lorentz: principles in multiscale systems biology in silico discovery of principles in multiscale...

Westerhoff et al., Leiden 20121116 Lorentz: Principles in multiscale Systems Biology

In silico discovery of principles in multiscale Systems Biology

Manchester Centre for Integrative Systems Biology

Doctoral Training Centre for Systems Biology from Molecules to Life

Hans V. Westerhoff and friends

Netherlands Institute for Systems Biology, Amsterdam


In silico discovery of principles in multiscale Systems Biology• The paradigm of the replica model• Discovery through replica modelling of reality:

– Time invariance and distributed control– Robust biology– Irreducible complexity– Drug target discovery– Hierarchies in scales: gene expression and time

• We have a problem• Multiscale ITFoM as a solution• Out of my comfort zone


• X=X(time, X0, e1, e2,.., en, enzyme parameters, [S])

The enzymes are like elementary particles for biology!

∙ chemical ─ reaction

Constituent equation:

𝑑𝑥𝑖=∑𝑗=1

𝑛

𝑁 𝑖𝑗 ∙𝑒 𝑗 ∙𝑣 𝑗(𝑥 ,𝑝)∙𝑑𝑡


The paradigm of the replica model• Model reality using multiscaling that does

not loose essential complexity• Genes/enzymes as elementary particles• Describe them with rate equations (v(X))• Describe metabolites with node equations

(dX/dt) = N.v)• Integrate• Repeat at higher scales in terms of

modules, keeping relationships with fine-grained levels


Silicon / virtual biochemical organisms



– Time invariance and distributed control– Irreducible complexity– Robust biology– Drug target discovery– Hierarchies in scales: gene expression and time



If the model is a replica, it is as complex as the real system, hence offers no advantages for understanding

Replica models can be used for computational investigations of reality

They greatly facilitate discovery ofPrinciples that govern reality


Hendrik Antoon Lorentz

• 1900: Maxwell equations are• invariant under the Lorentz

transformation

• Lorentz contraction

Westerhoff et al., Leiden 20121116 Lorentz: Principles in multiscale Systems Biology∙ chemical ─ reaction

Constituent equation:

𝑑𝑥𝑖=∑𝑗=1

𝑛

𝑁 𝑖𝑗 ∙𝑒 𝑗 ∙𝑣 𝑗(𝑥 ,𝑝)∙𝑑𝑡

Our transformation

𝑡′≡𝑡 /𝜆𝑒𝑖′≡ 𝜆 ∙𝑒𝑖

Seconds instead of minutes as time unit

All processes 60 times faster

There should be no effect


logarithm of time

lnJ

SS

n

j

xt

xe tCtCj

1

0)()(

Westerhoff (2008) J Theor Biol 252, 555 - 567

Law/principle of Systems Biology

Steady state or maximum:

C=Control of concentration by enzyme

𝐶1𝑥+𝐶2

𝑥+𝐶3𝑥+….+𝐶𝑛

𝑥=0lo

g of

con

cent

rati

on


Silicon / virtual biochemical organisms\validated in silico


The principle we discovered

E EP

F FP

G GP

For the maximum level of EP the phosphatases are equally important as the kinases

Transcription of ‘growth’genes

Growth factor

Simplicity: Control essentially in one component(the key gene/enzyme catalyzing the first irreversible step)

Irreducible complexity:Control is distributed And not even uniformly

Which is it?


MAP kinase signaling: which are the fragile steps?

0.03

0.06

-0.43

-0.18 0.21

0.00

0.43 0.01

-1.47

-1.12

-0.44

0.44

1.47

Hornberg et al. Oncogene

Healthy tissueCalculations based on

Schöberl model

At JWS/SiC

To discover & certify network principles of

robustness (and disease)

We need a definition of robustness

Definition of robustness

The percentage by which one can interfere

with a molecular process without reducing system

function by more than 1 %

Principle 1

Networking enhances robustness


Enzyme activity

Func

tion

Robustness is 1 for processes in isolation

1%1

%1

ffunctionindecrease

activityenzymeindecreasefei

Process in isolation

robustness of isolated processes =1

Is the robustness in networks larger?


