Complex Systems Biology
Life as Complicated System:
Enumeration of molecules, processes
detailed numerical models mimicking the life process
But understanding??
Life as Complex System:
Understand General features :robustness in development
irreversibility in differentiation
origin of heredity, ...
ÎGeneral Answer as a System Level?
Strategy:1) Search for universal features in cellular processes :extension of Dynamical Systems Theory2) Constructive Approach: (Exp & Theory)` construct simple system to catch universal features'`not to imitate'Constructive Biology Project at Komaba Clife grouptheme

experimenttheory

question

replicatingsystemin vitro
replication withenzymatic reaction

minority
controlorigin ofheredity;
evolvability

replicating cellwith internal
reactions

universal
statistics inreaction dynamics

condition forrecursive
growthcell differ.
development

differentiationof E Coilby interaction

emergence ofdifferentiation
rule from dynamics

irreversibility
robustness

morphogenesis

controlled
construction oftissues

self-consistency
between patternand dynamics

origin of
positional
Information

evolution

phenotypic diff.
by interaction

symbiotic
speciation

geno-pheno type
Relationshipcellsystem

experiment: Yomo; Asashima; Sugawara; Yasuda,..

• Q: Origin of heredity?
• * some molecules in a cell are regarded as‘’important’’, and control the behavior of celle.g., differentiation in roles between DNA
and protein,…
one hypothesis (KK & Yomo, 2002)
in a replicating system composing of mutuallycatalytic molecules, minority molecules play therole of heredity-carrier
Condition for heredity
preservation
controllability

X and Y mutually catalyze
the synthesis of each other;
Y is synthesized muchslower than X molecules.
Rate equation may leadto (active) Y moleculeof the concentr. < 1/N
A few Y molecules are necessary
to continue reproduction
tochasticmulation

divsionSelected are ‘rare’ stateswith a few Y molucules
Active Y molecules;(i) Preserved well,(ii)Control the behavior
Carrier of heredity

N molecules

N molecules

Expected from rate equation

Inactive X
Transition
Active X
Inactive Y

Active Y molecules
preserved

Active Y

Continuum Limit(rate equation ) is fine

Inactive Y molecules
Suppressed to ~0Essence of the mechanism;
1) discreteness in the molecule number 0,1,..
2) Preservation of rare states realized by fluctuations
3) Selection of such states according to growth condition
Cf. Without selection by growth
As dynamical systems, novel state is realized by discreteness inmolecule numbers?
novel --- not expected from continuum description?
(i.e., rate equation + noise (Langevin-type)i.e., distinct from noise-induced phenomena)
Yes(Togashi & KK 2001PRL, JSPJ 2003)
an example: Autocatalytic reaction loop
discreteness-induced symmetry breaking;4 Chemicals : X1, X2, X3, X4
Xi+Xi+1→Xi+1+Xi+1, X5≡X1– Reaction constant r=1 for all reactions.

Experimental verification

Importance ofMinority molecules
for replication
to continue
is confirmed
experimentally.

DNA polymerase gene
ribosome ,amino asidsATP.

Tth DNA polymerase

DNA ÅÆ enzyme
Autonomous Replicating
System (self-contained,In contrast to PCR)

acti vity of all clon es

Matsuura,
Yomo.,…
PNAS 2002

1.6
1.4
1.2
10.8
0.6
0.4
0.2
012g en e r a ti o n34

100 DNA molecule
Self-replication
Assay for DNA
molecule amplified

Dilution

Replication activity

10.8
0.6
0.4
0.2
0246

generation

81010 2 DNA molecules
Self-replication
Assay for DNA
molecules amplified

Dilution

Replication activity

10.8
0.6
0.4
0.2
012

generation

34

Constructive Biology Project at Komaba Clife group

○

theme

experiment

theoryquestion

replicatingsystem

in vitro
replication withenzymatic reaction

minority
controlorigin ofheredity;
evolvability

replicating cellwith internal
reactions

universal
statistics inreaction dynamics

condition forrecursive
growthcell differ.
development

differentiationof E Coilby interaction

emergence ofdifferentiation
rule from dynamics

irreversibility
robustness

morphogenesis

controlled
construction oftissuesself-consistency
between patternand dynamics

origin ofpositional
Information

evolution

phenotypic diff.
by interaction

symbioticspeciation

geno-pheno type
Relationshipcellsystem

experiment: Yomo; Asashima; Sugawara; Yasuda,..

