408 PRINCIPLES OF EMBRYOLOGY 



Thus if initially in a certain region the supply o£A is increased relative to 

 that of C, we find that P will be increased relative to Q by something 

 more than a proportionate amount, the excess being expressed by the last 

 term on the right. And if the rate of removal of P, (that is k^), is greater 

 than the rate at which P breaks down again into A and B, (that is kz), 

 this excess can be considerable. We can also see from expression (2) that 

 the exaggeration will be the more important the smaller the absolute 

 values of P and Q; and these will also be reduced if ^3 is fairly large, so 

 that P and Q are rapidly removed. 



■*■ A 



^ — — *■ 



Figure 19.1 



A system of competing chemical reactions, by which substances A, B and 

 C become converted into P or Q. See text. (From Waddington 1954a.) 



Without going into further details, we can see that if two autocatalytic 

 processes compete for raw materials, we may under some conditions find 

 that an initial change in the supply of the materials produces an exagger- 

 ated effect on the steady-state concentrations of the synthesised products, 

 and thus on the rates at which these products can be made available out- 

 side the system. 



If we suppose that .4, B, and C are the raw materials out of which two 

 genes manufacture their immediate products P and Q, we have now deve- 

 loped a picture by means of which we can see how a change in the con- 

 centrations of these raw materials leads to exaggerated differences in the 

 rate at which P and Q are passed out of the nucleus into the cytoplasm. 



It is, however, by no means the only model which might be appropri- 

 ate. As Delbriick (1949) has suggested, there might be direct interactions 

 between the two synthetic processes. These are perhaps most simply 

 formulated by supposing that P is destroyed at some rate proportional to 

 the concentration of Q (and vice versa). The equations for dPjdt and 

 dQjdt will then contain terms in PQ. If we regard the system as closed. 



