Kawato M, Suzuki R
Biol Cybern. 1981;40(2):139-49. doi: 10.1007/BF00344292.
A skeleton photoperiod consists of two short pulses which are applied on the circadian oscillator at times corresponding to the beginning and to the end of a continuous light stimulus. To study several problems in entrainment of circadian rhythms by skeleton photoperiods, we develop a simple diagrammatic solution of the steady state entrainment making use of phase transition curves which are directly gotten from phase response curves. The graphical method is simple and systematic to study entrainment by light cycles with various day lengths. As the method is also intuitive, we can easily examine three problems. (1) In Drosophila the phase relation (psi) between rhythm and light cycle is a continuous function of day length of skeleton photoperiods up to about 12 h, but a marked discontinuity (psi-jump) sets in between 13 and 14 h. By the diagrammatic method we find that psi-jump is mathematically a bifurcation phenomenon. (2) The action of photoperiods up to about 12 h is fully simulated by two 15-min skeleton pulses. Do 3-min skeleton pulses imitate the complete photoperiods? We find that pulse width is arbitrary to some extent. (3) Why skeleton photoperiods up to about 12 h are good models of complete photoperiods? The reason is the small amplitude and the nearly symmetrical form of phase response curves in the subjective day.
一个框架光周期由两个短脉冲组成，这两个短脉冲在与连续光刺激的开始和结束相对应的时间施加于昼夜节律振荡器上。为了研究框架光周期对昼夜节律的同步化中的几个问题，我们利用直接从相位响应曲线得到的相位转变曲线，开发了一种简单的稳态同步化图解法。该图解法简单且系统，可用于研究不同日长的光周期的同步化。由于该方法也很直观，我们可以轻松地研究三个问题。（1）在果蝇中，节律与光周期之间的相位关系（ψ）在框架光周期的日长达到约12小时之前是日长的连续函数，但在13至14小时之间会出现明显的不连续性（ψ跳跃）。通过图解法，我们发现ψ跳跃在数学上是一种分岔现象。（2）长达约12小时的光周期的作用可由两个15分钟的框架脉冲完全模拟。3分钟的框架脉冲能模拟完整的光周期吗？我们发现脉冲宽度在一定程度上是任意的。（3）为什么长达约12小时的框架光周期是完整光周期的良好模型？原因是主观日中相位响应曲线的幅度小且形式近乎对称。
