SLIDE 1
Active mechanics of cells
Tetsuya Hiraiwa The University of Tokyo
100μm
(HeLa cells)
Active mechanics of cells Tetsuya Hiraiwa The University of Tokyo - - PowerPoint PPT Presentation
Active mechanics of cells Tetsuya Hiraiwa The University of Tokyo - - PowerPoint PPT Presentation
Active mechanics of cells Tetsuya Hiraiwa The University of Tokyo 100m Active mechanics of cells Tetsuya Hiraiwa The University of Tokyo (HeLa cells) Table of contents My research subjects Multi-cellular scale (>>10m)
SLIDE 2
SLIDE 3
Table of contents
7/11/2016 3/18
Multi-cellular scale (>>10μm) Cellular scale (~ several 10μm) Subcellular scale (< 10μm)
My research subjects Contractility in actin-myosin cytoskeleton Chemotactic migration
- f eukaryotic cells
Epithelial tissue dynamics
destin ation
[Bray et al. Science ‘88.] [Salbreux et al., TCB ‘13]
SLIDE 4
[G. Salbreux et al., Trends in Cell Biol. 22, 536 (2013).]
~300nm 50nm
◇
2016/7/11 4/18 Contractility in actomyosin network
Cytoskeleton, controlling cell shape
F-actin network
Cell (HeLa )
[G. Charras et al., J. Cell Biol. ‘06]
[Image from: http://csls-db.c.u-tokyo.ac.jp/ search/detail?image_repository_id=341]
~7 nm
◇
Persistence length ~ 17μm
Cortical cytoskeleton
SLIDE 5
Mechanics of cortical cytoskeleton
2016/7/11 Contractility in actomyosin network 5/18
“How act.-myo. cytosk. gets contractile??”
− +
Myosin (Motor) F-actin
[Bray et al. Science ‘88.]
Contractile Contractile
[J.Sedzinski, M.Biro et al., Nature 476, 462 (2011).]
Cytokinesis (HeLa cell)
F-actins Myosin
Motor-induced force
SLIDE 6
(𝑗-th F-act.) 𝑡𝑗
Theoretical model
F-actin Passive crosslinker Myosin mini-filament
Motor-force 𝑔
0 on F-actins
Myosin-heads try to move twd. determined dirs. alg. F-act., (𝜈𝑒𝑡𝑗/𝑒𝑢 = −𝑒𝑉/𝑒𝑡𝑗 with the potential 𝑉 = −𝑔
0 𝑗 𝑡𝑗)
2016/7/11 6/18
Protein friction (−𝜈𝑒𝑡𝑗/𝑒𝑢)
Filaments can freely rotate ard. crosslnk.
Turnover
Contractility in actomyosin network
[TH and G. Salbreux, Phys. Rev. Lett. 116, 188101 (2016).]
SLIDE 7
Numerical results
2016/7/11 7/18 Contractility in actomyosin network
Details will be discussed on the poster
Without passive crosslinkers With passive crosslinkers
(w/o crosslnk. turnover) (with crosslnk. turnover)
→ Extensile (Diffusive) → Contractile
[TH and G. Salbreux, PRL 116, 188101 (2016).]
SLIDE 8
Table of contents
7/11/2016 8/18
Multi-cellular scale (>>10μm) Cellular scale (~ several 10μm) Subcellular scale (< 10μm)
My research subjects Contractility in actin-myosin cytoskeleton Chemotactic migration
- f eukaryotic cells
Epithelial tissue dynamics
destin ation
[Bray et al. Science ‘88.] [Salbreux et al., TCB ‘13]
SLIDE 9
Chemotactic migration of a eukaryotic cell
7/11/2016 Chemotactic migration 9/18
[ C. McCann et al.,
- J. Cell Science, 2010. ]
Chemotaxis of Dictyostelium discoideum (aca-)
Every 30 seconds for 90 minutes. Using phase-contrast microscopy with a 5× objective.
Chemoattractant (cAMP)
“Theor. model describing chemotaxis trajectory?”
