1 30 TEMPORAL ORGANIZATION IN CELLS 



It is worth noting that in the system without strong interactions between 

 components the condition x^ = .v,X; = jc} can never be satisfied, so that 

 entrainment cannot occur. This is seen from the following: 



00 

 -Pi 



Writing / = ^c{x]l2), this becomes 



00 



lA. = Y1 I t^i'^e-'dt 



-P(ciPi^l2) 



For j8 very small (6 very large), the integral is nearly r(3/2) = ^/(tt)/!. In the 

 limit of small jS we also have 



Zp 



so that 



' ^ wliScJ 



On the other hand 



1 



X{Xj 



Zpi^Pi J J 



-Pi -Pi 



Each of the integrals is easily transformed by the substitution t = jSc,oc^/2 to 

 the form 



00 



which for very small § is approximately 1/^c,. Using the approximate values for 

 the phase integrals in the limit of small ^, we get 



26 



TTy/{CiCj) 



The condition ^^ = x] therefore reduces to c-, = Cj, which is the same as 

 ^i^i/Qi = o^j^jIQj- This can be satisfied without requiring an identity of micro- 

 scopic parameters. But even with c, = Cj we get XjXj = I^/ttc,-, which clearly 

 can never be equal to a-^ = d/cj. In dynamic terms the reason for the absence of 

 entrainment in the system is simply that the type of coupling which we have 



