(a) Root mean square deviation RMSD between the experimental data (green bars in Fig. 3 (c, d)) and the simulated dwell time distributions for the three-cycle network as a function of the gating parameter for [ATP] = 10 (crosses) and [ATP] = 2 (circles).

<p>A lower deviation indicates an improved agreement between the experimental values and the distributions that result from the three-cycle network. For both concentrations, the RMSD decreases with increasing , until it saturates for , as indicated by the dashed line. The fluctuations for large values of arise from the variance in the simulations. The solid lines serve as a guide to the eye. (b) In case of a variable ATP binding rate , the agreement between the simulated dwell time distributions (symbols) and the experimental data (green bars) is further improved. The agreement is optimal for (red crosses), and is significantly improved in contrast to the distribution based on the experimental value of (red circles). The inset shows the RMSD as a function of , illustrating the minimal deviation for </p

(a) Typical stepping trajectory, i.e., spatial displacement as a function of time and (b) dwell time distribution of myosin V, adapted from [4].

<p>(a) In single-molecule experiments with a feedback loop, the data are monitored under constant external load. Hence, the distance between the bead monitoring the motor’s motion (upper gray trajectory, with the thin black line showing a filtered curve) and the trap center (black trajectory) remains constant. (b) Dwell time distribution of myosin V for saturating [ATP]. The solid line is a fit from Ref. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0055366#pone.0055366-Rief1" target="_blank">[4]</a> that involves two exponential functions with decay rates 150/s and 12.5/s.</p

Dwell time distributions (a) for high assisting forces, for (b) and (c, d) for substall and superstall resisting forces, for [ATP], [ADP] and zero [P] with the data from [<b>4]</b>, <b>[7]</b>.

<p>The blue lines show obtained using the single cycle network for . In (c) the distribution of forward steps, (brown, dashed line) agrees with the data that does not exhibit rapid events as in . (d) Forced backward stepping for leads to a single exponential decay (dashed violet line) that arises through the mechanical transition in the network in Fig. 2(b).</p

Transition rates for the uni-cycle network.

<p>Transition rates for the network displayed in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0055366#pone-0055366-g002" target="_blank">Fig. 2(a)</a> for , as determined experimentally in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0055366#pone.0055366-deLaCruz1" target="_blank">[3]</a> (*) and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0055366#pone.0055366-Rief1" target="_blank">[4]</a> (**), from simulations <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0055366#pone.0055366-Craig1" target="_blank">[35]</a> (^†), and earlier work <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0055366#pone.0055366-Bierbaum1" target="_blank">[19]</a>(^‡).</p

Dwell Time Distributions of the Molecular Motor Myosin V

<div><p>The dwell times between two successive steps of the two-headed molecular motor myosin V are governed by non-exponential distributions. These distributions have been determined experimentally for various control parameters such as nucleotide concentrations and external load force. First, we use a simplified network representation to determine the dwell time distributions of myosin V, with the associated dynamics described by a Markov process on networks with absorbing boundaries. Our approach provides a direct relation between the motor’s chemical kinetics and its stepping properties. In the absence of an external load, the theoretical distributions quantitatively agree with experimental findings for various nucleotide concentrations. Second, using a more complex branched network, which includes ADP release from the leading head, we are able to elucidate the motor’s gating effect. This effect is caused by an asymmetry in the chemical properties of the leading and the trailing head of the motor molecule. In the case of an external load acting on the motor, the corresponding dwell time distributions reveal details about the motor’s backsteps.</p> </div

Motor velocity as a function of external load for the network formed by the cycle (lines) compared to experimental data (symbols) for varying [ATP].

<p>In the experiments, the concentrations of ADP and P are believed to be rather small. In the calculations, we consider the limit of [ADP] = [P] = 0.</p

Chemomechanical networks based on the nucleotide states of the two motor heads at site , with chemical transitions shown as solid blue lines.

<p>The motor can reach states at the neighbouring sites and through mechanical transitions (dashed lines). The motor’s step velocity can be calculated by periodically repeating the networks at site along the spatial coordinate. (a) Uni-cycle network for myosin consisting of the chemomechanical cycle . Dashed red lines show mechanical transitions along the filament coordinate , which emerge from the state TD into the forward and from state DT into the backward direction. Solid lines refer to chemical transitions. The arrows indicate the direction of the transition, and infrequent transitions are shown in grey. This uni-cycle network applies to forces below the stall force . (b) Three-cycle network introduced in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0055366#pone.0055366-Bierbaum1" target="_blank">[19]</a> that captures the myosin’s stepping properties for both sub- and superstall load forces. The network includes ADP release from the leading head and additional forward and backward mechanical transitions for forced stepping (dashed violet line), with the dots pointing into the direction of hydrolysis. In addition to the network cycle , two cycles and are present. While the enzymatic cycle contains only chemical transitions, the mechanical cycle consists only of the mechanical transition . Thus, a spatial displacement can arise by means of the network cycle (dashed red lines) or the mechanical cycle (dashed violet lines).</p

(a–d) Dwell time distributions for different concentrations of ATP and ADP, with [P] = as discussed in the text.

<p>Comparison of distributions calculated using the uni-cycle network in Fig. 2(a) (blue solid lines) with experimental data (green bars) from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0055366#pone.0055366-Rief1" target="_blank">[4]</a>. Insets: Concentrations that apply to both experimental data theoretical curves are shown in the gray panels, while parameters specific to the theoretical results are given in the framed panels. In (a), (c–d), the experimental concentration of ADP is believed to be negligible. For saturating [ATP], (a,b) the dwell time distributions for the uni-cycle network (blue line) agree with those for the network shown in 2(b), for all gating parameters (data not shown). The symbols show simulated data for the network in 2(b) without gating (green circles) and gating with a 10-fold decelerated ADP release from the motor’s leading head (red circles).</p