Ｔｏｙ Cell Model with Catalytic Reaction
NetworkC.Furusawa & KK⚦⢩

ｋ species of chemicals 、Xo…Xｋ−１
number ---n０ 、n１ … nｋ−１

:（resource）

random catalytic reaction networkwith the path rate pfor the reaction
Ｘi＋Ｘj−＞Ｘk+Xj
some chemicals are penetrable
through the membrane with thediffusion coefficient D
resource chemicals are thustransformed into impenetrable
chemicals, leading to the growth in
Ｎ＝Σni, when it exceeds Nmax
the cell divides into twocell
reaction

:

:
:

:
:

catalyze:diffusion

mdeiummodel☆Growth speed, and fidelity in replication is
Maximum at Dc
Dc
1

growth speed
similarity

Growth0.15(only resources)
0.6

0.10

0.40.05
D = Dc0.00
0.001

DNo Growth

0.8

0.01
0.1
diffusion coefficient D

0.2

similarity H

growth speed (a.u.)

0.20※similarity is defined from innerproducts of composition vectors
between mother and daughtercells・0・Furusawa &KK,2003,PRL
Zipf’s Law is oberved at D = Dc

ni (number of molecules）

rank

Average number of each chemical ∝ 1/(its rank)Formation of cascade catalytic reaction★ 栄養から直接生成される成分の数を多くなるようパラメータを変えて、階層構造が判りやすくした例
100000ni

Catalyze chemicalsof higher rank
mainly４10000

３1000

２100

１

10Rank of ni

11101001000

10000

100000

１：minority molecules
２：catalyzed by 1, synthesized by resource
３：catalyzed by 2：

TheoryExperimentConfirmed by gene expression data
Human Liver1e-01

α= -1

1e-02

1e-03

ratio of mRNA

ratio of mRNA

1e-01

1e-04

ratio of mRNA

1e-01

1e+01

1e+02
rank

Human Kidney

1e-02

1e-03

1e-03

1e-04

1e+01

1e+02
rank

1e+03

1e+04

Human Colorectal Cancer
1e-01

1e-02

1e-03

1e-04

1e-04
1e+00

1e-02

1e-05
1e+00

1e+03

ratio of mRNA

1e-05
1e+00

Human Heart

1e+01

1e+02
rank

1e+03

1e+00

1e+01

1e+02
rank

1e+03

1e+04

Mouse ES cell

Mouse Fibroblast Cell
1e-01

1e-02

ratio of mRNA

ratio of mRNA

1e-01

α= -1

1e-03

1e-04

1e-02

1e-03

1e-04
1e-05
1e+00

1e+01

1e+02
rank

1e+03

1e+04

1e+00

C. elegans

1e+01

1e+02
rank

1e+03

Yeast
1e-01

ratio of mRNA

ratio of mRNA

1e-02

1e-03

1e-04

1e-05
1e+00

1e+01

1e+02
rank

1e+03

1e+04

1e-02

1e-03

1e-04
1e+00

1e+01

1e+02
rank

1e+03

So far average quantity of all components;
Next question: fluctuation by cells:
distribution of each Ni by cells

FurusawaKK,2003

Log normal distribution !

Each color gives
different chemical
speciesLOG SCALE

☆Heuristic explanation of log-normal distribution
Consider the case that a component X is catalyzed by other component
A, and replicate; the number --NX、NAd NX /dt = NX NA
thend log( NX )/dt = NA
If、 NA fluctuates around its mean < NA＞, with fluct. η（ｔ）

d log( NX )/dt = ＜NA＞ ＋ η（ｔ）

log( NX ) shows Brownian motion Æ NX log-normal dist.。
too, simplified, since no direct self-replication exists here
But with cascade catalytic reactions, fluctuations are
successively multiplied, (cf addition in central limit theorem.);Hence after logarithm, central limit th. Is applied☆Cascade leads to multiplicative propagation ofnoise (at critical region)
ＡＢＣＤＥ

Propagation of fluctuation, feedback to itsel
Leading to tail of log-normal typeCf. off-critical region

ＡFluctuations come in parallel:
Usual central limit theorem is valid

Experiment; protein abundances measured by fluorescenceLog-normal
Distribution
Confirmed
experimentally

Kashiwagi,Suzuki,YomoLarge phenotypic fluctuation Æ relevance to evolution (Sato et al., PNAS,2003)System for detecting the proper foldingof a protein
NRPGFP
Cimproper folding

interference

LowFluorescence
E. coli cellNRP

aggregation

GFPCproper folding
no interference

HighFluorescence
E. coli cellSchematic drawing of selection process〜2,000 clones
Eyes

Mutagenesis

1st screening

・・・・・ 〜30 clones
Spectrofluorometer
5〜8 clones

2nd screening

Spectrofluorometer
The highest clone

FACS analysis

``Response’’ --change of phenotype per generation per mutation

Fluctuation ---- Variance of phenotype of clone
Response proportional to Fluctuation
Organisms with larger phenotypic fluctuation- higher evolution speed; phenotypic plasticity also

