Abstract:Abstract. Motor-driven intracellular transport is a complex phenomenon where multiple motor proteins simultaneously attached on to a cargo engage in pulling activity, often leading to tug-of-war, displaying bidirectional motion. However, most mathematical and computational models ignore the details of the motor-cargo interaction. A few studies have focused on more realistic models of cargo transport by including elastic motor-cargo coupling, but either restrict the number of motors and/or use purely phenomenol… Show more
“…It is remarkable that the expression for stall force in this model, as given by eq.17, is simply the sum of stall forces p-3 [19] for details) in our calculations and numerical simulations are shown here.…”
mentioning
confidence: 66%
“…For a set of K identical motors, we use w ± i = w ± , θ i = θ for 1 ≤ i ≤ K. For set of N = K + D (K plus moving and D minus moving) motors, we choose w ± i = w ± , θ i = θ, for 1 ≤ i ≤ K and w ± i = w ∓ , θ i = 1 − θ, for K + 1 ≤ i ≤ N . A list of the parameters used in simulations are tabulated in tab.1; further details of simulations are to be found in [19]. For a cargo driven by a single motor (K = 1), ψ(∆ 1 ) obtained in computer simulations (symbols), for U e (x 0 ) = −f 1 s x 0 (corresponds to a constant force equal to the stall force of a single motor) and U e (x 0 ) = 0.05x 2 0 (akin to an optical trap) is compared with eq.15 for λ = A = 0 in fig.2(a).…”
We study a generic one-dimensional model for an intracellular cargo driven by N motor proteins against an external applied force. The model includes motor-cargo and motormotor interactions. The cargo motion is described by an over-damped Langevin equation, while motor dynamics is specified by hopping rates which follow a local detailed balance condition with respect to change in energy per hopping event. Based on this model, we show that the stall force, the mean external force corresponding to zero mean cargo velocity, is completely independent of the details of the interactions and is, therefore, always equal to the sum of the stall forces of the individual motors. This exact result is arrived on the basis of a simple assumption: the (macroscopic) state of stall of the cargo is analogous to a state of thermodynamic equilibrium, and is characterized by vanishing net probability current between any two microstates, with the latter specified by motor positions relative to the cargo. The corresponding probability distribution of the microstates under stall is also determined. These predictions are in complete agreement with numerical simulations, carried out using specific forms of interaction potentials. p-2
“…It is remarkable that the expression for stall force in this model, as given by eq.17, is simply the sum of stall forces p-3 [19] for details) in our calculations and numerical simulations are shown here.…”
mentioning
confidence: 66%
“…For a set of K identical motors, we use w ± i = w ± , θ i = θ for 1 ≤ i ≤ K. For set of N = K + D (K plus moving and D minus moving) motors, we choose w ± i = w ± , θ i = θ, for 1 ≤ i ≤ K and w ± i = w ∓ , θ i = 1 − θ, for K + 1 ≤ i ≤ N . A list of the parameters used in simulations are tabulated in tab.1; further details of simulations are to be found in [19]. For a cargo driven by a single motor (K = 1), ψ(∆ 1 ) obtained in computer simulations (symbols), for U e (x 0 ) = −f 1 s x 0 (corresponds to a constant force equal to the stall force of a single motor) and U e (x 0 ) = 0.05x 2 0 (akin to an optical trap) is compared with eq.15 for λ = A = 0 in fig.2(a).…”
We study a generic one-dimensional model for an intracellular cargo driven by N motor proteins against an external applied force. The model includes motor-cargo and motormotor interactions. The cargo motion is described by an over-damped Langevin equation, while motor dynamics is specified by hopping rates which follow a local detailed balance condition with respect to change in energy per hopping event. Based on this model, we show that the stall force, the mean external force corresponding to zero mean cargo velocity, is completely independent of the details of the interactions and is, therefore, always equal to the sum of the stall forces of the individual motors. This exact result is arrived on the basis of a simple assumption: the (macroscopic) state of stall of the cargo is analogous to a state of thermodynamic equilibrium, and is characterized by vanishing net probability current between any two microstates, with the latter specified by motor positions relative to the cargo. The corresponding probability distribution of the microstates under stall is also determined. These predictions are in complete agreement with numerical simulations, carried out using specific forms of interaction potentials. p-2
“…1. We model the stretching of this linkage upon motor stepping with a harmonic spring force of coupling constant k , whose typical stiffness is on the order of 10 −1 pN/nm 28,41,42 , or in the dimensionless microscopic units from Table 1, roughly 1–10.Figure 1Sketch of modeled one-dimensional motor-cargo system with harmonic coupling showing a single motor moving on a discrete lattice of positions n and the cargo moving continuously along a trajectory x ( t ).…”
Section: Methodsmentioning
confidence: 99%
“…A more common alternative to the Glauber ansatz is one with a formulation reminiscent of the Arrhenius equation for chemical reaction rates 18–20,28–31 . In this work, we classify this family of reaction rates as asymmetric exponential (AsEx) rates and further consider two variations of this ansatz.…”
Section: Methodsmentioning
confidence: 99%
“…However, this constraint is insufficient to generate a unique rate formulation, forcing a choice. We identify three of the popular model choices in the literature, which, absent a common nomenclature, we label: Glauber 26,27 , Product Asymmetric-Exchange (P-AsEx) 28–31 , and Difference Asymmetric-Exchange (D-AsEx) 18–20 .…”
Cells are complex structures which require considerable amounts of organization via transport of large intracellular cargo. While passive diffusion is often sufficiently fast for the transport of smaller cargo, active transport is necessary to organize large structures on the short timescales necessary for biological function. The main mechanism of this transport is by cargo attachment to motors which walk in a directed fashion along intracellular filaments. There are a number of models which seek to describe the motion of motors with attached cargo, from detailed microscopic to coarse phenomenological descriptions. We focus on the intermediate-detailed discrete stochastic hopping models, and explore how cargo transport changes depending on the number of motors, motor interaction, system constraints and rate formulations, which are derived from common thermodynamic assumptions. We find that, despite obeying the same detailed balance constraint, the choice of rate formulation considerably affects the characteristics of the overall motion of the system, with one rate formulation exhibiting novel behavior of loaded motor groups moving faster than a single unloaded motor.
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