Nonequilibrium physics
in multicellular systems
川口喬吾
Kyogo Kawaguchi
Riken BDR (from Sep 2018)1

Biology

Physics

Biology

Physics

Fundamental questions

TheoryNew experiments

Data analysis methods

Outline
1. Skin (tissue) homeostasis
Interacting particle system
2. Collective motion in cultured neural stem cells
Active nematics
3. Acknowledgements41. Skin homeostasis is maintained bynearest neighbor fate coupling[Science 352, 1471 (2016), Phys Rev E 96 012401 (2017), Cell Stem Cell 23, 677 (2018)]

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Tissue homeostasis:
Epidermal stem cells
are confined in a two-dimensional layer
Cross section
sketchDivision

Differentiation

Basal layer = stem cells(基底細胞層)Leblond, Walker (1956)

Turn over: 2-10 days

6Day 012

3514182024

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18

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18a18b13a26

24a12a

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11a
108b2123

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11
1316Day 2

12a109821
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Day 111b17a16a16b2117b
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19a26

Neighbor fate coupling?

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Neighbor fate coupling model= Voter model (DP2)- Model for “voters”- and critical coarsening- Universality class (two absorbing states)
Dornic et al. Phys. Rev. Lett. 87, 045701 (2001)
Hammal et al. Phys. Rev. Lett 94, 230601 (2005)8

~10 years ago:clonal analysis showed scaling behavior

Average cells / clone

Single cell labeling in live mice (Cre-induced)

Time post-labeling (weeks)
Clayton et al., Nature (2007)
Doupe et al., Dev. Cell (2010)
Klein & Simons, Development (2011)

Average number of cells
in surviving clones
Clone size distribution:
9Critical birth death model explains scaling

Division

Prob.

0.5
0.5
Differentiation
Average number of cells
in surviving clones
Clone size distribution:
Athreya and Ney “Branching Processes” (Dover)
Review: Klein & Simons, Development (2011)10

Summary of scaling: experiment and theory
Experiment(skin)2

Average clone size:

Cell autonomous
Fate(Critical birth death)

Coordinated fate (voter model)>2

Clone size
cumulative distribution:
Experiment:
Intestine[Lopez-Garcia et al. (2010)
Snippert et al. (2010)]
Seminiferous tubule[Klein et al., (2010)
Yoshida lab]

11Problem of 2D
Experiment(skin)

2

Cell autonomous
Fate

Coordinated fate (voter model)(Critical birth death)

Average clone size:>2Clone size
cumulative distribution:
Average cells / clone

Average size ofsurviving clone

Simulation/theory

Experiment

Time post-labeling (weeks)

12Fate coordination can be quantified
using “fluctuation test”

Blue – Red = 0 ± 1.5 (s.d.)

..

..

~𝑁𝑁

1/2

~𝑁𝑁 1/4

Blue – Red = 0 ± 0.5 (s.d.)Variance of net growth per cell

Data shows that fates of neighboring
cells are coordinatedVary window size
0.5124(in cellsize units)

Days

Time scale of coordination: 1-2 days

Length scale of coordination:

size of a single cell

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Modeling neighboring fate coupling by
local density feedback
From more data analysis:

Making model:

Cell Stem Cell 23, 677 (2018)

Cell density =Division

1-pp
Differentiation
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Modeling neighboring fate coupling by
local density feedback
Differentiation

Making model:

Division

Cell density =Division

1-pp
Differentiation
2L16

Deriving the voter model action
from particle dynamics
Many-body Langevin equation:-> Continuum dynamics of labeled cell density-> MSRDJ field theory-> linearize (around uniform density) -> lots of Gaussian integrals-> renormalization-> Voter model action (+ irrelevant terms)-> Dynamics:
Yamaguchi and Kawaguchi, in preparation17

Model has two regimes
separated at the interaction length scale
・Small scale regime:
critical birth death model (cell autonomous)
0.5
0.5
Crossover at L

2L

・Large scale regime:
voter model18

Crossover observed in skin data
Variance of net growth (per cell)

Cell autonomousregime
Voter modelregime

Vary window size
0.5
124(in cellsize units)

Window size (in cell size unit)

Feedback length scale (L) in the skin is the size of a single cell
= neighbor fate coupling19

Feedback length scale can bedifferent across tissues
L ～ single cell level (neighboring feedback)Signaling through adhesion, Notch-Delta, etc(ex: skin, intestinal crypt)

2L

L ～ scale of >10 cells
Tissue stretching/compression induced mechanical feedback
Quorum sensing, growth factor related feedback(ex: seminiferous tubule 精細管)
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2. Topological defects induce cell flow
[With Ryoichiro Kageyama and Masaki Sano, Nature 545 327 (2017)][Ongoing work with Masahito Uwamichi]

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Neural stem cells
20 um

Phase contrast image

Multipotent and culturable

GrowthLocal alignment at high density

Large scale image
Phase contrast

1 mmAngle

0180 degTopological defects in cell culture0180 deg+1/2-1/2

bioRxiv (Dec 13 th 2018)

Biopolar cell polarity axis(hepatocytes)
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Cell flow was induced by
topological defects+1/2 defect is the “sink”- 1/2 defect is the “source”

Geometry induced flow in active systems
Activity in nematic systems can induce
macroscopic active force =Spatial inhomogeneity in pattern
Extensile systems>0Contractile systems<0Q-tensor(measures the directionand extent of ordering)= 0 in passive systems
Blackwell et al., Soft Matter (2016)27

Geometry driven active transport
Mouse/rat brain:
Olfactory
bulb

Subventricularzone

Rostral migratory stream28Summary• Some concepts in nonequilibrium physics are usefulin understanding multicellular phenomena• Cell fate dynamics of skin stem cells
seem to follow the 2D voter model• Geometry induced flow in active systems
as a mechanism of cell flow control

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Tissue homeostasis
Experiments:

Kailin Mesa Katherine Cockburn David Gonzalez Valentina Greco(Yale School of Medicine)

Theory:Allon M. Klein
Harvard Medical School

Hiroki Yamaguchi Takahiro Sagawa
30
Univ. Tokyo

Active neural stem cells

Masaki Sano
Univ. Tokyo

Ryoichiro Kageyama
Kyoto Univ.

Masahito
UwamichiUniv. Tokyo
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Started lab in Kobe

Technical Staffs

Yuko Sakaide
Lisa Yamauchi
From FY 2019

Kyosuke Adachi
Yosuke Fukai
Daiki Nishiguchi
Visiting student

Uwamichi Masahito (U Tokyo) →32

Summary• Some concepts in nonequilibrium physics are usefulin understanding multicellular phenomena• Cell fate dynamics of skin stem cells
seem to follow the 2D voter model• Geometry induced flow in active systems
as a mechanism of cell flow control
Thank you!
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