So-called fluctuation-dissipation theorem in physics:
Force to change a variable x;
response ratio = (shift of x ) / force
fluctuation of x (without force)
response ratio proportional to fluctuation
Generalization::(mathematical formulation)
response ratio of some variable x against the changeof parameter a versus fluctuation of xP(x;a) x variable, a: control parameterchange of the parameter a Æpeak of P(x;a) ( i.e.,<x>average ) shifts< x > a +∆a − < x > a∝< (δ x) 2 > a =< ( x − < x >) 2 >∆a

(Evolution Speed per generation)

• Log-normal:: Is this the end of the story??
too universal as a theory of biology?
no need for high control?
Minority molecules?
Model including a loop of mutually catalytic reactions, Æcomponents in a small autocatalytic loop (hypercylce)
deviate to ‘Gaussian’; deviation possible either bysmall feedback loop or parallel paths (i.e., addition
instead of multiplication!)(KK,PRE 2003)‘important (control) partmay deviate??
(eg.,DNA)

Constructive Biology Project at Komaba Clife grouptheme

experiment

theoryquestion

replicating
systemin vitro
replication withenzymatic reaction

minority
controlorigin ofheredity;
evolvability

replicating cellwith internal
reactions

universal
statistics inreaction dynamics

condition forrecursive
growthcell differ.
development

differentiationof E Coilby interaction

emergence ofdifferentiation
rule from dynamics

irreversibility
robustness

morphogenesis

controlled
construction oftissues

self-consistency
between patternand dynamics

origin of
positional
Information

evolution

phenotypic diff.
by interaction

symbiotic
speciation

geno-pheno typeRelationshipcellsystem○○

experiment: Yomo; Asashima; Sugawara; Yasuda,..

Development and Differentiation
Question
Robustness in development under large fluctuation}(signal) molecules of few number -- relevant;Still robust process (e.g., development)
threshold mechanism only cannot explain robustness throughinteraction?
Loss of potency from totipotent cell (ES),to multipotent stem cell, and to determination
irreversible in normal development
reverse the time's arrow (Gurdon)
how to characterize?

Threshold

Evidence of fluctuations in Drosophillla egg(Leibler’s group, Nature)Isologous Diversification:internal dynamics and interaction : development
instability
distinct phenotypes
interaction-induceddx m= f m ( x1 , x 2 ,.., x k )dt

Example: chemical reaction network
specialize in the use of some path

phenotypesynchronous division:
no differentiation

Instability of homogeneous statethrough cell-cell interaction

formation of discrete types
with different chemicalcompositions:stabilize each otherrecursive production• (1) Synchronous oscillations of identical units
Up to some threshold number of units, all of them oscillate
synchronously, and their states are identical.}• (2) Differentiation of the phases of oscillations of internalstates. When the number of units exceeds the threshold, theylose identical and coherent dynamics. Although the state ofunits are different at an instance, averaged behaviors overperiods are essentially the same. Only the phase of oscillations
differs by units.
• (3) Differentiation of the amplitudes of internal states. At thisstage, the states are different even after taking the temporal
average over periods. It follows that the behavior of states(e.g., composition of chemicals, cycles of oscillations, andsoon) are differentiated.
• (4) Transfer of the differentiated state to the offspring byreproduction. This ``memory" is made possible through thetransfer of initial conditions (e.g., of chemicals) during thereproduction ( e.g., cell division).
• (5) Hierarchy of organized groups. This stage is the result ofsuccessive differentiation with time. Thus, the total system
consists of units of diverse behaviors, which forms acooperative society.

ÆWith the increase of the number

Distinct types are formed through instability in ‘developmentaldynamics’ and interaction (both types are necessary)

Robustness of developmental process
both states of each cell type and number
distribution of each cell type(1) against molecular fluctuations;(a few % fluctuations, ( ~ 100-1000 molecules))(2) against macroscopic damage;i.e., type A and type B, determined
but if type A is eliminated, then B dedifferentiates
and initial A-B cell ensemble is recovered(since A,B is stabilized each other)Differentiation of E Coli

Measurement by fluoresecent
proteins
Character of bacteria differentiate in a crowded condition(Kashiwagi, Yomo,…)Hierarchical differentiation from‘stem cell’;by taking initiallydynamics with instability (e.g.,chaotic)(higher order catalysis)

Furusawa & KK

Hierarchical differentiation from ‘stem cell’;by taking initially dynamics with instability (e.g., chaotic)(higher order catalysis)
Furusawa&KK

Generated Rule of Differentiation (example)
A1
A2
A3

A
S
B

Cf hematopoietic system(1)hierarchical differentiation:stem cell system(2) Stochastic Branching:stochastic model proposed in hematopoietic system(3) probability depends on # distrib. of cell types
with prob. pA for S Æ A
if #(A)
then pA―― global info. is embedded into internal cell statesÆSTABILITY(4) Differentiation of cell ensemble (tissue)――multiple stable distrib. { Ni }• Irreversibility: Lossof multipotency• diversity inchemicals• stability of thecellular state• growth speed
Prediction:
gene expression of stem cells diverse, weakrate of proliferation/differentiation dep. on cell distribution
If #(stem) proliferation is decreased externallythen proliferation increases
How to recover plasticity (clone, regeneration)

