Figure 4.
Motility diagrams for the three different microtubule gliding assays studied experimentally in Refs. (16–18) as a function of the parameters η and Nf/N: (A) For wild-type and mutant kinesin-1 motors (18), (B) for OSM-3 and kinesin-II motors (16), and (C) for Xklp1 and Xkid motors (17). (Open red circles) Numerical results for the lower and upper critical values ηl and ηu. (Solid blue and green curves) Obtained from analytical approximations of Eqs. 5 and 6, respectively (see also the Supporting Material). (Stars) Critical points. The region enclosed by red open circles represents the bistable motility regime. This is further illustrated by the insets in (A), which show velocity distributions from the master equation approach for values (a) η = 5.0, (b) η = 1.5, and (c) η = 0.5 at Nf/N = 0.5. In the bistable motility regime, the velocity distribution is bimodal (inset b), while there is only one stationary state with a unimodal velocity distribution outside of this region, corresponding to slow transport (inset a), or fast transport (inset c). The bifurcation diagram in Fig. 3 shows the detailed bifurcation behavior (vertical dashed black line) in diagram A. (Horizontal dashed green lines) Parameters explored experimentally in (A) Larson et al. (18) and (C) Bieling et al. (17). In Pan et al. (16), a value η = 3.3 outside the diagram B was realized experimentally.