Modeling the mechanochemistry of the $\varphi 29$ DNA translocation motor

We present a study of the DNA translocation of the bacteriophage $\varphi 29$ packaging molecular motor. From the available experimental information we present a model system based on a stochastic flashing potential, which reproduces the experimental observations such as detailed trajectories, steps and substeps, spatial correlation, and velocity. Moreover, the model allows the evaluation of the power and efficiency of this motor. We have found that the maximum power regime does not correspond with that of the maximum efficiency. This information can stimulate further experiments.

Figure 1

Flashing potential describing the motor cycle. The cycle starts with the dwell phase (orange/dark gray). Once the four ATPs are bound, the burst phase (blue/light gray) begins. The cycle is not fully depicted; in order to complete the cycles two additional substeps are necessary.

Figure 2

Left: Trajectory of the DNA as a function of time for different hindering forces. Right: Corresponding position histogram.

Figure 3

Spatial correlation of the two trajectories in Fig. 2 for a run of 10 s. $F_E=-8\mathrm{pN}$ (top) and $-40\mathrm{pN}$ (bottom).

Figure 4

Spatial correlations for three values of $t_r$, namely, $t_r=0$, 0.1, and 1 ms. The pull force applied is $F_E=-8\mathrm{pN}$.

Figure 5

Average velocity of the strand vs the external hindering force for different concentrations of ATP.

Figure 6

Average velocity of the strand vs [ATP] for different values of the external force.

Figure 7

Power of the motor as a function of the external force for different concentrations of [ATP].

Figure 8

Efficiency of the motor vs the force $F_E$ and two ATP concentrations.