Active Stresses and Self-organization in Cytoskeletal Networks

Transcription

1 Active Stresses and Self-organization in Cytoskeletal Networks Cytoskeleton: rich mechanics, dynamics and activity Mechanics: nonlinear elasticity, stiffening, anomalous stresses Active stresses and non-equilibrium fluctuations Disordered self-organization of acto-myosin Stability of networks by stress Inspiration for materials Collaborators: networks in vitro and in vivo Janmey, Schmidt, Weitz, Yao, Brangwynne, Silva, Koenderink, Mizuno, Gardel, Murrel theory of networks Broedersz, Sheinman, Levine, Mao, Lubensky

2 The cytoskeleton, a semiflexible composite The Cell intermediate filament F-actin microtubule Vale lab, UCSF

3 The cytoskeleton, a semiflexible composite Extracellular matrix The Cell fibrin intermediate filament F-actin microtubule blood clot Yuri Veklich and John Weisel Challenges: - origins of elasticity - nonlinear response - role of connectivity - motor/contractile activity

4 Nonlinear Elasticity: strain stiffening [biopolymers] 0.1 to 0.3 % PAM 5% G (Pa) Storm, et al. Nature (2005); also: Gardel et al., Science (2004); Gardel et al., PRL (2004); Lin et al., PRL (2010); & Yao et al., Biophys J (2010).

5 Nonlinear Elasticity: strain stiffening neurofilaments Flexible limit: Marko & Siggia 1994 Stiff limit: FCM, Kas, Janmey 1995 with Lin & Yao, et al., PRL (2010) & Biophys J (2010). & with Gardel, et al., Science, PRL (2004). see also Fixman & Kovac 1972

6 Non-equilibrium stiffening of active gels Design of artificial model system with cell-like activity Control of mechanics by motor activity Mizuno, Tardin, Schmidt, FCM, Science, (2007); FCM & Levine, PRL (2008); Koenderink et al., PNAS (2009).

7 Motion in Cells What governs motion in cell? -Directed/active processes -Random/thermal fluctuations -Non-directed active motion? w/ Brangwynne et al., PNAS 104: (2007); PRL 100: (2008); J Cell Biol, 183: 583 (2008); Trends Cell Biol, 19:423 (2009).

8 Thermal Motion, Equilibrium Fluctuations Fluctuation-Dissipation Theorem

9 Effect of molecular motors: Active gels Mizuno, et al., Science, (2007). No activity Vital, non-thermal motion With motor activity α (ω), ωc/2kt (m/n) fluctuations response ωc(ω)/2kt α (ω) α (ω), ωc/2kt (m/n) Equilib Frequency (Hz) Frequency (Hz) Along with these contractile fluctuations, there is a nearly 100-fold ATP-dependent stiffening of the network, which is consistent with tensions ~ few pn

10 Effect of molecular motors: Active gels with A Levine, PRL 2008; JPC 2009 Unbinding & release force fluctuations passive time active

11 Effect of molecular motors: Active gels with A Levine, PRL 2008; JPC 2009 Unbinding & release MSD 1 elastic active frequency time

12 Cell activity probed by injected beads Open symbols: 10 μm Blebbista5n treated (inhibit Myosin II motors). Lines: Sodium Azide + 2- deoxy- D- glucose treated (deplete ATP). with Guo and Weitz

13 Cell activity probed by injected beads Open symbols: 10 μm Blebbista5n treated (inhibit Myosin II motors). Lines: Sodium Azide + 2- deoxy- D- glucose treated (deplete ATP). Athermal Thermal with A Levine, PRL 2008 with Guo and Weitz

14 Athermal Fluctuations of MTs s with Brangwynne, Koenderink, Weitz, PNAS 2007, PRL 2008, JCB 2008.

15 Myosin coalescence, aggregation Martin, Kaschube & Wieschaus, Nature 2009

16 Contractile fluctuations and aggregation Green = myosin Red = actin Soares e Silva, Sturhmann, Depken, FCM, Koenderink, PNAS, see also Koehler, Schaller, Bausch, Nature Materials, 2011.

17 Contractile fluctuations and aggregation Green = myosin Red = actin Soares e Silva, Sturhmann, Depken, FCM, Koenderink, PNAS, see also Koehler, Schaller, Bausch, Nature Materials, 2011.

18 Buckling of actin leads to coalescence of aggregates Soares e Silva, Sturhmann, Depken, FCM, Koenderink, PNAS, 2011.

19 Buckling of actin leads to accumulation of actin and coalescence of aggregates Soares e Silva, Sturhmann, Depken, FCM, Koenderink, PNAS, 2011.

20 Connectivity and isostaticity 20 isostatic coordination J. C. Maxwell, Philos. Mag. 27, 27 (1864) S Alexander, Phys Rep 296, 65 (1998) M. Wyart et al., PRL. 101, (2008)

21 21 Connectivity and isostaticity isostatic coordination collagen (in vitro) S. Muenster actin-cortex vimemtin (in vitro) red blood cell (actin-spectrin) Y.-C.Lin J. C. Maxwell, Philos. Mag. 27, 27 (1864) S Alexander, Phys Rep 296, 65 (1998) M. Wyart et al., PRL. 101, (2008)

22 Critical behavior and shear-induced non-affine fluctuations D triangular lattice D FCC lattice shear modulus bend rigidity shear modulus bond occup. prob bond occup. prob. M B = 0 B > 0 CP Broedersz, X Mao, T Lubensky and FCM, Nature Phys (2011) T Tc

23 Phase diagram under load 23 rigid S Alexander (1998) Stress-induced stability of floppy networks See also Cai et al., J Cell Sci (2010). connectivity floppy stress/strain with Broedersz and Sheinman

24 Phase diagram under load 24 rigid S Alexander (1998) Stress-induced stability of floppy networks See also Cai et al., J Cell Sci (2010). connectivity floppy strain

25 Phase diagram under load 25 rigid flcuctuations S Alexander (1998) Stress-induced stability of floppy networks connectivity floppy strain

26 Phase diagram under load 26 rigid connectivity floppy Cai et al., J Cell Sci (2010). stress/strain with Broedersz and Sheinman

27 Phase diagram under load 27 rigid connectivity floppy Cai et al., J Cell Sci (2010). stress/strain with Broedersz and Sheinman

28 Active Stresses and Self-organization in Cytoskeletal Networks Cytoskeleton: rich mechanics, dynamics and activity Mechanics: nonlinear elasticity, stiffening, anomalous stresses Active stresses and non-equilibrium fluctuations Disordered self-organization of acto-myosin Stability of networks by stress Inspiration for materials Collaborators: networks in vitro and in vivo Janmey, Schmidt, Weitz, Yao, Brangwynne, Silva, Koenderink, Mizuno, Gardel, Murrel theory of networks Broedersz, Sheinman, Levine, Mao, Lubensky