Nonequilibrium physicsin multicellular systems

川口喬吾Kyogo Kawaguchi

Riken BDR (from Sep 2018)

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PhysicsBiology

PhysicsBiology

Fundamental questions

New experiments

Theory

Data analysis methods

Outline

1. Skin (tissue) homeostasisInteracting particle system

2. Collective motion in cultured neural stem cellsActive nematics

3. Acknowledgements

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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)]

Tissue homeostasis:Epidermal stem cellsare confined in a two-dimensional layer

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Leblond, Walker (1956)

Cross section sketch

Turn over: 2-10 days

Division Differentiation

Basal layer = stem cells(基底細胞層)

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*

**

Day 0 Day 1 Day 2

5

1 2 34

67

8 9 1011

12

1314* 15

16

18 19

20 2122

24 25 26

*

*25

12

3a

3b57

8 910

11

12a

1316a

16b18 19

212224 26*

17

2323

17

12

3a

3b5a

5b

7

8a

8b

910

11a

11b

12a

13a

13b

16a

16b17a

17b

18a

18b 19a21

22* 2624a

Neighbor fate coupling?

Neighbor fate coupling model= Voter model (DP2)

8Dornic et al. Phys. Rev. Lett. 87, 045701 (2001)Hammal et al. Phys. Rev. Lett 94, 230601 (2005)

- Model for “voters”- and critical coarsening- Universality class (two absorbing states)

~10 years ago:clonal analysis showed scaling behavior

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Clayton et al., Nature (2007)Doupe et al., Dev. Cell (2010)Klein & Simons, Development (2011)

Single cell labeling in live mice (Cre-induced)

Average number of cellsin surviving clones

Clone size distribution:

Time post-labeling (weeks)

Aver

age

cells

/ cl

one

Critical birth death model explains scaling

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0.5

0.5

Athreya and Ney “Branching Processes” (Dover) Review: Klein & Simons, Development (2011)

Prob.Division

Differentiation

Average number of cellsin surviving clones

Clone size distribution:

Summary of scaling: experiment and theory

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> 2

Cell autonomousFate

(Critical birth death)(voter model)Experiment

(skin) 2 Coordinated fate

Average clone size:

Clone size cumulative distribution:

Experiment:Intestine [Lopez-Garcia et al. (2010)

Snippert et al. (2010)]

Seminiferous tubule[Klein et al., (2010)Yoshida lab]

Average clone size:

Clone size cumulative distribution:

Problem of 2D

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> 2

Cell autonomousFate

(Critical birth death)(voter model) 2 Coordinated fate

Aver

age

size

of

surv

ivin

g cl

one

Time post-labeling (weeks)

Aver

age

cells

/ cl

one

Experiment(skin)

Simulation/theory Experiment

Fate coordination can be quantified using “fluctuation test”

..Blue – Red = 0 ± 1.5

..

Blue – Red = 0 ± 0.5(s.d.) (s.d.)

~𝑁𝑁1/2 ~𝑁𝑁1/4

Data shows that fates of neighboring cells are coordinated

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Time scale of coordination: 1-2 days Length scale of coordination:size of a single cell

Varia

nce

of n

et g

row

th p

er c

ell

Days

Vary window size0.5124

(in cellsize units)

Modeling neighboring fate coupling by local density feedback

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Division

Differentiation

1-p

p

From more data analysis:

Making model: Cell density =

Cell Stem Cell 23, 677 (2018)

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Division

Differentiation

1-p

p

Making model:

Differentiation Division

Modeling neighboring fate coupling by local density feedback

2L

Cell density =

Deriving the voter model actionfrom particle dynamics

17Yamaguchi and Kawaguchi, in preparation

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:

Model has two regimesseparated at the interaction length scale

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・Small scale regime:critical birth death model (cell autonomous)

・Large scale regime:voter model

2L

0.5

0.5

Crossover at L

Crossover observed in skin data

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

Vary window size0.5124

(in cellsize units)

Window size (in cell size unit)

Varia

nce

of n

et g

row

th (p

er c

ell)

Cell autonomousregime

Voter modelregime

Feedback length scale can be different across tissues

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L～ single cell level (neighboring feedback)

Signaling through adhesion, Notch-Delta, etc

(ex: skin, intestinal crypt)

L～ scale of >10 cells

Tissue stretching/compression induced mechanical feedback

Quorum sensing, growth factor related feedback

(ex: seminiferous tubule 精細管)

2L

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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]

Neural stem cells

Multipotent and culturable

20 um Phase contrast image

Growth

Local alignment at high density

Large scale image

1 mm

Phase contrast Angle 0 180 deg

Topological defects in cell culture

0 180 deg +1/2

-1/2

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bioRxiv (Dec 13th 2018)

Biopolar cell polarity axis(hepatocytes)

Cell flow was induced bytopological 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 =

Blackwell et al., Soft Matter (2016)

Q-tensor(measures the directionand extent of ordering)

> 0 < 0

= 0 in passive systems

Extensile systems Contractile systems

Spatial inhomogeneity in pattern

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Olfactorybulb

Subventricularzone

Rostral migratory stream

Geometry driven active transport

Mouse/rat brain:

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Summary

• Some concepts in nonequilibrium physics are usefulin understanding multicellular phenomena

• Cell fate dynamics of skin stem cellsseem to follow the 2D voter model

• Geometry induced flow in active systemsas a mechanism of cell flow control

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

Experiments:

Allon M. Klein Harvard Medical School

Tissue homeostasis

Hiroki Yamaguchi Takahiro SagawaUniv. Tokyo

Theory:

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Masaki SanoUniv. Tokyo

Ryoichiro KageyamaKyoto Univ.

MasahitoUwamichi

Univ. Tokyo

Active neural stem cells

Started lab in Kobe

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Technical StaffsYuko SakaideLisa Yamauchi

From FY 2019Kyosuke AdachiYosuke FukaiDaiki Nishiguchi

Visiting studentUwamichi Masahito (U Tokyo) →

Summary

• Some concepts in nonequilibrium physics are usefulin understanding multicellular phenomena

• Cell fate dynamics of skin stem cellsseem to follow the 2D voter model

• Geometry induced flow in active systemsas a mechanism of cell flow control

Thank you!33