8. APPLICATIONS AND PREDICTIONS 147 



periodically, but may occur as a microscopic consequence of the integrated 

 nature of the whole interacting epigenetic system of the anther cells. 



The modification required in the differential equations describing synthesis 

 and control of the /th species of mRNA and protein is 



(it Ar + krYr at 



The equation of protein synthesis remains unchanged, but mRNA synthesis is 

 now assumed to involve a self-replicating mechanism whereby messenger 

 molecules serve as templates for synthesis of more of the same messenger. 

 This has often been proposed as a mechanism of mRNA synthesis, and certain 

 species of RNA definitely do serve as their own templates such as ^.^ phage. 

 It remains a possiblity that other types of RNA, including mRNA, replicate 

 themselves, although it would appear that this is not the general mechanism 

 in bacteria. What the situation is in higher plants, such as the lily, remains to 

 be discovered. 



The other alteration in the kinetic equations is the assumption that the rate 

 of degradation of mRNA follows the law of mass action and varies with the 

 amount of mRNA present in the cell. This again is certainly a possibility, 

 although the introduction of this modification in the equations is dictated 

 more by the necessity of obtaining an integrable system, than by any logic 

 about the degradation kinetics of the mRNA for DNA-ase synthesis in lily 

 anthers. The effect of the modification is to make the equations more non- 

 linear than they were. This might be expected to have certain statistical conse- 

 quences, and we will now see what these are. 



Equations (93) can be rewritten in the form 



1 dXr _ ^r r 



Yr~di ~ A,+k,Y~ ' 



— = CC,Xr-Pr 



The steady states are the same as for the original equations, and we use the 

 same notation, p, and qr, for these quantities. We now introduce the transfor- 

 mations 



, Xy Af-\-kf If 

 x, = \og — , \+yr = 75 



where again Q,= A, + k,q,. Therefore A', =/),e'% and the differential equa- 

 tions take the form 



dXr 

 di 



t 'V'ryr J 



^Jl = oc,pXe-^^-l) = ^Xe-^>-l) 



