5. THE STATISTICAL MECHANICS OF THE EPIGENETIC SYSTEM 75 



which can nevertheless give some insight into the forces working to produce 

 organization and integration in biological systems, and it is to this end that 

 the present study is directed. 



To complete the spectrum of "thermodynamic" functions associated 

 with the present theory, we will now introduce the notion of work in an epi- 

 genetic context. This concept enters a statistical mechanics in association 

 with quantities which are called external parameters. These quantities define 

 the environment of the system, and when they change they cause the system to 

 change its " thermodynamic " state. In Chapter 2 we spent some time discussing 

 the notions of system and enviornment, for they are fundamental ideas which 

 underly experimental science. The scientist must always have some set of 

 pistons, levers, and screws, as Schrodinger has called them, to push his selected 

 system around and thus study its behaviour. In cell biology these "handles" 

 are such quantities as electric currents, chemical concentrations, doses of 

 ultraviolet light, temperature levels, mutant gene doses, etc. In embryology 

 many of the stimuli are not under direct experimental control, although 

 transplantation techniques, for example, place the "system", say a piece of 

 blastula ectoderm, in an environment which is known to produce a particular 

 stimulus such as the inside of the blastophore lip where primary induction 

 occurs. The scientist's goal is to relate environmental stimulus to system 

 response in some invariant manner, so that a certain set of conditions will 

 always produce the same result. Going further, he would like to obtain quan- 

 titative relations between the amount or intensity of the stimulus and the 

 amount of response. A sufficient set of variables for describing these relations 

 may be large or small and, of course, depends very much upon the type of 

 system which is being studied and the ambitions of the experimenter. In 

 studying the response of cells to stimuli, an experimenter usually selects a 

 clear marker for measuring his response, such as a membrane potential, an 

 enzyme activity, or a clonal type. He may enlarge either the number of 

 parameters in the environment or the number of variables in the system, and 

 the number of variables which the experimenter can study in response to 

 various stimuli, is limited only by the wealth of the institution which is buying 

 his equipment and paying the salaries of his technicians. 



However, it is the emphasis of a thermodynamic analysis to attempt to 

 bring some economy to the description of an experimental situation and to 

 discuss relations holding between quantities which describe general or macro- 

 scopic features of the system, rather than microscopic ones. For example, the 

 "microscopic" observation that the rate constants of enzymes increase with 

 increased temperature, might be used to try to derive a general relationship 

 between physical temperature and cell size, since it is also true in general that 

 as temperature increases cell size decreases, at least over a certain temperature 

 range (Mucibabic, 1956). In such a relation physical temperature would be 

 regarded as an external parameter. This does not appear to be a particularly 

 useful or enlightening relationship biologically, but it serves to illustrate the 

 type of law which a thermodynamic analysis seeks. More useful would be 

 the demonstration of relations holding, for example, between 6, the talandic 



