Reversible association with motor proteins (RAMP): A streptavidin-based method to manipulate organelle positioning

We report the development and characterization of a method, named reversible association with motor proteins (RAMP), for manipulation of organelle positioning within the cytoplasm. RAMP consists of coexpressing in cultured cells (i) an organellar protein fused to the streptavidin-binding peptide (SBP) and (ii) motor, neck, and coiled-coil domains from a plus-end–directed or minus-end–directed kinesin fused to streptavidin. The SBP–streptavidin interaction drives accumulation of organelles at the plus or minus end of microtubules, respectively. Importantly, competition of the streptavidin–SBP interaction by the addition of biotin to the culture medium rapidly dissociates the motor construct from the organelle, allowing restoration of normal patterns of organelle transport and distribution. A distinctive feature of this method is that organelles initially accumulate at either end of the microtubule network in the initial state and are subsequently released from this accumulation, allowing analyses of the movement of a synchronized population of organelles by endogenous motors.

In the bidirectional cargo transport model by Muller et al. [1], a cargo is transported by a team of N+ microtubule plus-end-directed and N-microtubule minus-directed motors which attach and detach from a microtubule stochastically with given on and off rates. The force-velocity relation for the motors was assumed to be a linear function of the applied load, and forcedissociation rate of the motors was assumed to be an exponentially increasing function of the load. When bound to the microtubule, the motor walks forward with the velocity " , which decreases linearly with the external force and reaches zero at the stall force The rates for unbinding of one of the bound motors from microtubule and for binding of an additional unbound motor to microtubule are found based on the assumption that (i) the presence of opposing motors induces a load force, and (ii) each plus-end directed motor feels the load 2 (and generates the force − 2 ), and each minus-end directed motor feels the load − 3 (and generates the force 3 ).
Thus, the force experienced by a cargo being pulled by pulled by 2 plus-end directed motors and 3 minus-end motors is given by The sign of the force is taken as positive if a load was on the plus-end directed motors (i.e., if the force pointed into the minus-end direction).
The net unbinding rate for the plus-end directed motor is where e+ indicates unloaded unbinding rate of single plus-end directed motor. The net rate for the binding of one plus-end directed motor is where p+ is the binding rate of a single plus-end directed motor. The index "+" labels the plus-end directed motors properties and index "−" labels the minus-end directed motors properties.
The cargo force 5 is determined by the condition that the plus-end directed motors, which experience the force 5 2 ⁄ , and the minus-end directed motors, which experience the force − 5 3 ⁄ , move with the same velocity, which is the cargo velocity 5 : Here, the sign of the velocity is taken positive in the plus-end direction and negative in the minusend direction.
In the case of stronger plus-end directed motors, 2 &2 > 3 &3 , the cargo force and velocity are given by the expressions and In this case, the cargo moves to the plus-end direction with velocity 5 > 0.
In the opposite case of the stronger minus-end directed motors (i.e., 2 &2 < 3 &3 ), in eqs. (6) and (7), the plus-end directed motor forward velocity "2 has to be replaced by its backward velocity (2 , and the minus motor backward velocity (3 has to be replaced by its forward velocity "3 . The cargo moves into the minus-end direction with velocity 5 < 0. In case an external force KLM is acting on the cargo, equation (2) can be written as 2 2 = − 3 3 + KLM (8) and 5 can be written as If cargo moves toward minus-end under an opposing force KLM (which is then negative), the plus motor forward velocity "2 should be replaced by its backward velocity (2 , and the minus motor backward velocity (3 by its forward velocity "3 Hence, in this case cargo velocity is given by In the next section, we described our model geometry and how bidirectional tug-of-war models was extended to understand organelle positing by a team consisting of KIF5B, KIF1Bβ and dynein motors in a WT HeLa cell line.

Tug-of war model for lysosome transport
We model the cell (HeLa) as hemisphere of radius (Rcell = 16 µm) and the nucleus was also considered as a hemisphere of radius (Rnucleus = 6 µm), as experiments were done with cells adhered to surface with average cell and nucleus diameters roughly ~ 32 µm and 12 µm, respectively (from microscopy images and measured using ImageJ). Microtubules were modelled as lines joining the nucleus to the cell periphery. We assumed that each cargo was transported along a separate microtubule and there was no steric hindrance among cargos while traveling on microtubules. Hence, assuming multiple cargos traveling on a single filament is not going to change our simulation results.
Due to the spherical symmetry of our model, we used spherical polar coordinates (r, θ, φ) to define the position of each cargo. The values of [0, /2] and [0,2 ] for each cargo were chosen randomly by Marsaglia's algorithm [2]. The initial radial position (r) of the cargo (central clustered, peripherally accumulated or normal steady-state distribution) was chosen according to the experiment to be modelled.
In our model, cargoes move radially along microtubules whose runs, pauses, reversals and detachments were simulated using bidirectional cargo transport model by Muller et al. [1].
Our WT HeLa cell line has only three different types of motors that move lysosomes [3]: kinesin-1 (KIF5B), kinesin-3 (KIF1Bβ) and dynein. Then, we had to extend the model from Muller Equation (2), which represents the force experienced by the cargo, is replaced by where Y , Z and [ represent number of kinesin-1 (KIF5B), dynein and kinesin-3 (KIF1Bβ) motors pulling the cargo, respectively.
The net unbinding rate for motors is given by and, force acting on the cargo is given by, If the plus end motors are weaker than the minus end motors i.
Z then the velocity of cargo is given by, and, force acting on the cargo is given by In our model, run lengths and run velocities, individual cargo trajectories were generated using the Gillespie algorithm as used by Muller et al. [1,4] for the motor attachment/detachment kinetics.
Simulations were performed to generate 500 cargo trajectories each trajectory starting from initial radial position (r) of the cargo (central clustered/peripherally accumulated/normal steadystate distribution) and randomly chosen angular position i.e. and . To model cargo release from the cell periphery (due to dissociation of mCh-KIF5B*-strep from lysosomes after biotin addition) we put r = Rcell for each cargo with Y = 1, Z = 2 and [ = 8 motors. To model cargo release from cell center (due to dissociation of strep-KIFC1*-mCh after biotin addition) we put r = Rnucleus for each cargo with Y = 1, Z = 2 and [ = 8 motors. For control experiment, i.e. normal steady-state distribution, the radial positions of the cargoes were chosen randomly between the value of Rnucleus and Rcell with Y = 1, Z = 2 [ = 8 motors.
In our simulations, cargo was allowed to move with the velocity 5 in the intervals between the attachment/detachment events. Simulations were performed until all motors were detached or a total simulation time of 30 minutes was reached. Parameters used in simulations are given in Supplementary Table 1. Binding rate (s -1 ) Ŷ 1.0 (for r < r0) # 0.0 (for r > r0) # Ẑ 5.0 [5] [ 6.0 [8,9] Unbinding rate (s -1 )

[6]
# Kinesin-1 motors were found to be active near the nucleus only, by Guardia et al. [10]. Hence, binding rate of kinesin-1 set to zero for r > r0. $ Kinesin-3 motors were found active away from nucleus [10]. Soppina et al. [8] predicted that binding rate of kinesin-3 increases due to the presence of K loop which has not been measured experimentally. The binding rate of kinesin-3 is predicted to be between 0.1 s -1 to 10.0 s -1 by Nishinari et al. [9]. r0 is the radial distance which was taken randomly between 8 µm and 10 µm in each microtubule in the cell.