The transition between strong and weak chaos in delay systems: stochastic modeling approach

We investigate the scaling behavior of the maximal Lyapunov exponent in chaotic systems with time delay. In the large-delay limit, it is known that one can distinguish between strong and weak chaos depending on the delay scaling, analogously to strong and weak instabilities for steady states and periodic orbits. Here we show that the Lyapunov exponent of chaotic systems shows significant differences in its scaling behavior compared to constant or periodic dynamics due to fluctuations in the linearized equations of motion. We reproduce the chaotic scaling properties with a linear delay system with multiplicative noise. We further derive analytic limit cases for the stochastic model illustrating the mechanisms of the emerging scaling laws

Stochastic switching in delay-coupled oscillators

A delay is known to induce multistability in periodic systems. Under influence of noise, coupled oscillators can switch between coexistent orbits with different frequencies and different oscillation patterns. For coupled phase oscillators we reduce the delay system to a nondelayed Langevin equation, which allows us to analytically compute the distribution of frequencies and their corresponding residence times. The number of stable periodic orbits scales with the roundtrip delay time and coupling strength, but the noisy system visits only a fraction of the orbits, which scales with the square root of the delay time and is independent of the coupling strength. In contrast, the residence time in the different orbits is mainly determined by the coupling strength and the number of oscillators, and only weakly dependent on the coupling delay. Finally we investigate the effect of a detuning between the oscillators. We demonstrate the generality of our results with delay-coupled FitzHugh-Nagumo oscillators

Autocorrelation properties of chaotic delay dynamical systems: A study on semiconductor lasers

We present a detailed experimental characterization of the autocorrelation properties of a delayed feedback semiconductor laser for different dynamical regimes. We show that in many cases the autocorrelation function of laser intensity dynamics can be approximated by the analytically derived autocorrelation function obtained from a linear stochastic model with delay. We extract a set of dynamic parameters from the fit with the analytic solutions and discuss the limits of validity of our approximation. The linear model captures multiple fundamental properties of delay systems, such as the shift and asymmetric broadening of the different delay echoes. Thus, our analysis provides significant additional insight into the relevant physical and dynamical properties of delayed feedback lasers

New AMD3100 derivatives for CXCR4 chemokine receptor targeted molecular imaging studies: synthesis, anti-HIV-1 evaluation and binding affinities

CXCR4 is a target of growing interest for the development of new therapeutic drugs and imaging agents as its role in multiple disease states has been demonstrated. AMD3100, a CXCR4 chemokine receptor antagonist that is in current clinical use as a haematopoietic stem cell mobilising drug, has been widely studied for its anti-HIV properties, potential to inhibit metastatic spread of certain cancers and, more recently, its ability to chelate radiometals for nuclear imaging. In this study, AMD3100 is functionalised on the phenyl moiety to investigate the influence of the structural modification on the anti-HIV-1 properties and receptor affinity in competition with anti-CXCR4 monoclonal antibodies and the natural ligand for CXCR4, CXCL12. The effect of complexation of nickel(II) in the cyclam cavities has been investigated. Two amino derivatives were obtained and are suitable intermediates for conjugation reactions to obtain CXCR4 molecular imaging agents. A fluorescent probe (BODIPY) and a precursor for 18F (positron emitting isotope) radiolabelling were conjugated to validate this route to new CXCR4 imaging agents

Acetate as a model for aspartate-based CXCR4 chemokine receptor binding of cobalt and nickel complexes of cross-bridged tetraazamacrocycles

A number of disease states including WHIM syndrome, HIV infection and cancer have been linked to the chemokine receptor CXCR4. High-affinity CXCR4 antagonist transition metal complexes of configurationally restricted bis-tetraazamacrocyclic ligands have been identified in previous studies. Recently synthesised and structurally characterised Co2+/Co3+ and Ni2+ acetate complexes of mono-macrocycle cross-bridged ligands have been used to mimic their known coordination interaction with the aspartate side chains on binding to CXCR4. Here, X-ray crystal structures for three Co2+/Co3+ acetate complexes and five Ni2+ acetate complexes are presented and demonstrate flexibility in the mode of binding to the acetate ligand concomitantly with the requisite cis-V-configured cross-bridged tetraazamacrocyle. Complexes of the smaller Co3+ metal ion exclusively bind acetate by chelating both oxygens of acetate. Larger Co2+ and Ni2+ metal ions in cross-bridged tetraazamacrocycles show a clear tendency to coordinate acetate in a monodentate fashion with a coordinated water molecule completing the octahedral coordination sphere. However, in unbridged tetraazamacrocycle acetate structures reported in the literature, the coordination preference is to chelate both acetate oxygens. We conclude that the short ethylene cross-bridge restricts the equatorial bulk of the macrocycle, prompting the metal ion to fill the equator with the larger monodentate acetate plus water ligand set. In unbridged ligand examples, the flexible macrocycle expands equatorially and generally only allows chelation of the sterically smaller acetate alone. These results provide insight for generation of optimised bis-macrocyclic CXCR4 antagonists utilising cobalt and nickel ions

