Exact stochastic simulations of intra-cellular transport by mechanically coupled molecular motors

Journal of Computational Science

Volumn 2, Issue 4, 2011, Pages 324-334

  Helmuth, Jo A ^a   Reboux, Sylvain ^a   Sbalzarini, Ivo F ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

Hybrid continuous discrete simulation; Hybrid stochastic deterministic model; Intra cellular transport; Motor proteins; Stochastic simulation algorithm

Indexed keywords

BIOCHEMICAL PROCESS; COMPUTATIONAL MODEL; CYTOSKELETONS; DIFFERENT TIME SCALE; HYBRID CONTINUOUS-DISCRETE SIMULATION; INTRA-CELLULAR TRANSPORT; LEVELS OF DETAIL; LIVE CELL; MODEL DYNAMICS; MOLECULAR MOTORS; MOTOR PROTEINS; NUMERICAL ERRORS; SIMULATION ALGORITHMS; SIMULATION APPROACH; STOCHASTIC SIMULATION ALGORITHMS; STOCHASTIC SIMULATIONS; TIME STEP; TRANSPORT DYNAMICS; TRANSPORT MODELS; VELOCITY AUTOCORRELATION FUNCTIONS;

ALGORITHMS; COMPUTATIONAL METHODS; DISCRETE EVENT SIMULATION; DYNAMICS; FREIGHT TRANSPORTATION; REGRESSION ANALYSIS; STOCHASTIC SYSTEMS;

STOCHASTIC MODELS;

EID: 82455208968     PISSN: 18777503     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jocs.2011.08.006     Document Type: Article

References (44)

