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Open AccessOpen Access JUSTC Life Sciences 06 April 2023

Intracellular transport by motor proteins with the same directionality

  • Department of Physics, University of Science and Technology of China, Hefei 230026, China

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https://doi.org/10.52396/JUSTC-2022-0140
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  • Author Bio:

    Kewei Xie is a graduate student under the tutelage of Prof. Qian Wang at the University of Science and Technology of China. His research focuses on the transport by motor proteins

    Qian Wang is a Professor at the University of Science and Technology of China. He received his Ph.D. degree from the University of Houston in 2012. His research focuses on developing analytical and theoretical tools to understand physical rules behind biological phenomena

  • Corresponding author: E-mail: wqq@ustc.edu.cn
  • Received Date: 30 September 2022
  • Accepted Date: 13 January 2023
    • Available Online: 06 April 2023
    Abstract

  • Abstract

    Active intracellular transport is mainly performed by a group of special nanomachines called motor proteins. During transport, cooperation between motor proteins significantly influences important transport features, such as distance and velocity. To understand this mechanism, we combine Gillespie simulation and analytical derivation to demonstrate how the mechanical properties of a single motor influence the cooperation between multiple motors, further regulating the transport distance. In addition, we build a deep learning model to help us quickly obtain the motor parameters. Our results shed light on the physical nature of intracellular transport by motor proteins with the same directionality.

    Graphical abstract

      Two kinesins on the microtubule.

    Abstract

    Active intracellular transport is mainly performed by a group of special nanomachines called motor proteins. During transport, cooperation between motor proteins significantly influences important transport features, such as distance and velocity. To understand this mechanism, we combine Gillespie simulation and analytical derivation to demonstrate how the mechanical properties of a single motor influence the cooperation between multiple motors, further regulating the transport distance. In addition, we build a deep learning model to help us quickly obtain the motor parameters. Our results shed light on the physical nature of intracellular transport by motor proteins with the same directionality.

    • Public Summary

    • We establish a theoretical framework to study transport by motors with the same directionality by combining simulation and analytical derivation.
    • Stronger binding between motors and microtubules leads to stronger cooperation between motors.
    • We introduce a deep learning method by which the motor parameters can be easily identified for expected transport features.