Universality?
checked a huge number of networks; only some fraction ofthem show chaotic dynamics & differentiation

Cells with such networks
with differentiation
higher growth speed as
an ensemble

Such networks are selectedChemical Gradient for Positional Information is generated
cell differentiation ÅÆ graidient for pattern
図９．５

Consolidation to Patterns

Constructive Biology Project at Komaba Clife grouptheme

experiment

theoryquestion

replicatingsystem

in vitro
replication withenzymatic reaction

minority
controlorigin ofheredity;
evolvability

replicating cellwith internal
reactions

universal
statistics inreaction dynamics

condition forrecursive
growthcell differ.
development

differentiationof E Coilby interaction

emergence ofdifferentiation
rule from dynamics

irreversibility
robustness

morphogenesis

controlled
construction oftissues

self-consistency
between patternand dynamics

origin of
positional
Information

evolution

phenotypic diff.
by interaction

symbiotic
speciation

geno-pheno type
Relationshipcellsystem○

experiment: Yomo; Asashima; Sugawara; Yasuda,..

•Evolution ( speciation )Recall underlying assumption in population genetics:
Selection by fitness=Function(Phenotype, environment)
but
assumption; Genotype ----> Phenotype: Single-Valued
determined uniquelythen Fitness=function(Genotype,environment)
individuals with little change in geneshould compete under the same niche???

Reconsider Genotype-Phenotype mapping
Consider seriously G -------[Development] Æ P;** G-P relationship can be one to many
(1) Isologous diversification(---theory so far)(2) Interaction-induced differentiation in experiments
bacteria (E.coli) Shapiro, Yomo, …..
(3) Low penetrance (often in mutants?)(---observation)
non-unique phenotypes (often in mutants)

Model with Evolution :Each unit Phenotype :: Variable X = ( X 1 , X 2 ,.., X k )Gene :: Parameter in the model
gje.g., reaction rate

( g1 , g 2 ,..., g k )Parameter
Variable(dynamical systems)
X(t=0)ÆX(t)Reproduction when maturity threshold condition(given by X) is satisfied
Mutation --- change in parameter in reproduction
Competition for survival:(remove a unit (randomly or with some condition)

Example of numerical simulation
Phenoptype(variable)

Ｇｅｎｅ （ｐａｒａｍｅｔｅｒ）

Suppress enzyme
activity by mutationAmplify enzyme
activity by mutation

Phenotypic change embedded into genetic change (cf Waddington)

Sympatric Speciation observed(1) First interaction-induced phenotype differentiation;
homogeneous state is destabilized by the interaction(2) Amplification of the difference through geno-pheno relation
Two groups form symbiotic relationship, and coevolve(3) Genetic Fixation and Isolation of Differentiated Groups
consolidation to genes(Example) chemical secreted out by one group are used as resources
for the other, and vice versa
create a niche each other and specialized in this created niche(4) Works for sexual reproduction case without assuming mating
preference
hybrid sterility as a result.
as its consequence mating preference evolves*＊Experimental Verification by Using E Coli in progress• Origin of heredity?
ÆMinority Control: use of rare fluctuations• How is recursive production of cells possible in theamidst of diversity and fluctuations?
Æ hierarchy of catalytic reactions formed:
Universal Statistics: amplification and regulation offluctuations. (Zipf’s law and log-normal distribution)
・ Biological relevance of such large fluctuations?
ÆPhenotypic Fluctuation ∝ Evolution Speed• Robustness of development under fluctuations?
Irreversibility of cell differentiation?
Æ phenotypic differentiation due to instability ofhomogeneous states, and formation of discrete
attracting states by cell-cell interaction. Loss ofplasticity in dynamics by the increase of cell number• How is speciation to discrete pheno-and genotypes possible under interaction amongorganisms?
ÆDynamic consolidation; fixation to slower timescale change( phenotype Ægenotype)
Flexibility of Unit and System
Regulation of Fluctuations
Loss of Plastic Dynamics
Universal Features:

Theory and Experiment• Collaborators:
Chikara Furusawa （Reaction network ofcell(Zipf‘s law,Log-normal), Cell-differentiation)
Tetsuya Yomo (all the experiments;sharing idea for all topics)
Katsuhiko Sato (fluctuation-responserelationship)
Akiko Kashiwagi, Takao Suzuki, Yoichiro Ito(experiments by Yomo’s group)・Most papers mentioned here are available at
http://chaos.c.u-tokyo.ac.jp