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. Author manuscript; available in PMC: 2016 Oct 7.

Published in final edited form as: Phys Rev E. 2016 Aug 29;94(2-1):022419. doi: 10.1103/PhysRevE.94.022419

FIG. 17 — Example phase-plane trajectories and density profiles (inset) for general boundary conditions. Insets show ρ_R + ρ_L (blue), ρ_R (red), and ρ_L (green). Red dots are kMC simulation results. The blue dot indicates the left boundary condition and the green dot the right boundary condition. (a) The blue line is $σ_{R} = α_{R} - \frac{1}{2}$ , and the green line is $σ_{L} = α_{L} - \frac{1}{2}$ . (b) The blue line is $σ_{L} = \frac{1}{2} - β_{L}$ , and the green line is $σ_{R} = \frac{1}{2} - β_{R}$ . (c) The blue line is $σ_{R} = α_{R} - \frac{1}{2}$ , and the green line is $σ_{R} = \frac{1}{2} - β_{R}$ . (d) The blue line is $σ_{L} = \frac{1}{2} - β_{L}$ , and the green line is $σ_{L} = α_{L} - \frac{1}{2}$ . The switching rate is 0.1 s⁻¹, bulk motor concentration c = 200 nM, and motor speed 5 μm s⁻¹; other parameters are the reference values of Table I. Arrows indicate the vector field, which has the mathematical form of Eqs. (12) and (13).