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 pushes 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 activation rate of the machine 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 behaviour as a function of the activation frequency, and the velocity follows a Michaelis-Menten (MM) law that arises naturally in this description. The estimation of the stall force of the motor follows a corrected MM law which yet is to be checked in experimental investigations. The results presented here agree with recent biological experimental findings.