64 



TEMPORAL ORGANIZATION IN CELLS 



Xi is not/7, but is always greater than this value. And if we assume a form of 

 self-replicating kinetics for messenger RNA synthesis, as we do in Chapter 8, 

 then an interesting discontinuity arises in the most probable value of X,-. 

 However, for the simple system with which we are now dealing the probability 

 distributions for the variables are very regular, most probable values coinciding 

 with steady state values. 



Consider now the phase averages of the functions defined by 





BG 



dG 



By, 



(30) 



These are loose analogues of kinetic energy in mechanical systems, and we may 

 expect that their phase averages will tell us something about the parameter 6, 

 the talandic temperature. 



00 00 



-Pi 



-Pi 



00 00 



-e J (x,+pd^(e-<^-")dx,l j e-^^J'dx, 



Pi 



-Pi 



= \-d[{Xi+Pi)e-''^'l^]^^^ + d J e-^V« Jx,| / J e-^V^^x,- 



d 



Now 



dG 



(^.•+/'/)^ = Ci(Xi + Pi)Xi 



= Ci(x]+PiXi) 



= c^[{X,-pd^+p^iX,-pd] 

 in the original variables. Therefore the result can be written in the form 



c,(X!-Piy+p,cxXi-Pi) = e 



(31) 



