Active mechanics of cells Tetsuya Hiraiwa The University of Tokyo
100μm Active mechanics of cells Tetsuya Hiraiwa The University of Tokyo (HeLa cells)
Table of contents My research subjects Multi-cellular scale (>>10μm) Epithelial tissue dynamics Cellular scale (~ several 10μm) Chemotactic migration ation destin of eukaryotic cells Subcellular Contractility in scale (< 10μm) [Bray et al. Science ‘88.] actin-myosin cytoskeleton [Salbreux et al., TCB ‘13] 7/11/2016 3/18
Cytoskeleton, controlling cell shape F-actin network ◇ Cortical cytoskeleton ~7 nm Cell (HeLa ) Persistence length ~ 17μm [Image from: http://csls-db.c.u-tokyo.ac.jp/ [G. Charras et al. , J. Cell Biol. ‘06] search/detail?image_repository_id=341] ◇ ~300 nm [G. Salbreux et al., Trends in Cell Biol. 22, 536 (2013).] 50nm 2016/7/11 Contractility in actomyosin network 4/18
Mechanics of cortical cytoskeleton Contractile Myosin + (Motor) Contractile F-actin − [Bray et al. Science ‘88.] Motor-induced force “How act. -myo. cytosk . gets contractile??” F-actins Myosin Cytokinesis (HeLa cell) [J.Sedzinski, M.Biro et al., Nature 476, 462 (2011).] 2016/7/11 Contractility in actomyosin network 5/18
Theoretical model [TH and G. Salbreux, Phys. Rev. Lett. 116, 188101 (2016).] F-actin Motor-force 𝑔 0 on F-actins Turnover ( 𝑗 -th F-act.) 𝑡 𝑗 Passive Myosin crosslinker mini-filament Filaments can freely Protein friction ( −𝜈𝑒𝑡 𝑗 /𝑒𝑢 ) rotate ard. crosslnk. Myosin-heads try to move twd. determined dirs. alg. F-act., ( 𝜈𝑒𝑡 𝑗 /𝑒𝑢 = −𝑒𝑉/𝑒𝑡 𝑗 with the potential 𝑉 = −𝑔 0 𝑗 𝑡 𝑗 ) 2016/7/11 Contractility in actomyosin network 6/18
Numerical results Without passive crosslinkers With passive crosslinkers → Extensile (Diffusive) → Contractile (w/o crosslnk. turnover) (with crosslnk. turnover) [TH and G. Salbreux, PRL 116, 188101 (2016).] Details will be discussed on the poster 2016/7/11 Contractility in actomyosin network 7/18
Table of contents My research subjects Multi-cellular scale (>>10μm) Epithelial tissue dynamics Cellular scale (~ several 10μm) Chemotactic migration ation destin of eukaryotic cells Subcellular Contractility in scale (< 10μm) [Bray et al. Science ‘88.] actin-myosin cytoskeleton [Salbreux et al., TCB ‘13] 7/11/2016 8/18
Chemotactic migration of a eukaryotic cell Chemoattractant (cAMP) Every 30 seconds for 90 minutes. [ C. McCann et al., Using J. Cell Science, 2010. ] phase-contrast microscopy with a 5 × objective. Chemotaxis of Dictyostelium discoideum (aca-) “ Theor . model describing chemotaxis trajectory?” 7/11/2016 Chemotactic migration 9/18
EoM of a cell as a self-driven object Responsiveness 𝑔 [TH et al., Physical Biology 11, 056002 (2014).] 𝑟 𝜈 𝑒 (Mechanical process) 𝑒𝑢 𝒚 = 𝜓𝒓 𝑙 𝑝𝑜 Force balance btw. friction and 𝒓 momentum generation alg. polarity ( 𝒓 ) 𝒘 = 𝑒𝒚 𝑒 Deterministic bias due to chem. grad. 𝑒𝑢 (Biol. pr.) 𝑒𝑢 𝒓 = 𝐽 𝑟 (1 − 𝑟 2 )𝒓 + 𝒈 .𝑡. + 𝝄 Polarity 𝑙 𝑝𝑔𝑔 dynamics 𝑤 𝑡 : constant speed ( = 𝜓/𝜈 ) Spontaneous polarity formation White Gaussian noise Gradient direction when polarity 𝒓 𝑡 (𝜄 𝑤 ) is spontaneously formed 20 μ m Distribution 𝑄 w/o spontaneous formation of polarity (Experiment) 𝐽 𝑟 = 100 migration direction 𝜄 𝑤 /𝜌 [ Fuller et al, 2009 ] ( 𝒈 .𝑡. = 0, 𝑇 with chemotact. bias 𝑇 = 0.1 , Dispers. 𝐸 of noise 𝝄 = 0.5) (using realistic Dicty. Parameters) 7/11/2016 Chemotactic migration 10/18
