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A drift-diffusion model for molecular motor transport in anisotropic filament bundles
1. | Courant Institute of Mathematical Sciences, New York University, 251 Mercer St, New York, NY 10012, United States |
2. | Courant Institute of Mathematical Sciences and Department of Biology, New York University, 251 Mercer St, New York, NY 10012, United States |
References:
[1] |
P. Baas, C. Nadar and K. Myers, Axonal transport of microtubules: The long and short of it, Traffic, 7 (2006), 490-498.
doi: 10.1111/j.1600-0854.2006.00392.x. |
[2] |
P. Bressloff and J. Newby, Stochastic models of intracellular transport, Reviews of Modern Physics, 85 (2013), 135-196.
doi: 10.1103/RevModPhys.85.135. |
[3] |
A. Friedman and G. Craciun, A model of intracellular transport of particles in an axon, Journal of Mathematical Biology, 51 (2005), 217-246.
doi: 10.1007/s00285-004-0285-3. |
[4] |
K. O. Friedrichs and P. D. Lax, Boundary value problems for first order operators, Communications on Pure and Applied Mathematics, 18 (1965), 355-388.
doi: 10.1002/cpa.3160180127. |
[5] |
W. Hancock, Bidirectional cargo transport: Moving beyond tug of war, Nature Reviews Molecular Cell Biology, 15 (2014), 615-628.
doi: 10.1038/nrm3853. |
[6] |
T. Hillen and H. Othmer, The diffusion limit of transport equations derived from velocity-jump processes, SIAM Journal on Applied Mathematics, 61 (2000), 751-775.
doi: 10.1137/S0036139999358167. |
[7] |
E. Keller and L. Segel, Initiation of slime mold aggregation viewed as an instability, Journal of Theoretical Biology, 26 (1970), 399-415.
doi: 10.1016/0022-5193(70)90092-5. |
[8] |
M. Kneussel and W. Wagner, Myosin motors at neuronal synapses: Drivers of membrane transport and actin dynamics, Nature Reviews Neuroscience, 14 (2013), 233-247.
doi: 10.1038/nrn3445. |
[9] |
A. Kunwar, S. Tripathy, J. Xu, M. Mattson, P. Anand, R. Sigua, M. Vershinin, R. McKenney, C. Yu, A. Mogilner and S. Gross, Mechanical stochastic tug-of-war models cannot explain bidirectional lipid-droplet transport, Proceedings of the National Academy of Sciences of the United States of America, 108 (2011), 18960-18965.
doi: 10.1073/pnas.1107841108. |
[10] |
A. Kuznetsov, Modelling active transport in drosophila unipolar motor neurons, Computer Methods in Biomechanics and Biomedical Engineering, 14 (2011), 1117-1131.
doi: 10.1080/10255842.2010.515983. |
[11] |
A. Kuznetsov and K. Hooman, Modeling traffic jams in intracellular transport in axons, International Journal of Heat and Mass Transfer, 51 (2008), 5695-5699, Biomedical-Related Special Issue.
doi: 10.1016/j.ijheatmasstransfer.2008.04.022. |
[12] |
I. Maly, Diffusion approximation of the stochastic process of microtubule assembly, Bulletin of Mathematical Biology, 64 (2002), 213-238.
doi: 10.1006/bulm.2001.0265. |
[13] |
D. Smith and R. Simmons, Models of motor-assisted transport of intracellular particles, Biophysical Journal, 80 (2001), 45-68.
doi: 10.1016/S0006-3495(01)75994-2. |
[14] |
M. Stone, F. Roegiers and M. Rolls, Microtubules have opposite orientation in axons and dendrites of drosophila neurons, Molecular Biology of the Cell, 19 (2008), 4122-4129.
