478 RHYTHMS IN PLANTS AND ANIMALS 



ship of daily rhythms to both Went's thermoperiodism (1957) and 

 the newer photoperiodic phenomena described by Highkin and Hanson 

 (1954) andHillman (1956). 



THE GENERALIZED OSCILLATOR MODEL 

 FOR CELLULAR CLOCKS 



We have discussed elsewhere (Bruce and Pittendrigh, 1957b; 

 Pittendrigh and Bruce, 1957; Pittendrigh, 1958) the general charac- 

 teristics of daily rhythms considered as clocks. The skepticism voiced 

 in some discussion at this symposium over use of the word "clock" 

 prompts us to note again the salient facts which have led us to this 

 usage. Persistent daily, tidal, and lunar rhythms stand sharply apart 

 from all other biological rhythms, such as heartbeat, for instance, in 

 two fundamental respects: (1) their natural period is an evolved 

 approximation to the period of an ecologically significant cosmic 

 period; (2) their period remains stable over a wide range of tempera- 

 tures, thus satisfying the functional prerequisite of an efficient time- 

 giver. In addition, it is noted that the feature of temperature inde- 

 pendence of period is uniquely associated with rhythms which have a 

 natural period matching a cosmic period and that all such rhythms 

 are temperature-independent. Clearly the universal concurrence of 

 these features is significant and implies that the systems they charac- 

 terize owe their existence to natural selection and that they serve to 

 measure time for the organism; in a word they are "clocks." 



Earlier papers from this laboratory (see especially Pittendrigh and 

 Bruce, 1957) have emphasized the fact that persistent daily rhythms 

 in a very wide range of organisms, from single-celled systems to 

 mammals, have many formal characteristics in common, and that 

 these characteristics are those of self-sustaining oscillators. We have 

 accordingly developed a generalized oscillator model for the discus- 

 sion of cellular clocks embodying the following principal propositions: 



1. The living cell possesses either as a distinct part or as a feature 

 of its overall organization a system that can develop a self-sustaining 

 oscillator, whose 



2. Natural Period is an evolved approximation to that of the solar 

 day, and 