64Cu PET Imaging of the CXCR4 Chemokine Receptor Using a Cross-Bridged Cyclam Bis-Tetraazamacrocyclic Antagonist

© 2020 by the Society of Nuclear Medicine and Molecular Imaging. Expression of the chemokine receptor chemokine C-X-C motif receptor 4 (CXCR4) plays an important role in cancer metastasis, in autoimmune diseases, and during stem cell-based repair processes after stroke and myocardial infarction. Previously reported PET imaging agents targeting CXCR4 suffer from either high nonspecific uptake or bind only to the human form of the receptor. The objective of this study was to develop a high-stability 64Cu-labeled small-molecule PET agent for imaging both human and murine CXCR4 chemokine receptors. Methods: Synthesis, radiochemistry, stability and radioligand binding assays were performed for the novel tracer 64Cu-CuCB-bicyclam. In vivo dynamic PET studies were performed on mice bearing U87 (CXCR4 low-expressing) and U87.CXCR4 (human-CXCR4 high-expressing) tumors. Biodistribution and receptor blocking studies were performed on CD1-IGS immunocompetent mice. CXCR4 expression on tumor and liver disaggregates was confirmed using a combination of immunohistochemistry, quantitative polymerase chain reaction, and Western blot. Results:64Cu-CuCB-bicyclam has a high affinity for both the human and the murine variants of the CXCR4 receptor (half-maximal inhibitory concentration, 8 nM [human]/2 nM [murine]) and can be obtained from the parent chelator that has low affinity. In vitro and in vivo studies demonstrate specific uptake in CXCR4-expressing cells that can be blocked by more than 90% using a higher-affinity antagonist, with limited uptake in non-CXCR4-expressing organs and high in vivo stability. The tracer was also able to selectively displace the CXCR4 antagonists AMD3100 and AMD3465 from the liver. Conclusion: The tetraazamacrocyclic small molecule 64Cu-CuCB-bicyclam has been shown to be an imaging agent for the CXCR4 receptor that is likely to be applicable across a range of species. It has high affinity and stability and is suitable for preclinical research in immunocompetent murine models

The transition between strong and weak chaos in delay systems: Stochastic modeling approach

We investigate the scaling behavior of the maximal Lyapunov exponent in chaotic systems with time delay. In the large-delay limit, it is known that one can distinguish between strong and weak chaos depending on the delay scaling, analogously to strong and weak instabilities for steady states and periodic orbits. Here we show that the Lyapunov exponent of chaotic systems shows significant differences in its scaling behavior compared to constant or periodic dynamics due to fluctuations in the linearized equations of motion. We reproduce the chaotic scaling properties with a linear delay system with multiplicative noise. We further derive analytic limit cases for the stochastic model illustrating the mechanisms of the emerging scaling laws

Discovery of inhibitors for the human chemokine receptors CXCR4 and CXCR7: screening applications on the FLIPR Tetra high-throughput cellular screening system

status: publishe

Stochastic switching in delay-coupled oscillators

A delay is known to induce multistability in periodic systems. Under influence of noise, coupled oscillators can switch between coexistent orbits with different frequencies and different oscillation patterns. For coupled phase oscillators we reduce the delay system to a nondelayed Langevin equation, which allows us to analytically compute the distribution of frequencies and their corresponding residence times. The number of stable periodic orbits scales with the roundtrip delay time and coupling strength, but the noisy system visits only a fraction of the orbits, which scales with the square root of the delay time and is independent of the coupling strength. In contrast, the residence time in the different orbits is mainly determined by the coupling strength and the number of oscillators, and only weakly dependent on the coupling delay. Finally we investigate the effect of a detuning between the oscillators. We demonstrate the generality of our results with delay-coupled FitzHugh-Nagumo oscillators