PHYSICAL REVIEW E 88, 022714 (2013) Transport dynamics of molecular motors that switch between an active and inactive state I. Pinkoviezky and N. S. Gov * Department of Chemical Physics, Weizmann Institute of Science, P.O. Box 26, Rehovot, Israel 76100 (Received 6 May 2013; revised manuscript received 11 June 2013; published 20 August 2013) Molecular motors are involved in key transport processes in the cell. Many of these motors can switch from an active to a nonactive state, either spontaneously or depending on their interaction with other molecules. When active, the motors move processively along the filaments, while when inactive they are stationary. We treat here the simple case of spontaneously switching motors, between the active and inactive states, along an open linear track. We use our recent analogy with vehicular traffic, where we go beyond the mean-field description. We map the phase diagram of this system, and find that it clearly breaks the symmetry between the different phases, as compared to the standard total asymmetric exclusion process. We make several predictions that may be testable using molecular motors in vitro and in living cells. DOI: 10.1103/PhysRevE.88.022714 PACS number(s): 87.10.−e, 05.20.−y, 05.60.Cd I. INTRODUCTION Unconventional myosin motors participate in many im- portant transport processes within the cell. Examples range from transporting cargo within the cell such as mRNA or mitochondria to anchoring organelles and even organizing the actin tracks on which they move [1]. Molecular motor traffic is usually modeled as a total asymmetric exclusion process (TASEP) with several general- izations. This includes incorporating attachment/detachment dynamics [2,3], the chemomechanical cycle [4,5], coupling the growth of the track to the occupation of motors [6–10], and many more. In the simplest version the TASEP is a one-dimensional driven lattice gas where particles hop asyn- chronously to the site on the right if it is empty. Already this simple one-dimensional process exhibits a rich phase diagram with both first- and second-order phase transitions [11]. Among many processes myosin motors play a key role in the formation of filopodia [12,13] [see illustration in Fig. 1(a)]. These structures are 1–10 μm[14] protrusions emanating from the cell’s membrane. In each filopodium there is a bundle of actin filaments which polymerize at the tip and depolymerize at the base of the filopodium. Due to this mechanism, the track itself is effectively moving backward. This backward (“retrograde”) motion is characterized by a retrograde velocity. Myosin motors enter the filopodium at the base, where the filopodium is open to the cell cytoplasm. Usually, myosin motors move toward the protrusion tip (the barbed end of the actin polymer), with the exception of Myo-VI. Several exper- iments have found [12,13,15–17] that in addition to the tip- directed motion of the motors (with velocity ∼0.5 μm/sec), a backward motion of the myosins is observed. The velocity of this motion is of the order of the retrograde velocity of the actin track (∼0.01 μm/sec) which suggests that this motion is due to jammed or inactive motors. It was further shown at the single-molecule level [16] that some myosin motors do not move forward but move backward with a velocity that matches the retrograde velocity of the actin, implying that they are inactive or jammed. * Corresponding author: nir.gov@weizmann.ac.il Further studies have shown that the tail domain of several myosins can interact with the motor domain thus sponta- neously inhibiting their own activity [18–20]. It was shown in [20] that the inhibited form corresponds to a monomeric form of the myosin. In this form the ATP hydrolysis rate is reduced substantially, but the residual ATP activity indicates that the motor can bind to the actin filament. The monomeric form is not processive and once an ATP hydrolysis cycle is completed the motor detaches. However since the ATP hydrolysis rate is reduced the motor can stay on the actin track for a long time. Another example of an inactive state is the myosin-IIIa motor [21] which is processive only in the presence of its cargo molecule. Even in the absence of the cargo the motor can still bind the actin filament, with reduced affinity [22]. In both cases the inactive form detaches more easily from the actin, which is a process that is beyond the current model. The fate of motors at the tip is not well characterized at present. It is considered that motors may get jammed on the filaments, detach, or participate in a variety of chemical reactions at the tip. Guided by these findings we consider here a simplified model based on TASEP where each particle can be in two states: active and inactive. When active, the motors move unidirectionally along the filaments, while when inactive they are stationary on the filaments. These two states describe in a coarse-grained manner the different possible conformations of the motors, which were discussed above. We will treat here the simple case of spontaneously switching motors, while more complex motor-motor interactions can also be present (see for example [22]). We extend the work presented in [23] on periodic systems to systems with open boundary conditions. Several works in the past dealt with particles with internal degrees of freedom either with a conservation law [24–26] or as a process with two tracks [27,28] (so particles with two different states can be at the same site). In [29]a process where the switching between states is dependent on the occupancy of adjacent site was studied. A process with more than one internal state was also considered in [30] but the current was calculated with a mean-field approximation (MFA), where in [23] we presented a treatment that treats correlations beyond the MFA, and demonstrated its need for describing this strongly correlated system. 022714-1 1539-3755/2013/88(2)/022714(10) ©2013 American Physical Society