Freie Universität Berlin
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Negative friction memory induces persistent motion
No full textWe investigate the mean-square displacement (MSD) for random motion governed by the generalized Langevin equation for memory functions that contain two different time scales: In the first model, the memory kernel consists of a delta peak and a single-exponential and in the second model of the sum of two exponentials. In particular, we investigate the scenario where the long-time exponential kernel contribution is negative. The competition between positive and negative friction memory contributions produces an enhanced transient persistent regime in the MSD, which is relevant for biological motility and active matter systems
Solving high-dimensional Hamilton-Jacobi-Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space
No full textOptimal control of diffusion processes is intimately connected to the problem of solving certain Hamilton-
Jacobi-Bellman equations. Building on recent machine learning inspired approaches towards high-dimensional
PDEs, we investigate the potential of iterative diffusion optimisation techniques, in particular considering applications
in importance sampling and rare event simulation. The choice of an appropriate loss function being
a central element in the algorithmic design, we develop a principled framework based on divergences between
path measures, encompassing various existing methods. Motivated by connections to forward-backward SDEs,
we propose and study the novel log-variance divergence, showing favourable properties of corresponding Monte
Carlo estimators. The promise of the developed approach is exemplified by a range of high-dimensional and
metastable numerical examples
Open Systems out of Equilibrium: Theory and Simulation
No full textWe consider the theoretical model of Bergmann and Lebowitz for open systems out of equilibriumand translate its principles in the adaptive resolution molecular dynamics technique (AdResS).We simulate Lennard-Jones fluids with open boundaries in a thermal gradient and find excellentagreement of the stationary responses with results obtained from the simulation of a larger, locallyforced closed system. The encouraging results pave the way for a computational treatment of opensystems far from equilibrium framed in a well-established theoretical model that avoids possiblenumerical artifacts and physical misinterpretations
Ranbow: A fast and accurate method for polyploid haplotype reconstruction
No full textReconstructing haplotypes from sequencing data is one of the major challenges in genetics. Haplotypes play a crucial role in many analyses, including genome-wide association studies and population genetics. Haplotype reconstruction becomes more difficult for higher numbers of homologous chromosomes, as it is often the case for polyploid plants. This complexity is compounded further by higher heterozygosity, which denotes the frequent presence of variants between haplotypes. We have designed Ranbow, a new tool for haplotype reconstruction of polyploid genome from short read sequencing data. Ranbow integrates all types of small variants in bi- and multi-allelic sites to reconstruct haplotypes. To evaluate Ranbow and currently available competing methods on real data, we have created and released a real gold standard dataset from sweet potato sequencing data. Our evaluations on real and simulated data clearly show Ranbow’s superior performance in terms of accuracy, haplotype length, memory usage, and running time. Specifically, Ranbow is one order of magnitude faster than the next best method. The efficiency and accuracy of Ranbow makes whole genome haplotype reconstruction of complex genome with higher ploidy feasible
Dimensionality Reduction of Complex Metastable Systems via Kernel Embeddings of Transition Manifolds
Get PDFAbstract
We present a novel kernel-based machine learning algorithm for identifying the
low-dimensional geometry of the effective dynamics of high-dimensional multiscale
stochastic systems. Recently, the authors developed a mathematical framework for the
computation of optimal reaction coordinates of such systems that is based on learning a
parameterization of a low-dimensional transition manifold in a certain function space.
In this article, we enhance this approach by embedding and learning this transition
manifold in a reproducing kernel Hilbert space, exploiting the favorable properties of
kernel embeddings. Under mild assumptions on the kernel, the manifold structure is
shown to be preserved under the embedding, and distortion bounds can be derived.
