Active Transport in Microtubules Networks

Transcription

1 Acive Transpor in Microubules Neworks Rony Granek Bioechnology Engineering, BGU Coworkers: Aviv Kahana, Gilad Kenan, Mario Feingold BGU Michael Elbaum WIS

2 An idealized animal cell

3 The cyoskeleon hp://img.sparknoes.com/figures/d/d479f5da67c08a54f986ae699069d7a/cyoskeleon.gif hp://campus.queens.edu/faculy/jannr/cells/cell/pics/cyoskeleon.jpg%0 Microubules are direcional: (-) ends originae from he cenrosome (MTOC)

4 Moor proeins Kinesin moves oward (+) end, Dynein oward (-) end. Low processiviy, ~1 s in bound sae (sep ime ~6ms). Velociy ~1µm/s.

5

6 Microubules Global order vs. local disorder

7 Quesions: Wha is he purpose of he finie moor processiviy? Wha is he effec of local disorder of he microubule nework on he acive ranspor in he cell?

8 In viro experimen: 3-D wih orienaional order

9 In viro sudy Fluorescenly labeled ssdna-proein complex including a nuclear localizaion signal (NLS) pepide. Moor proein assised ranspor. Paricle racking assays using a camera & designaed sofware. H. Salman, A. Abu-Arish, S. Oliel, A. Loyer, J. Klafer, R. Granek, and M. Elbaum, Biophys. J. (005)

10 Resuls Quesion: pl labeled complex wihou NLS an labeled complex wih NLS an+noc labeled complex wih NLS wihou microubules (desroyed by Nocodazole) Why does he acive ranspor appear as simple diffusion?

11 Acive ranspor Random velociy model in 1+1 dimensions y x Diffusion

12 Random velociy model in 1+1 dimensions Exac resul, Super-diffusion: y Scaling argumen: ( ) ~ 3/ G. Zumofen, J. Klafer, A. Blumen, PRA (1990) S. Redner, PRE (1997) J.-P. Bouchaud, A. Georges, P. Le Doussal, J. Physique (1987) y ( ) P ( ) v 0, x where P ( ) ~ 0, x 1/ The probabiliy of reurn o he origin in 1-D Simulaion resuls: Balanced racks (% up=% down) fis he heory of ZKB. diffusion wih drif a crossover from shor-ime super-diffusion y ( ) ~ 3/ o long-ime diffusion y ( ) ~ explained by a scaling argumen

13 RVM Unbalanced diffusion MSD Drif 1/ x pq / 0 x p q 0 define: x x 1/ pq 1 p q / 0 When >>1 RVM, when <<1 Diffusion For p=0.51 & q=0.49: =1 a =500

14 -D nework model Scaling argumen: x ( ) P ( ) v 0, y where P0, y y 1 ( ) The probabliy of reurn o he origin along he y axis, assuming Gaussian PDF By symmery x ( ) y ( ) ( ) ( ) ~ 4/3

15 More accurae self-consisen calculaion: From symmery x y Assuming Gaussian PDFs / 3 9 x y 1/ 3 v 4 / 3 / 3 4 / 3

16

17 -D nework model Self-consisen heory: x y ~ 4/3 Simulaion resuls: Balanced nework fis heory Unbalanced nework, long imes: unbalanced direcion RVM wih drif perpendicular direcion Long-ime diffusion y ~ x p qv

18 Slope=1.5 (4/3) Slope=1.0

19 Slope=1.33 Slope=1.45 (3/)

20 Processiviy dependence Slope=1.33 Processiviies - f

21 3-D nework model

22 More accurae self-consisen calculaion: Scaling argumen: 0, ) ( ) ( v P x yz where The probabliy of reurn o he origin in he y-z plane ) ( 1 ) ( 1 ) ( ) ( 0, 0, 0, z y P P P z y yz By symmery 3 ) ( ) ( ) ( ) ( r z y x r ~ ) ( 1/ ln τ v v A r.4 A Diffusion-like, bu acive (non-hermal) where v v is he mesh size,

23 Slope=0.96

24 In viro experimen: 3-D wih orienaional order z x y

25 In viro sudy Fluorescenly labeled ssdna-proein complex including a nuclear localizaion signal (NLS) pepide. Moor proein assised ranspor. Paricle racking assays using a camera & designaed sofware. H. Salman, A. Abu-Arish, S. Oliel, A. Loyer, J. Klafer, R. Granek, and M. Elbaum, Biophys. J. (005)

26 Resuls pl labeled complex wihou NLS an labeled complex wih NLS an+noc labeled complex wih NLS wihou microubules (desroyed by Nocodazole) Quesion: Why does he acive ranspor appear as simple diffusion?

27

28 Scaling argumen: x ( ) P ( ) v 0, yz where 1 P P ( ) P ( ) 0, yz 0, y 0, z y ( ) 1 D The probabliy of reurn o he origin in he y-z plane By symmery P P ( ) 0, 0, xz ( yz and ) ~ x ( ) y ( ) ( ) Diffusion-like, bu acive (non-hermal) More accurae self-consisen calculaion: A v D 4 / 3 1 / 3 ln τ v / 3 where v, is he mesh size v A 1.

29 Slope=0.63 ] / 3

30 3-D animal cell model

31 Simulaions of Firs Exi problem: Kinesin mediaed ranspor: (i) Probabiliy o arrive from he nucleus o he membrane unil ime. (ii) Probabiliy o arrive from he nucleus o a localized arge in he cell (e.g., ribosome) unil ime. Dynein mediaed ranspor: Probabiliy o arrive from he membrane o he nucleus unil ime.

32 Kinesin mediaed ranspor: From nucleus o membrane Many cells averaging

33 Dynein mediaed ranspor: From membrane o nucleus Many cells averaging

34 Kinesin mediaed ranspor: From nucleus o a localized arge (e.g. ribosome) Radiaive boundary condiions a he membrane Many cells averaging

35 Kinesin mediaed ranspor: From nucleus o a localized arge (e.g. ribosome) Reflecive boundary condiions a he membrane Many cells averaging

36 Shor imes

37 Wha else? Unusual Response o Force (?) f Assumpion Linear-like response of a single moor walking on a single MT: v v 0 f - mobiliy or v v 0 f i.e. sall force is f sall v 0

38 Along he force: x f linear response x x ~ 4 / 3 3/ for for * * * v 0 3 f 3 Perpendicular o he force: y ~ 4 / 3 for for * *

39 Conclusions: Increase of polariy (velociy) field and Euclidean dimensions leads o a decrease of he anomalous diffusion exponen. In 3-D disordered neworks acive ranspor may appear diffusive-like (wih minor logarihmic facors hining o is origin) consisen wih experimens. The finie, inermediae, processiviy of he microubule associaed moor proeins appears opimize he efficiency of ranspor beween he differen nework asks: ranspor from nucleus o he membrane and vice-versa, and beween localized cell comparmens. The local disorder of he microubule nework in he cell also appears o enhance he efficiency of ranspor beween differen locaions.

40 Thank you

41 Slope=1.50 Slope=1.01

42 Slope=1.333