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    • References(27)
  • [1]
    Vale R D. The molecular motor toolbox for intracellular transport. Cell, 2003, 112: 467–480. doi: 10.1016/S0092-8674(03)00111-9
    [2]
    Cross R A, McAinsh A. Prime movers: The mechanochemistry of mitotic kinesins. Nature Reviews Molecular Cell Biology, 2014, 15: 257–271. doi: 10.1038/nrm3768
    [3]
    Kolomeisky A B, Fisher M E. Molecular motors: A theorist’s perspective. Annual Review of Physical Chemistry, 2007, 58: 675–695. doi: 10.1146/annurev.physchem.58.032806.104532
    [4]
    Hirokawa N, Noda Y, Okada Y. Kinesin and dynein superfamily proteins in organelle transport and cell division. Current Opinion in Cell Biology, 1998, 10: 60–73. doi: 10.1016/S0955-0674(98)80087-2
    [5]
    Rath O, Kozielski F. Kinesins and cancer. Nature Reviews Cancer, 2012, 12: 527–539. doi: 10.1038/nrc3310
    [6]
    Millecamps S, Julien J P. Axonal transport deficits and neurodegenerative diseases. Nature Reviews Neuroscience, 2013, 14: 161–176. doi: 10.1038/nrn3380
    [7]
    Veigel C, Schmidt C F. Moving into the cell: Single-molecule studies of molecular motors in complex environments. Nature Reviews Molecular Cell Biology, 2011, 12: 163–176. doi: 10.1038/nrm3062
    [8]
    Pilling A D, Horiuchi D, Lively C M, et al. Kinesin-1 and dynein are the primary motors for fast transport of mitochondria in Drosophila motor axons. Molecular Biology of the Cell, 2006, 17: 2057–2068. doi: 10.1091/mbc.e05-06-0526
    [9]
    Kural C, Kim H, Syed S, et al. Kinesin and dynein move a peroxisome in vivo: A tug-of-war or coordinated movement. Science, 2005, 308: 1469–1472. doi: 10.1126/science.1108408
    [10]
    Gross S P. Hither and yon: A review of bi-directional microtubule-based transport. Physical Biology, 2004, 1: R1–R11. doi: 10.1088/1478-3967/1/2/R01
    [11]
    Welte M A. Bidirectional transport along microtubules. Current Biology, 2004, 14: R525–R537. doi: 10.1016/j.cub.2004.06.045
    [12]
    Kozielski F, Sack S, Marx A, et al. The crystal structure of dimeric kinesin and implications for microtubule-dependent motility. Cell, 1997, 91: 985–994. doi: 10.1016/S0092-8674(00)80489-4
    [13]
    Müller M J I, Klumpp S, Lipowsky R. Tug-of-war as a cooperative mechanism for bidirectional cargo transport by molecular motors. Proceedings of the National Academy of Sciences of the United States of America, 2008, 105: 4609–4614. doi: 10.1073/pnas.0706825105
    [14]
    Kunwar A, Tripathy S K, Xu J, et al. 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, 2011, 108: 18960–18965. doi: 10.1073/pnas.1107841108
    [15]
    Vu H T, Chakrabarti S, Hinczewski M, et al. Discrete step sizes of molecular motors lead to bimodal non-Gaussian velocity distributions under force. Physical Review Letters, 2016, 117: 078101. doi: 10.1103/PhysRevLett.117.078101
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    [17]
    Hancock W O. Bidirectional cargo transport: Moving beyond tug of war. Nature Reviews Molecular Cell Biology, 2014, 15: 615–628. doi: 10.1038/nrm3853
    [18]
    Xie K, Wang Q. Cooperation and competition coexist in bidirectional transport by motor proteins. The Journal of Physical Chemistry Letters, 2022, 13: 7336–7341. doi: 10.1021/acs.jpclett.2c01659
    [19]
    Gillespie D T. Exact stochastic simulation of coupled chemical-reactions. Journal of Physical Chemistry, 1977, 81: 2340–2361. doi: 10.1021/j100540a008
    [20]
    Schnitzer M J, Visscher K, Block S M. Force production by single kinesin motors. Nature Cell Biology, 2000, 2: 718–723. doi: 10.1038/35036345
    [21]
    Vale R D, Funatsu T, Pierce D W, et al. Direct observation of single kinesin molecules moving along microtubules. Nature, 1996, 380: 451–453. doi: 10.1038/380451a0
    [22]
    Leduc C, Campàs O, Zeldovich K B, et al. Cooperative extraction of membrane nanotubes by molecular motors. Proceedings of the National Academy of Sciences of the United States of America, 2004, 101: 17096–17101. doi: 10.1073/pnas.0406598101
    [23]
    Svoboda K, Block S M. Force and velocity measured for single kinesin molecules. Cell, 1994, 77: 773–784. doi: 10.1016/0092-8674(94)90060-4
    [24]
    Rogers A R, Driver J W, Constantinou P E, et al. Negative interference dominates collective transport of kinesin motors in the absence of load. Physical Chemistry Chemical Physics, 2009, 11: 4882–4889. doi: 10.1039/b900964g
    [25]
    Carter N J, Cross R A. Mechanics of the kinesin step. Nature, 2005, 435: 308–312. doi: 10.1038/nature03528
    [26]
    Oiwa K, Sakakibara H. Recent progress in dynein structure and mechanism. Current Opinion in Cell Biology, 2005, 17: 98–103. doi: 10.1016/j.ceb.2004.12.006
    [27]
    Avriel M. Nonlinear Programming: Analysis and Methods. Englewood Cliffs, NJ: Prentice-Hall, 1976
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    Figure  1.  (a) Schematic illustration of transport by two kinesins. Each kinesin can move stochastically in three modes: (i) moving forward; (ii) unbinding and (iii) binding. (b) The overall transport distance S as a function of the binding rate ${\pi}$. (c) ${\rm ln}\,S$ as a function of ${\rm e}^{-1/{F}_{\rm d}}$, where ${F}_{\rm d}$ is the detachment force. (d) S as a function of 1/${\varepsilon }_{0}$, where ${\varepsilon }_{0}$ is the detachment rate.