This leads to a more robust and more efficient algorithm compared to the previous
parameterization approaches
How to calculate pH-dependent binding rates for receptor-ligand systems based on thermodynamic simulations with different binding motifs
No full textMolecular simulations of ligand–receptor interactions are a computational challenge, especially when their association- (‘on’-rate) and dissociation- (‘off’-rate) mechanisms are working on vastly differing timescales. One way of tackling this multiscale problem is to compute the free-energy landscapes, where molecular dynamics (MD) trajectories are used to only produce certain statistical ensembles. The approach allows for deriving the transition rates between energy states as a function of the height of the activation-energy barriers. In this article, we derive the association rates of the opioids fentanyl and N-(3-fluoro-1-phenethylpiperidin-4-yl)-N-phenyl propionamide (NFEPP) in a μ-opioid receptor by combining the free-energy landscape approach with the square-root-approximation method (SQRA), which is a particularly robust version of Markov modelling. The novelty of this work is that we derive the association rates as a function of the pH level using only an ensemble of MD simulations. We also verify our MD-derived insights by reproducing the in vitro study performed by the Stein Lab
Single molecule mu-opioid receptor membrane-dynamics reveal agonist-specific dimer formation with super-resolved precision
No full textG-protein-coupled receptors (GPCRs) are key signaling proteins that mostly function as monomers, but for several receptors constitutive dimer formation has been described and in some cases is essential for function. Using single-molecule microscopy combined with super-resolution techniques on intact cells, we describe here a dynamic monomer–dimer equilibrium of µ-opioid receptors (µORs), where dimer formation is driven by specific agonists. The agonist DAMGO, but not morphine, induces dimer formation in a process that correlates both temporally and in its agonist- and phosphorylation-dependence with β-arrestin2 binding to the receptors. This dimerization is independent from, but may precede, µOR internalization. These data suggest a new level of GPCR regulation that links dimer formation to specific agonists and their downstream signals
Diffusion maps embedding and transition matrix analysis of the large-scale flow structure in turbulent Rayleigh-Bénard convection
No full textThree-dimensional potential vorticity structures for extreme precipitation events on the convective scale
Get PDFThree-dimensional potential vorticity (PV) structures on the convective scale during extreme precipitation events are investigated. Using the high resolution COSMO-REA2 data set, 3D composites of the PV, with and without Coriolis parameter and related variables, are evaluated for different classes of precipitation intensity. The development of a significant horizontal dipole structure in the immediate vicinity of the precipitation maximum and the updraft can be explained by the twisting term in the vorticity equation. This is because the vorticity equation is proportional to the PV equation for strong convective processes. This theoretical is important on the convective scale without the consideration of the Coriolis effect, which is a typical characteristic on the synoptic scale. In accordance to previous studies, the horizontal PV dipole is statistically confirmed by 3D composites of the PV and corresponding variables. We show that the dipole structures are especially distinct for the relative PV without Coriolis parameter and the relative vorticity. On the convective scale, the thermodynamical sources and sinks of the potential vorticity indicate the diabatic processes that are related to conservative vortex dynamics via the proportionality of the diabatic heating and the vertical velocity. This work confirms that the PV equation is an important tool in atmospheric dynamics that unifies the thermodynamical processes as well as the dynamical processes into one scalar
Computation and Optimal Perturbation of Finite-Time Coherent Sets for Aperiodic Flows Without Trajectory Integration
No full textUnderstanding the macroscopic behavior of dynamical systems is an important tool to unravel transport
mechanisms in complex flows. A decomposition of the state space into coherent sets is a popular
way to reveal this essential macroscopic evolution. To compute coherent sets from an aperiodic timedependent
dynamical system we consider the relevant transfer operators and their infinitesimal generators
on an augmented space-time manifold. This space-time generator approach avoids trajectory
integration and creates a convenient linearization of the aperiodic evolution. This linearization can
be further exploited to create a simple and effective spectral optimization methodology for diminishing
or enhancing coherence. We obtain explicit solutions for these optimization problems using
Lagrange multipliers and illustrate this technique by increasing and decreasing mixing of spatial
regions through small velocity field perturbations