1. Welte M.A. Bidirectional transport along microtubules. Curr. Biol. 2004, 14(13):525-537. 10.1016/j.cub.2004.06.045.
2. Mallik R., Petrov D., Lex S.A., King S.J., Gross S.P. Building complexity: an in vitro study of cytoplasmic dynein with in vivo implications. Curr. Biol. 2005, 15(23):2075-2085.
3. Levi V., Serpinskaya A.S., Gratton E., Gelfand V. Organelle transport along microtubules in xenopus melanophores: evidence for cooperation between multiple motors. Biophys. J. 2006, 90(1):318-327. 10.1529/biophysj.105.067843.
4. Helmuth J.A., Burckhardt C.J., Koumoutsakos P., Greber U.F., Sbalzarini I.F. A novel supervised trajectory segmentation algorithm identifies distinct types of human adenovirus motion in host cells. J. Struct. Biol. 2007, 159(3):347-358.
5. Gross S.P. Hither and yon: a review of bi-directional microtubule-based transport. Phys. Biol. 2004, 1(1-2):R1-R11. 10.1088/1478-3967/1/2/R01.
6. Nédélec F. Computer simulations reveal motor properties generating stable antiparallel microtubule interactions. J. Cell Biol. 2002, 158(6):1005-1015.
7. Carter N., Cross R. Mechanics of the kinesin step. Nature 2005, 435(7040):308-312. 10.1038/nature03528.
8. Klumpp S., Lipowsky R. Cooperative cargo transport by several molecular motors. Proc. Natl. Acad. Sci. U.S.A. 2005, 102(48):17284-17289.. 10.1073/pnas.0507363102.
9. Müller M.J.I., Klumpp S., Lipowsky R. Tug-of-war as a cooperative mechanism for bidirectional cargo transport by molecular motors. Proc. Natl. Acad. Sci. U.S.A. 2008, 105(12):4609-4614.
10. Korn C.B., Klumpp S., Lipowsky R., Schwarz U.S. Stochastic simulations of cargo transport by processive molecular motors. J. Chem. Phys. 2009, 131:245107. 10.1063/1.3279305.
11. Kunwar A., Mogilner A. Robust transport by multiple motors with nonlinear force-velocity relations and stochastic load sharing. Phys. Biol. 2010, 7(1):016012. 10.1088/1478-3975/7/1/016012.
12. Nedelec F., Foethke D. Collective Langevin dynamics of flexible cytoskeletal fibers. New J. Phys. 2007, 9:427.
13. Kunwar A., Vershinin M., Xu J., Gross S.P. Stepping, strain gating, and an unexpected force-velocity curve for multiple-motor-based transport. Curr. Biol. 2008, 18(16):1173-1183. 10.1016/j.cub.2008.07.027.
14. Beeg J., Klumpp S., Dimova R., Gracia R.S., Unger E., Lipowsky R. Transport of beads by several kinesin motors. Biophys. J. 2008, 94(2):532-541. 10.1529/biophysj.106.097881.
15. Gazzola M., Burckhardt C.J., Bayati B., Engelke M., Greber U.F., Koumoutsakos P. A stochastic model for microtubule motors describes the in vivo cytoplasmic transport of human adenovirus. PLoS Comp. Biol. 2009, 5(12):e1000623. 10.1371/journal.pcbi.1000623.
16. Soppina V., Rai A.K., Ramaiya A.J., Barak P., Mallik R. Tug-of-war between dissimilar teams of microtubule motors regulates transport and fission of endosomes. Proc. Natl. Acad. Sci. U.S.A. 2009, 106(46):19381-19386. 10.1073/pnas.0906524106.
17. Alfonsi A., Cancès E., Turinici G., Di Ventura B., Huisinga W. Adaptive simulation of hybrid stochastic and deterministic models for biochemical systems. in:E. Cancès, J.-F. Gerbeau (Eds.), ESAIM: Proceedings, vol. 14 2005, 1-13.
18. Salis H., Kaznessis Y. Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions. J. Chem. Phys. 2005, 122(5):054103. 10.1063/1.1835951.
19. Gillespie D.T. Stochastic simulation of chemical kinetics. Ann. Rev. Phys. Chem. 2007, 58:35-55.
20. Holzwarth G., Bonin K., Hill D.B. Forces required of kinesin during processive transport through cytoplasm. Biophys. J. 2002, 82(4):1784-1790.
21. Howard J. Mechanics of Motor Proteins and the Cytoskeleton 2001, Sinauer Associates, Sunderland.
22. Keller D., Bustamante C. The mechanochemistry of molecular motors. Biophys. J. 2000, 78(2):541-556.
23. Bustamante C., Chemla Y.R., Forde N.R., Izhaky D. Mechanical processes in biochemistry. Annu. Rev. Biochem. 2004, 73:705-748. 10.1146/annurev.biochem.72.121801.161542.
24. Rice S., Lin A.W., Safer D., Hart C.L., Naber N., Carragher B.O., Cain S.M., Pechatnikova E., Wilson-Kubalek E.M., Whittaker M., Pate E., Cooke R., Taylor E.W., Milligan R.A., Vale R.D. A structural change in the kinesin motor protein that drives motility. Nature 1999, 402(6763):778-784.
25. Mallik R., Carter B.C., Lex S.A., King S.J., Gross S.P. Cytoplasmic dynein functions as a gear in response to load. Nature 2004, 427(6975):649-652. 10.1038/nature02293.
26. Kardon J.R., Vale R.D. Regulators of the cytoplasmic dynein motor. Nat. Rev. Mol. Cell Bio. 2009, 10(12):854-865. 10.1038/nrm2804.
27. Kramers H.A. Brownian motion in a field of force and the diffusion model of chemical reactions. Physica 1940, 7:284-304.
28. Gillespie D.T. Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 1977, 81(25):2340-2361.
29. Gillespie D.T. A rigorous derivation of the chemical master equation. Physica A 1992, 188(1-3):404-425.
30. Gibson M.A., Bruck J. Efficient exact stochastic simulation of chemical systems with many species and many channels. J. Phys. Chem. A 2000, 104:1876-1889.
31. Shampine L.F., Gladwell I., Brankin R.W. Reliable solution of special event location problems for ODEs. ACM Trans. Math. Softw. 1991, 17(1):11-25.
32. Grabner G., Kecskeméthy A. An integrated Runge-Kutta root finding method for reliable collision detection in multibody systems. Multibody System Dynamics 2005, 14:301-316.
33. Hindmarsh A.C., Petzold L.R. Algorithms and software for ordinary differential equations and differential- algebraic equations, part II: higher-order methods and software packages. Comput. Phys. 1995, 9(2):148-155.
34. Ramaswamy R., González-Segredo N., Sbalzarini I.F. A new class of highly efficient exact stochastic simulation algorithms for chemical reaction networks. J. Chem. Phys. 2009, 130(24):244104.
35. Ramaswamy R., Sbalzarini I.F. A partial-propensity variant of the composition-rejection stochastic simulation algorithm for chemical reaction networks. J. Chem. Phys. 2010, 132(4):044102.
36. Gillespie D.T. The multivariate Langevin and Fokker-Planck equations. Am. J. Phys. 1996, 64(10):1246-1257.
37. van Kampen N.G. Stochastic Processes in Physics and Chemistry 2007, North Holland. 3rd ed.
38. Mallik R., Gross S.P. Molecular motors: strategies to get along. Curr. Biol. 2004, 14(22):971-982. 10.1016/j.cub.2004.10.046.
39. Mallik R., Gross S.P. Molecular motors as cargo transporters in the cell - the good, the bad and the ugly. Physica A 2006, 372(1):65-69. 10.1016/j.physa.2006.05.017.
40. Shtridelman Y., Cahyuti T., Townsend B., DeWitt D., Macosko J.C. Force-velocity curves of motor proteins cooperating in vivo. Cell Biochem. Biophys. 2008, 52(1):19-29. 10.1007/s12013-008-9021-8.
41. Gennerich A., Vale R.D. Walking the walk: how kinesin and dynein coordinate their steps. Curr. Opin. Cell Biol. 2009, 21(1):59-67.. 10.1016/j.ceb.2008.12.002.
42. Buchmann F.M. Simulation of stopped diffusions. J.Comput. Phys. 2005, 202:446-462.
43. Galassi M., Davies J., Theiler J., Gough B., Jungman G., Alken P., Booth M., Rossi F. GNU Scientific Library Reference Manual 2009, Network Theory Ltd, Bristol, UK. 3rd ed.
44. Hill D.B., Plaza M.J., Bonin K., Holzwarth G. Fast vesicle transport in PC12 neurites: velocities and forces. Eur. Biophys. J. Biophy. 2004, 33(7):623-632. 10.1007/s00249-004-0403-6.