A Closed Network of RNA Polymerase Flow Models for Analyzing Intracellular Transport

We present a network of several RNA polymerase flow models (RPFM) interconnected through a finite pool of resources. We prove that the network always approaches a steady-state by using tools from the theory of cooperative systems having a first integral. Through theoretical framework and simulations, our analysis shows that increasing any of the forward (backward) rates in any of the RPFMs yields a local effect, an increase (decrease) in the output rate of this RPFM, and a global effect, the output rate of other RPFMs all increases or all decreases. Through simulation, we also show that sometimes increase in backward rates in an RPFM is related to an increase in the total output rate of the network. We believe that the network of RPFMs can provide deep insights into analyzing many natural and artificial systems.