Robustness of vital flux of Trypanosomes vis-à-vis perturbation of various glycolytic steps

step Robustness

Glctr 1.1

GAPdh 42

HK 42

PGI 1546

PFK 234

ALD 38

TPI 482

GDH 66

GPO -251

PGK 61

PK 691

ATPase 2744

GlyK 389

Answer:

Yes, most robustnesses in networks in living organisms are large; average is 468 here

Question:

Is robustness higher (than 1) in networks of living cells?

Principle 2???

Trade-off???:

Does making the system more robust vis-à-vis one perturbation make it equally less robust for a

different perturbation???


Precise trade-off for robustness?

step Robustness

Robustness doubled glucose

transporter

Glctr 1.1 88

GAPdh 42 4

HK 42 20

PGI 1546 412

PFK 234 56.

ALD 38 3

TPI 482 64

GDH 66 6

GPO -251 -15

PGK 61 7

PK 691 73

ATPase 2744 313

GlyK 389 26

Sum (average) 6085 (468) 1055(81)

No, robustness is not conserved

No precise trade-off for robustness

Principle 2???

Trade-off???:

making the system more robust vis-à-vis one perturbation makes it less

robust for a different perturbation???

No principle then?No trade-off?

Yes, there is one!


Sum over all inverse robustnesses = 1= conserved

step 1/robustness

1/robustness (doubled glc transporter)

Glctr 0.887 0.011

GAPdh 0.024 0.249

HK 0.024 0.051

PGI 0.001 0.002

PFK 0.004 0.018

ALD 0.026 0.354

TPI 0.002 0.016

GDH 0.015 0.166

GPO -0.004 -0.068

PGK 0.016 0.144

PK 0.001 0.014

ATPase 0 0.003

GlyK 0.003 0.039

Sum 0.999 0.999


Trypanosomiasis


The most fragile step is…..

stepFragility=C=1/

robustness

1/robustness (doubled glc transporter)

Glucose transport 0.887 0.011

GAPdh 0.024 0.249

HK 0.024 0.051

PGI 0.001 0.002

PFK 0.004 0.018

ALD 0.026 0.354

TPI 0.002 0.016

GDH 0.015 0.166

GPO -0.004 -0.068

PGK 0.016 0.144

PK 0.001 0.014

ATPase 0 0.003

GlyK 0.003 0.039

Sum 0.999 0.999

?

?

Differential network-based drug design

Target where the difference between

parasite and host is the largest


Trypanosome in the host

T. brucei…..

us et al.

Holzhütter et al.

Red blood cell


TRYPANOSOMEERYTHROCYTE

GOODTARGET

Differential fragility analysis TRYP and ERY

Fragility of ATP synthesis flux

(Bakker, Holzhütter, Snoep, Westerhoff)

0.680.00

0.01

0.03

0.001

0.07

0.060.01

0.05

0.001

0.005

0.02

0.00

0.02

-0.01

0.00

0.00

0.03

0.940.00 0

0.00 FAIRTARGET

BADTARGET

BADTARGET


Haanstra


Fragilities of PGK mRNA and protein versus perturbations in ..

Fragility of for →:

Targeting the networks: multiple targets at the same time in hierarchical networks!

The multiscale problemand transcription

activation

• Time: • How to bridge the various time scales?

Molecular <1 s versus Cellular >1 h

• The multidimension problem:• How to enable regulation by 20

information flows rather than by 1?

A

A B

A B

C

A B

CD

AB

CD

B

C

D

C

B

A

D

D

D

C

The clock model for mammalian transcription activation


Slow macroscopic dynamics caused by, rapid, molecular processes!

Metivier, R. et al. Estrogen receptor-alpha directs ordered, cyclical, and combinatorial recruitment of cofactors on a natural target promoter. Cell 115, 751-763 (2003).

Karpova, T. S. et al. Concurrent fast and slow cycling of a transcriptional activator at an endogenous promoter. Science (New York, N.Y 319, 466-469 (2008).

Saramaki, A. et al. Cyclical chromatin looping and transcription factor association on the regulatory regions of the p21 (CDKN1A) gene in response to 1alpha,25-dihydroxyvitamin D3. J Biol Chem 284, 8073-8082, doi:M808090200 [pii]

Note! Transcription synchrony in population of cells!

Why?Well, we have ‘a’ problem

• Definitive cures are lacking for most

diseases

• The health care budget will cripple the

economy

• The life sciences are tremendously

successful but ….. not in empowering

medicine

• ………….


