1. INTRODUCTION 7 



than the general dynamic investigations mentioned above, and this will allow 

 us to draw quite specific conclusions concerning the macroscopic consequences 

 of our assumptions. 



It is unfortunate that the present study can make practically no use of 

 engineering procedures in analysing the dynamic properties of cellular control 

 systems, although the work should perhaps be regarded as a development of 

 one aspect of cybernetic theory. It is because the biologist is dealing with a 

 complex, organized system, that his approach to cell behaviour must be rather 

 different from that which the engineer has used so far. He cannot isolate a 

 component having only a few variables without missing the integrated be- 

 haviour of the whole system; he cannot linearize his problem without re- 

 moving the most important dynamic properties of the system; and he cannot 

 treat the control problem as the engineer does, i.e. to find that feed-back signal 

 which produces optimal behaviour in the system according to some defined 

 criterion. The biologist cannot always specify what the criterion of optimal 

 performance is for adaptive or regulatory processes in the cell; he has prac- 

 tically no control over feed-back signals ; and his primary problem is not to 

 find solutions to differential equations of low order. His job is to observe, 

 describe, and analyse a given functioning system, not to construct one which 

 gives a particular performance. Therefore it is hardly surprising that the bio- 

 logist must develop his own theories, and borrow what he can from the physi- 

 cist, whose attitude to the physical world is more akin to the biologist's than 

 is that of the engineer. The procedure of the present study is to discover con- 

 servation laws or invariants for a particular class of biochemical control 

 system, to construct a statistical mechanics for such a system, and to investigate 

 the macroscopic behaviour of the system in terms of variables of state analogous 

 to those of physics : energy, temperature, entropy, free energy, etc. What will 

 emerge from such a programme is a set of concepts which are strictly biological 

 in content and which bear no relation to their physical analogues so far as 

 the actual behaviour of the system is concerned, although there is a formal 

 mathematical relationship because we are using the same analytic construc- 

 tions as are used in classical physics. These macroscopic concepts will become 

 familiar and develop an intuitive content only if the experimental side of the 

 theory can be developed in the same way that the theoretical physical concepts 

 of energy and entropy have gained intuitive content through the years by 

 familiarity with their experimental implications. 



The analytical procedures which will be used in this attempt to bridge the 

 gap which presently exists between molecular biology and cell physiology are 

 strictly classical in the sense that only systems describable by differential 

 equations are considered, and of these only ones having a first integral of the 

 motion can be used to construct a statistical mechanics and " thermodynamics ". 

 This is certainly the easiest mathematical procedure, but it imposes severe 

 constraints upon the class of control system which can be studied. This 

 limitation may prove to be too great for a useful quantitative, predictive 

 theory of cellular behaviour, and then the logical procedure is to extend the 

 class of control system by loosening the analytic constraints. In mathematical 