    Figure  2.  (a) Three states during transport carried by two kinesins. (b) Comparison of the transport distance $S$ calculated by Eq. (9) and by simulations from the CC model. The input parameter is a 6-dimensional vector (${v}_{0}^{},{{\pi} }_{0},{\varepsilon }_{0},{F}_{\rm s},{F}_{\rm d},{k}^{}$). We repeat the calculation 104 times by randomly picking in the following parameter space: ${v}_{0}\in [160\;{\rm{nm}}/{\rm{s}},\;4000\;{\rm{nm}}/{\rm{s}}]$, ${{\pi} }_{0}\in [0.6\;{{\rm{s}}}^{-1},\;15\;{{\rm{s}}}^{-1}]$, ${\varepsilon }_{0}^{}\in [0.12\;{{\rm{s}}}^{-1},\;3\;{{\rm{s}}}^{-1}],$ ${F}_{\rm s}^{}\in [0.6\;{\rm pN},\;15\;{\rm pN}]$, ${F}_{\rm d}\in [0.36\;{\rm pN},\; $$ 9\;{\rm pN}]$, and ${k}\in [0.02\;{\rm pN/nm},\;0.5\;{\rm pN/nm}]$. (c) Comparison of $ {S}_{1} $ calculated by Eq. (12) and by simulations from the CC model. R represents the correlation coefficient.

    Figure  3.  (a) Error between the simulation and analytical calculation by Eq. (12) as a function of the elastic coefficient of kinesin, k. We define the error as $\eta = |{S_{\rm cal}} - {S_{\rm sim}}|/{S_{\rm sim}}$. (b) The distance S decays with the spring constant k. The blue line represents the Gillespie simulation result. The orange line represents the analytical result calculated by Eq. (12). The yellow line represents the analytical result calculated by Eq. (18). (c) and (d) are the same as (a) and (b) but the detachment force ${F}_{\rm d}\to \infty$.

    Figure  4.  (a) Deep learning neural network architecture. (b) The error of the deep learning changed by the number of training steps. (c) The error changed by the number of neurons and layers of the neural network. (d) The error changed by the size of the training set. (e) The distribution of errors.

