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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