Molecular motors are known to run on ATP, generating either rotation, or linear displacement. The latter type is observed in the enzymes that catalyze the replication of DNA. The speed of these linear motors has been measured and shown to depend on the tension applied to the DNA stand. The linear motor runs along a single-strand (ss) DNA molecule and replicates its template base, transforming it to a double-strand (ds) geometry through repeated capture and pairing in of the correct free nucleotides (dNTP). At the end of this catalytic cycle, the dsDNA reverts to two ss templates. The polymerase then repeats this catalytic process. The mechanical tension is applied during the replication process between the ds and ss ends. One of these ends is fixed at a stationary surface, and the other is attached to a plastic bead. The force creating the tension is applied with optical and magnetic tweezers.
We have developed a theoretical model that describes the speed of the linear motor as a function of the applied force and of the width of the resonances present in the processes that define the reaction rate. This width is a characteristic of each type of motor or enzyme, determining the phase space of the corresponding reactions. It can be determined from the quantum chemistry of the corresponding activation energies and reaction kinetics.
The above-mentioned resonances lead to a characteristic structure in the curve that expresses the dependence of the motor speed on the applied force or resulting tension, in a given embedding solution, at a given temperature. The speed is noticed to be optimal at a tension that corresponds to the fluctuating natural operating conditions of the motor. The analytical expression obtained by us opens the way for a derivation of the rate fluctuations present in the catalytic process, including also the quantum 1/f noise present in the motor speed.
Peter H. Handel
Department of Physics and Astronomy, University of Missouri-St. Louis
8001 Natural Bridge, St. Louis, MO 63121 USA
Phone: 314-5165021 Fax: 314-5166152