Multi-level Evolutionary Dynamics

Kunihiko KanekoUniv of TokyoCenter for Complex Systems Biology Universal Biology

• Life ~ A system that consists of diverse components and that maintains itself and can continue to produce itself --consequence

• Guiding Principle--Micro-macro Consistency:micro – many components (high-dimensional)macro – unit to sustain/ reproduce as a whole

(few degrees ?)molecule – cell, cell-tissue etc.

Steady (growth) state Constraint from macro to micro

Micro-macro relationship

Universal statistical lawComplex-systemsBiology

Consistency between Cell reproductionand molecule replication

Adaptation asa result of consistencybetween cell growth andgene expression dynamics

Consistency between Multicelluar developmentand cell reprodcution

Genotype

Catalytic reaction network

Phenotype

Evolutionary relationship on Robustness and Fluctuation

Phenotypic Plasticity vs SymbiosisOr Ecological diversification

Gene regulationnetwork

Molecule

Cell

Multicelluarity

Ecosystem

Stochsatic dynamics

Complex-Systems Biology : Consistency between different levels as guiding principle

TimescaleHeterogeneity

Consequence of Dynamical Systems rather than fitness

*1 consistency between molecular vs cell reproduction -- why diversity in compositions 10min

( - universal law in adaptation in chemical abundances)*2 consistency between genetic and phenotypic

changes 40min-- Direction in Evolution (Law for Phenotypic Evolution)

*3 consistency between cellular and multicellular--Origin of Multicellularity 20min--Isologous Diversification for robust cell society

*4 consistency between development and evolution--Evolution-Development Congruence 15min

Before optimization in evolution, consistency in multilevel dynamics predetermines necessity and possibility in phenotypic evolution

• Life ~ A system that consists of diverse components and that aintains itself and can continue to produce itself

• Why diversity??(i) To cope with diverse environmental changes?(ii) Not easy to find minimal set in the beginning/ just probabilistically higher?

Complexity in the beginning (Dyson 84)

(iii) To cope against parasitic processes…(iv) Competition for diverse, limited resources

among individuals ‘diversity transition’ ( Kamimura, KK,2014, arXiv)(dXi/dt=AiXi dXi/dt=Ci)

Artificial Replicating Cell with diversityMore than 5000 reaction steps run with 144 species of bio-molecules for the in liposome (oil emulsion) and self-replication, divide, evolve

EF-TuGDP

EF-Ts

EF-TsGTP

EF-G-GTP

IF1IF3 IF1

IF3IF2

ARS

IF2

MTF

RF1/2RF1/2 EF-GRF3

RRFEF-GRF3RRF

EF-TuEF-TsS1

GDPGTP

NDK

CK

ATPADP

AMPMK2 ADP

CKATP

EF-Tu-GDPR

F1/2

st

EF-Tu-GTP

PPiPPase

2Pi

f

Ichihashi,…Matsuura, Yomo,Nat. Comm 2014

Simplest Illustration of Diversity Transition

Only species with the highest aiSi remains(Darwinian selection)

(coexistence)

(1)

(Constrraint that sum of Si=1)

reaction rate a_iresource S_i

3-species example

Molecular replication vs Cell reproduction

Cell --- chemicals X1,X2,…Xn replicate with the aid of others (hypercycle) Grow and divide when the total number of molecules=N

Cf: Hypercycle introduced by Manfred Eigen for the issue of the origin of life (i.e., stable replicating system resolving the error catastrophe)

• If

When the resource flow is sufficient, most efficient hypercycle remains (3 species)

If the resource flow is limited, diverse components remain to form hypercylce-networks

Kamimura,Kaneko,2015

A) Diversity transition when resource flow goes below a threshold a la the simplest caseB) Negative Scaling relation between the abundances and resource (flow)

Reaction rate xi*xj (1/ ) (1/ ) assuming concentration is equally distributed among remaining species

KM

K M

KM

(1)

Kamimura,KK,2015,J Systems Chemistry +submitted

Similarity diagrambetween cells

Each axisCell Index

More clusters More coexsiting types

Kamimura and KKarXiv (2014)

Gene expression 

dynamics

Genom

ic change

Epigenetic change

(modification etc)

Cell state change

1 generation  Dozens  >100Embedding phenotypic change Genetic control

adaptation evolutionresponse memory

Micro-Macro : Multiple-time scale dynamics

＊ Consistency between dynamics with distinct time scales

Consistency between Developmental Process and Evolution  (Evo‐Devo Congruence)

