On-line references: *A Practical Guide to Optical Trapping* by Joshua Shaevitz https://www.eg.bucknell.edu/~phys310/experiments/Tweezers/OT_Practicle_Guide.pdf ~~ Work in progress ~~ Pictured below are simulations of molecular motors transporting microparticles that are subject to optical trap forces centered at $x = 0$. The key constraint is that the particles are constrained to one side of a plate that is located at $z=0$ and the motor is bound to a microtubule fixed to the plate. We assume the motor has a worm-like chain tether that has a contour length of 50 nm and is connected to the surface of the particle. #### Visualization of one optical trap run. A 20nm bead tethered to a kinesin-1-like motor. Black dots indicate where the motor is (phenomenologically) anchored. The anchor takes 8nm steps at rates depending on current load. The particle center location (blue) is the $(x,z)$-coordinate of the minimal potential energy of the motor-cargo-trap system. **Determination of the center of the particle through a balance-of-forces calculation is the key part of the model** Red dots indicate where the motor tether is bound to the cargo surface. | Motor Property | Notation | Value | Units | | -----------------------: | :------------: | :---: | :------------: | | Unburdened stepping rate | $v_0$ | 0.8 | $\mu/\text{m}$ | | Stall Force | $F_s$ | 7 | $\text{pN}$ | | Detachment Force | $F_\text{det}$ | 6.1 | $\text{pN}$ | | Trap Property | Connection | Notation | Value | Units | | -----------------: | :--------------: | :------: | :---: | :--------------------: | | Spring Constant | Trap <--> Cargo | $\alpha$ | 40 | $\text{pN}/\text{m}$ | | Contour Length | Motor <--> Cargo | $L_c$ | 0.5 | $\mu\text{m}/\text{m}$ | | Persistence Length | Motor <--> Cargo | $L_p$ | 0.002 | $\mu\text{m}/\text{m}$ | ![[fig_motor_cargo_trace_WLC.png]] ![[fig_motor_cargo_trace_Spring.png]] #### Animation We can also visualize these same paths through an animation. **Worm-like chain** run ![[mc_WLC_mov_R20zoom.gif]] **Hookean spring** run ![[mc_Spring_mov_R20zoom.gif]] --- The vertical direction of the force leads to faster detachment times. If we (unphysically) remove the interference of the wall, the runs are typically longer. Here is the run of a 10nm radius bead. ![[fig_motor_cargo_trace_NO_WALLWLC_R100.png]] and the associated time series ![[mc_WLC_mov_NO_WALL_R100zoom.gif]] Triple Bead Assay ![[tb_worm_mov_L1000.gif]] --- Large particle: $R = 500$ nm with worm-like chain motor-cargo tether ![[mc_WLC_mov_R500.gif]] --- $R = 500$ nm, with Hookean spring motor-cargo tether ![[mc_Spring_mov_R500.gif]] $R = 20$ nm, with worm-like chain motor-cargo tether ![[mc_WLC_mov_R20.gif]] $R = 20$ nm, with worm-like chain motor-cargo tether ![[mc_Spring_mov_R20.gif]]