Increased spending has not improved cancer mortality

1970 1975 1980 1985 1990 1995 2000 2005 20100

5

10

15

20

25

30

35

40

45

50

cumulative NCI funding (G$)

cancer mortality (/1000)

+2000 %

-10 %


Global prevalence of diabetes and impaired glucose tolerance (IGT) in 2010 and 2030

Boyle, 2011


genomicstranscriptomics

proteomics

metabolomics

structural biology

biophysics biologybiochemistry

physiology

Yet…We can measure almost everything now

http://en.wikibooks.org/wiki/File:Grafik_blutkreislauf.jpg


>1 trillion €/year spent on biomedical research: Tower of Babel?

Brueghel

health

disease


IT Future of Medicinea FET Flagship project

A CERN-like project:1.3 G€

Idea 1: Use computable replica model to organize and integrate the data


genomicstranscriptomics

proteomics

metabolomics

structural biology

biophysics biologybiochemistry

physiology

project all information into a computer replica

http://en.wikibooks.org/wiki/File:Grafik_blutkreislauf.jpg


Integration of all information through the ITFoM flagship into computable human

models!

Brueghel

An ICT model of the human

health

disease

Idea 2: to deal with otherwise impossible complexity

The human body is a computer using simple

principles

We should borrow its computation strategy

The virtual patient – a “person simulator”

New ICT for medicine

The virtual patient – a “person simulator”

And 7 billion of these…..:one man one vote := therapy

New ICT for medicine


Silicon / virtual biochemical human


Melanoma

Hepato-cyte

Red blood cell

Virtual heart

Integrating

Models

Models from Molecular Systems Biology

Physiological models from VPH

Statistical models

Epidemiological models

Clinical models

Patients’ concepts

…….

T. bruc

ei

Microbiome

Integration WP#6

Medical user and expertise

Instrumentation and assays

Medical WP1Analytical

WP2

Hard- & SoftwareWP#3

Data PipelinesWP#4

ComputationalWP#5

Programing industry & academia

Databases and repositories

Hardware

/Software industry

CoordinationWP#7

Final WP numbering and organization: blue is ICT, red is medical and green is analytical expertise. The end product

is ICT models of individual humans for individualized medicine.

4.6(I) Map

s

4.8(I) Mo

dels

4.7(I) Data

4.9(I) Too

ls

ICT-integration challengesmolecules – tissues - patients

4.5(I) Maps

4.7(I) Models

4.6(I) Data

4.8(I) Tools

ICT-modelling Strategies

4.1 (S) Watchmaker’s models (SiC)

4.2 (S) Engineer’s models

4.3 (S) Mechanic’s models (VPH)

4.4 (S) Learner’s models

4.5 (S) Combinations


Out of my comfort zone

• How to link down (enzyme MD)

Antreas Kalli

Use essential dynamicsReduce to essential statesCompute affinitiesValidate experimentallyInsert into enzyme kinetics



• Pathway complexity

Eytan Rubin, Mattias Reuss, and us and others

Use exometabolomics, FBA and objective functions to find where most of the flux is

Project SNPs into those pathways



• Parameter finding intracellular networksMartine SmitsBob van de Water

Rich data setsMultiple RNAi7 billion humans



• Cell heterogeneity

Single cell analyses



• Towards tissue• Katarina Wolf• David Basanta• Chris Adami• Andreas Deutsch

Transparent black box approachFocus on dominant behavior firstAgent based modelsEvolutionary games, but extended to continuous variablesAnd connect parameters between levels!



• True tissue dynamics and anatomy• Bernard Corfe

Transparent black box approachFocus on dominant behavior firstAgent based modelsEvolutionary games, but extended to continuous variablesAnd connect parameters between levels!



• Lifestyle and ethics• Angela Brand, Bernard Corfe

Insert substrates= food into pathwaysInsert movement as muscle activityInsert brain through measured hormone levels


In silico discovery of principles in multiscale Systems Biology

Manchester Centre for Integrative Systems Biology

Doctoral Training Centre for Systems Biology from Molecules to Life

friends

Netherlands Institute for Systems Biology, Amsterdam

lorentz: principles in multiscale systems biology in silico discovery of principles in multiscale...

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