Which phenotypic evolution is possible/ probable is predetermined

• Consistency between evo‐geno/ response‐fluctuation   a la Einstein and Waddington consequence of evolution of robustness and robustness in evolution

(i) evolutionary fluctuation‐response relationship:*Vip variance of phenotype ( fitness) over isogenic

individuals (Ve, Vnoise)Vip ∝ evolution speed

through evolution course bacteria evolution experiment + models (cell, gene‐regulation‐net),+Phenomenological Thoery

Evolution speed

Vip

Sato Ito Yomo KK; PNAS 2003,

μ=0.01 0.03

.0.05

Increase in fitness

Fluctuation Vip

EXPERIMENTCELL MODEL

Furusawa,KK2006KK, PLoSOne2007

(ii) Geno‐Pheno relationship on variances*Vip variance of fitness over isogenic individuals*Vg variance of average fitness over heterogenic popVip ∝ Vg ∝ evolution speed through evolution course confirmed; experiment, theory, models （ KK,Furusawa JTB2006, KK PLoSOne2007)

WHY?? result of robust evolution + distribution theory Robustness to noise ↑ Robustness to Mutation ↑Vip↓ Vg ↓

Isogenic individualsgene

phenotype Vip phenotype

Vg

μ ～μmax

μ

Viｐ=VgVg

Phenotype fluctuation of clone

Vip

WHY? (Phenomenological theory assuming evolutionary robustness) Consider 2-variable distrbP(x=phenotype,a=genotype) =exp(-V(x,a))Keep a single-peak (stability condition).

Hessian condition

Leads to relationship between Vip and Vg

KK,Furusawa, 2006 JTB

If mutation rate μ is small, Vg<Vip,Vg ~ (μ/μmax )Vip ∝ Vip

Vip=α～Vig= μC2

Consistency between pheno & geno also in Evolutionary Systems Biology 2012, ed. Soyer

• (i) Vip ≧ Vg ?（for stability?) ( **)(ii)error catastrophe at Vip ~ Vg                (**)

(where the evolution does not progress) (iii) Vg~(μ/μmax)Vip∝μVip

（∝evolution speed)      at least for small μ＊＊Consistent with the experiments,  but,,,,,Assumptions on P(x,a) and Robust Evolution??Why higher developmental noise leads to robust evolution?

(**) under selection of given trait. if μ is small:to be precisely Vig, variance those from a given phentype x: but Vig ~Vg if μ is small

Vg/(Vip+Vg) is known as heritability (smaller for important trait)

Gene expression dynamics model:: Relevance of Noise to evolution?Simple Model:Gene-net(dynamics of stochastic gene expression ) on/off state

xi – expression of gene i :on off

i jδij

ActivationRepressionJij=1,-1,0

M;total number of genes, ｋ: output genesGaussian white noise

Noise strength σ

(on) x＞θi (off) x<θi

• Fitness:  Starting from off of all genes, after development  genes  xi i=1、2、‥・・、k should be on（Target Gene Pattern)

Fitness F= －（Number of off xi）Genetic AlgorithmPopulation of N different genotypes(networks). Select those with higher <F> and mutate with rate μKeep N networks

If M=k=2

Most simulationsM=64K=8

generation

(1)Vip≧Vg forσ≧σc (2) Vg→Vip as

σ→σc (4) Vip∝Vg through

evolution course KK,PLosOne,2007

Small σ

generation

σ＜σｃ only tiny basinaround target orbitσ＞σc robustness evolvesproportional decrease in Vip &Vg Large basin for target attractor

Smooth developmental landscape

‘’Robustness transition by increasing noise’’

Difference in basin structure

After Evolution σ＞σc

σ＜σｃ: stay after evolution

Initial (most probable networks,Random)

Evolution of RobustnessIf developmental dynamics (gene expression) are under sufficient noise level, robustness to noise leads to robustness to mutation, through the evolution.Robustness ----- Insensitivity of Fitness (Phenotype) to system’s change –‘’Inverse’’ of phenotypic variances

Developmental Robustness to noise ---- VipRobustness to mutation in evolution ----VgVip ∝ Vg Developmental robustness is embedded into genetic (evolutionary) robustness for σ>σc

(data from 4 mutation rate values)

