Cooperative molecular motors moving back and forth

Abstract

We use a two-state ratchet model to study the cooperative bidirectional motion of molecular motors on cytoskeletal tracks with randomly alternating polarities. Our model is based on a previously proposed model [Badoual et al., Proc. Natl. Acad. Sci. USA 99, 6696 (2002)] for collective motor dynamics and, in addition, takes into account the cooperativity effect arising from the elastic tension that develops in the cytoskeletal track due to the joint action of the walking motors. We show, both computationally and analytically, that this additional cooperativity effect leads to a dramatic reduction in the characteristic reversal time of the bidirectional motion, especially in systems with a large number of motors. We also find that bidirectional motion takes place only on (almost) a-polar tracks, while on even slightly polar tracks the motion is unidirectional. We argue that the origin of these observations is the sensitive dependence of the cooperative dynamics on the difference between the number of motors typically working in and against the instantaneous direction of motion. † Authors with equal contributions 1

Duty ratio of cooperative molecular motors

“…The assumption that the actin filament is in mechanical equilibrium is also made in theoretical studies of intracellular cargo transport [8] and muscle constraction [27]) Our calculation shows that p eff is only slightly smaller than p. This result is very different from our previous findings for motility assays of bidirectional motion, where the elasticitymediated crosstalk effect is substantial. Finally, we note that although in both this and previous studies we found that p eff < p [11,28], the opposite relation cannot be excluded under certain conditions (e.g., when the filament experiences external forces as in single molecule experiments or muscle contraction). We intend to address this opposite scenario in a future publication, in which we investigate the variations in both p (the ATP-hydrolysis related attachment probability) and p eff (which also includes the contribution due to the elastic crosstalk effect) with the muscle contraction velocity.…”

“…These stress fluctuations are the origin of the elasticity-mediated crosstalk effect. Detailed analysis shows that the typical elastic energy stored in the actin filament scales as [10,11] …”

Biased Transport of Elastic Cytoskeletal Filaments with Alternating Polarities by Molecular Motors

“…This result was in marked contradiction with previous theoretical models which predicted that τ rev grows exponentially with N [4]. To resolve this disagreement, we have introduced a model that takes into account the elastic energy stored in the actin bundle due to the action of the working motors [10,11]. The elastic energy modifies the rates at which motors attach to and detach from the actin and eliminates the exponential dependence of τ rev on N .Our previous theoretical treatment of cooperative bidirectional motion was based on a mean field calculation of the actin elastic energy, ignoring both: (i) the sequential order of the polarities of the monomers, and (ii) the positions along the filament where the pulling forces of motors are applied.…”

“…The elastic energy modifies the rates at which motors attach to and detach from the actin and eliminates the exponential dependence of τ rev on N .Our previous theoretical treatment of cooperative bidirectional motion was based on a mean field calculation of the actin elastic energy, ignoring both: (i) the sequential order of the polarities of the monomers, and (ii) the positions along the filament where the pulling forces of motors are applied. The mean field elastic energy scales as E ∼ N N c , where N c is the number of attached motors [10,11]. Within the mean field picture, the bidirectional motion on perfectly a-polar tracks consisting of an equal number of monomers with right-pointing ("positive") and left-pointing ("negative") polarities has no bias, i.e., the intervals of motion in both directions occur with equal probability.…”

“…The results for N ≤ 28 have been derived using a full statistical calculation of the partition function, while for larger N they have been obtained from Monte Carlo simulations. The model parameters were assigned the following values which are representative of myosin II-actin systems [11,12]: βf 2 /2k = 0.002, q = 0.1, and f /λ 0 = 6 µm/sec. Both In the former it decreases with N , while in the latter it saturates and increases again for N > 600.…”