Universality in kinetic models of circadian rhythms in [Formula: see text].

Biological evolution has endowed the plant Arabidopsis thaliana with genetically regulated circadian rhythms. A number of authors have published kinetic models for these oscillating chemical reactions based on a network of interacting genes. To investigate the hypothesis that the Arabidopsis circadian dynamical system is poised near a Hopf bifurcation like some other biological oscillators, we varied the kinetic parameters in the models and searched for bifurcations. Finding that each model does exhibit a supercritical Hopf bifurcation, we performed a weakly nonlinear analysis near the bifurcation points to derive the Stuart-Landau amplitude equation. To illustrate a common dynamical structure, we scaled the numerical solutions to the models with the asymptotic solutions to the Stuart-Landau equation to collapse the circadian oscillations onto two universal curves-one for amplitude, and one for frequency. However, some models are close to bifurcation while others are far, some models are post-bifurcation while others are pre-bifurcation, and kinetic parameters that lead to a bifurcation in some models do not lead to a bifurcation in others. Future kinetic modeling can make use of our analysis to ensure models are consistent with each other and with the dynamics of the Arabidopsis circadian rhythm.

Theoretical estimation of retinal oxygenation in chronic diabetic retinopathy.

This paper uses computer modeling to estimate the progressive decline in oxygenation that occurs in the human diabetic retina after years of slowly progressive ischemic insult. An established model combines diffusion, saturable consumption, and blood capillary sources to determine the oxygen distribution across the retina. Incorporating long-term degradation of blood supply from the retinal capillaries into the model yields insight into the effects of progressive ischemia associated with prolonged hyperglycemia, suggesting time-scales over which therapeutic mitigation could have beneficial effect. A new extension of the model for oxygen distribution introduces a feedback mechanism for vasodilation and its potential to prolong healthy retinal function.

Transient turbulence in Taylor-Couette flow.

Recent studies have brought into question the view that at sufficiently high Reynolds number turbulence is an asymptotic state. We present direct observation of the decay of turbulent states in Taylor-Couette flow with lifetimes spanning five orders of magnitude. We also show that there is a regime where Taylor-Couette flow shares many of the decay characteristics observed in other shear flows, including Poisson statistics and the coexistence of laminar and turbulent patches. Our data suggest that for a range of Reynolds numbers characteristic decay times increase superexponentially with increasing Reynolds number but remain bounded in agreement with the most recent data from pipe flow. Our data are also consistent with recent theoretical predictions of lifetime scaling in transitional flows.

Photodynamic therapy for treatment of solid tumors--potential and technical challenges.

Photodynamic therapy (PDT) involves the administration of photosensitizer followed by local illumination with visible light of specific wavelength(s). In the presence of oxygen molecules, the light illumination of photosensitizer can lead to a series of photochemical reactions and consequently the generation of cytotoxic species. The quantity and location of PDT-induced cytotoxic species determine the nature and consequence of PDT. Much progress has been seen in both basic research and clinical application in recent years. Although the majority of approved PDT clinical protocols have primarily been used for the treatment of superficial lesions of both malignant and non-malignant diseases, interstitial PDT for the ablation of deep-seated solid tumors are now being investigated worldwide. The complexity of the geometry and non-homogeneity of solid tumor pose a great challenge on the implementation of minimally invasive interstitial PDT and the estimation of PDT dosimetry. This review will discuss the recent progress and technical challenges of various forms of interstitial PDT for the treatment of parenchymal and/or stromal tissues of solid tumors.

Biophotonic and other physical methods for characterizing oral mucosa.

This article discusses biophotonic and other physical methods for characterizing oral mucosa.