A Fast-Regulation Model for Transcription

The fast subsystem stationary state complies with chemical equilibrium, which is characterized by states D and Dp having equal chemical potentials. Concomitantly, there is no net flux of chemical energy associated with the fast subsystem. The stationary state of the slow subsystem does not comply with chemical equilibrium. Consequently the chemical potentials of states Dp + S and D + P + M obey the following inequality 

However, since fiop = IJ d + fJ-p, it follows from the above inequality that 

That is, the substrates out of which RNA molecules are made have a higher chemical potential than RNA molecules themselves. Thanks to this difference there exists a nonzero rate of conversion of S molecules into RNAs given by 

There exists also a chemical difference between state M and state Y (which represents the products of RNA degradation) /xm Mr - Furthermore, the RNA degradation rate equals the rate of production of this molecule in the stationary state. From all these considerations, the rate of heat dissipation in this system is 

In accordance to the first law of thermodynamics, energy has to be supplied to the system at the same rate to keep it constant. This occurs through the constant addition of S molecules and the constant removal of Y molecules. 

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