SLIDE 10
EoM of a cell as a self-driven object
𝑒 𝑒𝑢 𝒓 = 𝐽𝑟(1 − 𝑟2)𝒓 + 𝒈.𝑡. + 𝝄 𝜈 𝑒 𝑒𝑢 𝒚 = 𝜓𝒓
Deterministic bias due to chem. grad. White Gaussian noise
7/11/2016 Chemotactic migration 10/18
[TH et al., Physical Biology 11, 056002 (2014).]
𝒓
𝒘 = 𝑒𝒚 𝑒𝑢
𝑙𝑝𝑜 𝑙𝑝𝑔𝑔
𝑤𝑡: constant speed (= 𝜓/𝜈)
(Biol. pr.) Polarity dynamics (Mechanical process) Force balance btw. friction and momentum generation alg. polarity (𝒓)
Spontaneous polarity formation
Responsiveness 𝑔
𝑟
[ Fuller et al, 2009 ] 20 μm
(Experiment)
(𝒈.𝑡. = 0, 𝑇 with chemotact. bias 𝑇 = 0.1, Dispers. 𝐸 of noise 𝝄 = 0.5)
𝐽𝑟 = 100
Distribution 𝑄
𝑡(𝜄𝑤)
migration direction 𝜄𝑤/𝜌
(using realistic Dicty. Parameters)
when polarity 𝒓 is spontaneously formed w/o spontaneous formation of polarity
Gradient direction
SLIDE 11
Toward many cell system
𝑒 𝑒𝑢 𝒓𝑗 = 𝐽𝑟 1 − 𝑟𝑗2 𝒓𝑗 + 𝑲𝑗({𝒚𝑘}, {𝒓𝑘}) + 𝒈.𝑡. + 𝝄𝑗 𝜈 𝑒 𝑒𝑢 𝒚𝑗 = 𝜓𝒓𝑗 + 𝑳𝑗( 𝒚𝑘 )
7/11/2016 Chemotactic migration 11/18
Cell-cell avoidance
𝒚𝑗 𝒚𝑘
Alignment
𝑠
𝑗 -th cell Xenopus Neural Crest cells [E. Theveneau et al.
- Dev. Cell 19, 39 (2010).]
(Chemo- attractant)
SLIDE 12
Table of contents
7/11/2016 12/18
Multi-cellular scale (>>10μm) Cellular scale (~ several 10μm) Subcellular scale (< 10μm)
My research subjects Contractility in actin-myosin cytoskeleton Chemotactic migration
- f eukaryotic cells
Epithelial tissue dynamics
destin ation
[Bray et al. Science ‘88.] [Salbreux et al., TCB ‘13]
SLIDE 13
top view
Multicellular organism are covered by epithelial tissue
2016/7/11 13/18
[http://www.cdb.riken.jp/en/research/laboratory/wang.html]
Morphogenetic dynamics
Adherence junction and Actomyosin bundle Lateral view
[Y. Wang et al., Dev. Cell 25, 299 (2013).]
Drosophila embryogenesis Adhesion molecules (E-cadherin-GFP)
SLIDE 14
[ E. Kuranaga et al., Development 138, 1493 (2011).]
[ M. Suzanne et al., Curr. Biol ‘10.]
Epithelial tissue dynamics
“How can this long-term motion be realized?”
2016/7/11 14/18 Epithelial cell migration
25 h. after puparium
~100um
SLIDE 15
2016/7/11 15/18
・ Variational dynamics: 𝜈 𝑒
𝑒𝑢
𝑠𝑗 = − 𝜖𝐹({
𝑠𝑗}) 𝜖 𝑠𝑗
Model ― Cellular vertex model
Epithelial cell migration
[ D. B. Staple et al. Eur. Phys. J. E 33, 117 (2010). ] [T. Nagai and H. Honda, Phil. Mag. 81, 699 (2001).]
