Michaelis-Menten dynamics of a polymer chain out of a dichotomous   ATP-based motor
  We present a model of an ATP-fueled molecular machine which push a polymer through a pore channel. The machine acts between two levels (working-waiting), and the working one remains active for a fixed time giving a constant force. The machine activation rate can be put in relationship with the available ATP concentration in the solution, which gives the necessary energy supply. The translocation time shows a monotonic behavior as a function of the activation frequency and the velocity follows a Michaelis-Menten law that arises naturally in this description. The estimation of the stall force of the motor follows a corrected Michaelis-Menten law which still is to be checked in experimental investigation. The results presented agree with recent biological experimental findings. 
Alessandro Fiasconaro, Juan Jos\'e Mazo, Fernando Falo
cond-mat.soft physics.bio-ph q-bio.BM