Vlll PREFACE 



thermodynamic quantities, which are directly appHcable to the properties of 

 biological systems, developed on the basis of a dynamic theory of molecular 

 control processes. 



Therefore although the mathematics which is used in this study may seem 

 formidable, it really incorporates no more than the well-established procedures 

 used in physics, and more particularly in statistical mechanics, for the calcula- 

 tion and study of such quantities as temperature, entropy, and work. It did not 

 seem reasonable to attempt to make the book totally self-contained on this 

 side, for this would have meant writing first a text on statistical mechanics, of 

 which there are many excellent ones available. The strategy has been rather to 

 give a verbal explanation of the mathematical procedures which are introduced 

 at various points in the development of the theory, and also to interpret the 

 mathematical results obtained in terms of more familiar biochemical and phy- 

 siological notions. However, this unfortunately still leaves many pages of mathe- 

 matics which will mean little to most biologists. The greater part of the text 

 can actually be read without close attention to these pages. But if the treatment 

 of cellular processes given in this work in any way anticipates the future 

 development of biology, then sooner or later biologists will find it useful to 

 become familiar with the mathematical procedures used. On the other hand, 

 if the theory advanced falls by the wayside, then the biologist was quite right to 

 avoid any involvement in the mathematical details. 



For the scientist with a training in physics the book will offer no difficulties. 

 The biological background which is required is minimal, and except for certain 

 aspects of enzymology on the one hand and embryology on the other, the 

 exposition is self-contained. Actually the physicist will probably find the 

 mathematical treatment definitely lacking in the rigour to which he is accus- 

 tomed. The attempt has been to steer a middle course between physics and 

 biology, thus making the material accessible to scientists with a training on 

 either side. 



The basis of the theory presented here was developed while I was at the 

 Institute of Animal Genetics in Edinburgh as a graduate student, and at McGill 

 University as a post-doctoral fellow. It is a great pleasure for me to express my 

 indebtedness to Professor C. H. Waddington for his encouragement in the 

 pursuit of a theoretical study of biological processes, and for reading and sug- 

 gesting improvements in the manuscript, I would like also to thank Dr. H. 

 Kacser for discussions which clarified the groundwork of this analysis. In 

 addition I owe a debt of gratitude to friends at the Massachusetts Institute of 

 Technology who read and criticized various parts of the manuscript, especially 

 Karl Kornacker. 



Finally it is to the National Research Council of Canada that I am deeply 

 indebted for financial assitance in Edinburgh and in Montreal, without whose 

 generosity this study could not have been undertaken. 



Cambridge, Mass. 



August 1963 B.C.G. 



