Possible mechanisms for initiating macroscopic left-right asymmetry in developing organisms Chris Henley, Ricky Chachra, Jimmy Shen Cornell U. [Support: U.S. Dept. of Energy] APS March Meeting, Mar. 2, 2012 1
Key ideas Many animals (and plants) have systematic left-right (L/R) or chiral asymmetry. What mechanisms? Omitted story: Vertebrates heart, lungs, etc. story 1: molluscs shell twists right-handed (C. elegans similar) (short) story 2: plants roots/shoots twist w/species-dependent sense 2
Why left/right is a natural topic for physicists L/R must come from the microscopic chirality of organic molecules (under genetic control). Usually in biology spatial patterns come from diffusion of signals and regulatory interactions. Not this! (Passive diffusion has no L/R bias) mechanisms involve forces and motions (e.g. cytoskeleton) A priori symmetries constrain the mechanism 3
Two levels in any mechanism a) intracellular molecular, active 2D collective states b) intercellular mechanics body plan Problem of right-hand rule On either level, start with 2 orthogonal axes via spontaneous symmetry breaking: x a polarization z normal to membrane (or to a cell layer) Develop third y axis by SSB also (I assume) but need a small biasing field to ensure y =z x? (Each symbol has a concrete realization is the chirality.) 4
Story 1: Spiral cleavage in snails Experimental a) 1st 4 cells form a square 4 daughter cells on top with twist (WT in dextral sense). b) Twist depends on actin [ Y. Shibazaki et al (Kuroda lab) Curr Biol 14, 1462-1467 (2004)] 3 levels to show: (from top down) 1.1 Inter-cell mechanics 1.2 Intra-cell continuum 1.3 Intra-cell molecular 5
1.1 Inter-cell 2 scenarios: (a,b,c): latent-spindle (early action) (c,d,e): adhesionconstraint (delayed action) a) b) c) AB A B A B D C D C CD CD C C AB D D d) e) f) AB B A A B C D D CD C [Little black arrows = flow, 2-headed arrows = spindles] Flow arrows in same directions, 2 scenarios, give opposite results. 6
Looks like dextral L. Stagnalis (RIGHT) and its sinistral mutant. 7
1.2 Intra-cell level: continuum A minimal, ad-hoc, 2D theory. [Strempel et al arxiv:1112.3492 systematic] Say filaments exert clockwise (CW) forces on each other. 2D stress tensor: σ xy = σ yx = q(ρ(r)) q= skew pressure ; ρ(r) = density. Result: velocity v ẑ ρ. drives net currents wherever actomyosin density has a gradient. force pre division furrow actomyosin density E.g. around dividing cell s contractile ring (right). QED! N.B. Other chiral behaviors of actomyosin cortical layer seen in C. elegans egg polarization and in frog eggs 8
1.3 Intra-cell level: molecular A myosin bridge drives 2 actins past each other (green arrows). Each myosin motor spirals CCW in its step. Then result depends on relative alignment of the filaments: CCW drive bridge is away from membrane less drag (?). drive on left rides is closer to membrane more drag (?). (a) actin (c) membrane (b) (d) drag myosin II bridge 9
Story 2: Plants microtubule array on membrane Growing plants chirality correlates w/that of microtubule (mt) orientations spiraling around long axis of the (cylindrical) cells. [T. Hashimoto group, arabidopsis] Here we focus on dynamic rotations of mt array. 10
Expt l rotation: Left: raw image (labeled by rotation sense); right, motions in 1 domain at 20min intervals. [ J. Chan et al, 2007] 11
Microtubule (mt) simulation (w/j. X. Shen) Interaction of mt s are well(!) known from expts [Dixit & Cyr, Ambrose & Wasteneys] Collisions mt depolymerizes, or entrains whole 2D array becomes aligned. Handed interactions make array precess REMINDER symmetry principle: membrane must be involved. (a) mt branching at 30 : orientation of linking protein sterically constrained by nearby membrane. J. Chan observed asymmetry branching. Adopt this in simulations (next). OR (b) mt-mt collision L/R difference? (not yet checked!) 12
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Summary: active cortical layers. Story 1 Actomyosin (dividing animal cells) 1.1 Inter-cell level: Actin/myosin layer flows drive a twist around division axis. Depending when it acts, the same sense twist can drive opposite outcomes. Resembles dextral (WT)/sinistral mutant! 1.2 Intra-cell level, continuum theory for layer: actin-actin skew force mediated by myosin bridges antisymmetric stress tensor, flows 1.3 Intra-cellular, molecular level: screw motion of myosin II (filament s helical nature) along actin fibers next to membrane. Story 2: microtubule array] (elongating plant cells) Asymmetry in branching (binding molecule s chiral nature) Drives precession of array orientation. Either story: at molecular level, steric hindrance of membrane. 29
FURTHER CONCLUSIONS (EXTRA) Symmetry is key! Any of the mechanisms to produce L/R asymmetry must explicitly use 3 ingredients: dorsal/ventral asymmetry, or (in cell) in/out w.r.t membrane. anterior/posterior asymmetry, or (in cell) polarization, and helicity coming from the microscopic chirality of molecules. Chirality can enter by 1 screw mechanisms: translation along long helical fiber convert to rotation around axis (a) (processive?) motors (b) fiber-fiber collisions (c) changes of pitch of fiber 2 membrane-fiber binding proteins 30
Known chiral effects in actomyosin Xenopus egg: Time lapse shows fluorescently labeled points along several fibers: uniform shear. [ M. V. Danilchik et al Development 133, 4517-4526 (2006).] 1. Treated frog egg (above): incipient contractile ring (pre division) develops actin bundles shearing in leftward sense 2. C. elegans egg, after it polarizes and segregates actomyosin to anterior, that end twists around long axis 3. C. elegans at 8 cell stage (Wm. Wood). 4. Spiral cleavage in snail embryos at 8 cell stage, deciding adult chirality (Kuroda group)... 31