Kinetic discrimination of a polymerase in the presence of obstacles

One of the causes of high fidelity of copying in biological systems is kinetic discrimination. In this mechanism larger dissipation and copying velocity result in improved copying accuracy. We consider a model of a polymerase which simultaneously copies a single-stranded RNA and opens a single- to double-stranded junction serving as an obstacle. The presence of the obstacle slows down the motor, resulting in a change of its fidelity, which can be used to gain information about the motor and junction dynamics. We find that the motor's fidelity does not depend on details of the motor-junction interaction, such as whether the interaction is passive or active. Analysis of the copying fidelity can still be used as a tool for investigating the junction kinetics.

Figure 1

A simple model of a polymerase on a single-stranded DNA that serves as a template for copying. The motor is located on the border between a single- and double-stranded DNA. It can move forward while polymerizing an additional nucleotide onto the complementary strand, or it can move backward while removing a base from this strand. At the same time, the obstacle can move forward, or if the motor is far enough, the obstacle can move back, as the double strand closes.

Figure 2

(a) Mean polymerization velocity as a function of monomer concentration $\left[C\right]$. (b) The copying fidelity of the polymerase as a function of monomer concentration. In both panels, the lines represent the theoretical prediction, obtained from the steady-growth ansatz. Symbols represent the results from a Monte Carlo simulation of the model.

Figure 3

Schematic drawing of the potential of the elastic interaction between the polymerase and the junction as a function of the distance between them.

Figure 4

(a) Mean polymerization velocity as a function of monomer concentration $\left[C\right]$. Different curves represent different motor-junction interaction parameters, while kinetic parameters of the junction are kept constant ($q^{+}=1$). (b) The copying fidelity of the polymerase as a function of monomer concentration. Symbols correspond to results from stochastic simulations, whereas lines depict analytical results. The collapse of three lines onto a single curve shows that details of the interaction have no effect on the fidelity, namely, that the error rate for any value of $U_0$ and $n$ is the same as for the hard wall interaction. The solid line and the triangles correspond to a polymerase without an obstacle. Such a freely propagating polymerase exhibits considerably higher fidelity.