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Copyright information:Taken from "Simulation and analysis of spatio-temporal maps of gastrointestinal motility"http://www.biomedical-engineering-online.com/content/7/1/2BioMedical Engineering OnLine 2008;7():2-2.Published online 14 Jan 2008PMCID:PMC2254420. In this simulation, contractions at five separate locations oscillated in the same rhythms up and down (white double arrow), mimicking contraction and relaxation (period a). In the next period (b) the frequency of oscillation was doubled. In period (c), the oscillations contracted at the first frequency while they also propagated to the right. In period (d) the speed of propagation was doubled.
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Copyright information:Taken from "Simulation and analysis of spatio-temporal maps of gastrointestinal motility"http://www.biomedical-engineering-online.com/content/7/1/2BioMedical Engineering OnLine 2008;7():2-2.Published online 14 Jan 2008PMCID:PMC2254420. In this simulation, contractions at five separate locations oscillated in the same rhythms up and down (white double arrow), mimicking contraction and relaxation (period a). In the next period (b) the frequency of oscillation was doubled. In period (c), the oscillations contracted at the first frequency while they also propagated to the right. In period (d) the speed of propagation was doubled.
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Abstract Background Biochemical oscillations play an important role in maintaining physiological and cellular homeostasis in biological systems. The frequency and amplitude of oscillations are regulated to properly adapt to environments by numerous interactions within biomolecular networks. Despite the advances in our understanding of biochemical oscillators, the relationship between the network structure of an oscillator and its regulatory function still remains unclear. To investigate such a relationship in a systematic way, we have developed a novel analysis method called interaction perturbation analysis that enables direct modulation of the strength of every interaction and evaluates its consequence on the regulatory function. We have applied this new method to the analysis of three representative types of oscillators. Results The results of interaction perturbation analysis showed different regulatory features according to the network structure of the oscillator: (1) both frequency and amplitude were seldom modulated in simple negative feedback oscillators; (2) frequency could be tuned in amplified negative feedback oscillators; (3) amplitude could be modulated in the incoherently amplified negative feedback oscillators. A further analysis of naturally-occurring biochemical oscillator models supported such different regulatory features according to their network structures. Conclusions Our results provide a clear evidence that different network structures have different regulatory features in modulating the oscillation frequency and amplitude. Our findings may help to elucidate the fundamental regulatory roles of network structures in biochemical oscillations.
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Abstract Background Biochemical oscillations play an important role in maintaining physiological and cellular homeostasis in biological systems. The frequency and amplitude of oscillations are regulated to properly adapt to environments by numerous interactions within biomolecular networks. Despite the advances in our understanding of biochemical oscillators, the relationship between the network structure of an oscillator and its regulatory function still remains unclear. To investigate such a relationship in a systematic way, we have developed a novel analysis method called interaction perturbation analysis that enables direct modulation of the strength of every interaction and evaluates its consequence on the regulatory function. We have applied this new method to the analysis of three representative types of oscillators. Results The results of interaction perturbation analysis showed different regulatory features according to the network structure of the oscillator: (1) both frequency and amplitude were seldom modulated in simple negative feedback oscillators; (2) frequency could be tuned in amplified negative feedback oscillators; (3) amplitude could be modulated in the incoherently amplified negative feedback oscillators. A further analysis of naturally-occurring biochemical oscillator models supported such different regulatory features according to their network structures. Conclusions Our results provide a clear evidence that different network structures have different regulatory features in modulating the oscillation frequency and amplitude. Our findings may help to elucidate the fundamental regulatory roles of network structures in biochemical oscillations.
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This is the dataset of the various figures proposed in the article Fully integrated frequency references
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This is the dataset of the various figures proposed in the article Fully integrated frequency references
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Copyright information:Taken from "Dynamical signatures of cellular fluctuations and oscillator stability in peripheral circadian clocks"Molecular Systems Biology 2007;3():93-93.Published online 13 Mar 2007PMCID:PMC1847945.Copyright © 2007, EMBO and Nature Publishing Group () An extended Kuramoto model for the oscillator phases φ() and frequencies () describes coupled circadian phase oscillators. The total luminescence signal () is the sum of a population of initially oscillators each contributing a cosine signal centered around a constant with relative amplitude . Cell death follows a Poisson process with time constant τ reflected by the indicator variable θ() taking value 1 before (and 0 after) cell has died. The time-dependent frequencies and phases of the individual oscillators are subject to a stochastic differential equation (cf. Materials and methods and ). () Sample frequency trajectory; γ and σ are free constants representing the inverse memory of the frequency trajectories and the frequency dispersion, respectively. () Parameter listing. describes the intercellular coupling between the phases and is taken as all-to-all. More realistic coupling geometries are considered in .
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Copyright information:Taken from "Dynamical signatures of cellular fluctuations and oscillator stability in peripheral circadian clocks"Molecular Systems Biology 2007;3():93-93.Published online 13 Mar 2007PMCID:PMC1847945.Copyright © 2007, EMBO and Nature Publishing Group () An extended Kuramoto model for the oscillator phases φ() and frequencies () describes coupled circadian phase oscillators. The total luminescence signal () is the sum of a population of initially oscillators each contributing a cosine signal centered around a constant with relative amplitude . Cell death follows a Poisson process with time constant τ reflected by the indicator variable θ() taking value 1 before (and 0 after) cell has died. The time-dependent frequencies and phases of the individual oscillators are subject to a stochastic differential equation (cf. Materials and methods and ). () Sample frequency trajectory; γ and σ are free constants representing the inverse memory of the frequency trajectories and the frequency dispersion, respectively. () Parameter listing. describes the intercellular coupling between the phases and is taken as all-to-all. More realistic coupling geometries are considered in .
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Coherent control of the nitrogen-vacancy (NV) center in diamond’s triplet spin state has traditionally been accomplished with resonant ac magnetic fields. Here, we show that high-frequency stress resonant with the spin state splitting can also coherently control NV center spins. Because this mechanical drive is parity non-conserving, controlling spins with stress enables direct access to the magnetically forbidden |−1〉↔|+1〉 spin transition. Using a bulk-mode mechanical microresonator fabricated from single-crystal diamond, we apply intense ac stress to the diamond substrate and observe mechanically driven Rabi oscillations between the |−1〉 and |+1〉 states of an NV center spin ensemble. Additionally, we measure the inhomogeneous spin dephasing time (T2*) of the spin ensemble within this {−1,+1} subspace using a mechanical Ramsey sequence and compare it to the dephasing times measured with a magnetic Ramsey sequence for each of the three spin qubit combinations available within the NV center ground state. These results demonstrate coherent control of a spin with a mechanical resonator and could lead to the creation of a phase-sensitive Δ-system inside the NV center ground state with potential applications in quantum optomechanics and metrology.
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