shifted absorption, followed - after a lag equal to the propagation time of disturbances across the wind's acceleration region - by a response in high velocity blue-shifted absorption. Such arguments constrain the size of the acceleration region to ~10^12cm. We discuss possible mechanisms for periodic variations within the innermost 0.1AU of the disc, including the possibility that these variations indicate the presence of an embedded hot Jupiter.Comment: 20 pages, 23 figures. Accepted for publication in MNRAS. See http://www.ast.cam.ac.uk/~slp65/FUOripaperHRes.pdf for a pdf version of the paper with high-resolution images; footnote added to the titl

Target Zones in History and Theory: Lessons from an Austro-Hungarian Experiment (1896-1914)

The first known experiment with an exchange rate band took place in Austria- Hungary between 1896 and 1914. The rationale for introducing this policy rested on precisely those intuitions that the modern literature has emphasized: the band was designed to secure both exchange rate stability and monetary policy autonomy. However, unlike more recent experiences, such as the ERM, this policy was not undermined by credibility problems. The episode provides an ideal testing ground for some important ideas in modern macroeconomics: specifically, can formal rules, when faithfully adhered to, provide policy makers with some advantages such as short term autonomy? First, we find that a credible band has a "microeconomic" influence on exchange rate stability. By reducing uncertainty, a credible fluctuation band improves the quality of expectations, a channel that has been neglected in the modern literature. Second, we show that the standard test of the basic target zone model is flawed and develop an alternative methodology. We believe that these findings shed a new light on the economics of exchange rate bands

Quantitative Assessment of Molecular Dynamics Sampling for Flexible Systems

Molecular dynamics (MD) simulation is a natural method for the study of flexible molecules but at the same time is limited by the large size of the conformational space of these molecules. We ask by how much the MD sampling quality for flexible molecules can be improved by two means: the use of diverse sets of trajectories starting from different initial conformations to detect deviations between samples and sampling with enhanced methods such as accelerated MD (aMD) or scaled MD (sMD) that distort the energy landscape in controlled ways. To this end, we test the effects of these approaches on MD simulations of two flexible biomolecules in aqueous solution, Met-Enkephalin (5 amino acids) and HIV-1 gp120 V3 (a cycle of 35 amino acids). We assess the convergence of the sampling quantitatively with known, extensive measures of cluster number <i>N</i>_c and cluster distribution entropy <i>S</i>_c and with two new quantities, conformational overlap <i>O</i>_conf and density overlap <i>O</i>_dens, both conveniently ranging from 0 to 1. These new overlap measures quantify self-consistency of sampling in multitrajectory MD experiments, a necessary condition for converged sampling. A comprehensive assessment of sampling quality of MD experiments identifies the combination of diverse trajectory sets and aMD as the most efficient approach among those tested. However, analysis of <i>O</i>_dens between conventional and aMD trajectories also reveals that we have not completely corrected aMD sampling for the distorted energy landscape. Moreover, for V3, the courses of <i>N</i>_c and <i>O</i>_dens indicate that much higher resources than those generally invested today will probably be needed to achieve convergence. The comparative analysis also shows that conventional MD simulations with insufficient sampling can be easily misinterpreted as being converged

Intelligent Control for the BEES Flyer

This paper describes the effort to provide a preliminary capability analysis and a neural network based adaptive flight control system for the JPL-led BEES aircraft project. The BEES flyer was envisioned to be a small, autonomous platform with sensing and control systems mimicking those of biological systems for the purpose of scientific exploration on the surface of Mars. The platform is physically tightly constrained by the necessity of efficient packing within rockets for the trip to Mars. Given the physical constraints, the system is not an ideal configuration for aerodynamics or stability and control. The objectives of this effort are to evaluate the aerodynamics characteristics of the existing design, to make recommendaaons as to potential improvements and to provide a control system that stabilizes the existing aircraft for nominal flight and damaged conditions. Towards this several questions are raised and analyses are presented to arrive at answers to some of the questions raised. CART3D, a high-fidelity inviscid analysis package for conceptual and preliminary aerodynamic design, was used to compute a parametric set of solutions over the expected flight domain. Stability and control derivatives were extracted from the database and integrated with the neural flight control system. The Integrated Vehicle Modeling Environment (IVME) was also used for estimating aircraft geometric, inertial, and aerodynamic characteristics. A generic neural flight control system is used to provide adaptive control without the requirement for extensive gain scheduling or explicit system identification. The neural flight control system uses reference models to specify desired handling qualities in the roll, pitch, and yaw axes, and incorporates both pre-trained and on-line learning neural networks in the inverse model portion of the controller. Results are presented for the BEES aircraft in the subsonic regime for terrestrial and Martian environments