62 TEMPORAL ORGANIZATION IN CELLS 



00 



where Z^^ = J e-(i/^(cix<V2)^^. 



-Pi 



■ = r g-iV6)bi[yi-logO+yi)]^y. 



z. 



These phase integrals are written with steady state values for subscripts in 

 order to emphasize the fact that they are not functions of the system variables, 

 which are integrated out, but are functions of the parameters, which define 

 the steady state. They are also functions of Q. 



The importance of the canonical ensemble in physics is that it allows one to 

 study systems which are not isolated but are in thermal equilibrium with their 

 surroundings. The many duplicates of the initial system which surround it 

 and with which it can exchange energy may be regarded as a "heat bath" in 

 which the system is immersed. For physical systems Q is the thermodynamic 

 temperature of the ensemble while i/» is the free energy of the system in thermo- 

 dynamic equilibrium. In relation to the biochemical control mechanisms 

 which form the content of the present statistical mechanics d is again some kind 

 of "temperature" andi/( some kind of free energy, but we must discover what 

 these quantities in fact are and how they can be measured. Because there is a 

 formal and to some extent a literal equivalence between these new " epigenetic " 

 quantities and the familiar physical quantities, we shall retain the terms 

 temperature and free energy in order to draw upon the intuitive content of 

 these notions. However, we will prefix these terms by the word "talandic", 

 a neologism which is introduced here with some hesitation, since there may 

 be a concept already in use which would serve the present purpose as well. 

 The word derives from the Greek raAavrcocri?, meaning oscillation, and is 

 intended to emphasize the fact that all the quantities which arise in the present 

 study as tools for the investigation of epigenetic phenomena are properties of a 

 system whose fundamental dynamic characteristic is the occurrence of oscil- 

 lations. A better word would also carry the implication that the oscillations 

 occur as a result of control by feed-back, hence suggesting the use of the 

 terms "cybernetic temperature", "cybernetic entropy", etc., if it is found that 

 oscillatory phenomena of the type considered here are universal character- 

 istics of biological control systems employing negative feed-back. However, 

 in the absence of good evidence for this and in view of the fact that oscillations 

 may arise in biological systems independently of the presence of feed-back 

 (e.g. in Volterra type prey-predator systems), it seems preferable to use the 

 descriptive term talandic. 



The canonical ensemble is the appropriate tool for the study of talandic or 

 oscillatory properties in cells. With the further development of experimental 

 techniques whose resolution reaches the single cell, it is not unreasonable 

 to expect that continuous observation and measurement of the concentrations 

 of a molecular species in a single cell will be possible, and possibly even a few 

 species at a time. These species, say v in number, will not be isolated from the 