Toward many cell system Cell-cell avoidance 𝜈 𝑒 𝒚 𝑗 𝒚 𝑘 𝑒𝑢 𝒚 𝑗 = 𝜓𝒓 𝑗 + 𝑳 𝑗 ( 𝒚 𝑘 ) 𝑒 𝑒𝑢 𝒓 𝑗 = 𝐽 𝑟 1 − 𝑟 𝑗2 𝒓 𝑗 + 𝑲 𝑗 ({𝒚 𝑘 }, {𝒓 𝑘 }) + 𝒈 .𝑡. + 𝝄 𝑗 Alignment 𝑠 𝑗 -th cell (Chemo- attractant) Xenopus Neural Crest cells [E. Theveneau et al. Dev. Cell 19, 39 (2010).] 7/11/2016 Chemotactic migration 11/18
Table of contents My research subjects Multi-cellular scale (>>10μm) Epithelial tissue dynamics Cellular scale (~ several 10μm) Chemotactic migration ation destin of eukaryotic cells Subcellular Contractility in scale (< 10μm) [Bray et al. Science ‘88.] actin-myosin cytoskeleton [Salbreux et al., TCB ‘13] 7/11/2016 12/18
Multicellular organism are covered by Adhesion molecules epithelial tissue (E-cadherin-GFP) Drosophila embryogenesis [http://www.cdb.riken.jp/en/research/laboratory/wang.html] [Y. Wang et al., Dev. Cell 25, 299 (2013).] Adherence junction and Actomyosin bundle top view Lateral view 2016/7/11 Morphogenetic dynamics 13/18
Epithelial tissue dynamics ~100um 25 h. after puparium [ E. Kuranaga et al., [ M. Suzanne et al., Curr. Biol ‘10.] Development 138, 1493 (2011).] “How can this long - term motion be realized?” 2016/7/11 Epithelial cell migration 14/18
Model ― Cellular vertex model ~10μm 𝒔 𝒋 𝑗 < 𝒋, 𝒌 > 𝑘 E-cadherin ・ Variational dynamics: 𝜈 𝑒 𝑠 𝑗 = − 𝜖𝐹({ 𝑠 𝑗 }) 𝑒𝑢 𝜖 𝑠 𝑗 2 + 2 + <𝑗,𝑘>:𝑐𝑝𝑜𝑒𝑡 Λ 𝑗𝑘 𝑚 𝑗𝑘 𝐿 𝑞 𝐿 2 𝛽:𝑑𝑓𝑚𝑚𝑡 𝐵 𝛽 − 𝐵 0 2 𝛽:𝑑𝑓𝑚𝑚𝑡 𝑀 𝛽 − 𝑀 0 𝐹 𝑠 = 𝛽 Cell area ( 𝐵 α ) control Cell perimeter ( 𝑀 α ) control Bond-specific tension ( 𝑚 𝑗𝑘 : length of the ・ Junctional remodeling bond < 𝑗, 𝑘 > ) [T. Nagai and H. Honda, Phil. Mag. 81, 699 (2001).] [ D. B. Staple et al. Eur. Phys. J. E 33, 117 (2010). ] 2016/7/11 Epithelial cell migration 15/18
Introducing chirality in tension Myosin (II) distribution 𝜾 𝟏 = 𝝆/𝟓 In vivo Anterior- Bond specificity in tension 𝜇 𝑗𝑘 𝑢 Posterior axis (chirality in tension strength) 𝜇 𝑗𝑘 𝑢 = 𝛿 1 𝑢 × cos 2 (𝜄 𝑗𝑘 − 𝜄 0 ) 1+cos 2𝜌𝑔 𝑗𝑘 𝑢 (0) with 𝜄 0 = 45 ° and 𝛿 1 𝑢 = 𝛿 1 2 [K. Sato, TH, E. Maekawa, A. Isomura, T. Shibata and E. Kurenaga, Nat. Com. 6, 10074 (2015).] 2016/7/11 Epithelial cell migration 16/18
Model: Implementation 𝝐𝑭 𝒔 𝜷 , 𝜧 𝒋𝒌 𝝂 𝒆 𝒆𝒖 𝒔 𝒌 = − | 𝜧 𝒋𝒌 =𝝁 𝒋𝒌 𝒖 𝝐𝒔 𝒋 with 𝜇 𝑗𝑘 𝑢 = 𝛿 1 𝑢 × cos 2 (𝜄 𝑗𝑘 − 𝜄 0 ) × The direction in which tension is maximally strengthened Torque force Myosin (II) may be “actively” transported Bond 𝜖𝐹 𝑠 𝛽 , 𝛭 𝑗𝑘 Mechanical process : 𝜈 𝑒 𝑒𝑢 𝑠 𝑘 = − 𝜖 𝑠 𝑗 “ Mechano- active” 𝑒𝛭 𝑗𝑘 coupling Active process : τ 𝑒𝑢 = 0 = −(𝛭 𝑗𝑘 − 𝜇 𝑗𝑘 𝑢 ) 2016/7/11 Epithelial cell migration 17 /18
Numerical results Comp. with in vivo data A A (ex) bond angle distribution around AP axis In vivo P Before rotation During rotation Sim. A A [K. Sato, TH, E. Maekawa, A. Isomura, T. Shibata and E. Kuranaga, Nat. Com. 6, 10074 (2015).] 2016/7/11 Epithelial cell migration 18/18
Describing living cells’ dynamics Mechanics on active, dynamic motions of living cells (Cl.) Mechanical Finding the minimal ＋ eq. of motion “biological” assumption 2016/7/11 19/18
Acknowledgements On motor-induced contractiled stress in an isotropic network Dr. Guillaume Salbreux TH and G. Salbreux, Phys. Rev. Lett. 116, 188101 (2016) Dr. Fabio Staniscia Dr. Matthew Smith On theoretical modeling of chemotactic migration Thank you for your attention 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). 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).
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