Intracellular transport by single-headed kinesin KIF1A: Effects of single-motor mechanochemistry and steric interactions

In eukaryotic cells, many motor proteins can move simultaneously on a single microtubule track. This leads to interesting collective phenomena such as jamming. Recently we reported [Phys. Rev. Lett. 95, 118101 (2005)] a lattice-gas model which describes traffic of unconventional (single-headed) kinesins KIF1A. Here we generalize this model, introducing an interaction parameter $c$, to account for an interesting mechanochemical process. We have been able to extract all the parameters of the model, except $c$, from experimentally measured quantities. In contrast to earlier models of intracellular molecular motor traffic, our model assigns distinct “chemical” (or, conformational) states to each kinesin to account for the hydrolysis of adenosine triphosphate (ATP), the chemical fuel of the motor. Our model makes experimentally testable theoretical predictions. We determine the phase diagram of the model in planes spanned by experimentally controllable parameters, namely, the concentrations of kinesins and ATP. Furthermore, the phase-separated regime is studied in some detail using analytical methods and simulations to determine, e.g., the position of shocks. Comparison of our theoretical predictions with experimental results is expected to elucidate the nature of the mechanochemical process captured by the parameter $c$.

Figure 1

A biochemical cycle of a KIF1A motor (upper) and a three-valued discrete model for traffic of interacting KIF1A motors on a finite microtubule filament (lower). The states left to the dotted line in the upper figure correspond to strongly bound to microtubule states (state 1) while those right are weakly bound (state 2). 0 denotes an empty site, and only 2 can move either to the forward or backward site. Transition from 1 to 2 occurs at the same site which corresponds hydrolysis, and the detachment also happens in this process. The attachment is possible only at the empty sites. At the minus and plus ends the probabilities are different from those at sites in the bulk.

Figure 2

Schematic description of the three-state model of a single-headed kinesin motor that follows a Brownian ratchet mechanism. In the special case $2X\to 1X$, which has not been shown explicitly for the sake of simplicity, the rate constants would get modified following the prescriptions described in the text.

Figure 3

The two forms of the time-dependent potential used for implementing the Brownian ratchet mechanism.

Figure 4

The biochemical cycle of KIF1A is shown to define some important parameters which can be extracted from experimental data. See text for more details.

Figure 5

Fisher-Kolomeisky multistep chemical kinetic model of molecular motors.

Figure 6

In the absence of attachment and detachment, our model is equivalent to Fisher-Kolomeisky model shown in Fig. 5.

Figure 7

Fundamental diagram (i.e., flux-versus-density relation) for the traffic flow of KIF1A in our model.

Figure 8

(Color online) Space-time plot of the model system for $c=1$. Each row of squares represents the state of the system at one single instant of time whereas successive rows (in the upward direction) correspond to the state of the system with increasing time. The blue and red squares indicate kinesins in the states 1 and 2, respectively, while the white squares correspond to empty binding sites on the microtubule. Total number of binding sites is 600, and the configurations of the system are displayed for the last 1200 time steps of a simulation run up to a total of $2\times {10}^5$ time steps, starting from an initial state where all the binding sites on the microtubule were empty. The other model parameters are ${\omega }_a=0.3$, ${\omega }_d=0.2$, ${\omega }_h=400$, ${\omega }_f=600$, ${\omega }_s=200$, ${\omega }_b=50$ for bulk, and $\alpha =50$, ${\beta }_1={\beta }_2=700$, ${\gamma }_1={\gamma }_2=\delta =0$ for boundaries.

Figure 9

(Color online) An example of a density profile with shock obtained by integrating the mean-field equations as well as that of numerical result. Parameters are ${\omega }_h=200$, ${\omega }_a=0.01$.

Figure 10

Shock position as function of ${\omega }_a$ and ${\omega }_h$ obtained from STP simulations.

Figure 11

Variation of the shock positions with the interaction parameter $c$ for system size $L=3000$, ${\omega }_d=0.1$, and top: ${\omega }_s=55$, ${\omega }_f=145$, ${\omega }_a=0.007$, ${\omega }_h=180$; middle: ${\omega }_s=100$, ${\omega }_f=200$, ${\omega }_a=0.1$, ${\omega }_h=300$; bottom: ${\omega }_s=100$, ${\omega }_f=300$, ${\omega }_a=0.01$, ${\omega }_h=130$.

Figure 12

Phase diagram of this system without Langmuir dynamics.

Figure 13

(Color online) A “cometlike” structure formed by kinesins (red) on the microtubule (green). The high-density and low-density regions are clearly separated in this image. The white bar length is $2\mu \mathrm{m}$.

Figure 14

Schematic description of a general three-state model of a single molecular motor.