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Nambu and Living World: Symmetry Breaking and Pattern Selection in Cellular Mosaic Formation Noriaki OGAWA ( ) [ RIKEN QHP Lab. / iTHES ] in collaboration with: Tetsuo Hatsuda ( ) [RIKEN Hatsuda QHP Lab. / iTHES]

  1. Nambu and Living World: Symmetry Breaking and Pattern Selection in Cellular Mosaic Formation Noriaki OGAWA ( 小 川 軌 明 ) [ RIKEN QHP Lab. / iTHES ] in collaboration with: Tetsuo Hatsuda ( 初 田 哲 男 ) [RIKEN Hatsuda QHP Lab. / iTHES] Atsushi Mochizuki ( 望 月 敦 史 ) [RIKEN Mochizuki Theo. Bio. Lab. / iTHES] Masashi Tachikawa ( 立 川 正 志 ) [RIKEN Mochizuki Theo. Bio. Lab. / iTHES] 2015 November 17 Osaka CTSR - Kavli IPMU - RIKEN iTHES International workshop “Nambu and Science Frontier”

  2. Symmetry Breaking cf.) Talks by Watanabe, Oda, Noumi

  3. Noriaki OGAWA (RIKEN) Cone Cellular Mosaic on Fish Retina [T. Allison, website] [Flamarique, Proc.B , 2012] [OIST Developmental Neurobiology (Masai) Unit, website]

  4. Noriaki OGAWA (RIKEN) Vertebrate Eye & Retina Retina Cone cells: B UV R G [Figure: from Wikipedia]

  5. Noriaki OGAWA (RIKEN) Mosaic of Cone Cells on Fish Retina Zebrafish type Medaka type [T. Allison, website] p4mg c2mm [Flamarique, Proc.B , 2012] [OIST Developmental Neurobiology (Masai) Unit, website]

  6. Conventional Model and SSB

  7. Noriaki OGAWA (RIKEN) 2D Physical Modeling [Tohya-Mochizuki-Iwasa, 1999] ● C e l l u l a r - l e v e l , S q u a r e - l a t t i c e M o d e l ( e x t e n d e d P o t t s m o d e l ) – 1 site is , or “double cone” B UV RG R G – Binding energies between neighborhoods (binding proteins on the membranes) B UV – Effective temperature for fluctuation

  8. Noriaki OGAWA (RIKEN) Reproduction of Zebrafish-pattern [TMI 1999] [Mochizuki 2002] 2 3 3 3 3 o 2 2 2 2 2 R G r 3 3 3 3 3 3 2 2 2 2 2 3 3 3 3 B UV 2 2 2 2 2 2 3 3 3 3 Metropolis Simulation (stochastic replacements) (Random Initial State)

  9. Noriaki OGAWA (RIKEN) Reproduction of Zebrafish-pattern [TMI 1999] [Mochizuki 2002] 2 3 3 3 3 o 2 2 2 2 2 R G r 3 3 3 3 3 3 2 2 2 2 2 3 3 3 3 B UV 2 2 2 2 2 2 3 3 3 3 Metropolis Simulation (stochastic replacements)

  10. Noriaki OGAWA (RIKEN) Reproduction of Zebrafish-pattern [TMI 1999] [Mochizuki 2002] 2 3 3 3 3 o 2 2 2 2 2 R G r 3 3 3 3 3 3 2 2 2 2 2 3 3 3 3 B UV 2 2 2 2 2 2 3 3 3 3 Metropolis Simulation (stochastic replacements) (Spontaneous Symmetry Breaking)

  11. Noriaki OGAWA (RIKEN) Selected Direction in Nature ? “rotated Zebrafish pattern” Zebrafish Central Marginal Growth

  12. Retina Growing Model and Analysis

  13. Noriaki OGAWA (RIKEN) Retinal Growth : Schematics D. A. Cameron and S. S. Easter (1993) Visual Neurosci. 10: 375-384 D. L. Stenkamp et al. (1997) J. Comp. Neurol. 382: 272-284

  14. Noriaki OGAWA (RIKEN) Retinal Growth : Modeling Edge of retina “front-end” “new-layer” “Pool” of cone cells

  15. Noriaki OGAWA (RIKEN) Markov-Chain of Layers w ● P r o b . d i s t r i b u t i o n o f 1 l a y e r o f c e l l s – 6 states for 1 cell: – P i distribution for 6 w states Transition Matrix Markov-chain Inter-layer Layer-internal

  16. Noriaki OGAWA (RIKEN) Transition Matrix around T=0 Fluctuation term from T>0 Rotated Wild-type

  17. Noriaki OGAWA (RIKEN) Multi-stability at T=0 ? Wild-type (1) Wild-type (2) Rotated Grow

  18. Noriaki OGAWA (RIKEN) Growth of “Rotated” at T>0 ? Typical one-shot simulation: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ( w = 16 , T=0.5)