    [1]
    Vale R D. The molecular motor toolbox for intracellular transport. Cell, 2003, 112: 467–480. doi: 10.1016/S0092-8674(03)00111-9
    [2]
    Cross R A, McAinsh A. Prime movers: The mechanochemistry of mitotic kinesins. Nature Reviews Molecular Cell Biology, 2014, 15: 257–271. doi: 10.1038/nrm3768
    [3]
    Kolomeisky A B, Fisher M E. Molecular motors: A theorist’s perspective. Annual Review of Physical Chemistry, 2007, 58: 675–695. doi: 10.1146/annurev.physchem.58.032806.104532
    [4]
    Hirokawa N, Noda Y, Okada Y. Kinesin and dynein superfamily proteins in organelle transport and cell division. Current Opinion in Cell Biology, 1998, 10: 60–73. doi: 10.1016/S0955-0674(98)80087-2
    [5]
    Rath O, Kozielski F. Kinesins and cancer. Nature Reviews Cancer, 2012, 12: 527–539. doi: 10.1038/nrc3310
    [6]
    Millecamps S, Julien J P. Axonal transport deficits and neurodegenerative diseases. Nature Reviews Neuroscience, 2013, 14: 161–176. doi: 10.1038/nrn3380
    [7]
    Veigel C, Schmidt C F. Moving into the cell: Single-molecule studies of molecular motors in complex environments. Nature Reviews Molecular Cell Biology, 2011, 12: 163–176. doi: 10.1038/nrm3062
    [8]
    Pilling A D, Horiuchi D, Lively C M, et al. Kinesin-1 and dynein are the primary motors for fast transport of mitochondria in Drosophila motor axons. Molecular Biology of the Cell, 2006, 17: 2057–2068. doi: 10.1091/mbc.e05-06-0526
    [9]
    Kural C, Kim H, Syed S, et al. Kinesin and dynein move a peroxisome in vivo: A tug-of-war or coordinated movement. Science, 2005, 308: 1469–1472. doi: 10.1126/science.1108408
    [10]
    Gross S P. Hither and yon: A review of bi-directional microtubule-based transport. Physical Biology, 2004, 1: R1–R11. doi: 10.1088/1478-3967/1/2/R01
    [11]
    Welte M A. Bidirectional transport along microtubules. Current Biology, 2004, 14: R525–R537. doi: 10.1016/j.cub.2004.06.045
    [12]
    Kozielski F, Sack S, Marx A, et al. The crystal structure of dimeric kinesin and implications for microtubule-dependent motility. Cell, 1997, 91: 985–994. doi: 10.1016/S0092-8674(00)80489-4
    [13]
    Müller M J I, Klumpp S, Lipowsky R. Tug-of-war as a cooperative mechanism for bidirectional cargo transport by molecular motors. Proceedings of the National Academy of Sciences of the United States of America, 2008, 105: 4609–4614. doi: 10.1073/pnas.0706825105
    [14]
    Kunwar A, Tripathy S K, Xu J, et al. 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, 2011, 108: 18960–18965. doi: 10.1073/pnas.1107841108
    [15]
    Vu H T, Chakrabarti S, Hinczewski M, et al. Discrete step sizes of molecular motors lead to bimodal non-Gaussian velocity distributions under force. Physical Review Letters, 2016, 117: 078101. doi: 10.1103/PhysRevLett.117.078101
    [16]
    Vale R D, Malik F, Brown D. Directional instability of microtubule transport in the presence of kinesin and dynein, two opposite polarity motor proteins. Journal of Cell Biology, 1992, 119: 1589–1596. doi: 10.1083/jcb.119.6.1589
    [17]
    Hancock W O. Bidirectional cargo transport: Moving beyond tug of war. Nature Reviews Molecular Cell Biology, 2014, 15: 615–628. doi: 10.1038/nrm3853
    [18]
    Xie K, Wang Q. Cooperation and competition coexist in bidirectional transport by motor proteins. The Journal of Physical Chemistry Letters, 2022, 13: 7336–7341. doi: 10.1021/acs.jpclett.2c01659
    [19]
    Gillespie D T. Exact stochastic simulation of coupled chemical-reactions. Journal of Physical Chemistry, 1977, 81: 2340–2361. doi: 10.1021/j100540a008
    [20]
    Schnitzer M J, Visscher K, Block S M. Force production by single kinesin motors. Nature Cell Biology, 2000, 2: 718–723. doi: 10.1038/35036345
    [21]
    Vale R D, Funatsu T, Pierce D W, et al. Direct observation of single kinesin molecules moving along microtubules. Nature, 1996, 380: 451–453. doi: 10.1038/380451a0
    [22]
    Leduc C, Campàs O, Zeldovich K B, et al. Cooperative extraction of membrane nanotubes by molecular motors. Proceedings of the National Academy of Sciences of the United States of America, 2004, 101: 17096–17101. doi: 10.1073/pnas.0406598101
    [23]
    Svoboda K, Block S M. Force and velocity measured for single kinesin molecules. Cell, 1994, 77: 773–784. doi: 10.1016/0092-8674(94)90060-4
    [24]
    Rogers A R, Driver J W, Constantinou P E, et al. Negative interference dominates collective transport of kinesin motors in the absence of load. Physical Chemistry Chemical Physics, 2009, 11: 4882–4889. doi: 10.1039/b900964g
    [25]
    Carter N J, Cross R A. Mechanics of the kinesin step. Nature, 2005, 435: 308–312. doi: 10.1038/nature03528
    [26]
    Oiwa K, Sakakibara H. Recent progress in dynein structure and mechanism. Current Opinion in Cell Biology, 2005, 17: 98–103. doi: 10.1016/j.ceb.2004.12.006
    [27]
    Avriel M. Nonlinear Programming: Analysis and Methods. Englewood Cliffs, NJ: Prentice-Hall, 1976
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