Motor-driven intracellular transport is a complex phenomenon where multiple motor proteins attached  to a cargo are simultaneously engaged in pulling activity, often leading to tug-of-war and bidirectional motion. However, most mathematical and computational models ignore the details of the motor-cargo interaction. A few papers have studied more realistic models of cargo transport by including elastic motor-cargo coupling, but either restricts the number of motors and/or uses purely phenomenological forms for energy-dependent hopping rates. Here, we study a generic Model In which N motors are elastically coupled to a cargo, which itself is subject to thermal noise in the cytoplasm and  an additional external applied force. The motor-hopping rates are chosen to satisfy detailed balance with respect to the energy of stretching. The master equation is converted to a linear Fokker-Planck equation (LFPE), which yields the average positions of the cargo and motors, as well as their fluctuations and correlation functions. We apply this formalism to two specific forms of the hopping rates. Analytical results are obtained for mean cargo velocity , diffusion coefficient and the average force experienced by each motor for arbitrary N, and compared with numerical simulations. The expansion procedure also allows us to quantify load-sharing features among the cargo-bound motors. In general, we observe significant deviations between analytical predictions based on LFPE and the corresponding numerical results , which suggests a prominent role for higher order corrections .
Motor-driven cargo transport is a complex phenomenon where multiple motor proteins 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. Here, we study a generic model in which N motors are elastically coupled to a cargo, which itself is subjected to thermal noise in the cytoplasm and to an additional external applied force. The motor-hopping rates are chosen to satisfy detailed balance with respect to the energy of elastic stretching. With these assumptions, an (N+1)-variable master equation is constructed for dynamics of the motor-cargo complex. By expanding the hopping rates to linear order in fluctuations in motor positions, we obtain a linear Fokker-Planck equation . The deterministic equations governing the average quantities are separated out and explicit analytical expressions are obtained for the mean velocity and diffusion coefficient of the cargo. We also study the statistical features of the force experienced by an individual motor and quantitatively characterize the load-sharing among the cargo-bound motors. The mean cargo velocity and the effective diffusion coefficient are found to be decreasing functions of the stiffness. While increase in the number of motors N does not increase the velocity substantially, it decreases the effective diffusion coefficient which falls as 1/N asymptotically. We further show that the cargo-bound motors share the force exerted on the cargo equally only in the limit of vanishing elastic stiffness; as stiffness is increased, deviations from equal load sharing are observed. Numerical simulations agree with our analytical results where expected. Interestingly, we find in simulations that the stall force of a cargo elastically coupled to motors is independent of the stiffness .
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A few papers have studied more realistic models of cargo transport by including elastic motor-cargo coupling, but either restricts the number of motors and/or uses purely phenomenological forms for energy-dependent hopping rates.
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Model In
model in
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to
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stretching. The
elastic stretching. With these assumptions, an (N+1)-variable
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constructed for dynamics of the motor-cargo complex. By expanding the hopping rates to linear order in fluctuations in motor positions, we obtain
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(LFPE), which yields the average positions of the cargo and motors, as well as their fluctuations and correlation functions. We apply this formalism to two specific forms of the hopping rates. Analytical results
. The deterministic equations governing the average quantities are separated out and explicit analytical expressions
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mean cargo velocity , diffusion coefficient and the average
the mean velocity and diffusion coefficient of the cargo. We also study the statistical features of the
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each motor for arbitrary N, and compared with numerical simulations. The expansion procedure also allows us to quantify
an individual motor and quantitatively characterize the
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features
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In general, we observe significant deviations between analytical predictions based on LFPE and the corresponding numerical results , which suggests a prominent role for higher order corrections
The mean cargo velocity and the effective diffusion coefficient are found to be decreasing functions of the stiffness. While increase in the number of motors N does not increase the velocity substantially, it decreases the effective diffusion coefficient which falls as 1/N asymptotically. We further show that the cargo-bound motors share the force exerted on the cargo equally only in the limit of vanishing elastic stiffness; as stiffness is increased, deviations from equal load sharing are observed. Numerical simulations agree with our analytical results where expected. Interestingly, we find in simulations that the stall force of a cargo elastically coupled to motors is independent of the stiffness