  19. Noriaki OGAWA (RIKEN) Growth of “Rotated” at T>0 ? Typical one-shot simulation: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ( w = 16 , T=0.5)

  20. Noriaki OGAWA (RIKEN) Growth of “Rotated” at T>0 ? Typical one-shot simulation: 0 Rotated zebrafish 1 2 3 4 5 6 7 Dynamical 8 transition process 9 10 11 12 13 14 15 16 17 Wild zebrafish 18 19 20 ( w = 16 , T=0.5)

  21. Noriaki OGAWA (RIKEN) Monte-Carlo results “Agreement rates” along with growth From rotated pattern From random configuration I ( n ) I ( n ) ▲ ▲ ▲ 1.0 ● ● 1.0 ●● ● ● ● ●●●● ● ●● ●● ● ● ● ● ● ● ● ● ● ● ●●● ● ● ● ● ● ● ● ●● ●● ● ▲ ● ● ●● ● ● ● ●●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ▲ ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ▲ ● ● ● ● ● ● ● ● ● ● ● ▲ ● ● ● ● ● ● ● ● ▲ ● ● ● ● ● ▲ ● ● ● ● ● ● ● ● ● ● ▲ ● ● ● ● ● ● ● ● ● ● ● ● 0.8 ● ● ● ●● ● ● ● ● ● ● ● ● ● ● 0.8 ● ● ● ● ● ● ● ● ● ● ● ▲ ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ▲ ● ▲ ● ● ● ● ● ▲ ● ● ● ● ● ● ● ● 0.6 ● 0.6 ▲ ● ▲ ● ● ▲ ▲ ● ▲ ● ▲ ● ▲ ▲ ● ● 0.4 ● 0.4 ▲ ▲ ▲ ● ▲ ● ▲ ● ▲ ▲ ▲ ▲ 0.2 0.2 ▲ ● ● ▲ ● ▲ ▲ ▲ ▲ ▲ ▲ ● ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ● ● ● ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ● ▲ ▲ ▲ ● ● ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ● ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲▲ ▲ ▲ ▲ ▲ ● ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲▲▲ ▲ ▲ ▲ ▲ ● ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ● ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲▲ ▲▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲▲ ▲ ▲ ▲ ▲▲▲ ▲ ▲ ▲ ▲ ▲▲▲ ▲ ● ● ● 50 n ▲ ▲ ▲ ▲ ▲▲ ▲ 50 n ▲ 10 20 30 40 10 20 30 40 T=0.4 T=0.5 T=0.65 ( w = 16)

  22. Noriaki OGAWA (RIKEN) Eigen-spectrum of Transition Matrix (w = 4, T=0.5) Rotated Wild-type 1 0.2426 0.2426 0.2426 0.2426 0.00047 0.00045 0.00047 0.00045 -0.948 1 -1 -0.225 0.225 97% -0.948 -0.504 0.504 1 -1 0.910 1 1 -1 -1 0.865 -1 -1 -1 -1 0.8319 0.8076 0.8319 0.8076 0.864i 1 -0.97 i -1 0.97 i -0.864i 1 0.97 i -1 -0.97 i -0.863 0.024 0.024 0.024 0.024 1 -0.971 1 -0.971 0.321 1 1 1 1 0.0764 0.014 0.0764 0.014 …

  23. Pattern Selection Mechanism from Toy-Model

  24. Noriaki OGAWA (RIKEN) Directional Assymmetry of Bindings ? “rotated Zebrafish pattern” Zebrafish 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 2 R G 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 3 3 B UV 2 Horizontal (intra-layer) Vertical (inter-layer) bindings stronger bindings stronger

  25. Noriaki OGAWA (RIKEN) Simplified Toy-Model 2-states model Pattern α: AAAAA... Pattern β: BBBBB... Fluctuations U A A A U A B U B B U B V AA V AA V BB V BB A A B B U A U A U B U B V AA V BB V BA V BA A U A U B B B U B A U A V AA V BB V BB V AA A B B A U A U B U B U A U A + V BA = W = > U A + V AA U B + V BB U A + V AB

  26. Noriaki OGAWA (RIKEN) Simplified Toy-Model: fluctuations 2-states model Pattern α: AAAAA... Pattern β: BBBBB... Fluctuations

  27. Noriaki OGAWA (RIKEN) Intra-layer Energy governs Stability Fluctuations Eigen-spectrum Stationary distribution Larger layer-internal energy is favored.

  28. Noriaki OGAWA (RIKEN) Same Mechanism Working ? “rotated Zebrafish pattern” Zebrafish 2 R G 3 3 B UV 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 >

  29. Noriaki OGAWA (RIKEN) Summary ● P h y s i c a l m o d e l i n g o f growing retina. – E x p r e s s e d b y M a r k o v - c h a i n D y n a m i c a l S y s t e m . – Seed for symmetry breaking ● Only “Wild-type” pattern can survive. – “Dynamical selection” between two patterns with same static energy. – Agreement with observation in real animals. Thanks!

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