Vip(i) ∝Vg(i)over allcomponents i

Vip=Vg

Vip

Vg

Restriction among diverse componentsVip-Vg relationship

Vg(i)：Variation of i-th expression due to mutationVip(i)：Variation due to noise in dynamics

Isogenic individualsgene

phenotype Vip phenotype

Vg

If highly variable by noise,More easily evolvable

Fluctuation and response are two sides of coin

Vg(i),Vip(i) across different genes (proteins) also show proportionalityMeasure variance of gene expression for each gene i genetic variance Vg(i) ∝ isogenic variance Vip(i)

over different genes i, for given generation

Drosophila selection experiment Vip vs Vg across different phenotypes

Vip(i)

Vg(i)

Similarly, restriction among responses of all components ( transcriptional changes) through evolution

Vg(i)Responseby evolution

ΔlogX(i)_{G}

Proportion

Vip(i)〜proportional

Env-Evo Fluctuation Response RelationshipResponseto environment ΔlogX(i)_{Env} 〜proportional

Fluctuation

Genetic change

Environmental variation/ Noise

Last week reported the geno-pheno correspondence in high-dim expression dynamics both in response and fluctuation

Focus on steady‐growth cells  universal constraintall the components have to be roughly doubled within a cell division time)Ni(i=1,…,M) dNi/dt= μi Ni  exp(μi t);    all μi are equal;(M‐1) conditions  1‐dimensional line

Adaptation/evolution progresses on an iso-μi-line (‘quasi-static process’) in an M-dimensional state space

M(e.g. proteins) measurable by microarray

Concentration xi=Ni/V:  (dV/dt)/V= μ             （volume V)Temporal change of concentration x

Response under different stress strength E

dilution

In the linear regime

Susceptibility to stress

Steady-growth sustaining all components +Linear

Linearization w.r.t X(=log x)

Common proportionality for log-expression change δXj for all components j

KK,Furusawa,Yomo,Phys Rev X(2015)

＝ indep’t of j

O: no stressE,E’：osmotic pressure, heat, starvationLow, medium high

Put E Coli under different stress conditions; Measure gene

expressions

Transcriptome expreiment

A: low vs medium osmoB low vs medium heatC low vs medium starvation 

δX^E、δX^E’over few thousand genes

Expression changes under same stress with different strengths

Data fromMatsumotoetalBMCevolbiol2013

KK,Furusawa,Yomo,Phys Rev X (2015)

Growth Rate change

Log Expression change

Application to adaptive evolutionE: new environmental conditionー change in (log) expression δX（E,0） δμ(E,0)<0G: (Genetic) evolution under the environmental conditi(1)Assume represented a singe variable (projection)

ー change in (log) expression δX（E.G)rescover growth‐‐ ｜δμ（E,G）｜＜｜δμ（E.0）｜

０＜ δXi（E,G）/δXi（E,0） ＜１ commonreturn to original gene expression pattern

（Le Chatelier principle)

（Genssimilation Hypothesis)∝

(2)Linearization

(3)

Furusawa,KK Interface,2015

Confirmation by Toy Cell Model for Reproductionwith Catalytic Reaction Network 

（nutrient）

reaction

catalyze

cell

medium

diffusion

ｋ species of chemicals 、Xo…Xｋ－１

number ---n０ 、n１ … nｋ－１

resource chemicals are thus transformed into impenetrable chemicals, leading to the growth.

(a)Ｎ＝Σni exceeds Nmax (model 1) (b) when all chemicals exist (model 2),

the cell divides into two

random catalytic reaction networkwith the path rate p

for the reaction Ｘi＋Ｘj－＞Ｘk+Xj

model

・・・ K >>1 species

dX1/dt ∝ X0X4; rate equation;Stochastic model here

(Cf. Furusawak,KK, PRL 2003; PRL 2012)

□ Resource chemicals (<- environment) are transported with the aid of a given catalyst, transporter

TRANSPORTER

Facilitatetransport

Statistical Laws ( confirmed by experiments and simple toy cell models)

☑ Power Law in abundances across components （inverse proportionality between abundance and its rank)☑ Log-normal distribution for cell-cell variation☑Fold-change detection (Weber-Fechner Law)

Furusawa, KK, 2003, 2012, Furusawa et al 2005, KK Furusawa 2005,…

Human kidney, mouse ES yeast

generation

Switch environment

Recovery of growth rate by adaptive evolution to new environment

Grow

th rate

Let’s check evolution law in this catalytic reaction net model

Switch environment(composition of nutrient) and check response (--env)Mutate network and select those with higher growth –evo