・ Junctional remodeling
𝑗 𝑘
< 𝒋, 𝒌 >
𝐹 𝑠
𝛽
=
𝐿 2 𝛽:𝑑𝑓𝑚𝑚𝑡 𝐵𝛽 − 𝐵 0 2 + 𝐿𝑞 2 𝛽:𝑑𝑓𝑚𝑚𝑡 𝑀𝛽 − 𝑀 0 2 + <𝑗,𝑘>:𝑐𝑝𝑜𝑒𝑡 Λ𝑗𝑘𝑚𝑗𝑘
𝒔𝒋
~10μm Cell area (𝐵α) control Cell perimeter (𝑀α) control Bond-specific tension (𝑚𝑗𝑘: length of the bond < 𝑗, 𝑘 >) E-cadherin
SLIDE 16
Introducing chirality in tension
2016/7/11 16/18 Epithelial cell migration
Anterior- Posterior axis
Bond specificity in tension 𝜇𝑗𝑘 𝑢 (chirality in tension strength) 𝜾𝟏 = 𝝆/𝟓
𝜇𝑗𝑘 𝑢 = 𝛿1 𝑢 × cos2 (𝜄𝑗𝑘 − 𝜄0)
with 𝜄0 = 45° and 𝛿1 𝑢 = 𝛿1
(0) 1+cos 2𝜌𝑔𝑗𝑘𝑢 2
Myosin (II) distribution In vivo [K. Sato, TH, E. Maekawa, A. Isomura, T. Shibata and E. Kurenaga, Nat. Com. 6, 10074 (2015).]
SLIDE 17
Model: Implementation
2016/7/11 Epithelial cell migration 17 /18
The direction in which tension is maximally strengthened Bond
Torque force
×
Myosin (II) may be “actively” transported
𝝂 𝒆 𝒆𝒖 𝒔𝒌 = − 𝝐𝑭 𝒔𝜷 , 𝜧𝒋𝒌 𝝐𝒔𝒋 |𝜧𝒋𝒌=𝝁𝒋𝒌 𝒖
with 𝜇𝑗𝑘 𝑢 = 𝛿1 𝑢 × cos2(𝜄𝑗𝑘 − 𝜄0)
Mechanical process : 𝜈 𝑒
𝑒𝑢
𝑠
𝑘 = − 𝜖𝐹 𝑠𝛽 , 𝛭𝑗𝑘 𝜖 𝑠𝑗
Active process : τ
𝑒𝛭𝑗𝑘 𝑒𝑢 = 0 = −(𝛭𝑗𝑘 − 𝜇𝑗𝑘 𝑢 )
“Mechano-active” coupling
SLIDE 18
Numerical results
2016/7/11 Epithelial cell migration 18/18
[K. Sato, TH, E. Maekawa, A. Isomura, T. Shibata and E. Kuranaga, Nat. Com. 6, 10074 (2015).]
A P A
- Comp. with in vivo data
Sim. In vivo
(ex) bond angle distribution around AP axis
During rotation Before rotation
A A
SLIDE 19
2016/7/11 19/18
(Cl.) Mechanical
- eq. of motion
Describing living cells’ dynamics
Finding the minimal “biological” assumption
＋
Mechanics on active, dynamic motions of living cells
SLIDE 20
Acknowledgements
- Dr. Fabio Staniscia
- Dr. Matthew Smith
- Dr. Guillaume Salbreux
TH and G. Salbreux, Phys. Rev. Lett. 116, 188101 (2016)
On motor-induced contractiled stress in an isotropic network On a mechanism of epithelial migration
- Dr. Katsuhiko Sato, Dr. Tatsuo Shibata
- Dr. Erina Kuranaga, Dr. Emi Maekawa, Ayako Isomura
- K. Sato, TH, E. Maekawa, A. Isomura, T. Shibata and E. Kuranaga, Nat. Com. 6, 10074 (2015).
- K. Sato, TH and T. Shibata, Phys. Rev. Lett. 115, 188102 (2015).
On theoretical modeling of chemotactic migration
- Dr. Tatsuo Shibata, Dr. Akinori Baba, Dr. Masatoshi Nishikawa
- Dr. Akihiro Nagamatsu, Naohiro Akuzawa
TH, A. Nagamatsu, N. Akuzawa, M. Nishikawa and T. Shibata, Phys. Biol. 11, 056002 (2014).