RNA POLYMERASE ON DNA AS A FERMI SYSTEM: INTERNAL ENERGY, ENTROPY, HEAT CAPACITY, AND NEGATIVE TEMPERATURE

Abstract

The distribution function of RNA polymerase enzymes bound at specific and nonspecific sites of the DNA is studied by means of Fermi statistics. To this end, a model proposed earlier in the literature is used that consists of a finite number of discrete nonspecific binding sites and one specific site: the DNA promoter. Exact expressions for entropy, energy and specific heat as functions of the number of binding sites and the number of RNA enzymes are obtained. It is shown that the many-body system of bound RNA polymerase exhibits negative temperature at very low transcription rates. We speculate that negative temperature may be used as a thermodynamic mechanism to produce a pressure for transcription.