5-th generation

2oth generation

100 th generation

（１）Response by genetic change tends to cancel the change by environment（２）The two responses are proportional over all components

LeChatlier-type response common to all proteins

Expression Change by gene

Expression change by env

log(xe/x0)log(xg/x0)

XgXg Sl

ope in δX

－Δμ by env to by evol

Furusawa,KK Interface,2015

log (xe(i)/x0(i))

xo(i)

log(xg(i)/xo(i)

xe(i)xg(i)

Expression change after evolution

Expression change after environmental change Growth rate change

Theory line

Growth Rate

〜1000generations

Evolution Experiment of E Coli to adapt in stressed (ethanol) condition

Slope in expression changeVs growth rate change

Furusawa,KK Interface,2015

Furusawa'sGroup

Expression change after environmental switch

Evolutionary compenstation

Simulation (cell mdel)Experiment of E coli 

evolution

slope

 in th

e expressio

n change

Macro evolution theory dμ＝CdX+γdG－Δμ recovery of growth rate

Evolution of E Coli(Furusawa)

0

Evolutionary change

Scatter Plots over all genes

Response to environment

generation

Adaptive evolution ‐‐‐ cancelling the environmentally induced state change (expression change)

Application toadaptive evolution

slope

 in th

e expressio

n change

－Δμ recovery of growth rate

Furusawa,KK; Interface 2015

Vg(i)Responseby evolution

ΔlogX(i)_{G}

Proportion

Vip(i)〜proportional

Env-Evo Fluctuation Response RelationshipResponseto environment ΔlogX(i)_{Env} 〜proportional

Fluctuation

Genetic change

Environmental variation/ Noise

Last week reported the geno-pheno correspondence in high-dim expression dynamics both in response and fluctuation

Assumption

Theory for FluctuationLinearization

Genetic Assimilation(?)

Multicellular : Multi-level ConsistencyIntracellular dynamics (chemical reactions)Cell-cell interaction +growth(w competition)

MCO as Possible states allowing for robust Growth

Concentration of i-th component of m-th cell

Intra-cellular Interaction Growth-dilution

=0 Steady-state; intracellular balance

Growth-balance among agents

Differentiation from a same cell＋ balanced growth

As the number of cells (agents) increase resource limitation and interaction(cells interact and compete for resource) MCO as a necessity course?

Basic (Naive) Questions(1)Q1: How Diversification from a single cell is

achieved (Development)(2)Q2: Dhow Cells help each other for higher

growth as a community(3) Q3: Robustness as an ensemble of cells

Specific Example by Ensemble of Ｔｏｙ Cells with Catalytic Reaction Network 

（nutrient） cell

mediumdiffusion

ｋ species of chemicals 、Xo…Xｋ－１

number ---n０ 、n１ … nｋ－１

resource chemicals are transformed into impenetrable chemicals, leading to the growth. g(X)

Each type α has different networksInteraction ｈ-- due to diffusion of

penetrable components through Media+Competition of resources in Media■ Cell/Media volume ratio V strength of interaction &competition

random catalytic reaction networkwith the path rate p

for the reaction Ｘi＋qＸj－＞Ｘk+qXj

model

dX1/dt ∝ X0X4; rate equation;Stochastic model here

(Cf. Furusawak,KK, PRL 2003; PRL 2012)

□ Resource chemicals (<- environment) are transported with the aid of a given catalyst, transporter

……

• Several examples to show differentiation from a single cell with identical network with achievement of higher growth   ‐‐‐‐ common characteristics

Cell state with concentration oscillation fixed differentiation to few cell types with role differentiation under strong resource competition and interaction;Each type- Specification with fewer components +

symbiotic relationship Higher growth achieved

Example by 5 oomponents Yamagishi, Saito, KK(in prep)

Differentiate to1-3 richVs 2-4 rich types

The Next page is cut, as it includes unpublished material

(2) Strong InteractionSymbiotic relationship with the role differentiation(cf: comparative advantage in economics by Ricardo)

(1) Resource limitation No room to produce all chemicals: concentration on fewer components to enhance reactions: If concentrations are distributed to k chemical ( each is 1/k) then the sum of reaction rate for Xi+qXm-> Xj+qXm ~ (1/k) *k smaller k better some necessary catalyst may be missing

Catalyst(s) are exchanged to help each other cells

Mutually Dependent

Mutually help catalysis

Simplified image

Type α Type β

Primitive multicellularity with differentiation of roles

q+1

７synchronous division: no differentiation

Instability of homogeneous statethrough cell-cell interaction

formation of discrete types with different chemical compositions:stabilize each other

recursive production

Assuming oscillatory dynamics as a single cell

KK, Yomo1997,1999

Waddington’s Canalization (stability of each cell type)How genes guide this ?