doi: 10.1091/mbc.E07-10-1079. |
[15] |
R. Vale, The molecular motor toolbox for intracellular transport, Cell, 112 (2003), 467-480.
doi: 10.1016/S0092-8674(03)00111-9. |
[16] |
W. J. Walter, V. Beránek, E. Fischermeier and S. Diez, Tubulin acetylation alone does not affect kinesin-1 velocity and run length |
[17] |
F. Wanka and E. Van Zoelen, Cellular organelle transport and positioning by plasma streaming, Cellular and Molecular Biology Letters, 8 (2003), 1035-1045. |
show all references
References:
[1] |
P. Baas, C. Nadar and K. Myers, Axonal transport of microtubules: The long and short of it, Traffic, 7 (2006), 490-498.
doi: 10.1111/j.1600-0854.2006.00392.x. |
[2] |
P. Bressloff and J. Newby, Stochastic models of intracellular transport, Reviews of Modern Physics, 85 (2013), 135-196.
doi: 10.1103/RevModPhys.85.135. |
[3] |
A. Friedman and G. Craciun, A model of intracellular transport of particles in an axon, Journal of Mathematical Biology, 51 (2005), 217-246.
doi: 10.1007/s00285-004-0285-3. |
[4] |
K. O. Friedrichs and P. D. Lax, Boundary value problems for first order operators, Communications on Pure and Applied Mathematics, 18 (1965), 355-388.
doi: 10.1002/cpa.3160180127. |
[5] |
W. Hancock, Bidirectional cargo transport: Moving beyond tug of war, Nature Reviews Molecular Cell Biology, 15 (2014), 615-628.
doi: 10.1038/nrm3853. |
[6] |
T. Hillen and H. Othmer, The diffusion limit of transport equations derived from velocity-jump processes, SIAM Journal on Applied Mathematics, 61 (2000), 751-775.
doi: 10.1137/S0036139999358167. |
[7] |
E. Keller and L. Segel, Initiation of slime mold aggregation viewed as an instability, Journal of Theoretical Biology, 26 (1970), 399-415.
doi: 10.1016/0022-5193(70)90092-5. |
[8] |
M. Kneussel and W. Wagner, Myosin motors at neuronal synapses: Drivers of membrane transport and actin dynamics, Nature Reviews Neuroscience, 14 (2013), 233-247.
doi: 10.1038/nrn3445. |
[9] |
A. Kunwar, S. Tripathy, J. Xu, M. Mattson, P. Anand, R. Sigua, M. Vershinin, R. McKenney, C. Yu, A. Mogilner and S. Gross, Mechanical stochastic tug-of-war models cannot explain bidirectional lipid-droplet transport, Proceedings of the National Academy of Sciences of the United States of America, 108 (2011), 18960-18965.
doi: 10.1073/pnas.1107841108. |
[10] |
A. Kuznetsov, Modelling active transport in drosophila unipolar motor neurons, Computer Methods in Biomechanics and Biomedical Engineering, 14 (2011), 1117-1131.
doi: 10.1080/10255842.2010.515983. |
[11] |
A. Kuznetsov and K. Hooman, Modeling traffic jams in intracellular transport in axons, International Journal of Heat and Mass Transfer, 51 (2008), 5695-5699, Biomedical-Related Special Issue.
doi: 10.1016/j.ijheatmasstransfer.2008.04.022. |
[12] |
I. Maly, Diffusion approximation of the stochastic process of microtubule assembly, Bulletin of Mathematical Biology, 64 (2002), 213-238.
doi: 10.1006/bulm.2001.0265. |
[13] |
D. Smith and R. Simmons, Models of motor-assisted transport of intracellular particles, Biophysical Journal, 80 (2001), 45-68.
doi: 10.1016/S0006-3495(01)75994-2. |
[14] |
M. Stone, F. Roegiers and M. Rolls, Microtubules have opposite orientation in axons and dendrites of drosophila neurons, Molecular Biology of the Cell, 19 (2008), 4122-4129.
doi: 10.1091/mbc.E07-10-1079. |
[15] |
R. Vale, The molecular motor toolbox for intracellular transport, Cell, 112 (2003), 467-480.
doi: 10.1016/S0092-8674(03)00111-9. |
[16] |
W. J. Walter, V. Beránek, E. Fischermeier and S. Diez, Tubulin acetylation alone does not affect kinesin-1 velocity and run length |
[17] |
F. Wanka and E. Van Zoelen, Cellular organelle transport and positioning by plasma streaming, Cellular and Molecular Biology Letters, 8 (2003), 1035-1045. |
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