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In this article we review the application of the synchronization theory to the analysis of multivariate biological signals. We address the problem of phase estimation from data and detection and quantification of weak interaction, as well as quantification of the direction of coupling. We discuss the potentials as well as limitations and misinterpretations of the approach
We study synchronization transitions in a system of two coupled self-sustained chaotic oscillators. We demonstrate that with the increase of coupling strength the system first undergoes the transition to phase synchronization. With a further increase of coupling, a new synchronous regime is observed, where the states of two oscillators are nearly identical, but one system lags in time to the other. We describe thisregime as a state with correlated amplitudes and a constant phase shift. These transitions are traced in the Lyapunov spectrum.
Locking-based frequency measurement and synchronization of chaotic oscillators with complex dynamics
(2002)
Computation of the instantaneous phase and amplitude via the Hilbert Transform is a powerful tool of data analysis. This approach finds many applications in various science and engineering branches but is not proper for causal estimation because it requires knowledge of the signal’s past and future. However, several problems require real-time estimation of phase and amplitude; an illustrative example is phase-locked or amplitude-dependent stimulation in neuroscience. In this paper, we discuss and compare three causal algorithms that do not rely on the Hilbert Transform but exploit well-known physical phenomena, the synchronization and the resonance. After testing the algorithms on a synthetic data set, we illustrate their performance computing phase and amplitude for the accelerometer tremor measurements and a Parkinsonian patient’s beta-band brain activity.
A localized surface plasmon resonance biosensor in a flow-through configuration was applied for investigating kinetics of lectin binding to surface-grafted glycopolymer brushes. Polycarbonate filter membranes with pore sizes of 400 nm were coated with a 114-nm thick gold layer and used as substrate for surface-initiated atom-transfer radical polymerization of a glycomonomer. These grafted from glycopolymer brushes were further modified with two subsequent enzymatic reactions on the surface to yield an immobilized trisaccharide presenting brush. Specific binding of lectins including Clostridium difficile toxin A receptor domain to the glycopolymer brush surface could be investigated in a microfluidic setup with flow-through of the analytes and transmission surface plasmon resonance spectroscopy.
Glycan-protein interactions are essential biological processes with many disease-related modulations and variations. One of the key proteins involved in tumor progression and metastasis is galectin-3 (Gal-3). A lot of effort is put into the development of Gal-3 inhibitors as new therapeutic agents. The avidity of glycan-protein interactions is strongly enhanced by multivalent ligand presentation. Multivalent presentation of glycans can be accomplished by utilizing glycopolymers, which are polymers with pendent glycan groups. For the production of glycopolymers, glycomonomers are synthesized by a regioselective, microwave-assisted approach starting from lactose. The resulting methacrylamide derivatives are polymerized by RAFT and immobilized on gold surfaces using the trithiocarbonate group of the chain transfer agent. Surface plasmon resonance spectroscopy enables the label free kinetic characterization of Gal-3 binding to these multivalent glycopolymers. The measurements indicate oligomerization of Gal-3 upon exposure to multivalent environments and reveal strong specific interaction with the immobilized polymers.