III Robust developmentfrom Stem Cells: Dynamical-SystemsRepresentation of Waddington’s image on Cell Differentiation

Cell types as attractors(cf Kauffman mid60’s)

How differentiation starts?Stem cell?Robustness in cell society?

Increase in the cell number by divisionIn division put some noise in m,pbetween cells

Cell-cell interactions: diffusion of some protein

Diffusion of some protein

Model with Gene regulation network + Cell-cell interaction

N.Suzuki,C.Furusawa、KK(PLoSOne2012).

ee also Youtube, search with Suzuki,Furusawa,Kaneko

Dynamical Systems Mechanism

• Oscillatory DynamicsDesynchronized irregular oscillation by cell‐cell interaction some cells switch to a novel state(bifurcation & stabilized by interaction) Rate of differentiation or self‐renewal depends on the number ratio of each cell type  autonomous regulation

Mutually stabilizeCell number

Minimal GRN of 2 proteins (bit narrow in parameter range) （Goto,KK,Phys.Rev.E,2013)

Interaction Oscillatory to Fixed point

Saddle-Node Bifurcation on Invariant Curve induced by cell-cell interaction

Stable HierarchicalDifferentiation

Ratio A decreased thenDifferentiation rationS A is increasedStable ratio among cell types

pApS

pB

Hypothesis (Furusawa, KK 2001)Gene Expression dynamics

in stem cell = Oscillatory with itinerancy of several states cell-cell differentiationrobust differentiationLoss of Pluripotency== Loss of such dynamics

• Experimental Verification?• Pluripotency characterized by(i)  diversity of expressed genes(ii) Larger cell‐cell variation (exp. Heterogeneity confirmed)(iii) Oscillation in  gene expression 

Experimental confirmation     

Gene expression dynamics Itinerancy over several statesChang et al (Nature 08)

(Chambers et alNature07)

Kobayashi et al. Genes Development 2009

Oscillation of Hes1 expression~4hr for ESLost when differentiated

To recover Stemness increase in degrees of freedom (Furusawa,KK 2001) ?Yamanaka’s iPS (2006)by expressing 4 genes

Evolution‐Development Congruence?• Discussed by Haeckel as ontogeny recapitulates phylogeny   but too inaccurate, and dismissed

• ?But maybe some relationship between the two• Merit in numerical evo‐deveo

Numerical Evolution of development Cells in 1-dim line

Each cell has protein expression dynamics by GRNExternal morphogen gradient for input genesdiffusion of proteins

Evolve GRN by mutation Fitness: Given targetpattern for output genes

Kohsokabe & KKJ Exp Zoology B(in press)

Evo-devo congruencetopology (+ ordering) of stripe pattern formation agrees,

Rare exception

Comparison between evo and devo

For most (95%) examples, good evo-devo congruence

Evolution –‐ punctuated equilibrium  (need time for relevant mutation)Development – emergence of genes whose expression change slowly and control the output expression  works as a “ bifurcation parameter”

Why congruence?both evo and devo consist of quasistationary regime +

epoch for rapid stripe formation

Dynamical-systems explanation of evo-devo congruence stripe change --- bifurcation in mutation or in slow expression change; correspondence in bifurcations

Network explanation : Upstream forward network –produces a basic pattern working as boundary condition for later developmetal dynamicsDownstream added feedforward or feedback

Summary:(1) How compositional diversity in cells?(2) Law for Phenotypic EvolvabilityMCO (3) symbiotic differentiation Ricardo for MCO(4) isologous diversification(oscillatory-> fixed differentiation)

(4) Evolution-Development CongruneceCollaborators: Chikara Furusawa ;Atushi Kamimura; Takahiro KohsokabeJumpei Yamagishi, Nen Saito

Before optimization in evolution, consistency in multilevel dynamics predetermines necessity and possibility in phenotypic evolution