Plasticity and rectangularity in survival curves

Living systems inevitably undergo a progressive deterioration of physiological function with age and an increase of vulnerability to disease and death. To maintain health and survival, living systems should optimize survival strategies with adaptive interactions among molecules, cells, organs, individuals, and environments, which arises plasticity in survival curves of living systems. In general, survival dynamics in a population is mathematically depicted by a survival rate, which monotonically changes from 1 to 0 with age. It would be then useful to find an adequate function to describe complicated survival dynamics. Here we describe a flexible survival function, derived from the stretched exponential function by adopting an age-dependent shaping exponent. We note that the exponent is associated with the fractal-like scaling in cumulative mortality rate. The survival function well depicts general features in survival curves; healthy populations exhibit plasticity and evolve towards rectangular-like survival curves, as examples in humans or laboratory animals

Multichromophoric cyclodextrins. 3. Investigation of dynamics of energy hopping by frequency-domain fluorometry

A β-cyclodextrin labeled with seven naphthoyloxy chromophores was studied by steady-state and time-resolved fluorescence spectroscopy in order to get information on the dynamics of energy hopping between chromophores. The steady-state fluorescence anisotropy was recorded as a function of excitation wavelength in a mixture of methanol and ethanol at 110 K (rigid glass). The fluorescence anisotropy decay was obtained under the same conditions by the multifrequency phase-modulation technique upon excitation at 290 nm. The data were analyzed and interpreted on the basis of a theoretical model involving a unique rate constant for energy hopping between nearest neighbors. In particular, this model predicts a long-time leveling-off of the emission anisotropy at 1/7th of the fundamental anisotropy, which is confirmed by both steady-state and time-resolved data and thus indicates that there is no preferred mutual orientation between the chromophores. As regards the rate of energy hopping, an average value of 2 × 109 s-1 can be deduced from the comparison between the theoretical and experimental decays. This value is shown to be consistent with a dipole-dipole mechanism of energy transfer. © 1996 American Chemical Society