Chapter 4 

 THE DYNAMICS OF THE EPIGENETIC SYSTEM 



The Control Circuits 



Our primary concern in this chapter is to derive differential equations which 

 describe the dynamic properties of a certain class of control mechanisms for 

 macromolecular synthesis in cells. As we proceed with the argument, the 

 limitations of a strictly classical analysis in terms of differential equations and 

 integrals will become evident. The procedure will be to select an idealized 

 model of a metabolic feed-back control cycle which, however, incorporates 

 what are believed to be the essential features of the real system. The type of 

 unit component which we will study is that shown in Fig. 1 . L,- represents a 

 genetic locus which synthesizes mRNA in quantities represented by the 



variable Xi. This specific "signal" encounters a cellular structure R (a ribo- 

 some), where its activity results in the synthesis of a particular species of protein 

 in quantities denoted by the variable 7,-. The protein then travels to some 

 cellular locus, C, where it exerts an influence upon the metabolic state 

 either by enzyme action or by some other means (we will usually assume that 

 Yi is an enzyme). The result of this activity by the protein is the generation of a 

 metabolic species in quantity Mj, a fraction of which closes the control loop 

 by returning to the genetic locus, L,-, where it is assumed to act as a repressor 

 either alone or as a "co-repressor" coupled with another molecule, the 

 "aporepressor". If a separate operator locus exists for the control of genetic 

 activity at L,- then it is included for the purposes of the present discussion as part 

 of the locus Li itself. 



This is the simplest type of unit which will be considered, and in it the 



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