Active mechanics of cells. Tetsuya Hiraiwa The University of Tokyo

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1 Active mechanics of cells Tetsuya Hiraiwa The University of Tokyo

2 100μm Active mechanics of cells Tetsuya Hiraiwa The University of Tokyo (HeLa cells)

3 Cellular scale (~ several 10μm) Subcellular scale (< 10μm) Table of contents Multi-cellular scale (>>10μm) Contractility in actin-myosin cytoskeleton Epithelial tissue dynamics Chemotactic migration of eukaryotic cells My research subjects [Bray et al. Science 88.] [Salbreux et al., TCB 13] 7/11/2016 3/18 destin ation

4 ~7 nm Cytoskeleton, controlling cell shape F-actin network Cortical cytoskeleton Persistence length ~ 17μm [Image from: search/detail?image_repository_id=341] Cell (HeLa ) [G. Charras et al., J. Cell Biol. 06] [G. Salbreux et al., Trends in Cell Biol. 22, 536 (2013).] ~300nm 50nm 2016/7/11 Contractility in actomyosin network 4/18

5 Mechanics of cortical cytoskeleton Myosin (Motor) + F-actin Contractile Contractile Motor-induced force [Bray et al. Science 88.] How act.-myo. cytosk. gets contractile?? Cytokinesis (HeLa cell) F-actins Myosin [J.Sedzinski, M.Biro et al., Nature 476, 462 (2011).] 2016/7/11 Contractility in actomyosin network 5/18

6 Theoretical model [TH and G. Salbreux, Phys. Rev. Lett. 116, (2016).] Motor-force f 0 on F-actins F-actin Turnover (i-th F-act.) s i Myosin mini-filament Protein friction ( μds i /dt) Passive crosslinker Filaments can freely rotate ard. crosslnk. Myosin-heads try to move twd. determined dirs. alg. F-act., (μds i /dt = du/ds i with the potential U = f 0 i s i ) 2016/7/11 Contractility in actomyosin network 6/18

7 Numerical results Without passive crosslinkers Extensile (Diffusive) With passive crosslinkers Contractile (w/o crosslnk. turnover) (with crosslnk. turnover) [TH and G. Salbreux, PRL 116, (2016).] Details will be discussed on the poster 2016/7/11 Contractility in actomyosin network 7/18

8 Cellular scale (~ several 10μm) Table of contents Multi-cellular scale (>>10μm) Epithelial tissue dynamics Chemotactic migration of eukaryotic cells My research subjects destin ation Subcellular scale (< 10μm) Contractility in actin-myosin cytoskeleton [Bray et al. Science 88.] [Salbreux et al., TCB 13] 7/11/2016 8/18

9 Chemotactic migration of a eukaryotic cell Chemoattractant (camp) Every 30 seconds for 90 minutes. [ C. McCann et al., J. Cell Science, ] Using phase-contrast microscopy with a 5 objective. Chemotaxis of Dictyostelium discoideum (aca-) Theor. model describing chemotaxis trajectory? 7/11/2016 Chemotactic migration 9/18

10 Distribution P s (θ v ) v = dx dt EoM of a cell as a self-driven object q k on k off v s : constant speed (= χ/μ) 20 μm Responsiveness f q [TH et al., Physical Biology 11, (2014).] (Mechanical process) Force balance btw. friction and momentum generation alg. polarity (q) μ d x = χq dt Deterministic bias due to chem. grad. d dt q = I q(1 q 2 )q + f g.s. + ξ Spontaneous polarity formation (Biol. pr.) Polarity dynamics White Gaussian noise Gradient direction when polarity q is spontaneously formed (Experiment) [ Fuller et al, 2009 ] I q = 100 w/o spontaneous formation of polarity migration direction θ v /π (using realistic Dicty. Parameters) (f g.s. = 0, S with chemotact. bias S = 0.1, Dispers. D of noise ξ = 0.5) 7/11/2016 Chemotactic migration 10/18

11 d Toward many cell system μ d dt x i = χq i + K i ( x j ) dt q i = I q 1 q i 2 q i + J i ({x j }, {q j }) + f g.s. + ξ i Alignment Cell-cell avoidance x i x j r i -th cell Xenopus Neural Crest cells [E. Theveneau et al. Dev. Cell 19, 39 (2010).] 7/11/2016 Chemotactic migration 11/18 (Chemoattractant)

12 Cellular scale (~ several 10μm) Subcellular scale (< 10μm) Table of contents Multi-cellular scale (>>10μm) Contractility in actin-myosin cytoskeleton Epithelial tissue dynamics Chemotactic migration of eukaryotic cells My research subjects [Bray et al. Science 88.] [Salbreux et al., TCB 13] 7/11/ /18 destin ation

13 Multicellular organism are covered by epithelial tissue Adhesion molecules (E-cadherin-GFP) Drosophila embryogenesis [ [Y. Wang et al., Dev. Cell 25, 299 (2013).] Adherence junction and Actomyosin bundle Lateral view top view 2016/7/11 Morphogenetic dynamics 13/18

14 Epithelial tissue dynamics 25 h. after puparium ~100um [ M. Suzanne et al., Curr. Biol 10.] [ E. Kuranaga et al., Development 138, 1493 (2011).] How can this long-term motion be realized? 2016/7/11 Epithelial cell migration 14/18

15 ~10μm Model Cellular vertex model E-cadherin Variational dynamics: μ d dt r i = E({ r i}) r i Cell area (A α ) control Cell perimeter (L α ) control Bond-specific tension Junctional remodeling (l ij : length of the bond < i, j >) r i i < i, j > j E r α = K 2 α:cells A α A K p 2 α:cells L α L <i,j>:bonds Λ ij l ij [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

16 Introducing chirality in tension θ 0 = π/4 Myosin (II) distribution In vivo Anterior- Posterior axis Bond specificity in tension λ ij t (chirality in tension strength) λ ij t = γ 1 t cos 2 (θ ij θ 0 ) with θ 0 = 45 and γ 1 t = γ 1 (0) 1+cos 2πf ij t [K. Sato, TH, E. Maekawa, A. Isomura, T. Shibata and E. Kurenaga, Nat. Com. 6, (2015).] 2016/7/11 Epithelial cell migration 16/18 2

17 Model: Implementation μ d dt r j = E Myosin (II) may be actively transported with λ ij t = γ 1 t cos 2 (θ ij θ 0 ) Torque force r α, Λ ij r i The direction in which tension is maximally strengthened Bond Λij =λ ij t Mechano-active coupling Mechanical process : μ d dt r j = E r α, Λ ij r i Active process : τ dλ ij dt = 0 = (Λ ij λ ij t ) 2016/7/11 Epithelial cell migration 17 /18

18 Numerical results A A Comp. with in vivo data (ex) bond angle distribution around AP axis In vivo P Before rotation Sim. During rotation A A [K. Sato, TH, E. Maekawa, A. Isomura, T. Shibata and E. Kuranaga, Nat. Com. 6, (2015).] 2016/7/11 Epithelial cell migration 18/18

19 Describing living cells dynamics Mechanics on active, dynamic motions of living cells (Cl.) Mechanical eq. of motion + Finding the minimal biological assumption 2016/7/11 19/18

20 Dr. Fabio Staniscia Dr. Matthew Smith Acknowledgements On motor-induced contractiled stress in an isotropic network Dr. Guillaume Salbreux TH and G. Salbreux, Phys. Rev. Lett. 116, (2016) 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, (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, (2015). K. Sato, TH and T. Shibata, Phys. Rev. Lett. 115, (2015).